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In modern quantum field theory, one of the most important tasks is the calculation of loop integrals. Loop integrals appear when evaluating the Feynman diagrams with one or more loops by integrating over the internal momenta. Even though this problem has already been in place since the mid-twentieth century, we not only do not understand how to calculate all classes of these integrals beyond one loop, we do not even know in what class of functions the answer is expressed. To partially solve this problem, different variations of new functions called usually elliptic multiple polylogarithms have been introduced in the last decade. In this paper, we explore the possibilities and limitations of this class of functions. As a practical example, we chose the processes associated with the physics of heavy quarkonium at the two-loop level. | high energy physics theory |
We provide an approximation algorithm for k-means clustering in the one-round (aka non-interactive) local model of differential privacy (DP). This algorithm achieves an approximation ratio arbitrarily close to the best non private approximation algorithm, improving upon previously known algorithms that only guarantee large (constant) approximation ratios. Furthermore, this is the first constant-factor approximation algorithm for k-means that requires only one round of communication in the local DP model, positively resolving an open question of Stemmer (SODA 2020). Our algorithmic framework is quite flexible; we demonstrate this by showing that it also yields a similar near-optimal approximation algorithm in the (one-round) shuffle DP model. | computer science |
The underdoped phase diagram of the iron-based superconductors exemplifies the complexity common to many correlated materials. Indeed, multiple ordered states that break different symmetries but display comparable transition temperatures are present. Here, we argue that such a complexity can be understood within a simple unifying framework. This framework, built to respect the symmetries of the non-symmorphic space group of the FeAs/Se layer, consists of primary magnetically-ordered states and their vestigial phases that intertwine spin and orbital degrees of freedom. All vestigial phases have Ising-like and zero wave-vector order parameters, described in terms of composite spin order and exotic orbital-order patterns such as spin-orbital loop-currents, staggered atomic spin-orbit coupling, and emergent Rashba- and Dresselhaus-type spin-orbit interactions. Moreover, they host unusual phenomena, such as the electro-nematic effect, by which electric fields acts as transverse fields to the nematic order parameter, and the ferro-N\'eel effect, by which a uniform magnetic field induces N\'eel order. We discuss the experimental implications of our findings to iron-based superconductors and possible extensions to other correlated compounds with similar space groups. | condensed matter |
Statistical thinking partially depends upon an iterative process by which essential features of a problem setting are identified and mapped onto an abstract model or archetype, and then translated back into the context of the original problem setting (Wild and Pfannkuch 1999). Assessment in introductory statistics often relies on tasks that present students with data in context and expects them to choose and describe an appropriate model. This study explores post-secondary student responses to an alternative task that prompts students to clearly identify a sample, population, statistic, and parameter using a context of their own invention. The data include free text narrative responses of a random sample of 500 students from a sample of more than 1600 introductory statistics students. Results suggest that students' responses often portrayed sample and population accurately. Portrayals of statistic and parameter were less reliable and were associated with descriptions of a wide variety of other concepts. Responses frequently attributed a variable of some kind to the statistic, or a study design detail to the parameter. Implications for instruction and research are discussed, including a call for emphasis on a modeling paradigm in introductory statistics. | statistics |
We present a large-scale numerical study, supplemented by experimental observations, of a quasi-two-dimensional active system of polar rods and spherical beads confined between two horizontal plates and energised by vertical vibration. For low rod concentrations $\Phi_r$ we observe a direct phase transition, as bead concentration $\Phi_b$ is increased, from the isotropic phase to a homogeneous flock. For $\Phi_r$ above a threshold value, an ordered band dense in both rods and beads occurs between the disordered phase and the homogeneous flock, in both experiments and simulations. Within the size ranges accessible we observe only a single band, whose width increases with $\Phi_r$. Deep in the ordered state, we observe broken-symmetry "sound" modes and giant number fluctuations. The direction-dependent sound speeds and the scaling of fluctuations are consistent with the predictions of field theories of flocking, but sound damping rates show departures from such theories. At very high densities we see phase separation into rod-rich and bead-rich regions, both of which move coherently. | condensed matter |
In this paper we present numerical analysis of the phase transition of the area-interaction model, which is a standard model of Statistical Mechanics. The theoretical results are based on a recent paper by Dereudre \& Houdebert \cite{dereudre_houdebert_2018_SharpTransitionWR} which provides a complete phase diagram except on a bounded (implicit) domain. With our numerical analysis we give an approximative explicit description of this domain. %This region is related to the theoretical function $\beta \mapsto \widetilde{z}_c^a(\beta, 1)$ which is percolation threshold of the model, for given $\beta$. %We provide a numerical approximation of this function in order to fully understand the phase diagram. Furthermore our numerical results confirm the still unproven conjecture stating that non-uniqueness holds if and only if $z= \beta$ is large enough, with a value of the threshold obtained from the simulation of $\beta_c \simeq 1.726$. | mathematics |
We show that if X_n is a variety of cxn-matrices that is stable under the group Sym([n]) of column permutations and if forgetting the last column maps X_n into X_{n-1}, then the number of Sym([n])-orbits on irreducible components of X_n is a quasipolynomial in n for all sufficiently large n. To this end, we introduce the category of affine FI^op-schemes of width one, review existing literature on such schemes, and establish several new structural results about them. In particular, we show that under a shift and a localisation, any width-one FI^op-scheme becomes of product form, where X_n=Y^n for some scheme Y in affine c-space. Furthermore, to any FI^op-scheme of width one we associate a component functor from the category FI of finite sets with injections to the category PF of finite sets with partially defined maps. We present a combinatorial model for these functors and use this model to prove that Sym([n])-orbits of components of X_n, for all n, correspond bijectively to orbits of a groupoid acting on the integral points in certain rational polyhedral cones. Using the orbit-counting lemma for groupoids and theorems on quasipolynomiality of lattice point counts, this yields our Main Theorem. | mathematics |
We introduce a notion of $F$-concavity which largely generalizes the usual concavity. By the use of the notions of closedness under positive scalar multiplication and closedness under positive exponentiation we characterize power concavity and power log-concavity among nontrivial $F$-concavities, respectively. In particular, we have a characterization of log-concavity as the only $F$-concavity which is closed both under positive scalar multiplication and positive exponentiation. Furthermore, we discuss the strongest $F$-concavity preserved by the Dirichlet heat flow, characterizing log-concavity also in this connection. | mathematics |
Purpose: Identify and examine the associations between health behaviors and increased risk of adolescent suicide attempts, while controlling for socioeconomic and demographic differences. Design: A data-driven analysis using cross-sectional data. Setting: Communities in the state of Montana from 1999 to 2017. Subjects: Selected 22,447 adolescents of whom 1,631 adolescents attempted suicide at least once. Measures: Overall 29 variables (predictors) accounting for psychological behaviors, illegal substances consumption, daily activities at schools and demographic backgrounds, were considered. Analysis: A library of machine learning algorithms along with the traditionally-used logistic regression were used to model and predict suicide attempt risk. Model performances (goodness-of-fit and predictive accuracy) were measured using accuracy, precision, recall and F-score metrics. Results: The non-parametric Bayesian tree ensemble model outperformed all other models, with 80.0% accuracy in goodness-of-fit (F-score:0.802) and 78.2% in predictive accuracy (F-score:0.785). Key health-behaviors identified include: being sad/hopeless, followed by safety concerns at school, physical fighting, inhalant usage, illegal drugs consumption at school, current cigarette usage, and having first sex at an early age (below 15 years of age). Additionally, the minority groups (American Indian/Alaska Natives, Hispanics/Latinos), and females are also found to be highly vulnerable to attempting suicides. Conclusion: Significant contribution of this work is understanding the key health-behaviors and health disparities that lead to higher frequency of suicide attempts among adolescents, while accounting for the non-linearity and complex interactions among the outcome and the exposure variables. | statistics |
In this paper we address the problem of generating all elements obtained by the saturation of an initial set by some operations. More precisely, we prove that we can generate the closure of a boolean relation (a set of boolean vectors) by polymorphisms with a polynomial delay. Therefore we can compute with polynomial delay the closure of a family of sets by any set of "set operations": union, intersection, symmetric difference, subsets, supersets $\dots$). To do so, we study the $Membership_{\mathcal{F}}$ problem: for a set of operations $\mathcal{F}$, decide whether an element belongs to the closure by $\mathcal{F}$ of a family of elements. In the boolean case, we prove that $Membership_{\mathcal{F}}$ is in P for any set of boolean operations $\mathcal{F}$. When the input vectors are over a domain larger than two elements, we prove that the generic enumeration method fails, since $Membership_{\mathcal{F}}$ is NP-hard for some $\mathcal{F}$. We also study the problem of generating minimal or maximal elements of closures and prove that some of them are related to well known enumeration problems such as the enumeration of the circuits of a matroid or the enumeration of maximal independent sets of a hypergraph. This article improves on previous works of the same authors. | computer science |
In this work, we extend existing well-posedness by noise results for the stochastic transport and continuity equations by treating them as special cases of the linear advection equation of $k$-forms, which arises naturally in geometric fluid dynamics. In particular, we prove the existence and uniqueness of weak $L^p$-solutions to the stochastic linear advection equation of $k$-forms that is driven by a H\"older continuous, $W^{1,1}_{loc}$ drift and smooth diffusion vector fields, such that the equation without noise admits infinitely many solutions. | mathematics |
A decomposition of the non-equilibrium stationary state of a quadratic Fermi system influenced by linear baths is obtained and used to establish a simulation protocol in terms of tensor states. The scheme is then applied to examine the occurrence of uncoupled Majorana fermions in Kitaev chains subject to baths on the ends. The resulting phase diagram is compared against the topological characterization of the equilibrium chain and the protocol efficiency is studied with respect to this model | quantum physics |
Here we studied the possible diffusion speed for relativistic fluid in different effective quantum chromodynamics models: Nambu-Jona-Lasinio (NJL), Polyakov loop extended NJL, entangled PNJL (EPNJL) model. | high energy physics phenomenology |
Extreme high-energy peaked BL Lac objects (EHBLs) are an emerging class of blazars with exceptional spectral properties. The non-thermal emission of the relativistic jet peaks in the spectral energy distribution (SED) plot with the synchrotron emission in X-rays and with the gamma-ray emission in the TeV range or above. These high photon energies may represent a challenge for the standard modeling of these sources. They are important for the implications on the indirect measurements of the extragalactic background light, the intergalactic magnetic field estimate, and the possible origin of extragalactic high-energy neutrinos. In this paper, we perform a comparative study of the multi-wavelength spectra of 32 EHBL objects detected by the Swift-BAT telescope in the hard X-ray band and by the Fermi-LAT telescope in the high-energy gamma-ray band. The source sample presents uniform spectral properties in the broad-band SEDs, except for the TeV gamma-ray band where an interesting bimodality seems to emerge. This suggests that the EHBL class is not homogeneous, and a possible sub-classification of the EHBLs may be unveiled. Furthermore, in order to increase the number of EHBLs and settle their statistics, we discuss the potential detectability of the 14 currently TeV gamma-ray undetected sources in our sample by the Cherenkov telescopes. | astrophysics |
We introduce a high-temperature droplet epitaxy procedure, based on the control of the arsenization dynamics of nanoscale droplets of liquid Ga on GaAs(111)A surfaces. The use of high temperatures for the self-assembly of droplet epitaxy quantum dots solves major issues related to material defects, introduced during the droplet epitaxy fabrication process, which limited its use for single and entangled photon sources for quantum photonics applications. We identify the region in the parameter space which allows quantum dots to self-assemble with the desired emission wavelength and highly symmetric shape while maintaining a high optical quality. The role of the growth parameters during the droplet arsenization is discussed and modelled. | condensed matter |
Rayleigh-B\'enard convection (RBC) and Taylor-Couette Flow (TCF) are two paradigmatic fluid dynamical systems frequently discussed together because of their many similarities despite their different geometries and forcing. Often these analogies require approximations, but in the limit of large radii where TCF becomes rotating plane Couette flow (RPC) exact relations can be established. When the flows are restricted to two spatial degrees of freedom there is an exact specification that maps the three velocity components in RPC to the two velocity components and one temperature field in RBC. Using this, we deduce several relations between both flows: (i) The Rayleigh number $Ra$ in convection and the Reynolds $Re$ and rotation $R_\Omega$ number in RPC flow are related by $Ra= Re^2 R_\Omega (1-R_\Omega)$. (ii) Heat and angular momentum transport differ by $(1-R_\Omega)$, explaining why angular momentum transport is not symmetric around $R_\Omega=1/2$ even though the relation between $Ra$ and $R_\Omega$ has this symmetry. This relationship leads to a predicted value of $R_\Omega$ that maximizes the angular momentum transport that agrees remarkably well with existing numerical simulations of the full 3D system. (iii) One variable in both flows satisfy a maximum principle i.e., the fields' extrema occur at the walls. Accordingly, backflow events in shear flow \emph{cannot} occur in this two-dimensional setting. (iv) For free slip boundary conditions on the axial and radial velocity components, previous rigorous analysis for RBC implies that the azimuthal momentum transport in RPC is bounded from above by $Re^{5/6}$ with a scaling exponent smaller than the anticipated $Re^1$. | physics |
Recent BELLE measurements provide the cross section for single hadron production in $e^+e^-$ annihilations, differential in thrust and in the hadron transverse momentum with respect to the thrust axis. Universality breaking effects due to process-dependent soft factors make it very difficult to relate this cross sections to those corresponding to hadron-pair production in $e^+e^-$ annihilations, where transverse momentum dependent (TMD) factorization can be applied. The correspondence between these two cross sections is examined in the framework of the Collins-Soper-Sterman factorization, in the collinear as well as in the TMD approach. We propose a scheme that allows to relate the TMD parton densities defined in 1-hadron and in 2-hadron processes, neatly separating, within the soft and collinear parts, the non-perturbative terms from the contributions that can be calculated perturbatively. The regularization of rapidity divergences introduces cut-offs, the arbitrariness of which will be properly reabsorbed by means of a mechanism closely reminiscent of a gauge transformation. In this way, we restore the possibility to perform global phenomenological studies of TMD physics, simultaneously analyzing data belonging to different hadron classes. | high energy physics phenomenology |
Dead time effects have been considered a major limitation for fast data acquisition in various time-correlated single photon counting applications, since a commonly adopted approach for dead time mitigation is to operate in the low-flux regime where dead time effects can be ignored. Through the application of lidar ranging, this work explores the empirical distribution of detection times in the presence of dead time and demonstrates that an accurate statistical model can result in reduced ranging error with shorter data acquisition time when operating in the high-flux regime. Specifically, we show that the empirical distribution of detection times converges to the stationary distribution of a Markov chain. Depth estimation can then be performed by passing the empirical distribution through a filter matched to the stationary distribution. Moreover, based on the Markov chain model, we formulate the recovery of arrival distribution from detection distribution as a nonlinear inverse problem and solve it via provably convergent mathematical optimization. By comparing per-detection Fisher information for depth estimation from high- and low-flux detection time distributions, we provide an analytical basis for possible improvement of ranging performance resulting from the presence of dead time. Finally, we demonstrate the effectiveness of our formulation and algorithm via simulations of lidar ranging. | electrical engineering and systems science |
We study fragmentation in electron-positron annihilation assuming a di-jet situation, using variables defined independent of any frame. In a collinear situation some of the variables are centered around zero with the small deviations attributed to intrinsic transverse momenta and large deviations attributed to additional hard subprocesses. Of course there is a gradual transition. Our modest goal is to show that covariantly defined variables are well suited to get a feeling for the magnitude of intrinsic transverse momenta. | high energy physics phenomenology |
In the low energy effective theory of the weak interaction, a macroscopic force arises when pairs of neutrinos are exchanged. We calculate the neutrino Casimir force between plates, allowing for two different mass eigenstates within the loop. We also provide the general potential between point sources. We discuss the possibility of distinguishing whether neutrinos are Majorana or Dirac fermions using these quantum forces. | high energy physics phenomenology |
We investigate the connection between the intrinsic C IV absorption line variability and the continuum flux changes of broad absorption line (BAL) quasars using a sample of 78 sources in the Stripe 82 region. The absorption trough variability parameters are measured using the archival multi-epoch spectroscopic data from the Sloan Digital Sky Survey (SDSS), and the continuum flux variability parameters are estimated from the photometric light curves obtained by the SDSS and the Catalina Real-Time Survey (CRTS) surveys. We find evidence for weak correlations (\rho ~ 0.3) between the intrinsic C IV absorption line variability and the quasar continuum variability for the final sample of 78 BAL quasars. The correlation strengths improve (\rho ~0.5) for the "high-SNR" sample sources that have higher spectral signal-to-noise ratio. Using two sub-sets of the high-SNR sample differing on the absorption trough depth, we find that the shallow trough sub-set shows an even stronger correlation (\rho ~ 0.6), whereas the deep trough sub-set does not show any correlation between the absorption line variability and the continuum variability. These results point to the important role of saturation effects in the correlation between the absorption line variability and the continuum variability of BAL quasars. Considering other effects that can also smear the correlation, we conclude that the actual correlation between the absorption line and continuum variability is even stronger. | astrophysics |
The Rivlin-Ericksen model is one of the oldest models in fluid dynamics to describe non-Newtonian properties. The model comes with two independent transports at second order. In this paper, we study the relativistic origin of the Rivlin-Ericksen fluid. Starting from a relativistic Weyl invariant uncharged fluid in $3+1$ dimensions, we reduce it over light-cone directions and obtain a generic non-relativistic uncharged fluid in one lower dimension with all possible second order terms in the constitutive relations. We observe that the Rivlin-Ericksen fluid is a subclass of our generalised non-relativistic system. We also compute the holographic values of all the non-relativistic second order transports and find that three of them satisfy a universal constraint relation. | high energy physics theory |
Scale-free outbursts of activity are commonly observed in physical, geological, and biological systems. The idea of self-organized criticality (SOC), introduced back in 1987 by Bak, Tang and Wiesenfeld suggests that, under certain circumstances, natural systems can seemingly self-tune to a critical state with its concomitant power-laws and scaling. Theoretical progress allowed for a rationalization of how SOC works by relating its critical properties to those of a standard non-equilibrium second-order phase transition that separates an active state in which dynamical activity reverberates indefinitely, from an absorbing or quiescent state where activity eventually ceases. Here, we briefly review these ideas as well as a recent closely-related concept: self-organized bistability (SOB). In SOB, the very same type of feedback operates in a system characterized by a discontinuos phase transition, which has no critical point but instead presents bistability between active and quiescent states. SOB also leads to scale-invariant avalanches of activity but, in this case, with a different type of scaling and coexisting with anomalously large outbursts. Moreover, SOB explains experiments with real sandpiles more closely than SOC. We review similarities and differences between SOC and SOB by presenting and analyzing them under a common theoretical framework, covering recent results as well as possible future developments. We also discuss other related concepts for "imperfect" self-organization such as "self-organized quasi-criticality" and "self-organized collective oscillations", of relevance in e.g. neuroscience, with the aim of providing an overview of feedback mechanisms for self-organization to the edge of a phase transition. | condensed matter |
In 2D materials, the quantum confinement and van der Waals-type interlayer interactions largely govern the fundamental electronic and optical properties, and the dielectric screening plays a dominant role in the excitonic properties. This suggests strongly layer-dependent properties, and a central topic is to characterize and control the interlayer interactions in 2D materials and heterostructures. Black phosphorus is an emerging 2D semiconductor with unusually strong interlayer interactions and widely tunable direct bandgaps from the monolayer to the bulk, offering us an ideal platform to probe the layer-dependent properties and the crossover from 2D to 3D (i.e., the scaling effects). In this review, we present a comprehensive and thorough summary of the fundamental physical properties of black phosphorus, with a special focus on the layer-dependence characters, including the electronic band structures, optical absorption and photoluminescence, and excitonic properties, as well as the band structure engineering by means of electrical gating, strain, and electrochemical intercalation. Finally, we give an outlook for the future research. | condensed matter |
We present a weak formulation and discretization of the system discovery problem from noisy measurement data. This method of learning differential equations from data fits into a new class of algorithms that replace pointwise derivative approximations with linear transformations and a variance reduction technique. Our approach improves on the standard SINDy algorithm by orders of magnitude. We first show that in the noise-free regime, this so-called Weak SINDy (WSINDy) framework is capable of recovering the dynamic coefficients to very high accuracy, with the number of significant digits equal to the tolerance of the data simulation scheme. Next we show that the weak form naturally accounts for white noise by identifying the correct nonlinearities with coefficient error scaling favorably with the signal-to-noise ratio while significantly reducing the size of linear systems in the algorithm. In doing so, we combine the ease of implementation of the SINDy algorithm with the natural noise-reduction of integration to arrive at a more robust and user-friendly method of sparse recovery that correctly identifies systems in both small-noise and large-noise regimes. | mathematics |
We investigate the Hong-Ou-Mandel (HOM) effect $-$ a two-photon quantum-interference effect $-$ in the space-time of a rotating spherical mass. In particular, we analyze a common-path HOM setup restricted to the surface of the earth and show that, in principle, general-relativistic frame-dragging induces observable shifts in the HOM dip. For completeness and correspondence with current literature, we also analyze the emergence of gravitational time-dilation effects in HOM interference, for a dual-arm configuration. The formalism thus presented establishes a basis for encoding general-relativistic effects into local, multi-photon, quantum-interference experiments. Demonstration of these instances would signify genuine observations of quantum and general relativistic effects, in tandem, and would also extend the domain of validity of general relativity, to the arena of quantized electromagnetic fields. | quantum physics |
In an industrial internet setting, ensuring the trustworthiness of process data is a must when data-driven algorithms operate in the upper layers of the control system. Unfortunately, the common place in an industrial setting is to find time series heavily corrupted by noise and outliers. Typical methods for cleaning the data include the use of smoothing filters or model-based observers. In this work, a purely data-driven learning-based approach is proposed based on a combination of convolutional and recurrent neural networks, in an auto-encoder configuration. Results show that the proposed technique outperforms classical methods in both a simulated example and an application using real process data from an industrial facility. | electrical engineering and systems science |
Caging is a promising tool which allows a robot to manipulate an object without directly reasoning about the contact dynamics involved. Furthermore, caging also provides useful guarantees in terms of robustness to uncertainty, and often serves as a way-point to a grasp. Unfortunately, previous work on caging is often based on computational geometry or discrete topology tools, causing restriction on gripper geometry, and difficulty on integration into larger manipulation frameworks. In this paper, we develop a convex-combinatorial model to characterize caging from an optimization perspective. More specifically, we study the configuration space of the object, where the fingers act as obstacles that enclose the configuration of the object. The convex-combinatorial nature of this approach provides guarantees on optimality, convergence and scalability, and its optimization nature makes it adaptable for further applications on robot manipulation tasks. | computer science |
The explosion of time series data in recent years has brought a flourish of new time series analysis methods, for forecasting, clustering, classification and other tasks. The evaluation of these new methods requires either collecting or simulating a diverse set of time series benchmarking data to enable reliable comparisons against alternative approaches. We propose GeneRAting TIme Series with diverse and controllable characteristics, named GRATIS, with the use of mixture autoregressive (MAR) models. We simulate sets of time series using MAR models and investigate the diversity and coverage of the generated time series in a time series feature space. By tuning the parameters of the MAR models, GRATIS is also able to efficiently generate new time series with controllable features. In general, as a costless surrogate to the traditional data collection approach, GRATIS can be used as an evaluation tool for tasks such as time series forecasting and classification. We illustrate the usefulness of our time series generation process through a time series forecasting application. | statistics |
We prove a convergence result for a family of Yang-Mills connections over an elliptic $K3$ surface $M$ as the fibers collapse. In particular, assume $M$ is projective, admits a section, and has singular fibers of Kodaira type $I_1$ and type $II$. Let $\Xi_{t_k}$ be a sequence of $SU(n)$ connections on a principal $SU(n)$ bundle over $M$, that are anti-self-dual with respect to a sequence of Ricci flat metrics collapsing the fibers of $M$. Given certain non-degeneracy assumptions on the spectral covers induced by $\bar\partial_{\Xi_{t_k}}$, we show that away from a finite number of fibers, the curvature $F_{\Xi_{t_k}}$ is locally bounded in $C^0$, the connections converge along a subsequence (and modulo unitary gauge change) in $L^p_1$ to a limiting $L^p_1$ connection $\Xi_0$, and the restriction of $\Xi_0$ to any fiber is $C^{1,\alpha}$ gauge equivalent to a flat connection with holomorphic structure determined by the sequence of spectral covers. Additionally, we relate the connections $\Xi_{t_k}$ to a converging family of special Lagrangian multi-sections in the mirror HyperK\"ahler structure, addressing a conjecture of Fukaya in this setting. | mathematics |
In this paper, we consider the data-driven model invalidation problem for Lipschitz continuous systems, where instead of given mathematical models, only prior noisy sampled data of the systems are available. We show that this data-driven model invalidation problem can be solved using a tractable feasibility check. Our proposed approach consists of two main components: (i) a data-driven abstraction part that uses the noisy sampled data to over-approximate the unknown Lipschitz continuous dynamics with upper and lower functions, and (ii) an optimization-based model invalidation component that determines the incompatibility of the data-driven abstraction with a newly observed length-T output trajectory. Finally, we discuss several methods to reduce the computational complexity of the algorithm and demonstrate their effectiveness with a simulation example of swarm intent identification. | electrical engineering and systems science |
This is the second part of a two-paper series that establishes the uniqueness and regularity of a threshold energy wave map that does not scatter in both time directions. Consider the two-sphere valued equivariant energy critical wave maps equation on 1+2 dimensional Minkowski space, with equivariance class k > 3. It is known that every topologically trivial wave map with energy less than twice that of the unique k-equivariant harmonic map Q scatters in both time directions. We study maps with precisely the threshold energy, i.e., twice the energy of Q. In the first part of the series we gave a refined construction of a threshold wave map that asymptotically decouples into a superposition of two harmonic maps (bubbles), one of which is concentrating in scale. In this paper, we show that this solution is the unique (up to the natural invariances of the equation) two-bubble wave map. Combined with our earlier work we can now give an exact description of every threshold wave map. | mathematics |
We investigate the thermal instability of a smooth equilibrium state, in which the density function satisfies Schwarzschild's (instability) condition, to a compressible heat-conducting viscous flow without heat conductivity in the presence of a uniform gravitational field in a three-dimensional bounded domain. We show that the equilibrium state is linearly unstable by a modified variational method. Then, based on the constructed linearly unstable solutions and a local well-posedness result of classical solutions to the original nonlinear problem, we further construct the initial data of linearly unstable solutions to be the one of the original nonlinear problem, and establish an appropriate energy estimate of Gronwall-type. With the help of the established energy estimate, we finally show that the equilibrium state is nonlinearly unstable in the sense of Hadamard by a careful bootstrap instability argument. | mathematics |
We demonstrate how noise can be turned into an advantage for optical sensing using a nonlinear cavity. The cavity is driven by a continuous wave laser into the regime of optical bistability. Due to the influence of fluctuations, the cavity randomly switches between two states. By analyzing residence times in these two states, perturbations to the resonance frequency of the cavity can be detected. Here, such an analysis is presented as a function of the strength of the perturbation and of the noise. By increasing the standard deviation of the noise, we find that the detection speed increases monotonically while the sensitivity peaks at a finite value of the noise strength. Furthermore, we discuss how noise-assisted sensing can be optimized in state-of-the-art experimental platforms, relying solely on the minimum amount of noise present in the cavity due to its dissipation. These results open new perspectives for the ultrafast detection of nanoparticles, contaminants, gases, or other perturbations to the resonance frequency of an optical resonator, at low powers and in noisy environments. | physics |
We show how to compute conformal blocks of operators in arbitrary Lorentz representations using the formalism described in arXiv:1905.00036 and arXiv:1905.00434, and present several explicit examples of blocks derived via this method. The procedure for obtaining the blocks has been reduced to (1) determining the relevant group theoretic structures and (2) applying appropriate predetermined substitution rules. The most transparent expressions for the blocks we find are expressed in terms of specific substitutions on the Gegenbauer polynomials. In our examples, we study operators which transform as scalars, symmetric tensors, two-index antisymmetric tensors, as well as mixed representations of the Lorentz group. | high energy physics theory |
A new scheme to determine the neutrino mass matrix is proposed using atomic de-excitation between two states of a few eV energy spacing. The determination of the smallest neutrino mass of the order of 1 meV and neutrino mass type, Majorana or Dirac, becomes possible, if one can coherently excite more than 1 gram of atoms using two lasers. | high energy physics phenomenology |
We derive Next-to-Eikonal (NEik) corrections to the background quark propagator, which stem from (i) considering a finite longitudinal width target instead of an infinitely thin shockwave and (ii) including the interaction of the quark with the transverse components of the background field. These two different corrections to the eikonal approximation combine together and provides a gauge covariant expression for the quark propagator at NEik accuracy. We then apply our results to quark (or antiquark) scattering on a nucleus at NEik accuracy, considering both unpolarized cross section and helicity asymmetry. | high energy physics phenomenology |
In wireless control systems, remote control of plants is achieved through closing of the control loop over a wireless channel. As wireless communication is noisy and subject to packet dropouts, proper allocation of limited resources, e.g. transmission power, across plants is critical for maintaining reliable operation. In this paper, we formulate the design of an optimal resource allocation policy that uses current plant states and wireless channel states to assign resources used to send control actuation information back to plants. While this problem is challenging due to its infinite dimensionality and need for explicit system model and state knowledge, we propose the use of deep reinforcement learning techniques to find neural network-based resource allocation policies. In particular, we use model-free policy gradient methods to directly learn continuous power allocation policies without knowledge of plant dynamics or communication models. Numerical simulations demonstrate the strong performance of learned policies relative to baseline resource allocation methods in settings where state information is available both with and without noise. | electrical engineering and systems science |
Within the framework of the AdS/CMT correspondence asymptotically anti-de Sitter black holes in four space-time dimensions can be used to analyse transport properties in two space dimensions. A non-linear renormalisation group equation for the conductivity in two dimensions is derived in this model and, as an example of its application, both the Ohmic and Hall DC and AC conductivities are studied in the presence of a magnetic field, using a bulk dyonic solution of the Einstein-Maxwell equations in asymptotically AdS$_4$ space-time. The ${\cal Q}$-factor of the cyclotron resonance is shown to decrease as the temperature is increased and increase as the charge density is increased in a fixed magnetic field. Likewise the dissipative Ohmic conductivity at resonance increases as the temperature is decreased and as the charge density is increased. The analysis also involves a discussion of the piezoelectric effect in the context of the AdS/CMT framework. | high energy physics theory |
Positrons play a major role in the emission of solar gamma-rays at energies from a few hundred keV to >1 GeV. Although the processes leading to positron production in the solar atmosphere are well known, the origin of the underlying energetic particles that interact with the ambient particles is poorly understood. With the aim of understanding the full gamma-ray spectrum of the Sun, I review the key emission mechanisms that contribute to the observed gamma-ray spectrum, focusing on the ones involving positrons. In particular, I review the processes involved in the 0.511 MeV positron annihilation line and the positronium continuum emissions at low energies, and the pion continuum emission at high energies in solar eruptions. It is thought that particles accelerated at the flare reconnection and at the shock driven by coronal mass ejections are responsible for the observed gamma-ray features. Based on some recent developments I suggest that energetic particles from both mechanisms may contribute to the observed gamma-ray spectrum in the impulsive phase, while the shock mechanism is responsible for the extended phase. | astrophysics |
Entanglement distillation is a key primitive for distributing high-quality entanglement between remote locations. Probabilistic noiseless linear amplification based on the quantum scissors is a candidate for entanglement distillation from noisy continuous-variable (CV) entangled states. Being a non-Gaussian operation, quantum scissors is challenging to analyze. We present a derivation of the non-Gaussian state heralded by multiple quantum scissors in a pure loss channel with two-mode squeezed vacuum input. We choose the reverse coherent information (RCI)---a proven lower bound on the distillable entanglement of a quantum state under one-way local operations and classical communication (LOCC), as our figure of merit. We evaluate a Gaussian lower bound on the RCI of the heralded state. We show that it can exceed the unlimited two-way LOCCassisted direct transmission entanglement distillation capacity of the pure loss channel. The optimal heralded Gaussian RCI with two quantum scissors is found to be significantly more than that with a single quantum scissors, albeit at the cost of decreased success probability. Our results fortify the possibility of a quantum repeater scheme for CV quantum states using the quantum scissors. | quantum physics |
Extending constructions by Gabriel and Zisman, we develop a functorial framework for the cohomology and homology of simplicial sets with very general coefficient systems given by functors on simplex categories into abelian categories. Furthermore we construct Leray type spectral sequences for any map of simplicial sets. We also show that these constructions generalise and unify the various existing versions of cohomology and homology of small categories and as a bonus provide new insight into their functoriality. | mathematics |
The high-speed implementation and robustness against of non-adiabatic holonomic quantum computation provide a new idea for overcoming the difficulty of quantum system interacting with the environment easily decoherence, which realizing large-scale quantum computer construction. Here, we show that a high-fidelity quantum gates to implement non-adiabatic holonomic quantum computation under solid-state spin in Nitrogen-Vacancy(NV) centers, providing an extensible experimental platform that has the potential for room-temperature quantum computing, which has increased attention recent years. Compared with the previous method, we can implement both the one and two-qubit gates by varying the amplitude and phase of the microwave pulse applied to control the non-Abelian geometric phase acquired by NV centers. We also find that our proposed scheme may be implemented in the current experiment to discuss the gate fidelity with the experimental parameters. Therefore, the scheme adopts a new method to achieve high-fidelity non-adiabatic holonomic quantum computation. | quantum physics |
We employ the epidemic Renormalization Group (eRG) framework to understand, reproduce and predict the COVID-19 pandemic diffusion across the US. The human mobility across different geographical US divisions is modelled via open source flight data alongside the impact of social distancing for each such division. We analyse the impact of the vaccination strategy on the current pandemic wave dynamics in the US. We observe that the ongoing vaccination campaign will not impact the current pandemic wave and therefore strict social distancing measures must still be enacted. To curb the current and the next waves our results indisputably show that vaccinations alone are not enough and strict social distancing measures are required until sufficient immunity is achieved. Our results are essential for a successful vaccination strategy in the US. | physics |
During the Parker Solar Probe's (PSP) first perihelion pass, the spacecraft reached within a heliocentric distance of \(\sim 37~R_\odot\) and observed numerous magnetic and flow structures characterized by sharp gradients. To better understand these intermittent structures in the young solar wind, an important property to examine is their degree of correlation in time and space. To this end, we use the well-tested Partial Variance of Increments (PVI) technique to identify intermittent events in FIELDS and SWEAP observations of magnetic and proton-velocity fields (respectively) during PSP's first solar encounter, when the spacecraft was within 0.25 au from the Sun. We then examine distributions of waiting times between events with varying separation and PVI thresholds. We find power-law distributions for waiting times shorter than a characteristic scale comparable to the correlation time, suggesting a high degree of correlation that may originate in a clustering process. Waiting times longer than this characteristic time are better described by an exponential, suggesting a random memory-less Poisson process at play. These findings are consistent with near-Earth observations of solar wind turbulence. The present study complements the one by Dudok de Wit et al. (2020, present volume), which focuses on waiting times between observed "switchbacks" in the radial magnetic field. | physics |
In 1980, Antonio Aurilia, Hermann Nicolai and I constructed an N=8 supergravity with a positive exponential potential for one of the 70 scalar fields by adapting the dimensional reduction of 11D supergravity to allow for a non-zero 4-form field-strength in 4D. This model, now viewed as a particular gauged maximal supergravity, had little influence at the time because it does not have a maximally-symmetric vacuum. However, as shown here, it does have a domain-wall solution, which lifts to the M2-brane solution of D=11 supergravity. The possibility of a similar construction for other branes of M-theory is also explored. | high energy physics theory |
In this paper, we give a partial solution to a new isomorphism problem about $2$-$(v,k,k-1)$ designs from disjoint difference families in finite fields and Galois rings. Our results are obtained by carefully calculating and bounding some block intersection numbers, and we give insight on the limitations of this technique. Moreover, we present results on cyclotomic numbers and on the structure of Galois rings of characteristic $p^2$. | mathematics |
We introduce a reinforcement learning environment based on Heroic - Magic Duel, a 1 v 1 action strategy game. This domain is non-trivial for several reasons: it is a real-time game, the state space is large, the information given to the player before and at each step of a match is imperfect, and distribution of actions is dynamic. Our main contribution is a deep reinforcement learning agent playing the game at a competitive level that we trained using PPO and self-play with multiple competing agents, employing only a simple reward of $\pm 1$ depending on the outcome of a single match. Our best self-play agent, obtains around $65\%$ win rate against the existing AI and over $50\%$ win rate against a top human player. | computer science |
High-fidelity manipulation is the key for the physical realization of fault-tolerant quantum computation. Here, we present a protocol to realize universal nonadiabatic geometric gates for silicon-based spin qubits. We find that the advantage of geometric gates over dynamical gates depends crucially on the evolution loop for the construction of the geometric phase. Under appropriate evolution loops, both the geometric single-qubit gates and the CNOT gate can outperform their dynamical counterparts for both systematic and detuning noises. We also perform randomized benchmarking using noise amplitudes consistent with experiments in silicon. For the static noise model, the averaged fidelities of geometric gates are around 99.90\% or above, while for the time-dependent $1/f$-type noise, the fidelities are around 99.98\% when only the detuning noise is present. We also show that the improvement in fidelities of the geometric gates over dynamical ones typically increases with the exponent $\alpha$ of the $1/f$ noise, and the ratio can be as high as 4 when $\alpha\approx 3$. Our results suggest that geometric gates with judiciously chosen evolution loops can be a powerful way to realize high-fidelity quantum gates. | quantum physics |
Owing to its capacity for unique (bio)-chemical specificity, microscopy withmid-IR illumination holds tremendous promise for a wide range of biomedical and industrial applications. The primary limitation, however, remains detection; with current mid-IR detection technology often marrying inferior technical capabilities with prohibitive costs. This has lead to approaches that shift detection towavelengths into the visible regime, where vastly superior silicon-based cameratechnology is available. Here, we experimentally show how nonlinear interferometry with entangled light can provide a powerful tool for mid-IR microscopy, while only requiring near-infrared detection with a standard CMOS camera. In this proof-of-principle implementation, we demonstrate intensity imaging overa broad wavelength range covering 3.4-4.3um and demonstrate a spatial resolution of 35um for images containing 650 resolved elements. Moreover, we demonstrate our technique is fit for purpose, acquiring microscopic images of biological tissue samples in the mid-IR. These results open a new perspective for potential relevance of quantum imaging techniques in the life sciences. | physics |
Image denoising is a classical signal processing problem that has received significant interest within the image processing community during the past two decades. Most of the algorithms for image denoising has focused on the paradigm of non-local similarity, where image blocks in the neighborhood that are similar, are collected to build a basis for reconstruction. Through rigorous experimentation, this paper reviews multiple aspects of image denoising algorithm development based on non-local similarity. Firstly, the concept of non-local similarity as a foundational quality that exists in natural images has not received adequate attention. Secondly, the image denoising algorithms that are developed are a combination of multiple building blocks, making comparison among them a tedious task. Finally, most of the work surrounding image denoising presents performance results based on Peak-Signal-to-Noise Ratio (PSNR) between a denoised image and a reference image (which is perturbed with Additive White Gaussian Noise). This paper starts with a statistical analysis on non-local similarity and its effectiveness under various noise levels, followed by a theoretical comparison of different state-of-the-art image denoising algorithms. Finally, we argue for a methodological overhaul to incorporate no-reference image quality measures and unprocessed images (raw) during performance evaluation of image denoising algorithms. | computer science |
Recently, a practical approach to holographic renormalization has been developed based on the Hamilton-Jacobi formulation. Using a simple Einstein-scalar theory, we clarify that this approach does not conflict with the Hamiltonian constraint as it seems. Then we apply it to the holographic renormalization of massive gravity. We assume that the shift vector is falling off fast enough asymptotically. We derive the counterterms up to the boundary dimension d=4. Interestingly, we find that the conformal anomaly can even occur in odd dimensions, which is different from the Einstein gravity. We check that the counterterms cancel the divergent part of the on-shell action at the background level. At the perturbation level, they are also applicable in several time-dependent cases. | high energy physics theory |
In this paper, we present a method for finding approximate Nash equilibria in a broad class of reachability games. These games are often used to formulate both collision avoidance and goal satisfaction. Our method is computationally efficient, running in real-time for scenarios involving multiple players and more than ten state dimensions. The proposed approach forms a family of increasingly exact approximations to the original game. Our results characterize the quality of these approximations and show operation in a receding horizon, minimally-invasive control context. Additionally, as a special case, our method reduces to local gradient-based optimization in the single-player (optimal control) setting, for which a wide variety of efficient algorithms exist. | electrical engineering and systems science |
Correlations in multiparticle systems are constrained by restrictions from quantum mechanics. A prominent example for these restrictions are monogamy relations, limiting the amount of entanglement between pairs of particles in a three-particle system. A powerful tool to study correlation constraints is the notion of sector lengths. These quantify, for different $k$, the amount of $k$-partite correlations in a quantum state in a basis-independent manner. We derive tight bounds on the sector lengths in multi-qubit states and highlight applications of these bounds to entanglement detection, monogamy relations and the $n$-representability problem. For the case of two- and three qubits we characterize the possible sector lengths completely and prove a symmetrized version of strong subadditivity for the linear entropy. | quantum physics |
Photoluminescence spectra have been investigated in erbium doped GaLaS(O) glasses. The samples demonstrate intense green emission bands centered at around 525 and 550 nm due to up-conversion processes in erbium ions. The theoretical description of up-conversion intensity as a function of excitation intensity has been offered. It is based on a solution of a system of rate equations taking into account three up-conversion transitions. | physics |
A class of classical affine W-algebras are shown to be isomorphic as differential algebras to the coordinate rings of double coset spaces of certain prounipotent proalgebraic groups. As an application, integrable Hamiltonian hierarchies associated with them are constructed geometrically, generalizing the corresponding result of Feigin-Frenkel and Enriquez-Frenkel for the principal cases. | mathematics |
We study the Fourier coefficients b(k,T) of the net baryon number density in strongly interacting matter at finite temperature. We show that singularities in the complex chemical potential plane connected with phase transitions are reflected in the asymptotic behavior of the coefficients at large k. We derive the scaling properties of b(k,T) near a second order phase transition in the O(4) and Z(2) universality classes. The impact of first order and crossover transitions is also examined. The scaling properties of b(k,T) are linked to the QCD phase diagram in the temperature and complex chemical potential plane. | high energy physics phenomenology |
We introduce a method for finding flux vacua of type IIB string theory in which the flux superpotential is exponentially small and at the same time one or more complex structure moduli are stabilized exponentially near to conifold points. | high energy physics theory |
In recent years, the filtering-clustering problems have been a central topic in statistics and machine learning, especially the $\ell_1$-trend filtering and $\ell_2$-convex clustering problems. In practice, such structured problems are typically solved by first-order algorithms despite the extremely ill-conditioned structures of difference operator matrices. Inspired by the desire to analyze the convergence rates of these algorithms, we show that for a large class of filtering-clustering problems, a \textit{global error bound} condition is satisfied for the dual filtering-clustering problems when a certain regularization is chosen. Based on this result, we show that many first-order algorithms attain the \textit{optimal rate of convergence} in different settings. In particular, we establish a generalized dual gradient ascent (GDGA) algorithmic framework with several subroutines. In deterministic setting when the subroutine is accelerated gradient descent (AGD), the resulting algorithm attains the linear convergence. This linear convergence also holds for the finite-sum setting in which the subroutine is the Katyusha algorithm. We also demonstrate that the GDGA with stochastic gradient descent (SGD) subroutine attains the optimal rate of convergence up to the logarithmic factor, shedding the light to the possibility of solving the filtering-clustering problems efficiently in online setting. Experiments conducted on $\ell_1$-trend filtering problems illustrate the favorable performance of our algorithms over other competing algorithms. | statistics |
Kibble-Zurek mechanism (KZM) is a universal framework which could in principle describe phase transition phenomenon in any system with required symmetry properties. However, a conflicting observation termed anti-KZ behavior has been reported in the study of ferroelectric phase transition, in which slower driving results in more topological defects [S. M. Griffin, et al. Phys. Rev. X. 2, 041022 (2012)]. Although this research is significant, its experimental simulations have been scarce until now. In this work, we experimentally demonstrate anti-KZ behavior under noisy control field in three kinds of quantum phase transition protocols using a single trapped Yb ion. The density of defects is studied as a function of the quench time and the noise intensity. We experimentally verify that the optimal quench time to minimize excitation scales as a universal power law of the noise intensity. Our research sets a stage for quantum simulation of such anti-KZ behavior in two-level systems and reveals the limitations of the adiabatic protocols such as quantum annealing. | quantum physics |
Proximal splitting-based convex optimization is a promising approach to linear inverse problems because we can use some prior knowledge of the unknown variables explicitly. In this paper, we firstly analyze the asymptotic property of the proximity operator for the squared loss function, which appears in the update equations of some proximal splitting methods for linear inverse problems. The analysis shows that the output of the proximity operator can be characterized with a scalar random variable in the large system limit. Moreover, we investigate the asymptotic behavior of the Douglas-Rachford algorithm, which is one of the famous proximal splitting methods. From the asymptotic result, we can predict the evolution of the mean-square-error (MSE) in the algorithm for large-scale linear inverse problems. Simulation results demonstrate that the MSE performance of the Douglas-Rachford algorithm can be well predicted by the analytical result in compressed sensing with the $\ell_{1}$ optimization. | electrical engineering and systems science |
In this work, we show fundamental low temperature (T) magnetic and Ic responses of a magnetic Josephson Junction (MJJ) S/F/S heterostructure - Nb/ Co56Fe24B20 /Nb. The ultra-thin Co56Fe24B20 (CFB) films (0.6-1.3 nm) were deposited onto two separate buffer layers: 150 nm Nb/5 nm Cu and 150 nm Nb/ (1 nm Cu/0.5 nm Nb)6/1 nm Cu. Both film sets were capped with 5 nm Cu/50 nm Nb. Magnetic results show reduced switching distributions in patterned arrays measured at near liquid Helium temperature (~ 10 K), with the incorporation of the (1 nm Cu/0.5 nm Nb)6/1 nm multilayer. In electrical devices, the critical current (Ic) through the CFB layer decays exponentially with increasing ferromagnetic layer thickness and shows a dip in Ic at 0.8 nm, characteristic of a change in the equilibrium Josephson phase in an S/F/S structure. | condensed matter |
Autonomous digital sky surveys such as Pan-STARRS have the ability to image a very large number of galactic and extra-galactic objects, and the large and complex nature of the image data reinforces the use of automation. Here we describe the design and implementation of a data analysis process for automatic broad morphology annotation of galaxies, and applied it to the data of Pan-STARRS DR1. The process is based on filters followed by a two-step convolutional neural network (CNN) classification. Training samples are generated by using an augmented and balanced set of manually classified galaxies. Results are evaluated for accuracy by comparison to the annotation of Pan-STARRS included in a previous broad morphology catalog of SDSS galaxies. Our analysis shows that a CNN combined with several filters is an effective approach for annotating the galaxies and removing unclean images. The catalog contains morphology labels for 1,662,190 galaxies with ~95% accuracy. The accuracy can be further improved by selecting labels above certain confidence thresholds. The catalog is publicly available. | astrophysics |
Satyendra Nath Bose's attempt to describe the quantum statistical aspects of light consistently in terms of particles, and Einstein's generalisation, lead to the concept of Bosons as a class of quanta obeying `Bose-Einstein statistics'. Their identity as a class came in sharp contrast when the Pauli exclusion principle and the Dirac equation revealed the other class called Fermions, obeying `Fermi-Dirac statistics'. Spin, and spin alone, is the determining factor of the multiparticle behaviour of fundamental quanta. This is the basis of the Spin-Statistics Connection. While it is known that the overall theoretical picture is consistent, the physical reason for the connection is unknown. Further, the class difference is sensitive only to the total spin in a quantum aggregate, as spectacularly seen in superconductivity and superfluidity, and in the Bose-Einstein condensation of neutral atomic gas. Can we grasp the true reason behind the difference in the collective behaviour of Bosons and Fermions? An explorer's journey demanding logical and physical consistency of what we already know takes us to the hidden factors in the relation between spin and the statistics of quanta. The surprising answer is in the domain of gravity, that too, on a cosmic scale. | physics |
The continuous penetration of distributed energy resources (DER) in the electric power grid is driving a new paradigm shift towards transactive energy system (TES), an active and more sustainable system characterized by distributed generation and energy exchanges among consumers and producers in the network. This transition, however, comes with challenges such as dealing with the nonlinear and non-convex power flows of the system, determining an optimal transaction price to maximize overall system welfare, and ensuring fairness for all participants. In this paper, we propose a three-stage transactive energy framework that aims to address these challenges. In the first stage, the cost without trading is calculated which will serve as the reference in the profit maximization problem in the next stage. DER dispatch, power flows and initial transaction payments/incentives of the participants will then be determined in the second stage. A benefit allocation algorithm is applied in the third control stage to determine the optimal transaction price and final payments/incentives that will ensure fairness for trading participants. The proposed framework was tested in an IEEE 33-bus system and results show that fair benefits are given for all participants during trading and the system operates within the network and economic constraints. | electrical engineering and systems science |
Along the way initiated by Carleo and Troyer [1], we construct the neural-network quantum state of transverse-field Ising model(TFIM) by an unsupervised machine learning method. Such a wave function is a map from the spin-configuration space to the complex number field determined by an array of network parameters. To get the ground state of the system, values of the network parameters are calculated by a Stochastic Reconfiguration(SR) method. We provide for this SR method an understanding from action principle and information geometry aspects. With this quantum state, we calculate key observables of the system, the energy, correlation function, correlation length, magnetic moment and susceptibility. As innovations, we provide a high efficiency method and use it to calculate entanglement entropy (EE) of the system and get results consistent with previous work very well. | condensed matter |
Asteroseismology is an exceptional tool for studying stars by using the properties of observed modes of oscillation. So far the process of performing an asteroseismic analysis of a star has remained somewhat esoteric and inaccessible to non-experts. In this software paper we describe PBjam, an open-source Python package for analyzing the frequency spectra of solar-like oscillators in a simple but principled and automated way. The aim of PBjam is to provide a set of easy-to-use tools to extract information about the radial and quadrupole oscillations in stars that oscillate like the Sun, which may then be used to infer bulk properties such as stellar mass, radius and age or even structure. Asteroseismology and its data analysis methods are becoming increasingly important as space-based photometric observatories are producing a wealth of new data, allowing asteroseismology to be applied in a wide range of contexts such as exoplanet, stellar structure and evolution, and Galactic population studies. | astrophysics |
Current arrow spine measurements rely on statically hanging a known weight at the shaft center and measuring the maximum deflection. This archaic method of measuring arrow stiffness ignores dynamic nature of the arrow when released from the bow. For this project, we built an apparatus to measure the dynamic characteristics of the arrow to better indicate arrow performance. Using stochastic perturbations from a voice coil actuator and displacement measurements, we successfully estimated the natural frequency, damping parameter, and mechanical stiffness of carbon, wood, and aluminum arrows of varying spines. Parameter estimates using a second order parameterized model showed agreement with the manufacturer rated spine values. In addition, high cycle fatigue testing was completed on each arrow material but showed no significant changes in arrow parameters. | electrical engineering and systems science |
In a recent work, a contribution to the Nernst current of a Dirac or Weyl semimetal coming from the conformal anomaly was reported. Being originated from an anomaly - a vacuum contribution -, a non-zero transport coefficient was predicted at zero temperature and chemical potential. In this work we perform a Kubo formula calculation of the thermoelectrical coefficient and confirm that the result agrees with the quantum field theory estimation in the limit of zero temperature and chemical potential. For finite chemical potential {\mu} around {\mu} = 0 the transverse Seebeck coefficient shows a plateau indicating that only the zero conformal Landau levels contributes to this intrinsic effect. This result opens the way to the experimental observation of a geometric anomaly which is much harder to explore than the standard chiral anomaly. | condensed matter |
We classify and characterize all invertible anomalies and all allowed topological terms related to various Standard Models (SM), Grand Unified Theories (GUT), and Beyond Standard Model (BSM) physics. By all anomalies, we mean the inclusion of (1) perturbative/local anomalies captured by perturbative Feynman diagram loop calculations, classified by $\mathbb{Z}$ free classes, and (2) non-perturbative/global anomalies, classified by finite group $\mathbb{Z}_N$ torsion classes. Our work built from [arXiv:1812.11967] fuses the math tools of Adams spectral sequence, Thom-Madsen-Tillmann spectra, and Freed-Hopkins theorem. For example, we compute bordism groups $\Omega^{G}_d$ and their invertible topological field theory invariants, which characterize $d$d topological terms and $(d-1)$d anomalies, protected by the following symmetry group $G$: $Spin\times \frac{SU(3)\times SU(2)\times U(1)}{\mathbb{Z}_q}$ for SM with $q=1,2,3,6$; $\frac{Spin \times Spin(n)}{\mathbb{Z}_2^F}$ or $Spin \times Spin(n)$ for SO(10) or SO(18) GUT as $n=10, 18$; $Spin \times SU(n)$ for Georgi-Glashow SU(5) GUT as $n=5$; $\frac{Spin\times \frac{SU(4)\times(SU(2)\times SU(2))}{\mathbb{Z}_{q'}}}{\mathbb{Z}_2^F}$ for Pati-Salam GUT as $q'=1,2$; and others. For SM with an extra discrete symmetry, we obtain new anomaly matching conditions of $\mathbb{Z}_{16}$, $\mathbb{Z}_{4}$, and $\mathbb{Z}_{2}$ classes in 4d beyond the familiar Witten anomaly. Our approach offers an alternative view of all anomaly matching conditions built from the lower-energy (B)SM or GUT, in contrast to high-energy Quantum Gravity or String Theory Landscape v.s. Swampland program, as bottom-up/top-down complements. Symmetries and anomalies provide constraints of kinematics, we further suggest constraints of quantum gauge dynamics, and new predictions of possible extended defects/excitations plus hidden BSM non-perturbative topological sectors. | high energy physics theory |
A variational solution procedure is reported for the many-particle no-pair Dirac-Coulomb-Breit Hamiltonian aiming at a parts-per-billion (ppb) convergence of the atomic and molecular energies, described within the fixed nuclei approximation. The procedure is tested for nuclear charge numbers from $Z=1$ (hydrogen) to $28$ (iron). Already for the lowest $Z$ values, a significant difference is observed from leading-order Foldy-Woythusen perturbation theory, but the observed deviations are smaller than the estimated self-energy and vacuum polarization corrections. | quantum physics |
The cosmic background radiation has been observed to deviate from the Planck law expected from a blackbody at $\sim$ 2.7 K at frequencies below $\sim 3$ GHz. We discuss the abundance of the low-energy photons from the perspective of nonequilibrium statistical mechanics. We propose a mechanism of stochastic frequency-diffusion, the counterpart to stochastic acceleration for charged particles in a turbulent plasma, to modify the standard Kompaneets equation. The resulting violation of the Einstein relation allows to take advantage of low-frequency localization and finally leads to photon cooling. The new equation predicts a frequency distribution in agreement with the absolute temperature measurements of the cosmic background radiation down to about 20 MHz, for which we offer here an updated compilation. In that sense, the so called 'space roar' we observe today is interpreted as a nonequilibrium echo of the early universe, and of nonequilibrium conditions in the primordial plasma more specifically. | astrophysics |
Perfusion imaging is the current gold standard for acute ischemic stroke analysis. It allows quantification of the salvageable and non-salvageable tissue regions (penumbra and core areas respectively). In clinical settings, the singular value decomposition (SVD) deconvolution is one of the most accepted and used approaches for generating interpretable and physically meaningful maps. Though this method has been widely validated in experimental and clinical settings, it might produce suboptimal results because the chosen inputs to the model cannot guarantee optimal performance. For the most critical input, the arterial input function (AIF), it is still controversial how and where it should be chosen even though the method is very sensitive to this input. In this work we propose an AIF selection approach that is optimized for maximal core lesion segmentation performance. The AIF is regressed by a neural network optimized through a differentiable SVD deconvolution, aiming to maximize core lesion segmentation agreement with ground truth data. To our knowledge, this is the first work exploiting a differentiable deconvolution model with neural networks. We show that our approach is able to generate AIFs without any manual annotation, and hence avoiding manual rater's influences. The method achieves manual expert performance in the ISLES18 dataset. We conclude that the methodology opens new possibilities for improving perfusion imaging quantification with deep neural networks. | electrical engineering and systems science |
We identify vertex operator algebras (VOAs) of a class of Argyres-Douglas (AD) matters with two types of non-abelian flavor symmetries. They are the $W$ algebra defined using nilpotent orbit with partition $[q^m,1^s]$. Gauging above AD matters, we can find VOAs for more general $\mathcal{N}=2$ SCFTs engineered from 6d $(2,0)$ theories. For example, the VOA for general $(A_{N-1}, A_{k-1})$ theory is found as the coset of a collection of above $W$ algebras. Various new interesting properties of 2d VOAs such as level-rank duality, conformal embedding, collapsing levels, coset constructions for known VOAs can be derived from 4d theory. | high energy physics theory |
The temperature dependence of quantum Hall conductivities is studied in the context of the AdS/CMT paradigm using a model with a bulk theory consisting of (3+1)-dimensional Einstein-Maxwell action coupled to a dilaton and an axion, with a negative cosmological constant. We consider a solution which has a Lifshitz like geometry with a dyonic black-brane in the bulk. There is an $Sl(2,R)$ action in the bulk corresponding to electromagnetic duality, which maps between classical solutions, and is broken to $Sl(2,Z)$ by Dirac quantisation of dyons. This bulk $Sl(2,Z)$ action translates to an action of the modular group on the 2-dimensional transverse conductivities. The temperature dependence of the infra-red conductivities is then linked to modular forms via gradient flow and the resulting flow diagrams show remarkable agreement with existing experimental data on the temperature flow of both integral and fractional quantum Hall conductivities. | high energy physics theory |
We discuss prospects of searching for a dark photon ($A'$) which serves as mediator between Standard model (SM) particles and light dark matter (LDM) by using the combined results from the NA64 experiment at the CERN SPS running in high-energy electron (NA64e) and muon (NA64$\mu$) modes. We discuss the most natural values and upper bounds on the $A'$ coupling constant to LDM and show they are lying in the range accessible at NA64. While for the projected $ 5\times10^{12}$ electrons on target (EOT) NA64e is able to probe the scalar and Majorana LDM scenarios, the combined NA64e and NA64$\mu$ results with $\simeq 10^{13}$ EOT and a few $10^{13}$ MOT, respectively, will allow covering significant region in the parameter space of the most interesting LDM models. This makes NA64e and NA64$\mu$ extremely complementary to each other and increases significantly the discovery potential of sub-GeV DM. | high energy physics phenomenology |
Magnetic Eternally Collapsing Objects (MECO) have been proposed as the central engines of galactic black hole candidates (GBHC) and supermassive active galactic nuclei (AGN). Previous work has shown that their luminosities and spectral and timing characteristics are in good agreement with observations. These features and the formation of jets are generated primarily by the interactions of accretion disks with an intrinsically magnetic central MECO. The interaction of accretion disks with the anchored magnetic fields of the central objects permits a unified description of properties for GBHC, AGN, neutron stars in low mass x-ray binaries and dwarf novae systems. The previously published MECO models have been based on a quasistatic Schwarzschild metric of General Relativity; however, the only essential feature of this metric is its ability to produce extreme gravitational redshifts. For reasons discussed in this article, an alternative development based on a quasistatic exponential metric is considered here. | physics |
Supermassive stars (SMSs) are candidates for being progenitors of supermassive quasars at high redshifts. However, their formation process requires strong mechanisms that would be able to extract the angular momentum of the gas that the SMSs accrete. We investigate under which conditions the magnetic coupling between an accreting SMS and its winds can remove enough angular momentum for accretion to proceed from a Keplerian disc. We numerically computed the rotational properties of accreting SMSs that rotate at the $\Omega\Gamma$-limit and estimated the magnetic field that is required to maintain the rotation velocity at this limit using prescriptions from magnetohydrodynamical simulations of stellar winds. We find that a magnetic field of 10 kG at the stellar surface is required to satisfy the constraints on stellar rotation from the $\Omega\Gamma$-limit. Magnetic coupling between the envelope of SMSs and their winds could allow for SMS formation by accretion from a Keplerian disc, provided the magnetic field is at the upper end of present-day observed stellar fields. Such fields are consistent with primordial origins. | astrophysics |
An implementation and an application of the combination of the genetic algorithm and Newton's method for solving a system of nonlinear equations is presented. The method first uses the advantage of the robustness of the genetic algorithm for guessing the rough location of the roots, then it uses the advantage of a good rate of convergence of Newton's method. An effective application of the method for the positioning problem of multiple small rovers proposed for the use in asteroid exploration is shown. | mathematics |
A two-stage stochastic optimization model for the design of the closed-loop cable layout of an Offshore Wind Farm (OWF) is presented. The model consists on a Mixed Integer Linear Program (MILP) with scenario numeration incorporation to account for both wind power and cable failure stochasticity. The objective function supports simultaneous optimization of: (i) Initial investment (network topology and cable sizing), (ii) Total electrical power losses costs, and (iii) Reliability costs due to energy curtailment from cables failures. The mathematical optimization program is embedded in an iterative framework called PCI (Progressive Contingency Incorporation), in order to simplify the full problem while still including its global optimum. The applicability of the method is demonstrated by tackling a real-world instance. Results show the functionality of the tool in quantifying the economic profitability when applying stochastic optimization compared to a deterministic approach, given certain values of failure parameters. | electrical engineering and systems science |
Variational inference (VI) is a widely used framework in Bayesian estimation. For most of the non-Gaussian statistical models, it is infeasible to find an analytically tractable solution to estimate the posterior distributions of the parameters. Recently, an improved framework, namely the extended variational inference (EVI), has been introduced and applied to derive analytically tractable solution by employing lower-bound approximation to the variational objective function. Two conditions required for EVI implementation, namely the weak condition and the strong condition, are discussed and compared in this paper. In practical implementation, the convergence of the EVI depends on the selection of the lower-bound approximation, no matter with the weak condition or the strong condition. In general, two approximation strategies, the single lower-bound (SLB) approximation and the multiple lower-bounds (MLB) approximation, can be applied to carry out the lower-bound approximation. To clarify the differences between the SLB and the MLB, we will also discuss the convergence properties of the aforementioned two approximations. Extensive comparisons are made based on some existing EVI-based non-Gaussian statistical models. Theoretical analysis are conducted to demonstrate the differences between the weak and the strong conditions. Qualitative and quantitative experimental results are presented to show the advantages of the SLB approximation. | statistics |
We present a methodology based on \textit{ex-situ} (post-growth) electrochemistry to control the oxygen concentration in thin films of the superconducting oxide La$_2$CuO$_{4+y}$ grown epitaxially on substrates of isostructural LaSrAlO$_4$. The superconducting transition temperature, which depends on the oxygen concentration, can be tuned by adjusting the pH level of the base solution used for the electrochemical reaction. As our main finding, we demonstrate that the dopant oxygens can either occupy the interstitial layer in an orientationally disordered state or organize into a crystalline phase via a mechanism in which dopant oxygens are inserted into the substrate, changing the lattice symmetry of both the substrate and the epitaxial film. We discuss this mechanism, and describe the resulting methodology as a platform to be explored in thin films of other transition metal oxides. | condensed matter |
Identifying the start time of a sequence of symbols received at the receiver, commonly referred to as \emph{frame synchronization}, is a critical task for achieving good performance in digital communications systems employing time-multiplexed transmission. In this work we focus on \emph{frame synchronization} for linear channels with memory in which the channel impulse response is periodic and the additive Gaussian noise is correlated and cyclostationary. Such channels appear in many communications scenarios, including narrowband power line communications and interference-limited wireless communications. We derive frame synchronization algorithms based on simplifications of the optimal likelihood-ratio test, assuming the channel impulse response is unknown at the receiver, which is applicable to many practical scenarios. The computational complexity of each of the derived algorithms is characterized, and a procedure for selecting nearly optimal synchronization sequences is proposed. The algorithms derived in this work achieve better performance than the noncoherent correlation detector, and, in fact, facilitate a controlled tradeoff between complexity and performance. | electrical engineering and systems science |
We perform an analysis of the $b\to c\tau\nu$ data, including $R(D^{(*)})$, $R(J/\psi)$, $P_\tau(D^{*})$ and $F_L^{D^*}$, within and beyond the Standard Model (SM). We fit the $B\to D^{(*)}$ hadronic form factors in the HQET parametrization to the lattice and the light-cone sum rule (LCSR) results, applying the general strong unitarity bounds corresponding to $J^P=1^-$, $1^+$, $0^-$ and $0^+$. Using the obtained HQET relations between helicity amplitudes, we give the strong unitarity bounds on individual helicity amplitudes, which can be used in the BGL fits. Using the fitted form factors and taking into account the most recent Belle measurement of $R(D^{(*)})$ we investigate the model-independent and the leptoquark model explanations of the $b\to c\tau\nu$ anomalies. Specifically, we consider the one-operator, the two-operator new physics (NP) scenarios and the NP models with a single $R_2$, $S_1$ or $U_1$ leptoquark which is supposed to be able to address the $b\to c\tau\nu$ anomalies, and our results show that the $R_2$ leptoquark model is in tension with the limit $\mathcal B(B_c\to \tau\nu)<10\%$. Furthermore, we give predictions for the various observables in the SM and the NP scenarios/leptoquark models based on the present form factor study and the analysis of NP. | high energy physics phenomenology |
Knee osteoarthritis (OA) is the most common musculoskeletal disease in the world. In primary healthcare, knee OA is diagnosed using clinical examination and radiographic assessment. Osteoarthritis Research Society International (OARSI) atlas of OA radiographic features allows to perform independent assessment of knee osteophytes, joint space narrowing and other knee features. This provides a fine-grained OA severity assessment of the knee, compared to the gold standard and most commonly used Kellgren-Lawrence (KL) composite score. However, both OARSI and KL grading systems suffer from moderate inter-rater agreement, and therefore, the use of computer-aided methods could help to improve the reliability of the process. In this study, we developed a robust, automatic method to simultaneously predict KL and OARSI grades in knee radiographs. Our method is based on Deep Learning and leverages an ensemble of deep residual networks with 50 layers, squeeze-excitation and ResNeXt blocks. Here, we used transfer learning from ImageNet with a fine-tuning on the whole Osteoarthritis Initiative (OAI) dataset. An independent testing of our model was performed on the whole Multicenter Osteoarthritis Study (MOST) dataset. Our multi-task method yielded Cohen's kappa coefficients of 0.82 for KL-grade and 0.79, 0.84, 0.94, 0.83, 0.84, 0.90 for femoral osteophytes, tibial osteophytes and joint space narrowing for lateral and medial compartments respectively. Furthermore, our method yielded area under the ROC curve of 0.98 and average precision of 0.98 for detecting the presence of radiographic OA (KL $\geq 2$), which is better than the current state-of-the-art. | electrical engineering and systems science |
Significant progress has been made using fMRI to characterize the brain changes that occur in ASD, a complex neuro-developmental disorder. However, due to the high dimensionality and low signal-to-noise ratio of fMRI, embedding informative and robust brain regional fMRI representations for both graph-level classification and region-level functional difference detection tasks between ASD and healthy control (HC) groups is difficult. Here, we model the whole brain fMRI as a graph, which preserves geometrical and temporal information and use a Graph Neural Network (GNN) to learn from the graph-structured fMRI data. We investigate the potential of including mutual information (MI) loss (Infomax), which is an unsupervised term encouraging large MI of each nodal representation and its corresponding graph-level summarized representation to learn a better graph embedding. Specifically, this work developed a pipeline including a GNN encoder, a classifier and a discriminator, which forces the encoded nodal representations to both benefit classification and reveal the common nodal patterns in a graph. We simultaneously optimize graph-level classification loss and Infomax. We demonstrated that Infomax graph embedding improves classification performance as a regularization term. Furthermore, we found separable nodal representations of ASD and HC groups in prefrontal cortex, cingulate cortex, visual regions, and other social, emotional and execution related brain regions. In contrast with GNN with classification loss only, the proposed pipeline can facilitate training more robust ASD classification models. Moreover, the separable nodal representations can detect the functional differences between the two groups and contribute to revealing new ASD biomarkers. | electrical engineering and systems science |
The vanishing of the Higgs quartic coupling at a high energy scale may be explained by Intermediate Scale Supersymmetry, where supersymmetry breaks at $(10^9$-$10^{12})$ GeV. The possible range of supersymmetry breaking scales can be narrowed down by precise measurements of the top quark mass and the strong coupling constant. On the other hand, nuclear recoil experiments can probe Higgsino or sneutrino dark matter up to a mass of $10^{12}$ GeV. We derive the correlation between the dark matter mass and precision measurements of standard model parameters, including supersymmetric threshold corrections. The dark matter mass is bounded from above as a function of the top quark mass and the strong coupling constant. The top quark mass and the strong coupling constant are bounded from above and below respectively for a given dark matter mass. We also discuss how the observed dark matter abundance can be explained by freeze-out or freeze-in during a matter-dominated era after inflation, with the inflaton condensate being dissipated by thermal effects. | high energy physics phenomenology |
Novel display technologies aim at providing the users with increasingly immersive experiences. In this regard, it is a long-sought dream to generate three-dimensional (3D) scenes with high resolution and continuous depth, which can be overlaid with the real world. Current attempts to do so, however, fail in providing either truly 3D information, or a large viewing area and angle, strongly limiting the user immersion. Here, we report a proof-of-concept solution for this problem, and realize a compact holographic 3D near-eye display with a large exit pupil of 10mm x 8.66mm. The 3D image is generated from a highly transparent Huygens metasurface hologram with large (>10^8) pixel count and subwavelength pixels, fabricated via deep-ultraviolet immersion photolithography on 300 mm glass wafers. We experimentally demonstrate high quality virtual 3D scenes with ~50k active data points and continuous depth ranging from 0.5m to 2m, overlaid with the real world and easily viewed by naked eye. To do so, we introduce a new design method for holographic near-eye displays that, inherently, is able to provide both parallax and accommodation cues, fundamentally solving the vergence-accommodation conflict that exists in current commercial 3D displays. | physics |
Solutions to the Stokes equations written in terms of a small number of hydrodynamic image singularities have been a useful tool in theoretical and numerical computations for nearly fifty years. In this article, we extend the catalogue of known solutions by deriving the flow expressions due to a general point torque and point source in the presence of a stationary sphere with either a no-slip or a stress-free (no shear) boundary condition. For an axisymmetric point torque and a no-slip sphere the image system simplifies to a single image point torque, reminiscent of the solution for a point charge outside an equipotential sphere in electrostatics. By symmetry, this also gives a simple representation of the solution due to an axisymmetric point torque inside a rigid spherical shell. In all remaining cases, the solution can be described by a collection of physically intuitive point and line singularities. Our results will be useful for the theoretical modelling of the propulsion of microswimmers and efficient numerical implementation of far-field hydrodynamic interactions in this geometry. | physics |
We theoretically demonstrate dynamically selective bidirectional emission and absorption of a single itinerant microwave photon in a waveguide. The proposed device is an artificial molecule composed of two qubits coupled to a waveguide a quarter-wavelength apart. By using simulations based on the input--output theory, we show that upon preparing an appropriate entangled state of the two qubits, a photon is emitted directionally as a result of the destructive interference occurring either at the right or left of the qubits. Moreover, we demonstrate that this artificial molecule possesses the capability of absorbing and transmitting an incoming photon on-demand, a feature essential to the creation of a fully inter-connected one-dimensional quantum network, in which quantum information can be exchanged between any two given nodes. | quantum physics |
In fifth generation (5G) and beyond Internet of Things (IoT), it becomes increasingly important to serve a massive number of IoT devices outside the coverage of terrestrial cellular networks. Due to their own limitations, unmanned aerial vehicles (UAVs) and satellites need to coordinate with each other in the coverage holes of 5G, leading to a cognitive satellite-UAV network (CSUN). In this paper, we investigate multi-domain resource allocation for CSUNs consisting of a satellite and a swarm of UAVs, so as to improve the efficiency of massive access in wide areas. Particularly, the cell-free on-demand coverage is established to overcome the cost-ineffectiveness of conventional cellular architecture. Opportunistic spectrum sharing is also implemented to cope with the spectrum scarcity problem. To this end, a process-oriented optimization framework is proposed for jointly allocating subchannels, transmit power and hovering times, which considers the whole flight process of UAVs and uses only the slowly-varying large-scale channel state information (CSI). Under the on-board energy constraints of UAVs and interference temperature constraints from UAV swarm to satellite users, we present iterative multi-domain resource allocation algorithms to improve network efficiency with guaranteed user fairness. Simulation results demonstrate the superiority of the proposed algorithms. Moreover, the adaptive cell-free coverage pattern is observed, which implies a promising way to efficiently serve wide-area IoT devices in the upcoming sixth generation (6G) era. | electrical engineering and systems science |
The incommensurate stacking of multi-layered two-dimensional materials is a challenging problem from a theoretical perspective and an intriguing avenue for manipulating their physical properties. Here we present a multi-scale model to obtain the mechanical relaxation pattern of twisted trilayer van der Waals (vdW) heterostructures with two independent twist angles, a generally incommensurate system without a supercell description. We adopt the configuration space as a natural description of such incommensurate layered materials, based on the local environment of atomic positions, bypassing the need for commensurate approximations. To obtain the relaxation pattern, we perform energy minimization with respect to the relaxation displacement vectors. We use a continuum model in combination with the Generalized Stacking Fault energy to describe the interlayer coupling, obtained from first-principles calculations based on Density Functional Theory. We show that the relaxation patterns of twisted trilayer graphene and $\mathrm{WSe_2}$ are "moir\'e of moir\'e", as a result of the incommensurate coupling two bilayer moir\'e patterns. We also show that, in contrast to the symmetry-preserving in-plane relaxation in twisted bilayers, trilayer relaxation can break the two-fold rotational symmetry about the xy-plane when the two twist angles are equal. | condensed matter |
We present a proximal augmented Lagrangian based solver for general convex quadratic programs (QPs), relying on semismooth Newton iterations with exact line search to solve the inner subproblems. The exact line search reduces in this case to finding the zero of a one-dimensional monotone, piecewise affine function and can be carried out very efficiently. Our algorithm requires the solution of a linear system at every iteration, but as the matrix to be factorized depends on the active constraints, efficient sparse factorization updates can be employed like in active-set methods. Both primal and dual residuals can be enforced down to strict tolerances and otherwise infeasibility can be detected from intermediate iterates. A C implementation of the proposed algorithm is tested and benchmarked against other state-of-the-art QP solvers for a large variety of problem data and shown to compare favorably against these solvers. | mathematics |
Spectrum cartography constructs maps of metrics such as channel gain or received signal power across a geographic area of interest using spatially distributed sensor measurements. Applications of these maps include network planning, interference coordination, power control, localization, and cognitive radios to name a few. Since existing spectrum cartography techniques require accurate estimates of the sensor locations, their performance is drastically impaired by multipath affecting the positioning pilot signals, as occurs in indoor or dense urban scenarios. To overcome such a limitation, this paper introduces a novel paradigm for spectrum cartography, where estimation of spectral maps relies on features of these positioning signals rather than on location estimates. Specific learning algorithms are built upon this approach and offer a markedly improved estimation performance than existing approaches relying on localization, as demonstrated by simulation studies in indoor scenarios. | electrical engineering and systems science |
The correct interpretation of the large amount of complex data from next-generation (in particular, space-based) observational facilities requires a very strong theoretical underpinning. One can thus predict that in the near future the use of atmospheric models obtained through the use of three-dimensional (3-D) radiation magnetohydrodynamics (RMHD) codes, coupled with advanced radiative transfer treatment including non-local thermodynamic equilibrium (non-LTE) effects and polarisation, will become the norm. In particular, stellar brightness variability in cool (i. e., spectral type F, G, K, and M) stars can be induced by several different effects, besides pulsation. We briefly discuss some literature results and mention some of our recent progress. Finally, we attempt to peek into the future of understanding this important aspect of the life of stars. | astrophysics |
We extend the cosmological bootstrap to correlators involving massless particles with spin. In de Sitter space, these correlators are constrained both by symmetries and by locality. In particular, the de Sitter isometries become conformal symmetries on the future boundary of the spacetime, which are reflected in a set of Ward identities that the boundary correlators must satisfy. We solve these Ward identities by acting with weight-shifting operators on scalar seed solutions. Using this weight-shifting approach, we derive three- and four-point correlators of massless spin-1 and spin-2 fields with conformally coupled scalars. Four-point functions arising from tree-level exchange are singular in particular kinematic configurations, and the coefficients of these singularities satisfy certain factorization properties. We show that in many cases these factorization limits fix the structure of the correlators uniquely, without having to solve the conformal Ward identities. The additional constraint of locality for massless spinning particles manifests itself as current conservation on the boundary. We find that the four-point functions only satisfy current conservation if the s, t, and u-channels are related to each other, leading to nontrivial constraints on the couplings between the conserved currents and other operators in the theory. For spin-1 currents this implies charge conservation, while for spin-2 currents we recover the equivalence principle from a purely boundary perspective. For multiple spin-1 fields, we recover the structure of Yang-Mills theory. Finally, we apply our methods to slow-roll inflation and derive a few phenomenologically relevant scalar-tensor three-point functions. | high energy physics theory |
We demonstrate the capability of block-copolymer templating to tune the refractive indices of functional oxides over a broad range by structuring materials on the 20-1000 atoms scale, with simple one-pot synthesis. The presented method is then combined with genetic algorithm-based optimization to explore its application for anti-reflection coating design. Merging these techniques allows for the realization of a minimal two-layer anti-reflection stack for silicon with broadband reflectivity of just 3% from the nominal value of 38%, over a 120{\deg} angular span, validated by fabrication followed by optical measurements. | condensed matter |
In recent years, there has been an explosion of AI research on counterfactual explanations as a solution to the problem of eXplainable AI (XAI). These explanations seem to offer technical, psychological and legal benefits over other explanation techniques. We survey 100 distinct counterfactual explanation methods reported in the literature. This survey addresses the extent to which these methods have been adequately evaluated, both psychologically and computationally, and quantifies the shortfalls occurring. For instance, only 21% of these methods have been user tested. Five key deficits in the evaluation of these methods are detailed and a roadmap, with standardised benchmark evaluations, is proposed to resolve the issues arising; issues, that currently effectively block scientific progress in this field. | computer science |
An external magnetic field can induce a transition in $\alpha$-RuCl$_3$ from an ordered zigzag state to a disordered state that is possibly related to the Kitaev quantum spin liquid. Here we present new field dependent inelastic neutron scattering and magnetocaloric effect measurements implying the existence of an additional transition out of the quantum spin liquid phase at an upper field limit $B_u$. The neutron scattering shows three distinct regimes of magnetic response. In the low field ordered state the response shows magnon peaks; the intermediate field regime shows only continuum scattering, and above $B_u$ the response shows sharp magnon peaks at the lower bound of a strong continuum. Measurable dispersion of magnon modes along the $(0,0,L)$ direction implies non-negligible inter-plane interactions. Combining the magnetocaloric effect measurements with other data a $T-B$ phase diagram is constructed. The results constrain the range where one might expect to observe quantum spin liquid behavior in $\alpha$-RuCl$_3$. | condensed matter |
We shall study the wall crossing behavior of moduli of stable sheaves on an elliptic surface. | mathematics |
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