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Let C be a general element in the locus of curves in M_g lying on some K3
surface, where g is congruent to 3 mod 4 and greater than or equal to 15.
Following Mukai's ideas, we show how to reconstruct the K3 surface as a
Fourier-Mukai transform of a Brill-Noether locus of rank two vector bundles on
C.
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When a d-dimensional quantum system is subjected to a periodic drive, it may
be treated as a (d+1)-dimensional system, where the extra dimension is a
synthetic one. In this work, we take these ideas to the next level by showing
that non-uniform potentials, and particularly edges, in the synthetic dimension
are created whenever the dynamics of system has a memory component. We
demonstrate that topological states appear on the edges of these synthetic
dimensions and can be used as a basis for a wave packet construction. Such
systems may act as an optical isolator which allows transmission of light in a
directional way. We supplement our ideas by an example of a physical system
that shows this type of physics.
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We quantify the rigidity of branching microstructures in shape memory alloys
undergoing cubic-to-tetragonal transformations in the geometrically linearized
theory by making use of Tartar's H-measures. The main result is a
$B^{2/3}_{1,\infty}$-estimate for the characteristic functions of twins, which
heuristically suggests that the larger-scale interfaces can cluster on a set of
Hausdorff-dimension $3-\frac{2}{3}$. We provide evidence indicating that the
dimension is optimal. Furthermore, we get an essentially local lower bound for
the blow-up behavior of the limiting energy density close to a habit plane.
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Close binaries ($a_{bin} < 20$ au) are known to harbor planets, yet planet
formation is unlikely to succeed in such systems. Studying the dynamics of
disks in close binaries can help to understand how those planets could have
formed. We study the impact that numerical and physical parameters have on the
dynamics of disks in close binaries. We use the $\gamma$-Cephei system as an
example and focus on disk quantities such as disk eccentricity and the
precession rate as indicators for the dynamical state of the disks. We simulate
disks in close binaries by performing two-dimensional radiative hydrodynamical
simulations using a modified version of the Fargo code. First, we perform a
parameter study for different numerical parameters to confirm that our results
are robust. In the second part, we study the effects of different masses and
different viscosities on the disks' dynamics. Previous studies on radiative
disks in close binaries used too low resolutions and too small simulation
domains, which impacted the disk's dynamics. We find that radiative disks in
close binaries, after an initialization phase, become eccentric with mean
eccentricities between 0.06 to 0.27 and display a slow retrograde precession
with periods ranging from $4 - 40T_{bin}$ which depends quadratically on the
disk's mean aspect ratio. In general, the disks show a coherent, rigid
precession which can be broken, however, by changes in the opacity law reducing
the overall eccentricity of the disk.
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This paper has been withdrawn by the author because the result of this paper
was already obtained.
|
The complexity of psychological principles underscore a significant societal
challenge, given the vast social implications of psychological problems.
Bridging the gap between understanding these principles and their actual
clinical and real-world applications demands rigorous exploration and adept
implementation. In recent times, the swift advancement of highly adaptive and
reusable artificial intelligence (AI) models has emerged as a promising way to
unlock unprecedented capabilities in the realm of psychology. This paper
emphasizes the importance of performance validation for these large-scale AI
models, emphasizing the need to offer a comprehensive assessment of their
verification from diverse perspectives. Moreover, we review the cutting-edge
advancements and practical implementations of these expansive models in
psychology, highlighting pivotal work spanning areas such as social media
analytics, clinical nursing insights, vigilant community monitoring, and the
nuanced exploration of psychological theories. Based on our review, we project
an acceleration in the progress of psychological fields, driven by these
large-scale AI models. These future generalist AI models harbor the potential
to substantially curtail labor costs and alleviate social stress. However, this
forward momentum will not be without its set of challenges, especially when
considering the paradigm changes and upgrades required for medical
instrumentation and related applications.
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Physical systems are often neither completely closed nor completely open, but
instead they are best described by dynamical systems with partial escape or
absorption. In this paper we introduce classical measures that explain the main
properties of resonance eigenfunctions of chaotic quantum systems with partial
escape. We construct a family of conditionally-invariant measures with varying
decay rates by interpolating between the natural measures of the forward and
backward dynamics. Numerical simulations in a representative system show that
our classical measures correctly describe the main features of the quantum
eigenfunctions: their multi-fractal phase space distribution, their product
structure along stable/unstable directions, and their dependence on the decay
rate. The (Jensen-Shannon) distance between classical and quantum measures goes
to zero in the semiclassical limit for long- and short-lived eigenfunctions,
while it remains finite for intermediate cases.
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A time-space traffic (TS) diagram, which presents traffic states in
time-space cells with color, is an important traffic analysis and visualization
tool. Despite its importance for transportation research and engineering, most
TS diagrams that have already existed or are being produced are too coarse to
exhibit detailed traffic dynamics due to the limitations of existing
information technology and traffic infrastructure investment. To increase the
resolution of a TS diagram and enable it to present ample traffic details, this
paper introduces the TS diagram refinement problem and proposes a multiple
linear regression-based model to solve the problem. Two tests, which attempt to
increase the resolution of a TS diagram 4 and 16 times, are carried out to
evaluate the performance of the proposed model. Data collected at different
times, in different locations and even in different countries are employed to
thoroughly evaluate the accuracy and transferability of the proposed model.
Strict tests with diverse data show that the proposed model, despite its
simplicity, is able to refine a TS diagram with promising accuracy and reliable
transferability. The proposed refinement model will "save" widely existing TS
diagrams from their blurry "faces" and enable TS diagrams to show more traffic
details.
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In the present paper, we construct two classes of non-weight modules
$\Omega(\lambda,\alpha,\beta)\otimes\mathrm{Ind}(M)$ and
$\mathcal{M}\big(V,\Omega(\lambda,\alpha,\beta)\big)$ over the twisted
Heisenberg-Virasoro algebra, which are both associated with the modules
$\Omega(\lambda,\alpha,\beta)$.
We present the necessary and sufficient conditions under which modules in
these two classes are irreducible and isomorphic, and also show that the
irreducible modules in these two classes are new. Finally, we construct
non-weight modules $\mathrm{Ind}_{\underline y,\lambda}(\C_{RS})$ and
$\mathrm{Ind}_{\underline z,\lambda}(\C_{PQ})$ over the twisted
Heisenberg-Virasoro algebra and then apply the established results to give
irreducible conditions for $\mathrm{Ind}_{\underline y,\lambda}(\C_{RS})$ and
$\mathrm{Ind}_{\underline z,\lambda}(\C_{PQ})$.
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We verified operational approach based on direct measurement of entanglement
degree for bipartite systems. In particular spectral distributions of single
counts and coincidence for pure biphoton states generated by train of short
pump pulses have been measured and entanglement quantifier calculated. The
approach gives upper bound of entanglement stored in total biphoton states,
which can reach extremely high value up to $10^{4}-10^{5}$.
|
We report a comprehensive set of density functional theory calculations on
the family of layered antiferromagnetic manganese pnictides (Ba, Ca,
Sr)$\mathrm{Mn}_2\mathrm{(P, As, Sb)}_2$. We characterize all components to the
linear magnetoelectric (ME) tensor $\alpha$ which are parsed into their
contributions from spin and orbital moments for both lattice-mediated and their
clamped-ion electronic analogs. Our main results show that the orbital
magnetization components cannot be neglected in these systems. The ME response
is dominated by electronic effects with total $\alpha$ values exceeding those
of the prototypical $\mathrm{Cr}_2\mathrm{O}_3$ (i.e. $\alpha \simeq$ 6.79 ps/m
in $\mathrm{BaMn}_2\mathrm{As}_2$). We also identify a strong correlation with
the computed ME susceptibility on pnictogen substitution in the trigonal
subfamily albeit with weaker amplitudes ($\alpha \simeq$ 0.2-1.7 ps/m).
Additionally, we provide the dependence of these predictions on the Hubbard +U
correction, at the level of the local density approximation, which show large
variations on the calculated ME coefficients in the tetragonal compounds
highlighting the role of strong correlation in these compounds.
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Defocusing mechanism provides a way to construct chaotic (hyperbolic)
billiards with focusing components by separating all regular components of the
boundary of a billiard table sufficiently far away from each focusing
component. If all focusing components of the boundary of the billiard table are
circular arcs, then the above separation requirement reduces to that all
circles obtained by completion of focusing components are contained in the
billiard table. In the present paper we demonstrate that a class of convex
tables--asymmetric lemons, whose boundary consists of two circular arcs,
generate hyperbolic billiards. This result is quite surprising because the
focusing components of the asymmetric lemon table are extremely close to each
other, and because these tables are perturbations of the first convex ergodic
billiard constructed more than forty years ago.
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Following Roe and others (see, e.g., [MR1451755]), we (re)develop coarse
geometry from the foundations, taking a categorical point of view. In this
paper, we concentrate on the discrete case in which topology plays no role. Our
theory is particularly suited to the development of the_Roe (C*-)algebras_
C*(X) and their K-theory on the analytic side; we also hope that it will be of
use in the strictly geometric/algebraic setting of controlled topology and
algebra. We leave these topics to future papers.
Crucial to our approach are nonunital coarse spaces, and what we call
_locally proper_ maps (which are actually implicit in [MR1988817]). Our_coarse
category_ Crs generalizes the usual one: its objects are nonunital coarse
spaces and its morphisms (locally proper) coarse maps modulo_closeness_. Crs is
much richer than the usual unital coarse category. As such, it has all nonzero
limits and all colimits. We examine various other categorical issues. E.g., Crs
does not have a terminal object, so we substitute a_termination functor_ which
will be important in the development of exponential objects (i.e., "function
spaces") and also leads to a notion of_quotient coarse spaces_. To connect our
methods with the standard methods, we also examine the relationship between Crs
and the usual coarse category of Roe.
Finally we briefly discuss some basic examples and applications. Topics
include_metric coarse spaces_,_continuous control_ [MR1277522], metric and
continuously controlled_coarse simplices_,_sigma-coarse spaces_ [MR2225040],
and the relation between quotient coarse spaces and the K-theory of Roe
algebras (of particular interest for continuously controlled coarse spaces).
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Approximately half of the planets discovered by NASA's Kepler mission are in
systems where just a single planet transits its host star, and the remaining
planets are observed to be in multi-planet systems. Recent analyses have
reported a dichotomy in the eccentricity distribution displayed by systems
where a single planet transits compared with that displayed by the multi-planet
systems. Using $N$-body simulations, we examine the hypothesis that this
dichotomy has arisen because inner systems of super-Earths are frequently
accompanied by outer systems of giant planets that can become dynamically
unstable and perturb the inner systems. Our initial conditions are constructed
using a subset of the known Kepler five-planet systems as templates for the
inner systems, and systems of outer giant planets with masses between those of
Neptune and Saturn that are centred on orbital radii $2 \le a_{\rm p} \le 10$
au. The parameters of the outer systems are chosen so that they are always
below an assumed radial velocity detection threshold of 3 ms$^{-1}$. The
results show an inverse relation between the mean eccentricities and the
multiplicites of the systems. Performing synthetic transit observation of the
final systems reveals dichotomies in both the eccentricity and multiplicity
distributions that are close to being in agreement with the Kepler data. Hence,
understanding the observed orbital and physical properties of the compact
systems of super-Earths discovered by Kepler may require holistic modelling
that couples the dynamics of both inner and outer systems of planets during and
after the epoch of formation.
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We give an explicit minimal graded free resolution, in terms of
representations of the symmetric group $S_d$, of a Galois-theoretic
configuration of $d$ points in $\mathbb{P}^{d-2}$ that was studied by Bhargava
in the context of ring parametrizations. When applied to the geometric generic
fiber of a simply branched degree $d$ cover of $\mathbb{P}^1$ by a relatively
canonically embedded curve $C$, our construction gives a new interpretation for
the splitting types of the syzygy bundles appearing in its relative minimal
resolution. Concretely, our work implies that all these splitting types consist
of scrollar invariants of resolvent covers. This vastly generalizes a prior
observation due to Casnati, namely that the first syzygy bundle of a degree $4$
cover splits according to the scrollar invariants of its cubic resolvent. Our
work also shows that the splitting types of the syzygy bundles, together with
the multi-set of scrollar invariants, belong to a much larger class of
multi-sets of invariants that can be attached to $C \to \mathbb{P}^1$: one for
each irreducible representation of $S_d$, i.e., one for each partition of $d$.
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The space of the structure (0,3)-tensors of the covariant derivatives of the
structure endomorphism and the metric on almost contact B-metric manifolds is
considered. A known decomposition of this space in orthogonal and invariant
subspaces with respect to the action of the structure group is used. We
determine the corresponding components of the structure tensor and consider the
case of the lowest dimension 3 of the studied manifolds. Some examples are
commented.
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In this paper we have given a generalisation of the earlier work by Prigogine
et al. who have constructed a phenomenological model of entropy production via
particle creation in the very early universe generated out of the vacuum rather
than from a singularity, by including radiation also as the energy source and
tried to develop an alternative cosmological model in which particle creation
prevents the big bang. We developed Radiation dominated model of the universe
which shows a general tendency that (i) it originates from instability of
vacuum rather than from a singularity. (ii) Up to a characteristic time
cosmological quantities like density, pressure, Hubble constant and expansion
parameter vary rapidly with time. (iii) After the characteristic time these
quantities settles down and the models are turned into de-sitter type model
with uniform matter, radiation, creation densities and Hubble's constant H. The
de-sitter regime survives during a decay time then connects continuously to a
usual adiabatic matter radiation RW universe.The interesting thing in the paper
is that we have related the phenomenological radiation dominated model to
macroscopic model of quantum particle creation in the early universe giving
rise to the present observed value of cosmic background radiation . It is also
found that the dust filled model tallies exactly with that of the Prigogine's
one, which justifies that our model is generalized Prigogine's model. Although
the model originates from instability of vacuum rather than from a singularity,
still there is a couple of unavoidable singularities in the model.
|
Gerbes are locally connected presheaves of groupoids. They are classified up
to local weak equivalence by path components in a 2-cocycle category taking
values in all sheaves of groups, their isomorphisms and homotopies. If F is a
full presheaf of sheaves of groups, isomorphisms and homotopies, then [*,BF] is
isomorphic to equivalence classes of gerbes locally equivalent to groups
appearing in F. Giraud's non-abelian cohomology object of equivalence classes
of gerbes with band L is isomorphic to morphisms in the homotopy category from
the point * to the homotopy fibre over L for a map defined on BF and taking
values in the classifying space for the stack completion of the fundamental
groupoid of F.
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We observed a distinct peak in the $\Lambda p$ invariant mass spectrum of
$^{3}{\rm He}(K^-, \, \Lambda p)n$, well below the mass threshold of $m_K + 2
m_p$. By selecting a relatively large momentum-transfer region $q = 350 \sim
650$ MeV/$c$, one can clearly separate the peak from the quasi-free process,
$\overline{K}N \rightarrow \overline{K}N$ followed by the non-resonant
absorption by the two spectator-nucleons $\overline{K}NN \rightarrow \Lambda N
$. We found that the simplest fit to the observed peak gives us a Breit-Wigner
pole position at $B_{\rm {\it Kpp}} = 47 \pm 3 \, (stat.) \,^{+3}_{-6}
\,(sys.)$ MeV having a width $\Gamma_{\rm {\it Kpp}} = 115 \pm 7 \, (stat.)
\,^{+10}_{-9} \,(sys.)$ MeV, and the $S$-wave Gaussian reaction form-factor
parameter $Q_{\rm {\it Kpp}} = 381 \pm 14 \, (stat.)\,^{+57}_{-0} \,(sys.)$
MeV/$c$, as a new form of the nuclear bound system with strangeness --
"$K^-pp$".
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With the aim of investigating whether stellar sources can account for the
>10^8 Msun dust masses inferred from mm/sub-mm observations of samples of
5<z<6.4 quasars,we develop a chemical evolution model which follows the
evolution of metals and dust on the stellar characteristic lifetimes, taking
into account dust destruction mechanisms.Using a grid of stellar dust yields as
a function of the initial mass and metallicity over the range 1-40 Msun and 0-1
Zsun,we show that the role of AGB stars in cosmic dust evolution at high
redshift might have been over-looked.We apply the chemical evolution model with
dust to the host galaxy of the most distant quasar at z=6.4, SDSS
J1148+5251.Given the current uncertainties on the star formation history of the
host galaxy, we have considered two models: (i) a star formation history
obtained in a numerical simulation by Li et al.(2007) which predicts that a
large stellar bulge is already formed at z=6.4,and (ii) a constant star
formation rate of 1000 Msun/yr, as suggested by the observations if most of the
FIR luminosity is due to young stars.The total mass of dust predicted at z=6.4
by the first model is 2x10^8Msun,within the range of values inferred by
observations,with a substantial contribution (80%) of AGB-dust.When a constant
star formation rate is adopted,the contribution of AGB-dust decreases to 50%
but the total mass of dust formed is a factor 2 smaller.Both models predict a
rapid enrichment of the ISM with metals and a relatively mild evolution of the
carbon abundance,in agreement with observational constraints. This supports the
idea that stellar sources can account for the dust observed but show that the
contribution of AGB stars to dust production cannot be neglected, even at the
most extreme redshifts currently accessible to observations.
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Generalized Goppa codes are defined by a code locator set $\mathcal{L}$ of
polynomials and a Goppa polynomial $G(x)$. When the degree of all code locator
polynomials in $\mathcal{L}$ is one, generalized Goppa codes are classical
Goppa codes. In this work, binary generalized Goppa codes are investigated.
First, a parity-check matrix for these codes with code locators of any degree
is derived. A careful selection of the code locators leads to a lower bound on
the minimum Hamming distance of generalized Goppa codes which improves upon
previously known bounds. A quadratic-time decoding algorithm is presented which
can decode errors up to half of the minimum distance. Interleaved generalized
Goppa codes are introduced and a joint decoding algorithm is presented which
can decode errors beyond half the minimum distance with high probability.
Finally, some code parameters and how they apply to the Classic McEliece
post-quantum cryptosystem are shown.
|
A relativistic gas in a Schwarzschild metric is studied within the framework
of a relativistic Boltzmann equation in the presence of gravitational fields,
where Marle's model for the collision operator of the Boltzmann equation is
employed. The transport coefficients of bulk and shear viscosities and thermal
conductivity are determined from the Chapman-Enskog method. It is shown that
the transport coefficients depend on the gravitational potential. Expressions
for the transport coefficients in the presence of weak gravitational fields in
the non-relativistic (low temperatures) and ultra-relativistic (high
temperatures) limiting cases are given. Apart from the temperature gradient the
heat flux has two relativistic terms. The first one, proposed by Eckart, is due
to the inertia of energy and represents an isothermal heat flux when matter is
accelerated. The other, suggested by Tolman, is proportional to the
gravitational potential gradient and indicates that -- in the absence of an
acceleration field -- a state of equilibrium of a relativistic gas in a
gravitational field can be attained only if the temperature gradient is
counterbalanced by a gravitational potential gradient.
|
Generative adversarial network (GAN) has achieved impressive success on
cross-domain generation, but it faces difficulty in cross-modal generation due
to the lack of a common distribution between heterogeneous data. Most existing
methods of conditional based cross-modal GANs adopt the strategy of
one-directional transfer and have achieved preliminary success on text-to-image
transfer. Instead of learning the transfer between different modalities, we aim
to learn a synchronous latent space representing the cross-modal common
concept. A novel network component named synchronizer is proposed in this work
to judge whether the paired data is synchronous/corresponding or not, which can
constrain the latent space of generators in the GANs. Our GAN model, named as
SyncGAN, can successfully generate synchronous data (e.g., a pair of image and
sound) from identical random noise. For transforming data from one modality to
another, we recover the latent code by inverting the mappings of a generator
and use it to generate data of different modality. In addition, the proposed
model can achieve semi-supervised learning, which makes our model more flexible
for practical applications.
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This paper is devoted to the study of the long wave approximation for water
waves under the influence of the gravity and a Coriolis forcing. We start by
deriving a generalization of the Boussinesq equations in 1D (in space) and we
rigorously justify them as an asymptotic model of the water waves equations.
These new Boussinesq equations are not the classical Boussinesq equations. A
new term due to the vorticity and the Coriolis forcing appears that can not be
neglected. Then, we study the Boussinesq regime and we derive and fully justify
different asymptotic models when the bottom is flat : a linear equation linked
to the Klein-Gordon equation admitting the so-called Poincar{\'e} waves; the
Ostrovsky equation, which is a generalization of the KdV equation in presence
of a Coriolis forcing, when the rotation is weak; and finally the KdV equation
when the rotation is very weak. Therefore, this work provides the first
mathematical justification of the Ostrovsky equation. Finally, we derive a
generalization of the Green-Naghdi equations in 1D in space for small
topography variations and we show that this model is consistent with the water
waves equations.
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When exposed to high magnetic fields, certain materials manifest an exotic
superconducting (SC) phase that has attracted considerable attention. A
proposed explanation for the origin of the high-field SC phase is the
Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state. This state is characterized by
inhomogeneous superconductivity, where the Cooper pairs have finite
center-of-mass momenta. Recently, the high-field SC phase was observed in FeSe,
and it was deemed to originate from the FFLO state. Here, we synthesize FeSe
single crystals with different levels of disorder. The level of disorder is
expressed by the ratio of the mean free path to the coherence length and ranges
between 35 and 1.2. The upper critical field \textit{B}$_{\rm{c}2}$ was
obtained by both resistivity and magnetic torque measurements over a wide range
of temperatures, which went as low as $\sim$0.5 K, and magnetic fields, which
went up to $\sim$38 T along the \textit{c} axis and in the \textit{ab} plane.
In the high-field region parallel to the \textit{ab} plane, an unusual SC phase
was confirmed in all the crystals, and the phase was found to be robust against
disorder. This result suggests that the high-field SC phase in FeSe is not a
conventional FFLO state.
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We derive global analytic representations of fundamental solutions for a
class of linear parabolic systems with full coupling of first order derivative
terms where coefficient may depend on space and time. Pointwise convergence of
the global analytic expansion is proved. This leads to analytic representations
of solutions of initial-boundary problems of first and second type in terms of
convolution integrals or convolution integrals and linear integral equations.
The results have both analytical and numerical impact. Analytically, our
representations of fundamental solutions of coupled parabolic systems may be
used to define generalized stochastic processes. Moreover, some classical
analytical results based on a priori estimates of elliptic equations are a
simple corollary of our main result. Numerically, accurate, stable and
efficient schemes for computation and error estimates in strong norms can be
obtained for a considerable class of Cauchy- and initial-boundary problems of
parabolic type. Furthermore, there are obvious and less obvious applications to
finance and physics. Warning: The argument given in the current version is only
valid in special cases (essentially the scalar case). A more involved argument
is needed for systems and will be communicated soon in a replacement,
|
Gravitational interactions between the Large Magellanic Cloud (LMC) and the
stellar and dark matter halo of the Milky Way are expected to give rise to
disequilibrium phenomena in the outer Milky Way. A local wake is predicted to
trail the orbit of the LMC, while a large-scale over-density is predicted to
exist across a large area of the northern Galactic hemisphere. Here we present
the detection of both the local wake and Northern over-density (hereafter the
"collective response") in an all-sky star map of the Galaxy based on 1301 stars
at 60<R_gal<100 kpc. The location of the wake is in good agreement with an
N-body simulation that includes the dynamical effect of the LMC on the Milky
Way halo. The density contrast of the wake and collective response are both
stronger in the data than in the simulation. The detection of a strong local
wake is independent evidence that the Magellanic Clouds are on their first
orbit around the Milky Way. The wake traces the path of the LMC, which will
provide insight into the orbit of the LMC, which in turn is a sensitive probe
of the mass of the LMC and the Milky Way. These data demonstrate that the outer
halo is not in dynamical equilibrium, as is often assumed. The morphology and
strength of the wake could be used to test the nature of dark matter and
gravity.
|
An experimental study of the production of up-going charged particles in
inelastic interactions of down-going underground muons is reported, using data
obtained from the MACRO detector at the Gran Sasso Laboratory. In a sample of
12.2 10^6 single muons, corresponding to a detector livetime of 1.55 y, 243
events are observed having an up-going particle associated with a down-going
muon. These events are analysed to determine the range and emission angle
distributions of the up-going particle, corrected for detection and
reconstruction efficiency. Measurements of the muon neutrino flux by
underground detectors are often based on the observation of through-going and
stopping muons produced in $\nu_\mu$ interactions in the rock below the
detector. Up-going particles produced by an undetected down-going muon are a
potential background source in these measurements. The implications of this
background for neutrino studies using MACRO are discussed.
|
We have developed a fully coupled-channel complex scaling method (ccCSM) for
the study of the most essential kaonic nucleus, $``K^-pp,"$ which is a resonant
state of a $\bar{K}NN$-$\pi\Sigma N$-$\pi\Lambda N$ coupled-channel system
based on a theoretical viewpoint. By employing the ccCSM and imposing the
correct boundary condition of resonance, the coupled-channel problem is
completely solved using a phenomenological energy-independent potential. As a
result of the ccCSM calculation of $``K^-pp,"$ in which all three channels are
treated explicitly, we have obtained three-body resonance as a Gamow state. The
resonance pole indicates that the binding energy of $``K^-pp"$ and the half
value of its mesonic decay width are 51 MeV and 16 MeV, respectively. In the
analysis of the resonant wave function obtained using the ccCSM, we clarify the
spatial configuration and channel compositions of $``K^-pp."$ Compared with
past studies of single-channel calculations based on effective $\bar{K}N$
potentials, the current study provides a guideline for the determination of the
$\bar{K}N$ energy to be used in effective potentials.
|
We present the stellar population analysis of a sample of 12 dwarf elliptical
galaxies, observed with the SAURON integral field unit, using the full-spectrum
fitting method. We show that star formation histories (SFHs) resolved into two
populations can be recovered even within a limited wavelength range, provided
that high S/N data is used. We confirm that dEs have had complex SFHs, with
star formation extending to (more) recent epochs: for the majority of our
galaxies star formation activity was either still strong a few ($\lesssim$ 5)
Gyr ago or they experienced a secondary burst of star formation roughly at that
time. This latter possibility is in agreement with the proposed dE formation
scenario where tidal harassment drives the gas remaining in their progenitors
inwards and induces a star formation episode. For one of our field galaxies,
ID0918, we find a correlation between its stellar population and kinematic
properties, pointing to a possible merger origin of its kinematically-decoupled
core. One of our cluster objects, VCC1431, appears to be composed exclusively
of an old population ($\gtrsim$ 10-12 Gyr). Combining this with our earlier
dynamical results, we conclude that the galaxy was either ram-pressure stripped
early on in its evolution in a group environment and subsequently tidally
heated, or that it evolved in situ in the cluster's central parts, compact
enough to avoid tidal disruption. These are only two of the examples
illustrating the SFH richness of these objects confirmed with our data.
|
Semantic Web is, without a doubt, gaining momentum in both industry and
academia. The word "Semantic" refers to "meaning" - a semantic web is a web of
meaning. In this fast changing and result oriented practical world, gone are
the days where an individual had to struggle for finding information on the
Internet where knowledge management was the major issue. The semantic web has a
vision of linking, integrating and analysing data from various data sources and
forming a new information stream, hence a web of databases connected with each
other and machines interacting with other machines to yield results which are
user oriented and accurate. With the emergence of Semantic Web framework the
na\"ive approach of searching information on the syntactic web is clich\'e.
This paper proposes an optimised semantic searching of keywords exemplified by
simulation an ontology of Indian universities with a proposed algorithm which
ramifies the effective semantic retrieval of information which is easy to
access and time saving.
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The sets of $k$-free integers in general quadratic number fields are studied,
with special emphasis on (extended) symmetries and their impact on the
topological dynamical systems induced by such integers. We establish
correspondences between number-theoretic and dynamical quantities, and use
symmetries and entropy to distinguish the systems.
|
The effective potential V in a massless self-coupled scalar theory and
massless scalar electrodynamics is considered. Both the MS and Coleman-Weinberg
renormalization schemes are examined. The renormalization scheme dependence of
V is determined. Upon summing all of the logarithmic contributions to V, it is
shown that the implicit and explicit dependence on the renormalization scale
{\mu} cancels. In addition, if there is spontaneous symmetry breaking, then the
dependence on the background field {\Phi} cancels, leaving V flat but with
non-perturbative contributions. The quartic scalar coupling in the
Coleman-Weinberg renormalization scheme consequently vanishes.
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It has long been known, since the classical work of (Arora, Karger,
Karpinski, JCSS~99), that \MC\ admits a PTAS on dense graphs, and more
generally, \kCSP\ admits a PTAS on "dense" instances with $\Omega(n^k)$
constraints. In this paper we extend and generalize their exhaustive sampling
approach, presenting a framework for $(1-\eps)$-approximating any \kCSP\
problem in \emph{sub-exponential} time while significantly relaxing the
denseness requirement on the input instance. Specifically, we prove that for
any constants $\delta \in (0, 1]$ and $\eps > 0$, we can approximate \kCSP\
problems with $\Omega(n^{k-1+\delta})$ constraints within a factor of
$(1-\eps)$ in time $2^{O(n^{1-\delta}\ln n /\eps^3)}$. The framework is quite
general and includes classical optimization problems, such as \MC, {\sc
Max}-DICUT, \kSAT, and (with a slight extension) $k$-{\sc Densest Subgraph}, as
special cases. For \MC\ in particular (where $k=2$), it gives an approximation
scheme that runs in time sub-exponential in $n$ even for "almost-sparse"
instances (graphs with $n^{1+\delta}$ edges). We prove that our results are
essentially best possible, assuming the ETH. First, the density requirement
cannot be relaxed further: there exists a constant $r < 1$ such that for all
$\delta > 0$, \kSAT\ instances with $O(n^{k-1})$ clauses cannot be approximated
within a ratio better than $r$ in time $2^{O(n^{1-\delta})}$. Second, the
running time of our algorithm is almost tight \emph{for all densities}. Even
for \MC\ there exists $r<1$ such that for all $\delta' > \delta >0$, \MC\
instances with $n^{1+\delta}$ edges cannot be approximated within a ratio
better than $r$ in time $2^{n^{1-\delta'}}$.
|
Measurements of the de Haas - van Alphen effect in the normal state of the
heavy Fermion superconductor CeCoIn5 have been carried out using a torque
cantilever at temperatures ranging from 20 to 500 mK and in fields up to 18
tesla. Angular dependent measurements of the extremal Fermi surface areas
reveal a more extreme two dimensional sheet than is found in either CeRhIn5 or
CeIrIn5. The effective masses of the measured frequencies range from 9 to 20
m*/m0.
|
We propose a novel and generic calibration technique for four-factor
foreign-exchange hybrid local-stochastic volatility models with stochastic
short rates. We build upon the particle method introduced by Guyon and
Labord\`ere [Nonlinear Option Pricing, Chapter 11, Chapman and Hall, 2013] and
combine it with new variance reduction techniques in order to accelerate
convergence. We use control variates derived from a calibrated pure local
volatility model, a two-factor Heston-type LSV model (both with deterministic
rates), and the stochastic (CIR) short rates. The method can be applied to a
large class of hybrid LSV models and is not restricted to our particular choice
of the diffusion. The calibration procedure is performed on real-world market
data for the EUR-USD currency pair and has a comparable run-time to the PDE
calibration of a two-factor LSV model alone.
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Using scattering amplitudes, we obtain the potential contributions to
conservative binary dynamics in general relativity at fourth post-Minkowskian
order, ${\cal O}(G^4)$. As in previous lower-order calculations, we harness
powerful tools from the modern scattering amplitudes program including
generalized unitarity, the double copy, and advanced multiloop integration
methods, in combination with effective field theory. The classical amplitude
involves polylogarithms with up to transcendental weight two and elliptic
integrals. We derive the radial action directly from the amplitude, and
determine the corresponding Hamiltonian in isotropic gauge. Our results are in
agreement with known overlapping terms up to sixth post-Newtonian order, and
with the probe limit. We also determine the post-Minkowskian energy loss from
radiation emission at ${\cal O}(G^3)$ via its relation to the tail effect.
|
In the present work, we report a systematic theoretical study of the $\log
ft$ values for the forbidden $\beta^-$ decay transitions in the $^{208}$Pb
region. For this, we have considered $^{206}$Hg $\rightarrow$ $^{206}$Tl,
$^{208}$Hg $\rightarrow$ $^{208}$Tl, $^{206}$Tl $\rightarrow$ $^{206}$Pb and
$^{208}$Tl $\rightarrow$ $^{208}$Pb transitions. We have performed shell model
calculations using KHH7B interaction in valence shell 58-114 for protons and
100-164 for neutrons by considering ${\it 1p-1h}$ excitations for both protons
and neutrons simultaneously for daughter nuclei. This study presents the first
shell model results of $\beta^-$-decay corresponding to the recent experimental
data.
|
Mirage mediation reduces the fine-tuning in the minimal supersymmetric
standard model by dynamically arranging a cancellation between anomaly-mediated
and modulus-mediated supersymmetry breaking. We explore the conditions under
which a mirage "messenger scale" is generated near the weak scale and the
little hierarchy problem is solved. We do this by explicitly including the
dynamics of the SUSY-breaking sector needed to cancel the cosmological
constant. The most plausible scenario for generating a low mirage scale does
not readily admit an extra-dimensional interpretation. We also review the
possibilities for solving the mu/Bmu problem in such theories, a potential
hidden source of fine-tuning.
|
In an earlier paper we introduced rectangular diagrams of surfaces and showed
that any isotopy class of a surface in the three-sphere can be presented by a
rectangular diagram. Here we study transformations of those diagrams and
introduce moves that allow transition between diagrams representing isotopic
surfaces. We also introduce more general combinatorial objects called mirror
diagrams and various moves for them that can be used to transform presentations
of isotopic surfaces to each other. The moves can be divided into two types so
that, vaguely speaking, type~I moves commute with type~II ones. This
commutation is the matter of the main technical result of the paper. We use it
as well as a relation of the moves to Giroux's convex surfaces to propose a new
method for distinguishing Legendrian knots. We apply this method to show that
two Legendrian knots having topological type $6_2$ are not equivalent. More
applications of the method will be a subject of subsequent papers.
|
Learning from imbalanced data is one of the most significant challenges in
real-world classification tasks. In such cases, neural networks performance is
substantially impaired due to preference towards the majority class. Existing
approaches attempt to eliminate the bias through data re-sampling or
re-weighting the loss in the learning process. Still, these methods tend to
overfit the minority samples and perform poorly when the structure of the
minority class is highly irregular. Here, we propose a novel deep meta-learning
technique to augment a given imbalanced dataset with new minority instances.
These additional data are incorporated in the classifier's deep-learning
process, and their contributions are learned explicitly. The advantage of the
proposed method is demonstrated on synthetic and real-world datasets with
various imbalance ratios.
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We examine the elements of the balance equation of entropy in open quantum
evolutions and their response as we go from a Markovian to a non-Markovian
situation. In particular, we look at the heat current and entropy production
rate in the non-Markovian reduced evolution, as well as a Markovian limit of
the same, experienced by one of two interacting systems immersed in a Markovian
bath. The analysis naturally leads us to define a heat current deficit and an
entropy production rate deficit, which are differences between the global and
local versions of the corresponding quantities. The investigation leads, in
certain cases, to a complementarity of the time-integrated heat current deficit
and the relative entropy of entanglement between the two systems.
|
The structure of multivariate semisimple codes over a finite chain ring $R$
is established using the structure of the residue field $\bar R$. Multivariate
codes extend in a natural way the univariate cyclic and negacyclic codes and
include some non-trivial codes over $R$. The structure of the dual codes in the
semisimple abelian case is also derived and some conditions on the existence of
selfdual codes over $R$ are studied.
|
We show that the homotopy colimit construction for diagrams of categories
with an operad action, recently introduced by Fiedorowicz, Stelzer and Vogt,
has the desired homotopy type for diagrams of weak braided monoidal categories.
This provides a more flexible way to realize E-2 spaces categorically.
|
In this paper we derive the canonical distribution as a stationary solution
of the Liouville equation for the classical dissipative system. Dissipative
classical systems can have stationary states look like canonical Gibbs
distributions. The condition for non-potential forces which leads to this
stationary solution is very simple: the power of the non-potential forces must
be directly proportional to the velocity of the Gibbs phase (phase entropy
density) change. The example of the canonical distribution for a linear
oscillator with friction is considered.
|
Skew Boolean algebras (skew BA) and Boolean-like algebras (nBA) are
one-pointed and n-pointed noncommutative generalisation of Boolean algebras,
respectively. We show that any nBA is a cluster of n isomorphic right-handed
skew BAs, axiomatised here as the variety of skew star algebras. The variety of
skew star algebras is shown to be term equivalent to the variety of nBAs. We
use skew BAs in order to develop a general theory of multideals for nBAs. We
also provide a representation theorem for right-handed skew BAs in terms of
nBAs of n-partitions.
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We propose a new model about diffusion of a product which includes a memory
of how many adopters or advertisements a non-adopter met, where (non-)adopters
mean people (not) possessing the product. This effect is lacking in the Bass
model. As an application, we utilize the model to fit the iPod sales data, and
so the better agreement is obtained than the Bass model.
|
In this paper, a mathematical analysis of the global dynamics of a viral
infection model in vivo is carried out. We study the dynamics of a hepatitis C
virus (HCV) model, under therapy, that considers both extracellular and
intracellular levels of infection. At present most mathematical modeling of
viral kinetics after treatment only addresses the process of infection of a
cell by the virus and the release of virions by the cell, while the processes
taking place inside the cell are not included. We prove that the solutions of
the new model with positive initial values are positive, exist globally in time
and are bounded. The model has two virus-free steady states. They are
distinguished by the fact that viral RNA is absent inside the cells in the
first state and present inside the cells in the second. There are basic
reproduction numbers associated to each of these steady states. If the basic
reproduction number of the first steady state is less than one then that state
is asymptotically stable. If the basic reproduction number of the first steady
state is greater than one and that of the second less than one then the second
steady state is asymptotically stable. If both basic reproduction numbers are
greater than one then we obtain various conclusions which depend on different
restrictions on the parameters of the model. Under increasingly strong
assumptions we prove that there is at least one positive steady state (infected
equilibrium), that there is a unique positive steady state and that the
positive steady state is stable. We also give a condition under which every
positive solution converges to a positive steady state. This is proved by
methods of Li and Muldowney. Finally, we illustrate the theoretical results by
numerical simulations.
|
Collective mode dynamics of the helical magnets coupled to electric
polarization via spin-orbit interaction is studied theoretically. The soft
modes associated with the ferroelectricity are not the transverse optical
phonons, as expected from the Lyddane-Sachs-Teller relation, but are the spin
waves hybridized with the electric polarization. This leads to the Drude-like
dielectric function $\epsilon(\omega)$ in the limit of zero magnetic
anisotropy. There are two more low-lying modes; phason of the spiral and
rotation of helical plane along the polarization axis. The roles of these soft
modes in the neutron scattering and antiferromagnetic resonance are revealed,
and a novel experiment to detect the dynamical magneto-electric coupling is
proposed.
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A general class of cosmological models driven by a non-local scalar field
inspired by string field theories is studied. In particular cases the scalar
field is a string dilaton or a string tachyon. A distinguished feature of these
models is a crossing of the phantom divide. We reveal the nature of this
phenomena showing that it is caused by an equivalence of the initial non-local
model to a model with an infinite number of local fields some of which are
ghosts. Deformations of the model that admit exact solutions are constructed.
These deformations contain locking potentials that stabilize solutions.
Bouncing and accelerating solutions are presented.
|
Elliptic curves with a known number of points over a given prime field with n
elements are often needed for use in cryptography. In the context of primality
proving, Atkin and Morain suggested the use of the theory of complex
multiplication to construct such curves. One of the steps in this method is the
calculation of a root modulo n of the Hilbert class polynomial H(X) for a
fundamental discriminant D. The usual way is to compute H(X) over the integers
and then to find the root modulo n. We present a modified version of the
Chinese remainder theorem (CRT) to compute H(X) modulo n directly from the
knowledge of H(X) modulo enough small primes. Our complexity analysis suggests
that asymptotically our algorithm is an improvement over previously known
methods.
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Motivated by recent work indicating that the UV continuum in AGN may be
produced by reradiation of energy absorbed from X-rays irradiating an accretion
disk, we present a calculation of the vertical structures and ultraviolet
spectra of X-ray irradiated accretion disks around massive non-rotating black
holes. After finding the radial dependence of vertically-integrated quantities
for these disks, we solve the equations of hydrostatic equilibrium, energy
balance, and frequency-dependent radiation transfer as functions of altitude.
To solve the last set of equations, we use a variable Eddington factor method.
We include electron scattering, free-free, and HI, HeI, and HeII bound-free
opacities and the corresponding continuum cooling processes.
While the overall spectral shape predicted by X-ray irradiation may be
compatible with observations, the Lyman edge emission feature it predicts is
not. This finding raises questions for many otherwise plausible models in which
X-ray irradiation plays a major role.
|
Understanding system-bath correlations in open quantum systems is essential
for various quantum information and technology applications. Derivations of
most master equations (MEs) for the dynamics of open systems require
approximations that mask dependence of the system dynamics on correlations,
since the MEs focus on reduced system dynamics. Here we demonstrate that the
most common MEs indeed contain hidden information about explicit
system-environment correlation. We unfold these correlations by recasting the
MEs into a universal form in which the system-bath correlation operator
appears. The equations include the Lindblad, Redfield, second-order
time-convolutionless, second-order Nakajima-Zwanzig, and second-order universal
Lindblad-like cases. We further illustrate our results in an example, which
implies that the second-order universal Lindblad-like equation captures
correlation more accurately than other standard techniques.
|
The ANTARES detector is the largest deep sea underwater neutrino telescope in
operation. The apparatus comprises a matrix of 885 photomultiplier tubes (PMTs)
which detect the Cherenkov light emitted by the charged leptons produced in the
charged current interactions of high energy neutrinos with the matter inside or
near the detector. Reconstruction of the muon track and energy can be achieved
using the time, position and charge information of the hits arriving to the
PMTs. A good calibration of the detector is necessary in order to ensure its
optimal performance. This contribution reviews the different calibration
systems and methods developed by the ANTARES Collaboration.
|
We evaluate quasielastic double-differential antineutrino cross sections
obtained in a phenomenological model based on the superscaling behavior of
electron scattering data and estimate the contribution of the vector
meson-exchange currents in the 2p-2h sector. We show that the impact of
meson-exchange currents for charge-changing antineutrino reactions is much
larger than in the neutrino case.
|
In this paper, we define Orlov-Schulman's operators $M_L$, $M_R$, and then
use them to construct the additional symmetries of the bigraded Toda hierarchy
(BTH). We further show that these additional symmetries form an interesting
infinite dimensional Lie algebra known as a Block type Lie algebra, whose
structure theory and representation theory have recently received much
attention in literature. By acting on two different spaces under the weak
W-constraints we find in particular two representations of this Block type Lie
algebra.
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The state of a quantum system acquires a phase factor, called the geometric
phase, when taken around a closed trajectory in the parameter space, which
depends only on the geometry of the parameter space. Due to its sensitive
nature, the geometric phase is instrumental in capturing weak effects such as
the acceleration-induced non-inertial quantum field theoretic effects. In this
paper, we study the geometric phase response of a circularly rotating detector
inside an electromagnetic cavity. Using the cavity, the non-inertial
contribution to the geometric phase can be isolated from or strengthened
relative to the inertial contribution. We show that the accumulative nature of
the geometric phase may facilitate the experimental observation of the
resulting, otherwise feeble, non-inertial contribution to the modified field
correlations inside the cavity. Specifically, we show that the atom acquires an
experimentally detectable geometric phase at accelerations of the order of
$\sim 10^{7}$ m/s$^2$ which is experimentally feasible.
|
We provide a numerical validation of a recently proposed phenomenological
theory to characterize the space-time statistical properties of a turbulent
puff, both in terms of bulk properties, such as the mean velocity, temperature
and size, and scaling laws for velocity and temperature differences both in the
viscous and in the inertial range of scales. In particular, apart from the more
classical shear-dominated puff turbulence, our main focus is on the recently
discovered new regime where turbulent fluctuations are dominated by buoyancy.
The theory is based on an adiabaticity hypothesis which assumes that
small-scale turbulent fluctuations rapidly relax to the slower large-scale
dynamics, leading to a generalization of the classical Kolmogorov and
Kolmogorov-Obukhov-Corrsin theories for a turbulent puff hosting a scalar
field. We validate our theory by means of massive direct numerical simulations
finding excellent agreement.
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We estimate polarizabilities of atoms in molecules without electron density,
using a Voronoi tesselation approach instead of conventional density
partitioning schemes. The resulting atomic dispersion coefficients are
calculated, as well as many-body dispersion effects on intermolecular potential
energies. We also estimate contributions from multipole electrostatics and
compare them to dispersion. We assess the performance of the resulting
intermolecular interaction model from dispersion and electrostatics for more
than 1,300 neutral and charged, small organic molecular dimers. Applications to
water clusters, the benzene crystal, the anti-cancer drug
ellipticine---intercalated between two Watson-Crick DNA base pairs, as well as
six macro-molecular host-guest complexes highlight the potential of this method
and help to identify points of future improvement. The mean absolute error made
by the combination of static electrostatics with many-body dispersion reduces
at larger distances, while it plateaus for two-body dispersion, in conflict
with the common assumption that the simple $1/R^6$ correction will yield proper
dissociative tails. Overall, the method achieves an accuracy well within
conventional molecular force fields while exhibiting a simple parametrization
protocol.
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We estimate the total population of near-Earth objects (NEOs) in the Solar
System, using an extensive, `Solar System to pixels' fake-asteroid simulation
to debias detections of real NEOs by the ATLAS survey. Down to absolute
magnitudes $H=25$ and 27.6 (diameters of $\sim 34$ and 10 meters, respectively,
for 15% albedo), we find total populations of $(3.72 \pm 0.49) \times 10^5$ and
$(1.59 \pm 0.45) \times 10^7$ NEOs, respectively. Most plausible sources of
error tend toward underestimation, so the true populations are likely larger.
We find the distribution of $H$ magnitudes steepens for NEOs fainter than $H
\sim 22.5$, making small asteroids more common than extrapolation from brighter
$H$ mags would predict. Our simulation indicates a strong bias against
detecting small but dangerous asteroids that encounter Earth with high relative
velocities -- i.e., asteroids in highly inclined and/or eccentric orbits.
Worldwide NEO discovery statistics indicate this bias affects global NEO
detection capability, to the point that an observational census of small
asteroids in such orbits is probably not currently feasible. Prompt and
aggressive followup of NEO candidates, combined with closer collaborations
between segments of the global NEO community, can increase detection rates for
these dangerous objects.
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We study the dynamics of cold atoms subjected to {\em pairs} of closely
time-spaced $\delta$-kicks from standing waves of light. The classical phase
space of this system is partitioned into momentum cells separated by trapping
regions. In a certain range of parameters it is shown that the classical motion
is well described by a process of anomalous diffusion. We investigate in detail
the impact of the underlying classical anomalous diffusion on the quantum
dynamics with special emphasis on the phenomenon of dynamical localization.
Based on the study of the quantum density of probability, its second moment and
the return probability we identify a region of weak dynamical localization
where the quantum diffusion is still anomalous but the diffusion rate is slower
than in the classical case. Moreover we examine how other relevant time scales
such as the quantum-classical breaking time or the one related to the beginning
of full dynamical localization are modified by the classical anomalous
diffusion. Finally we discuss the relevance of our results for the
understanding of the role of classical cantori in quantum mechanics.
|
Several years ago, G. Brodin, A. P. Misra, and M. Marklund considered "Spin
Contribution to the Ponderomotive Force in a Plasma" Phys. Rev. Lett.
\textbf{105}, 105004 (2010). They applied a two fluid model of electron gas
where spin-up and spin-down electrons are considered as two different species.
Their approach to this problem appears to be in disagreement with the Pauli
equation. The correct model is presented in this comment.
|
We analyze the light curves of 413 radio sources at submillimeter wavelengths
using data from the Submillimeter Array calibrator database. The database
includes more than 20,000 observations at 1.3 and 0.8 mm that span 13 years. We
model the light curves as a damped random walk and determine a characteristic
time scale $\tau$ at which the variability amplitude saturates. For the vast
majority of sources, primarily blazars and BL Lac objects, we find only lower
limits on $\tau$. For two nearby low luminosity active galactic nuclei, M81 and
M87, however, we measure $\tau=1.6^{+3.0}_{-0.9}$ days and
$\tau=45^{+61}_{-24}$ days, respectively ($2\sigma$ errors). Including the
previously measured $\tau=0.33\pm 0.16$ days for Sgr A*, we show an
approximately linear correlation between $\tau$ and black hole mass for these
nearby LLAGN. Other LLAGN with spectra that peak in the submm are expected to
follow this correlation. These characteristic time scales are comparable to the
minimum time scale for emission processes close to an event horizon, and
suggest that the underlying physics may be independent of black hole mass,
accretion rate, and jet luminosity.
|
Bose-Einstein condensate dark matter model and Randall-Sundrum type 2
brane-world theory are tested with galactic rotation curves. Analytical
expressions are derived for the rotational velocities of test particles around
the galactic center in both cases. The velocity profiles are fitted to the
observed rotation curve data of high surface brightness and low surface
brightness galaxies. The brane-world model fits better the rotation curves with
asymptotically flat behaviour.
|
Nowadays, there exists an abundance of theoretical approaches towards the
mesonic spectrum, ranging from confinement models of all kinds, i.e.,
glueballs, and quark-antiquark, multiquark and hybrid configurations, to models
in which only mesonic degrees of freedom are taken into account. Nature seems
to come out somewhere in the middle, neither preferring pure bound states, nor
effective meson-meson physics with only coupling constants and possibly form
factors. As a matter of fact, apart from a few exceptions, like pions and
kaons, Nature does not allow us to study mesonic bound states of any kind,
which is equivalent to saying that such states do not really exist. Hence,
instead of extrapolating from pions and kaons to the remainder of the meson
family, it is more democratic to consider pions and kaons mesonic resonances
that happen to come out below the lowest threshold for strong decay.
Nevertheless, confinement is an important ingredient for understanding the many
regularities observed in mesonic spectra. Therefore, excluding quark degrees of
freedom is also not the most obvious way of describing mesons in general, and
scalars and axial-vectors in particular.
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A new paradigm is required to facilitate the demand for the huge data storage
capacity and faster data processing in the future. Nano structures such as
magnetic skyrmions have been predicted to address this issues as these vortex
structures are the smallest particle-like magnetic features and are
topologically protected from crystallographic defects or magnetic disorder. We
report here stable skyrmions at room temperature and with zero applied field in
ebeam evaporated Ir Fe Ir MgO thin film stacks. Micromagnetic simulations show
that these skyrmions are induced by interfacial Dzyaloshinskii Moriya
interactions between the ferromagnetic and heavy metal ultra thin layers values
in the range between 3.1 to 3.6. We also show the field dependencies of the
skyrmion width and density. The room temperature zero field width is 110 nm,
approximately comparable to the value showed by Fert et al and Boulle et al for
the multi stacks thin film. DFT calculations corroborate our experimental
results by predicting a DMI value of 3.67.
|
Evolution in the measured rest frame ultraviolet spectral slope and
ultraviolet to optical flux ratios indicate a rapid evolution in the dust
obscuration of galaxies during the first 3 billion years of cosmic time (z>4).
This evolution implies a change in the average interstellar medium properties,
but the measurements are systematically uncertain due to untested assumptions,
and the inability to measure heavily obscured regions of the galaxies. Previous
attempts to directly measure the interstellar medium in normal galaxies at
these redshifts have failed for a number of reasons with one notable exception.
Here we report measurements of the [CII] gas and dust emission in 9 typical
(~1-4L*) star-forming galaxies ~1 billon years after the big bang (z~5-6). We
find these galaxies have >12x less thermal emission compared with similar
systems ~2 billion years later, and enhanced [CII] emission relative to the
far-infrared continuum, confirming a strong evolution in the interstellar
medium properties in the early universe. The gas is distributed over scales of
1-8 kpc, and shows diverse dynamics within the sample. These results are
consistent with early galaxies having significantly less dust than typical
galaxies seen at z<3 and being comparable to local low-metallicity systems.
|
Group twirling is crucial in quantum information processing, particularly in
randomized benchmarking and random compiling. While protocols based on Pauli
twirling have been effectively crafted to transform arbitrary noise channels
into Pauli channels for Clifford gates -- thereby facilitating efficient
benchmarking and mitigating worst-case errors -- practical twirling groups for
multi-qubit non-Clifford gates are lacking. In this work, we study the issue of
finding twirling groups for generic quantum gates within a widely used circuit
structure in randomized benchmarking or random compiling. For multi-qubit
controlled phase gates, which are essential in both the quantum Fourier
transform and quantum search algorithms, we identify optimal twirling groups
within the realm of classically replaceable unitary operations. In contrast to
the simplicity of the Pauli twirling group for Clifford gates, the optimal
groups for such gates are much larger, highlighting the overhead of tailoring
noise channels in the presence of global non-Clifford gates.
|
Intermediate mass protostarsprovide a bridge between theories of low- and
high-mass star formation. Emerging molecular outflows can be used to determine
the influence of fragmentation and multiplicity on protostellar evolution
through the correlation of outflow forces of intermediate mass protostars with
the luminosity. The aim of this paper is to derive outflow forces from outflows
of six intermediate mass protostellar regions and validate the apparent
correlation between total luminosity and outflow force seen in earlier work, as
well as remove uncertainties caused by different methodology. By comparing CO
6--5 observations obtained with APEX with non-LTE radiative transfer model
predictions, optical depths, temperatures, densities of the gas of the
molecular outflows are derived. Outflow forces, dynamical timescales and
kinetic luminosities are subsequently calculated. Outflow parameters, including
the forces, were derived for all sources. Temperatures in excess of 50 K were
found for all flows, in line with recent low-mass results. However, comparison
with other studies could not corroborate conclusions from earlier work on
intermediate mass protostars which hypothesized that fragmentation enhances
outflow forces in clustered intermediate mass star formation. Any enhancement
in comparison with the classical relation between outflow force and luminosity
can be attributed the use of a higher excitation line and improvement in
methods; They are in line with results from low-mass protostars using similar
techniques. The role of fragmentation on outflows is an important ingredient to
understand clustered star formation and the link between low and high-mass star
formation. However, detailed information on spatial scales of a few 100 AU,
covering all individual members is needed to make the necessary progress.
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A compelling use case of offline reinforcement learning (RL) is to obtain a
policy initialization from existing datasets followed by fast online
fine-tuning with limited interaction. However, existing offline RL methods tend
to behave poorly during fine-tuning. In this paper, we devise an approach for
learning an effective initialization from offline data that also enables fast
online fine-tuning capabilities. Our approach, calibrated Q-learning (Cal-QL),
accomplishes this by learning a conservative value function initialization that
underestimates the value of the learned policy from offline data, while also
being calibrated, in the sense that the learned Q-values are at a reasonable
scale. We refer to this property as calibration, and define it formally as
providing a lower bound on the true value function of the learned policy and an
upper bound on the value of some other (suboptimal) reference policy, which may
simply be the behavior policy. We show that offline RL algorithms that learn
such calibrated value functions lead to effective online fine-tuning, enabling
us to take the benefits of offline initializations in online fine-tuning. In
practice, Cal-QL can be implemented on top of the conservative Q learning (CQL)
for offline RL within a one-line code change. Empirically, Cal-QL outperforms
state-of-the-art methods on 9/11 fine-tuning benchmark tasks that we study in
this paper. Code and video are available at https://nakamotoo.github.io/Cal-QL
|
We present explicit expressions for the correlation functions of interacting
fermions in one dimension which are valid for arbitrary system sizes and
temperatures. The result applies to a number of very different strongly
correlated systems, including mesoscopic quantum wires, quantum Hall edges,
spin chains and quasi-one-dimensional metals. It is for example possible to
calculate Coulomb blockade oscillations from our expression and determine their
dependence on interaction strength and temperature. Numerical simulations show
excellent agreement with the analytical results.
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We present a generic algorithm for computing discrete logarithms in a finite
abelian p-group H, improving the Pohlig-Hellman algorithm and its
generalization to noncyclic groups by Teske. We then give a direct method to
compute a basis for H without using a relation matrix. The problem of computing
a basis for some or all of the Sylow p-subgroups of an arbitrary finite abelian
group G is addressed, yielding a Monte Carlo algorithm to compute the structure
of G using O(|G|^0.5) group operations. These results also improve generic
algorithms for extracting pth roots in G.
|
A fundamental gap in the current understanding of galaxies concerns the
thermodynamical evolution of the ordinary, baryonic matter. On one hand,
radiative emission drastically decreases the thermal energy content of the
interstellar plasma (ISM), inducing a slow cooling flow toward the centre. On
the other hand, the active galactic nucleus (AGN) struggles to prevent the
runaway cooling catastrophe, injecting huge amount of energy in the ISM. The
present study intends to deeply investigate the role of mechanical AGN feedback
in (isolated or massive) elliptical galaxies, extending and completing the mass
range of tested cosmic environments. Our previously successful feedback models,
in galaxy clusters and groups, demonstrated that AGN outflows, self-regulated
by cold gas accretion, are able to properly quench the cooling flow, without
destroying the cool core. Via 3D hydrodynamic simulations (FLASH 3.3),
including also stellar evolution, we show that massive mechanical AGN outflows
can indeed solve the cooling flow problem for the entire life of the galaxy, at
the same time reproducing typical observational features and constraints, such
as buoyant underdense bubbles, elliptical shock cocoons, sonic ripples,
dredge-up of metals, subsonic turbulence, and extended filamentary or nuclear
cold gas. In order to avoid overheating and totally emptying the isolated
galaxy, the frequent mechanical AGN feedback should be less powerful and
efficient (~1.e-4), compared to the heating required for more massive and bound
ellipticals surrounded by the intragroup medium (efficiency ~1.e-3).
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We present an end-to-end model using streaming physiological time series to
predict near-term risk for hypoxemia, a rare, but life-threatening condition
known to cause serious patient harm during surgery. Inspired by the fact that a
hypoxemia event is defined based on a future sequence of low SpO2 (i.e., blood
oxygen saturation) instances, we propose the hybrid inference network (hiNet)
that makes hybrid inference on both future low SpO2 instances and hypoxemia
outcomes. hiNet integrates 1) a joint sequence autoencoder that simultaneously
optimizes a discriminative decoder for label prediction, and 2) two auxiliary
decoders trained for data reconstruction and forecast, which seamlessly learn
contextual latent representations that capture the transition from present
states to future states. All decoders share a memory-based encoder that helps
capture the global dynamics of patient measurement. For a large surgical cohort
of 72,081 surgeries at a major academic medical center, our model outperforms
strong baselines including the model used by the state-of-the-art hypoxemia
prediction system. With its capability to make real-time predictions of
near-term hypoxemic at clinically acceptable alarm rates, hiNet shows promise
in improving clinical decision making and easing burden of perioperative care.
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Besides achieving secure communication between two spatially-separated
parties, another important issue in modern cryptography is related to secure
communication in time, i.e., the possibility to confidentially store
information on a memory for later retrieval. Here we explore this possibility
in the setting of quantum reading, which exploits quantum entanglement to
efficiently read data from a memory whereas classical strategies (e.g., based
on coherent states or their mixtures) cannot retrieve any information. From
this point of view, the technique of quantum reading can provide a new form of
technological security for data storage.
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The hadronization process for quarks combining into two mesons, q\bar q\to
MM' at temperature T is described within the SU(3) Nambu- Jona-Lasinio model
with finite current quark masses. Invariant matrix elements, cross-sections and
transition rates are calculated to leading order in a 1/N_c expansion. Four
independent classes, u\bar d, u\bar s, u\bar u and s\bar s\to hadrons are
analysed, and the yield is found to be dominated by pion production. Threshold
behaviour is determined by the exothermic or endothermic nature of the
processes constituting the hadronization class. A strong suppression of
transition rates is found at the pionic Mott temperature T_{M\pi}=212 MeV, at
which the pion becomes a resonant state. The mean time for hadronization is
calculated to be 2-4 fm/c near the Mott temperature. The calculation of
strangeness changing processes indicates that hadronization accounts for a 1%
increase in the absolute value of the kaon to pion ratio at T=150 MeV.
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We investigate the photon polarization tensor at finite temperature in the
presence of a static and homogeneous external magnetic field. In our scheme,
the Matsubara frequency summation is performed after Poisson summation, which
will be taken easily and convergent quickly in the frame of proper time
representation. Moreover, the dependence of Landau levels is expressed
explicitly. It demonstrates the convergence of summing Landau levels as it has
to be. Consequently, there is no necessary to truncate the Landau level in a
numerical estimation. At zero temperature, the Lowest Landau Level (LLL)
approximation is analytically satisfied for the imaginary parts of the vacuum
photon polarization tensor. Our results examine that, the LLL approximation is
not enough for the thermal photon polarization tensor, it gains the
contribution not only from the lowest Landau level but also up to the
finite-$n$ levels. Such large imaginary ones only show up at finite
temperatures, which is the so called Landau damping. It originates from the
absorption of soft fields by hard plasma constituents, which is a universal
feature of plasma systems. Finally, it was argued that the summation of
Matsubara frequency is not commuted with Landau level ones, such conjecture is
excluded in our calculations.
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We study the stimulated scattering instabilities of an intense linearly
polarized electromagnetic wave (EMW) in a relativistic plasma with degenerate
electrons. Starting from a relativistic hydrodynamic model and the Maxwell's
equations, we derive coupled nonlinear equations for low-frequency electron and
ion plasma oscillations that are driven by the EMW's ponderomotive force. The
nonlinear dispersion relations are then obtained from the coupled nonlinear
equations which reveal stimulated Raman scattering (SRS), stimulated Brillouin
scattering (SBS), and modulational instabilities (MIs) of EMWs. It is shown
that the thermal pressure of ions and the relativistic degenerate pressure of
electrons significantly modify the characteristics of SRS, SBS, and MIs.
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In 2003, Kechris, Pestov and Todorcevic showed that the structure of certain
separable metric spaces - called ultrahomogeneous - is closely related to the
combinatorial behavior of the class of their finite metric spaces. The purpose
of the present paper is to explore the different aspects of this connection.
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We study spin transport in lateral spin valves with constricted channels.
Using electromigration, we modulate the spin accumulation by continuously
varying the width of the non-magnetic channel at a single location. By fitting
the non-local spin signal data as a function of the non-magnetic channel
resistance, we extract all the relevant parameters regarding spin transport
from a single device. Simulations show that constricting the channel blocks the
diffusion of the accumulated spins rather than causing spin flipping. This
result could be used to improve the design of future spintronic devices devoted
to information processing.
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Granular materials are characterized by large collections of discrete
particles of sizes larger than one micron, where the particle-particle
interactions are significantly more important than the particle-fluid
interactions. These flows can be successfully modeled by the existing Kinetic
Theory (KT) models when they are in the dilute regime with low
particle-particle collision frequencies, yielding results that agree well with
the simulation results of the event-driven hard sphere model or the more
sophisticated soft-sphere Discrete Element Method (DEM). However, these KT
models become less accurate for granular flows with soft particles (low
particle stiffness) at high particle-particle collision frequencies when the
predicted collision interval (the time of free flight for a particle prior to
the next collision) is comparable to the collision duration; there is a large
discrepancy between the results of these KT models and those from the DEM
models. In this work we develop a new KT model that could be used to model
granular systems of high collision frequencies with a finite particle
stiffness. This is done by modifying the fluctuation energy dissipation rate to
incorporate the ratio of collision duration to collision interval, a parameter
that is determined by both the collision frequency and particle stiffness. We
use a linear-spring-dashpot collision scheme to model the elastic potential
energy in the system and to uncover the relationship between the constitutive
relations of KT and the ratio of collision duration to collision interval.
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A model for planar phenomena introduced by Jackiw and Pi and described by a
Lagrangian including a Chern-Simons term is considered. The associated
equations of motion, among which a 2+1 gauged nonlinear Schr\"odinger equation,
are rewritten into a gauge independent form involving the modulus of the matter
field. Application of a Painlev\'e analysis, as adapted to partial differential
equations by Weiss, Tabor and Carnevale, shows up resonance values that are all
integer. However, compatibility conditions need be considered which cannot be
satisfied consistently in general. Such a result suggests that the examined
equations are not integrable, but provides tools for the investigation of the
integrability of different reductions. This in particular puts forward the
familiar integrable Liouville and 1+1 nonlinear Schr\"odinger equations.
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New data on the anomalous magnetic moment of the muon together with the b->s
gamma decay rate and Higgs limits are considered within the supergravity
inspired constrained minimal supersymmetric model. We perform a global
statistical chi2 analysis of these data and show that the allowed region of
parameter space is bounded from below by the Higgs limit, which depends on the
trilinear coupling and from above by the anomalous magnetic moment.
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The electronic charge density plays a central role in determining the
behavior of matter at the atomic scale, but its computational evaluation
requires demanding electronic-structure calculations. We introduce an
atom-centered, symmetry-adapted framework to machine-learn the valence charge
density based on a small number of reference calculations. The model is highly
transferable, meaning it can be trained on electronic-structure data of small
molecules and used to predict the charge density of larger compounds with low,
linear-scaling cost. Applications are shown for various hydrocarbon molecules
of increasing complexity and flexibility, and demonstrate the accuracy of the
model when predicting the density on octane and octatetraene after training
exclusively on butane and butadiene. This transferable, data-driven model can
be used to interpret experiments, initialize electronic structure calculations,
and compute electrostatic interactions in molecules and condensed-phase
systems.
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We investigate and demonstrate the use of convolutional neural networks
(CNNs) for the task of distinguishing between merging and non-merging galaxies
in simulated images, and for the first time at high redshifts (i.e. $z=2$). We
extract images of merging and non-merging galaxies from the Illustris-1
cosmological simulation and apply observational and experimental noise that
mimics that from the Hubble Space Telescope; the data without noise form a
"pristine" data set and that with noise form a "noisy" data set. The test set
classification accuracy of the CNN is $79\%$ for pristine and $76\%$ for noisy.
The CNN outperforms a Random Forest classifier, which was shown to be superior
to conventional one- or two-dimensional statistical methods (Concentration,
Asymmetry, the Gini, $M_{20}$ statistics etc.), which are commonly used when
classifying merging galaxies. We also investigate the selection effects of the
classifier with respect to merger state and star formation rate, finding no
bias. Finally, we extract Grad-CAMs (Gradient-weighted Class Activation
Mapping) from the results to further assess and interrogate the fidelity of the
classification model.
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Inertial-range scaling behavior of high-order (up to order N=51) structure
functions of a passively advected vector field has been analyzed in the
framework of the rapid-change model with strong small-scale anisotropy with the
aid of the renormalization group and the operator-product expansion. It has
been shown that in inertial range the leading terms of the structure functions
are coordinate independent, but powerlike corrections appear with the same
anomalous scaling exponents as for the passively advected scalar field. These
exponents depend on anisotropy parameters in such a way that a specific
hierarchy related to the degree of anisotropy is observed. Deviations from
power-law behavior like oscillations or logarithmic behavior in the corrections
to structure functions have not been found.
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Accurate channel estimation is essential for broadband wireless
communications. As wireless channels often exhibit sparse structure, the
adaptive sparse channel estimation algorithms based on normalized least mean
square (NLMS) have been proposed, e.g., the zero-attracting NLMS (ZA-NLMS)
algorithm and reweighted zero-attracting NLMS (RZA-NLMS). In these NLMS-based
algorithms, the step size used to iteratively update the channel estimate is a
critical parameter to control the estimation accuracy and the convergence speed
(so the computational cost). However, invariable step-size (ISS) is usually
used in conventional algorithms, which leads to provide performance loss or/and
low convergence speed as well as high computational cost. To solve these
problems, based on the observation that large step size is preferred for fast
convergence while small step size is preferred for accurate estimation, we
propose to replace the ISS by variable step size (VSS) in conventional
NLMS-based algorithms to improve the adaptive sparse channel estimation in
terms of bit error rate (BER) and mean square error (MSE) metrics. The proposed
VSS-ZA-NLMS and VSS-RZA-NLMS algorithms adopt VSS, which can be adaptive to the
estimation error in each iteration, i.e., large step size is used in the case
of large estimation error to accelerate the convergence speed, while small step
size is used when the estimation error is small to improve the steady-state
estimation accuracy. Simulation results are provided to validate the
effectiveness of the proposed scheme.
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We investigate whether the quark gluon plasma (QGP) is created in small
colliding systems from analyses of various hadron yields and their ratios in
proton-proton (p+p), proton-lead (p+Pb) and lead-lead (Pb+Pb) collisions at LHC
energies. Recently, the ALICE Collaboration reports enhancement of yield ratio
of multi-strange hadrons to charged pions as a function of multiplicity at
mid-rapidity. Motivated by these results, we develop the dynamical core-corona
initialization framework and find that our results describe tendencies of the
ALICE data especially for multi-strange hadrons. These results indicate that
the QGP is partly formed in high multiplicity events in small colliding
systems.
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We use open string field theory to study the dynamics of unstable branes in
the bosonic string theory, in the background of a generic linear dilaton. We
find a simple exact solution describing a dynamical interpolation between the
perturbative vacuum and the recently discovered nonperturbative tachyon vacuum.
In our solution, the open string tachyon increases exponentially along a null
direction, after which nonlinearities set in and cause the solution to
asymptote to a static state. In particular, the wild oscillations of the open
string fields which plague the time-like rolling tachyon solution are entirely
absent. Our model thus represents the first example proving that the true
tachyon vacuum of open string field theory can be realized as the endpoint of a
dynamical transition from the perturbative vacuum.
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Transmission spectra are differential measurements that utilize stellar
illumination to probe transiting exoplanet atmospheres. Any spectral difference
between the illuminating light source and the disk-integrated stellar spectrum
due to starspots and faculae will be imprinted in the observed transmission
spectrum. However, few constraints exist for the extent of photospheric
heterogeneities in M dwarfs. Here, we model spot and faculae covering fractions
consistent with observed photometric variabilities for M dwarfs and the
associated 0.3-5.5 $\mu$m stellar contamination spectra. We find that large
ranges of spot and faculae covering fractions are consistent with observations
and corrections assuming a linear relation between variability amplitude and
covering fractions generally underestimate the stellar contamination. Using
realistic estimates for spot and faculae covering fractions, we find stellar
contamination can be more than $10 \times$ larger than transit depth changes
expected for atmospheric features in rocky exoplanets. We also find that
stellar spectral contamination can lead to systematic errors in radius and
therefore the derived density of small planets. In the case of the TRAPPIST-1
system, we show that TRAPPIST-1's rotational variability is consistent with
spot covering fractions $f_{spot} = 8^{+18}_{-7}\%$ and faculae covering
fractions $f_{fac} = 54^{+16}_{-46}\%$. The associated stellar contamination
signals alter transit depths of the TRAPPIST-1 planets at wavelengths of
interest for planetary atmospheric species by roughly 1-15 $\times$ the
strength of planetary features, significantly complicating $JWST$ follow-up
observations of this system. Similarly, we find stellar contamination can lead
to underestimates of bulk densities of the TRAPPIST-1 planets of $\Delta(\rho)
= -3^{+3}_{-8} \%$, thus leading to overestimates of their volatile contents.
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We briefly review the existing psi(2S) data taken at RHIC, the Tevatron and
the LHC. We systematically compare them with colour-singlet-model predictions
as a function of the center-of-mass energy, of the quarkonium rapidity and of
the quarkonium transverse momentum. The overall agreement is good except for
large transverse momenta. This points at the existence of large NNLO
corrections or points at colour-octet dominance.
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The transport of many kinds of singular structures in a medium, such as
vortex points/lines/sheets in fluids, dislocation loops in crystalline plastic
solids, or topological singularities in magnetism, can be expressed in terms of
the geometric (Lie) transport equation \[
\frac{\mathrm{d}}{\mathrm{d} t} T_t + \mathcal{L}_{b_t} T_t = 0 \] for a
time-indexed family of integral or normal $k$-currents $t \mapsto T_t$ in
$\mathbb{R}^d$. Here, $b_t$ is the driving vector field and $\mathcal{L}_{b_t}
T_t$ is the Lie derivative of $T_t$ with respect to $b_t$. Written in
coordinates for different values of $k$, this PDE encompasses the classical
transport equation ($k = d$), the continuity equation ($k = 0$), as well as the
equations for the transport of dislocation lines in crystals ($k = 1$) and
membranes in liquids ($k =d-1$). The top-dimensional and bottom-dimensional
cases have received a great deal of attention in connection with the
DiPerna--Lions and Ambrosio theories of Regular Lagrangian Flows. On the other
hand, very little is rigorously known at present in the
intermediate-dimensional cases. This work develops the theory of the geometric
transport equation for arbitrary $k$ and in the case of boundaryless currents
$T_t$, covering in particular existence and uniqueness of solutions, structure
theorems, rectifiability, and a number of Rademacher-type differentiability
results. The latter yield, given an absolutely continuous (in time) path $t
\mapsto T_t$, the existence almost everywhere of a ''geometric derivative'',
namely a driving vector field $b_t$. This subtle question turns out to be
intimately related to the critical set of the evolution, a new notion
introduced in this work, which is closely related to Sard's theorem and
concerns singularities that are ''smeared out in time''. Our differentiability
results are sharp, which we demonstrate through an explicit example.
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The practical importance of inference with robustness against large
bandwidths for causal effects in regression discontinuity and kink designs is
widely recognized. Existing robust methods cover many cases, but do not handle
uniform inference for CDF and quantile processes in fuzzy designs, despite its
use in the recent literature in empirical microeconomics. In this light, this
paper extends the literature by developing a unified framework of inference
with robustness against large bandwidths that applies to uniform inference for
quantile treatment effects in fuzzy designs, as well as all the other cases of
sharp/fuzzy mean/quantile regression discontinuity/kink designs. We present
Monte Carlo simulation studies and an empirical application for evaluations of
the Oklahoma pre-K program.
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We investigate the aggregation and phase separation of thin, living T.
tubifex worms that behave as active polymers. Randomly dispersed active worms
spontaneously aggregate to form compact, highly entangled blobs, a process
similar to polymer phase separation, and for which we observe power-law growth
kinetics. We find that the phase separation of active polymerlike worms does
not occur through Ostwald ripening, but through active motion and coalescence
of the phase domains. Interestingly, the growth mechanism differs from
conventional growth by droplet coalescence: the diffusion constant
characterizing the random motion of a worm blob is independent of its size, a
phenomenon that can be explained from the fact that the active random motion
arises from the worms at the surface of the blob. This leads to a fundamentally
different phase-separation mechanism that may be unique to active polymers.
|
We determine all pairs of real numbers $(\alpha, \beta)$ such that the
dilated floor functions $\lfloor \alpha x\rfloor$ and $\lfloor \beta x\rfloor$
commute under composition, i.e., such that $\lfloor \alpha \lfloor \beta
x\rfloor\rfloor = \lfloor \beta \lfloor \alpha x\rfloor\rfloor$ holds for all
real $x$.
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Two measurements of $A$ and $B$ are carried out one after the other. The
measurements of $A$ are controlled by the parameter $\lambda_A$ in the Kraus
operator, where the measurements of $B$ are controlled by the parameter
$\lambda_B$. Strong measurements imply that the parameters in the Kraus
operators approach infinite large values while weak measurements are carried
out when the parameters approach zero. Here we prove that by repeating on the
two successive measurements of $A$ and $B$ then: (1) Average over all
measurements of $A$ is invariant of the measurement strength parameters
$\lambda_A$ and $\lambda_B$. It implies that all surprising results obtained in
weak measurements of $A$ are washed out when the average is taken. (2) If the
operators $\hat A$ and $\hat B$ commute then the mean value of $B$ as obtained
by taking the average of the results for $B$ over all measurements is invariant
of $\lambda_A$ and $\lambda_B$. Moreover it is exactly equal to the expectation
value of $\hat B$ as expected for strong measurements of $B$. (3) If $\hat A$
and $\hat B$ do not commute \textit{and} another condition given in this paper
is satisfied then the mean value of the results obtained for $B$ depends on the
value of $\lambda_A$ and not on the value of $\lambda_B$. An illustrative
possible experiment to show the effect of the strength of the measurements of A
on the results obtained for the measurements of B is given.
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Von Neumann's psycho-physical parallelism requires the existence of an
interaction between subjective experiences and material systems. A hypothesis
is proposed that amends physics in a way that connects subjective states with
physical states, and a general model of the interaction is provided. A specific
example shows how the theory applies to pain consciousness. The implications
concerning quantum mechanical state creation and reduction are discussed, and
some mechanisms are suggested to seed the process. An experiment that tests the
hypothesis is described elsewhere. Key Words: von Neumann, psycho-physical,
consciousness, state reduction, state collapse, macroscopic superpositions,
conscious observer.
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Self-scaled barrier functions on self-scaled cones were introduced through a
set of axioms in 1994 by Y.E. Nesterov and M.J. Todd as a tool for the
construction of long-step interior point algorithms. This paper provides firm
foundation for these objects by exhibiting their symmetry properties, their
intimate ties with the symmetry groups of their domains of definition, and
subsequently their decomposition into irreducible parts and algebraic
classification theory. In a first part we recall the characterisation of the
family of self-scaled cones as the set of symmetric cones and develop a
primal-dual symmetric viewpoint on self-scaled barriers, results that were
first discovered by the second author. We then show in a short, simple proof
that any pointed, convex cone decomposes into a direct sum of irreducible
components in a unique way, a result which can also be of independent interest.
We then show that any self-scaled barrier function decomposes in an essentially
unique way into a direct sum of self-scaled barriers defined on the irreducible
components of the underlying symmetric cone. Finally, we present a complete
algebraic classification of self-scaled barrier functions using the
correspondence between symmetric cones and Euclidean Jordan algebras.
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First-order, rhombohedral to orthorhombic, stress-induced phase transitions
have been evidenced by bulk charge-stress measurements and X-ray diffraction
derived lattice strain measurements in [001]c-poled PZN-4.5PT. The transitions
are induced by uniaxial, compressive loads applied either along or
perpendicular to the poling direction. In each case, they occur via rotation of
the polar vector in the Cm monoclinic plane and the induced lattice strain is
hysteretic yet reversible. Although no depoling is observed in the transverse
mode, net depolarization is observed under longitudinal stress which is
important for the use of [001]c-poled PZN-PT and PMN-PT single crystals in
Tonpilz-type underwater projectors.
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In recent years two Krylov subspace methods have been proposed for solving
skew symmetric linear systems, one based on the minimum residual condition, the
other on the Galerkin condition. We give new, algorithm-independent proofs that
in exact arithmetic the iterates for these methods are identical to the
iterates for the conjugate gradient method applied to the normal equations and
the classic Craig's method, respectively, both of which select iterates from a
Krylov subspace of lower dimension. More generally, we show that projecting an
approximate solution from the original subspace to the lower-dimensional one
cannot increase the norm of the error or residual.
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Subsets and Splits
Filtered Text Samples
Retrieves 100 samples of text containing the specific phrase "You are a helpful assistant", providing limited insight into the dataset.
Helpful Assistant Text Samples
Returns a limited set of rows containing the phrase 'helpful assistant' in the text, providing basic filtering of relevant entries.