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• Publication . Preprint . Article . 2018

## The Spitzer-IRAC/MIPS Extragalactic Survey (SIMES): II enhanced nuclear accretion rate in galaxy groups at z$\sim$0.2

Open Access English
Authors:
Ivano Baronchelli; G. Rodighiero; Harry I. Teplitz; Claudia Scarlata; Alberto Franceschini; S. Berta; Laia Barrufet; Mattia Vaccari; Matteo Bonato; Laure Ciesla; +15 more
Publisher: HAL CCSD
Countries: France, Italy, United States
Project: EC | HELP (607254)

For a sample of star forming galaxies in the redshift interval 0.15$<$z$<$0.3, we study how both the relative strength of the AGN infra-red emission, compared to that due to the star formation (SF), and the numerical fraction of AGNs, change as a function of the total stellar mass of the hosting galaxy group (M$^{*}_{\mathrm{group}}$), between $10^{10.25}$ and $10^{11.9}$M$_{\odot}$. Using a multi-component SED fitting analysis, we separate the contribution of stars, AGN torus and star formation to the total emission at different wavelengths. This technique is applied to a new multi-wavelength data-set in the SIMES field (23 not redundant photometric bands), spanning the wavelength range from the UV (GALEX) to the far-IR (Herschel) and including crucial AKARI and WISE mid-IR observations (4.5 \mu m$<\lambda<$24 \mu m), where the BH thermal emission is stronger. This new photometric catalog, that includes our best photo-z estimates, is released through the NASA/IPAC Infrared Science Archive (IRSA). Groups are identified through a friends of friends algorithm ($\sim$62% purity, $\sim$51% completeness). We identified a total of 45 galaxies requiring an AGN emission component, 35 of which in groups and 10 in the field. We find BHAR$\propto ($M$^{*}_{\mathrm{group}})^{1.21\pm0.27}$ and (BHAR/SFR)$\propto ($M$^{*}_{\mathrm{group}})^{1.04\pm0.24}$ while, in the same range of M$^{*}_{\mathrm{group}}$, we do not observe any sensible change in the numerical fraction of AGNs. Our results indicate that the nuclear activity (i.e. the BHAR and the BHAR/SFR ratio) is enhanced when galaxies are located in more massive and richer groups. Comment: 31 pages, 23 figures

• Publication . Article . Preprint . 2021

## Contrasting processing tomato cultivars unlink yield and pollen viability under heat stress

Open Access English
Authors:
Golan Miller; Avital Beery; Prashant Kumar Singh; Fengde Wang; Rotem Zelingher; Etel Motenko; Michal Lieberman-Lazarovich;

pmc:

pmid:

Publisher: Oxford University Press
Country: France

Abstract Climate change is causing temperature increment in crop production areas worldwide, generating conditions of heat stress that negatively affect crop productivity. Tomato (Solanum lycopersicum), a major vegetable crop, is highly susceptible to conditions of heat stress. When tomato plants are exposed to ambient day/night temperatures that exceed 32 °C/20 °C, respectively, during the reproductive phase, fruit set and fruit weight are reduced, leading to a significant decrease in yield. Processing tomato cultivars are cultivated in open fields, where environmental conditions are not controlled; therefore, plants are exposed to multiple abiotic stresses, including heat stress. Nonetheless, information on stress response in processing tomatoes is very limited. Understanding the physiological response of modern processing tomato cultivars to heat stress may facilitate the development of thermotolerant cultivars. Here, we compared two tomato processing cultivars, H4107 and H9780, that we found to be constantly differing in yield performance. Using field and temperature-controlled greenhouse experiments, we show that the observed difference in yield is attributed to the occurrence of heat stress conditions. In addition, fruit set and seed production were significantly higher in the thermotolerant cultivar H4107, compared with H9780. Despite the general acceptance of pollen viability as a measure of thermotolerance, there was no difference in the percentage of viable pollen between H4107 and H9780 under either of the conditions tested. In addition to observations of similar pollen germination and bud abscission rates, our results suggest that processing tomato cultivars may present a particular case, in which pollen performance is not determining reproductive thermotolerance. Our results also demonstrate the value of combining controlled and uncontrolled experimental settings, in order to validate and identify heat stress-related responses, thus facilitating the development of thermotolerant processing tomato cultivars. Our paper deals with the response of tomato plants to high temperatures. Tomato is an important crop, and tomato plants are very sensitive to high temperatures. Therefore, the increase in temperatures due to climate change poses a threat to tomato production. We found that a specific tomato cultivar is heat stress-tolerant, with better productivity under high temperatures. Usually, such tolerance is linked with pollen grains viability. Interestingly, in our case, pollen characteristics were eliminated as a causal factor for heat stress tolerance, meaning that other factors are involved. Follow-up studies are performed towards the development of heat-tolerant tomato.

• Publication . Article . Other literature type . Preprint . 2019

## Cooperative Games With Bounded Dependency Degree

Open Access
Authors:
Igarashi, Ayumi; Izsak, Rani; Elkind, Edith;
Publisher: Association for the Advancement of Artificial Intelligence (AAAI)
Country: United Kingdom
Project: EC | ACCORD (639945)

Cooperative games provide a framework to study cooperation among self-interested agents. They offer a number of solution concepts describing how the outcome of the cooperation should be shared among the players. Unfortunately, computational problems associated with many of these solution concepts tend to be intractable---NP-hard or worse. In this paper, we incorporate complexity measures recently proposed by Feige and Izsak (2013), called dependency degree and supermodular degree, into the complexity analysis of cooperative games. We show that many computational problems for cooperative games become tractable for games whose dependency degree or supermodular degree are bounded. In particular, we prove that simple games admit efficient algorithms for various solution concepts when the supermodular degree is small; further, we show that computing the Shapley value is always in FPT with respect to the dependency degree. Finally, we note that, while determining the dependency among players is computationally hard, there are efficient algorithms for special classes of games. 10 pages, full version of accepted AAAI-18 paper

• Publication . Preprint . Article . 2021

## Making the most of potential: potential games and genotypic convergence

Open Access English
Authors:
Omer Edhan; Ziv Hellman; Ilan Nehama;

pmc:

pmid:

Publisher: The Royal Society
Country: United Kingdom

AbstractWe consider genotypic convergence of populations and show that under fixed fitness asexual and haploid sexual populations attain monomorphic convergence (even under genetic linkage between loci) to basins of attraction with locally exponential convergence rates; the same convergence obtains in single locus diploid sexual reproduction but to polymorphic populations. Furthermore, we show that there is a unified underlying theory underlying these convergences: all of them can be interpreted as instantiations of players in a potential game implementing a multiplicative weights updating algorithm to converge to equilibrium, making use of the Baum–Eagon Theorem. To analyse varying environments, we introduce the concept of ‘virtual convergence’, under which, even if fixation is not attained, the population nevertheless achieves the fitness growth rate it would have had under convergence to an optimal genotype. Virtual convergence is attained by asexual, haploid sexual, and multi-locus diploid reproducing populations, even if environments vary arbitrarily. We also study conditions for true monomorphic convergence in asexually reproducing populations in varying environments.

• Publication . Preprint . Conference object . Article . 2019

## Learning Context Graph for Person Search

Open Access
Authors:
Yichao Yan; Qiang Zhang; Bingbing Ni; Wendong Zhang; Minghao Xu; Xiaokang Yang;
Publisher: IEEE

Person re-identification has achieved great progress with deep convolutional neural networks. However, most previous methods focus on learning individual appearance feature embedding, and it is hard for the models to handle difficult situations with different illumination, large pose variance and occlusion. In this work, we take a step further and consider employing context information for person search. For a probe-gallery pair, we first propose a contextual instance expansion module, which employs a relative attention module to search and filter useful context information in the scene. We also build a graph learning framework to effectively employ context pairs to update target similarity. These two modules are built on top of a joint detection and instance feature learning framework, which improves the discriminativeness of the learned features. The proposed framework achieves state-of-the-art performance on two widely used person search datasets. To appear in CVPR 2019

• Publication . Article . Preprint . 2020

## A bright, high rotation-measure FRB that skewers the M33 halo

Open Access
Authors:
Liam Connor; J. van Leeuwen; L. C. Oostrum; Emily Petroff; Yogesh Maan; Elizabeth A. K. Adams; Jisk Attema; J. E. Bast; Oliver M. Boersma; H. Dénes; +31 more
Publisher: Oxford University Press (OUP)
Country: Netherlands
Project: NWO | ARTS - the Apertif Radio ... (10066), EC | RadioNet (730562), EC | ALERT (617199), NWO | Microporous membranes fro... (5831), NWO | ARGOThe Apertif Radio – G... (31150)

ABSTRACT We report the detection of a bright fast radio burst, FRB 191108, with Apertif on the Westerbork Synthesis Radio Telescope. The interferometer allows us to localize the FRB to a narrow 5 arcsec × 7 arcmin ellipse by employing both multibeam information within the Apertif phased-array feed beam pattern, and across different tied-array beams. The resulting sightline passes close to Local Group galaxy M33, with an impact parameter of only 18 kpc with respect to the core. It also traverses the much larger circumgalactic medium (CGM) of M31, the Andromeda Galaxy. We find that the shared plasma of the Local Group galaxies could contribute ∼10 per cent of its dispersion measure of 588 pc cm−3. FRB 191108 has a Faraday rotation measure (RM) of +474 $\pm \, 3$ rad m−2, which is too large to be explained by either the Milky Way or the intergalactic medium. Based on the more moderate RMs of other extragalactic sources that traverse the halo of M33, we conclude that the dense magnetized plasma resides in the host galaxy. The FRB exhibits frequency structure on two scales, one that is consistent with quenched Galactic scintillation and broader spectral structure with Δν ≈ 40 MHz. If the latter is due to scattering in the shared M33/M31 CGM, our results constrain the Local Group plasma environment. We found no accompanying persistent radio sources in the Apertif imaging survey data.

• Publication . Article . Preprint . 2019

## Algorithms for deletion problems on split graphs

Open Access English
Authors:
Dekel Tsur;

Abstract In the Split to Block Vertex Deletion and Split to Threshold Vertex Deletion problems the input is a split graph G and an integer k, and the goal is to decide whether there is a set S of vertices of size at most k such that G − S is a block graph and G − S is a threshold graph, respectively. In this paper we give algorithms for these problems whose running times are O ⁎ ( 2.076 k ) and O ⁎ ( 1.619 k ) , respectively.

• Publication . Preprint . Conference object . Article . 2020 . Embargo End Date: 01 Jan 2020

## Lifting with Simple Gadgets and Applications to Circuit and Proof Complexity

Open Access
Authors:
Susanna F. de Rezende; Or Meir; Jakob Nordström; Toniann Pitassi; Robert Robere; Marc Vinyals;
Publisher: arXiv
Project: NSERC , EC | UTHOTP (279611)

We significantly strengthen and generalize the theorem lifting Nullstellensatz degree to monotone span program size by Pitassi and Robere (2018) so that it works for any gadget with high enough rank, in particular, for useful gadgets such as equality and greater-than. We apply our generalized theorem to solve three open problems: •We present the first result that demonstrates a separation in proof power for cutting planes with unbounded versus polynomially bounded coefficients. Specifically, we exhibit CNF formulas that can be refuted in quadratic length and constant line space in cutting planes with unbounded coefficients, but for which there are no refutations in subexponential length and subpolynomial line space if coefficients are restricted to be of polynomial magnitude. •We give the first explicit separation between monotone Boolean formulas and monotone real formulas. Specifically, we give an explicit family of functions that can be computed with monotone real formulas of nearly linear size but require monotone Boolean formulas of exponential size. Previously only a non-explicit separation was known. •We give the strongest separation to-date between monotone Boolean formulas and monotone Boolean circuits. Namely, we show that the classical GEN problem, which has polynomial-size monotone Boolean circuits, requires monotone Boolean formulas of size $2^{\Omega(n/\text{polylog}(n))}$ . An important technical ingredient, which may be of independent interest, is that we show that the Nullstellensatz degree of refuting the pebbling formula over a DAG $G$ over any field coincides exactly with the reversible pebbling price of $G$ . In particular, this implies that the standard decision tree complexity and the parity decision tree complexity of the corresponding falsified clause search problem are equal. This is an extended abstract. The full version of the paper is available at https://arxiv.org/abs/2001.02144.

• Publication . Article . Preprint . 2021

## Distributed Source Simulation With No Communication

Open Access English
Authors:
Tomer Berg; Ofer Shayevitz; Young-Han Kim; Lele Wang;
Project: NSERC , EC | InfoInt (639573)

We consider the problem of distributed source simulation with no communication, in which Alice and Bob observe sequences $U^{n}$ and $V^{n}$ respectively, drawn from a joint distribution $p_{UV}^ {\otimes n}$ , and wish to locally generate sequences $X^{n}$ and $Y^{n}$ respectively with a joint distribution that is close (in KL divergence) to $p_{XY}^ {\otimes n}$ . We provide a single-letter condition under which such a simulation is asymptotically possible with a vanishing KL divergence. Our condition is nontrivial only in the case where the Gacs-Korner (GK) common information between $U$ and $V$ is nonzero, and we conjecture that only scalar Markov chains $X-U-V-Y$ can be simulated otherwise. Motivated by this conjecture, we further examine the case where both $p_{UV}$ and $p_{XY}$ are doubly symmetric binary sources with parameters $p,q\leq 1/2$ respectively. While it is trivial that in this case $p\leq q$ is both necessary and sufficient, we use Fourier analytic tools to show that when $p$ is close to $q$ then any successful simulation is close to being scalar in the total variation sense.

• Publication . Article . Preprint . 2020

## Induced equators in flag spheres

Open Access English
Authors:
Maria Chudnovsky; Eran Nevo;
Project: EC | PROGEOCOM (320924), NSF | Forbidding Induced Subgra... (1763817)

We propose a combinatorial approach to the following strengthening of Gal's conjecture: $\gamma(\Delta)\ge \gamma(E)$ coefficientwise, where $\Delta$ is a flag homology sphere and $E\subseteq \Delta$ an induced homology sphere of codimension $1$. We provide partial evidence in favor of this approach, and prove a nontrivial nonlinear inequality that follows from the above conjecture, for boundary complexes of flag $d$-polytopes: $h_1(\Delta) h_i(\Delta) \ge (d-i+1)h_{i-1}(\Delta) + (i+1) h_{i+1}(\Delta)$ for all $0\le i\le d$. Comment: 12 pages

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• Publication . Preprint . Article . 2018

## The Spitzer-IRAC/MIPS Extragalactic Survey (SIMES): II enhanced nuclear accretion rate in galaxy groups at z$\sim$0.2

Open Access English
Authors:
Ivano Baronchelli; G. Rodighiero; Harry I. Teplitz; Claudia Scarlata; Alberto Franceschini; S. Berta; Laia Barrufet; Mattia Vaccari; Matteo Bonato; Laure Ciesla; +15 more
Publisher: HAL CCSD
Countries: France, Italy, United States
Project: EC | HELP (607254)

For a sample of star forming galaxies in the redshift interval 0.15$<$z$<$0.3, we study how both the relative strength of the AGN infra-red emission, compared to that due to the star formation (SF), and the numerical fraction of AGNs, change as a function of the total stellar mass of the hosting galaxy group (M$^{*}_{\mathrm{group}}$), between $10^{10.25}$ and $10^{11.9}$M$_{\odot}$. Using a multi-component SED fitting analysis, we separate the contribution of stars, AGN torus and star formation to the total emission at different wavelengths. This technique is applied to a new multi-wavelength data-set in the SIMES field (23 not redundant photometric bands), spanning the wavelength range from the UV (GALEX) to the far-IR (Herschel) and including crucial AKARI and WISE mid-IR observations (4.5 \mu m$<\lambda<$24 \mu m), where the BH thermal emission is stronger. This new photometric catalog, that includes our best photo-z estimates, is released through the NASA/IPAC Infrared Science Archive (IRSA). Groups are identified through a friends of friends algorithm ($\sim$62% purity, $\sim$51% completeness). We identified a total of 45 galaxies requiring an AGN emission component, 35 of which in groups and 10 in the field. We find BHAR$\propto ($M$^{*}_{\mathrm{group}})^{1.21\pm0.27}$ and (BHAR/SFR)$\propto ($M$^{*}_{\mathrm{group}})^{1.04\pm0.24}$ while, in the same range of M$^{*}_{\mathrm{group}}$, we do not observe any sensible change in the numerical fraction of AGNs. Our results indicate that the nuclear activity (i.e. the BHAR and the BHAR/SFR ratio) is enhanced when galaxies are located in more massive and richer groups. Comment: 31 pages, 23 figures

• Publication . Article . Preprint . 2021

## Contrasting processing tomato cultivars unlink yield and pollen viability under heat stress

Open Access English
Authors:
Golan Miller; Avital Beery; Prashant Kumar Singh; Fengde Wang; Rotem Zelingher; Etel Motenko; Michal Lieberman-Lazarovich;

pmc:

pmid:

Publisher: Oxford University Press
Country: France

Abstract Climate change is causing temperature increment in crop production areas worldwide, generating conditions of heat stress that negatively affect crop productivity. Tomato (Solanum lycopersicum), a major vegetable crop, is highly susceptible to conditions of heat stress. When tomato plants are exposed to ambient day/night temperatures that exceed 32 °C/20 °C, respectively, during the reproductive phase, fruit set and fruit weight are reduced, leading to a significant decrease in yield. Processing tomato cultivars are cultivated in open fields, where environmental conditions are not controlled; therefore, plants are exposed to multiple abiotic stresses, including heat stress. Nonetheless, information on stress response in processing tomatoes is very limited. Understanding the physiological response of modern processing tomato cultivars to heat stress may facilitate the development of thermotolerant cultivars. Here, we compared two tomato processing cultivars, H4107 and H9780, that we found to be constantly differing in yield performance. Using field and temperature-controlled greenhouse experiments, we show that the observed difference in yield is attributed to the occurrence of heat stress conditions. In addition, fruit set and seed production were significantly higher in the thermotolerant cultivar H4107, compared with H9780. Despite the general acceptance of pollen viability as a measure of thermotolerance, there was no difference in the percentage of viable pollen between H4107 and H9780 under either of the conditions tested. In addition to observations of similar pollen germination and bud abscission rates, our results suggest that processing tomato cultivars may present a particular case, in which pollen performance is not determining reproductive thermotolerance. Our results also demonstrate the value of combining controlled and uncontrolled experimental settings, in order to validate and identify heat stress-related responses, thus facilitating the development of thermotolerant processing tomato cultivars. Our paper deals with the response of tomato plants to high temperatures. Tomato is an important crop, and tomato plants are very sensitive to high temperatures. Therefore, the increase in temperatures due to climate change poses a threat to tomato production. We found that a specific tomato cultivar is heat stress-tolerant, with better productivity under high temperatures. Usually, such tolerance is linked with pollen grains viability. Interestingly, in our case, pollen characteristics were eliminated as a causal factor for heat stress tolerance, meaning that other factors are involved. Follow-up studies are performed towards the development of heat-tolerant tomato.

• Publication . Article . Other literature type . Preprint . 2019

## Cooperative Games With Bounded Dependency Degree

Open Access
Authors:
Igarashi, Ayumi; Izsak, Rani; Elkind, Edith;
Publisher: Association for the Advancement of Artificial Intelligence (AAAI)
Country: United Kingdom
Project: EC | ACCORD (639945)

Cooperative games provide a framework to study cooperation among self-interested agents. They offer a number of solution concepts describing how the outcome of the cooperation should be shared among the players. Unfortunately, computational problems associated with many of these solution concepts tend to be intractable---NP-hard or worse. In this paper, we incorporate complexity measures recently proposed by Feige and Izsak (2013), called dependency degree and supermodular degree, into the complexity analysis of cooperative games. We show that many computational problems for cooperative games become tractable for games whose dependency degree or supermodular degree are bounded. In particular, we prove that simple games admit efficient algorithms for various solution concepts when the supermodular degree is small; further, we show that computing the Shapley value is always in FPT with respect to the dependency degree. Finally, we note that, while determining the dependency among players is computationally hard, there are efficient algorithms for special classes of games. 10 pages, full version of accepted AAAI-18 paper

• Publication . Preprint . Article . 2021

## Making the most of potential: potential games and genotypic convergence

Open Access English
Authors:
Omer Edhan; Ziv Hellman; Ilan Nehama;

pmc:

pmid:

Publisher: The Royal Society
Country: United Kingdom

AbstractWe consider genotypic convergence of populations and show that under fixed fitness asexual and haploid sexual populations attain monomorphic convergence (even under genetic linkage between loci) to basins of attraction with locally exponential convergence rates; the same convergence obtains in single locus diploid sexual reproduction but to polymorphic populations. Furthermore, we show that there is a unified underlying theory underlying these convergences: all of them can be interpreted as instantiations of players in a potential game implementing a multiplicative weights updating algorithm to converge to equilibrium, making use of the Baum–Eagon Theorem. To analyse varying environments, we introduce the concept of ‘virtual convergence’, under which, even if fixation is not attained, the population nevertheless achieves the fitness growth rate it would have had under convergence to an optimal genotype. Virtual convergence is attained by asexual, haploid sexual, and multi-locus diploid reproducing populations, even if environments vary arbitrarily. We also study conditions for true monomorphic convergence in asexually reproducing populations in varying environments.

• Publication . Preprint . Conference object . Article . 2019

## Learning Context Graph for Person Search

Open Access
Authors:
Yichao Yan; Qiang Zhang; Bingbing Ni; Wendong Zhang; Minghao Xu; Xiaokang Yang;
Publisher: IEEE

Person re-identification has achieved great progress with deep convolutional neural networks. However, most previous methods focus on learning individual appearance feature embedding, and it is hard for the models to handle difficult situations with different illumination, large pose variance and occlusion. In this work, we take a step further and consider employing context information for person search. For a probe-gallery pair, we first propose a contextual instance expansion module, which employs a relative attention module to search and filter useful context information in the scene. We also build a graph learning framework to effectively employ context pairs to update target similarity. These two modules are built on top of a joint detection and instance feature learning framework, which improves the discriminativeness of the learned features. The proposed framework achieves state-of-the-art performance on two widely used person search datasets. To appear in CVPR 2019

• Publication . Article . Preprint . 2020

## A bright, high rotation-measure FRB that skewers the M33 halo

Open Access
Authors:
Liam Connor; J. van Leeuwen; L. C. Oostrum; Emily Petroff; Yogesh Maan; Elizabeth A. K. Adams; Jisk Attema; J. E. Bast; Oliver M. Boersma; H. Dénes; +31 more
Publisher: Oxford University Press (OUP)
Country: Netherlands
Project: NWO | ARTS - the Apertif Radio ... (10066), EC | RadioNet (730562), EC | ALERT (617199), NWO | Microporous membranes fro... (5831), NWO | ARGOThe Apertif Radio – G... (31150)

ABSTRACT We report the detection of a bright fast radio burst, FRB 191108, with Apertif on the Westerbork Synthesis Radio Telescope. The interferometer allows us to localize the FRB to a narrow 5 arcsec × 7 arcmin ellipse by employing both multibeam information within the Apertif phased-array feed beam pattern, and across different tied-array beams. The resulting sightline passes close to Local Group galaxy M33, with an impact parameter of only 18 kpc with respect to the core. It also traverses the much larger circumgalactic medium (CGM) of M31, the Andromeda Galaxy. We find that the shared plasma of the Local Group galaxies could contribute ∼10 per cent of its dispersion measure of 588 pc cm−3. FRB 191108 has a Faraday rotation measure (RM) of +474 $\pm \, 3$ rad m−2, which is too large to be explained by either the Milky Way or the intergalactic medium. Based on the more moderate RMs of other extragalactic sources that traverse the halo of M33, we conclude that the dense magnetized plasma resides in the host galaxy. The FRB exhibits frequency structure on two scales, one that is consistent with quenched Galactic scintillation and broader spectral structure with Δν ≈ 40 MHz. If the latter is due to scattering in the shared M33/M31 CGM, our results constrain the Local Group plasma environment. We found no accompanying persistent radio sources in the Apertif imaging survey data.

• Publication . Article . Preprint . 2019

## Algorithms for deletion problems on split graphs

Open Access English
Authors:
Dekel Tsur;

Abstract In the Split to Block Vertex Deletion and Split to Threshold Vertex Deletion problems the input is a split graph G and an integer k, and the goal is to decide whether there is a set S of vertices of size at most k such that G − S is a block graph and G − S is a threshold graph, respectively. In this paper we give algorithms for these problems whose running times are O ⁎ ( 2.076 k ) and O ⁎ ( 1.619 k ) , respectively.

• Publication . Preprint . Conference object . Article . 2020 . Embargo End Date: 01 Jan 2020

## Lifting with Simple Gadgets and Applications to Circuit and Proof Complexity

Open Access
Authors:
Susanna F. de Rezende; Or Meir; Jakob Nordström; Toniann Pitassi; Robert Robere; Marc Vinyals;
Publisher: arXiv
Project: NSERC , EC | UTHOTP (279611)

We significantly strengthen and generalize the theorem lifting Nullstellensatz degree to monotone span program size by Pitassi and Robere (2018) so that it works for any gadget with high enough rank, in particular, for useful gadgets such as equality and greater-than. We apply our generalized theorem to solve three open problems: •We present the first result that demonstrates a separation in proof power for cutting planes with unbounded versus polynomially bounded coefficients. Specifically, we exhibit CNF formulas that can be refuted in quadratic length and constant line space in cutting planes with unbounded coefficients, but for which there are no refutations in subexponential length and subpolynomial line space if coefficients are restricted to be of polynomial magnitude. •We give the first explicit separation between monotone Boolean formulas and monotone real formulas. Specifically, we give an explicit family of functions that can be computed with monotone real formulas of nearly linear size but require monotone Boolean formulas of exponential size. Previously only a non-explicit separation was known. •We give the strongest separation to-date between monotone Boolean formulas and monotone Boolean circuits. Namely, we show that the classical GEN problem, which has polynomial-size monotone Boolean circuits, requires monotone Boolean formulas of size $2^{\Omega(n/\text{polylog}(n))}$ . An important technical ingredient, which may be of independent interest, is that we show that the Nullstellensatz degree of refuting the pebbling formula over a DAG $G$ over any field coincides exactly with the reversible pebbling price of $G$ . In particular, this implies that the standard decision tree complexity and the parity decision tree complexity of the corresponding falsified clause search problem are equal. This is an extended abstract. The full version of the paper is available at https://arxiv.org/abs/2001.02144.

• Publication . Article . Preprint . 2021

## Distributed Source Simulation With No Communication

Open Access English
Authors:
Tomer Berg; Ofer Shayevitz; Young-Han Kim; Lele Wang;
Project: NSERC , EC | InfoInt (639573)

We consider the problem of distributed source simulation with no communication, in which Alice and Bob observe sequences $U^{n}$ and $V^{n}$ respectively, drawn from a joint distribution $p_{UV}^ {\otimes n}$ , and wish to locally generate sequences $X^{n}$ and $Y^{n}$ respectively with a joint distribution that is close (in KL divergence) to $p_{XY}^ {\otimes n}$ . We provide a single-letter condition under which such a simulation is asymptotically possible with a vanishing KL divergence. Our condition is nontrivial only in the case where the Gacs-Korner (GK) common information between $U$ and $V$ is nonzero, and we conjecture that only scalar Markov chains $X-U-V-Y$ can be simulated otherwise. Motivated by this conjecture, we further examine the case where both $p_{UV}$ and $p_{XY}$ are doubly symmetric binary sources with parameters $p,q\leq 1/2$ respectively. While it is trivial that in this case $p\leq q$ is both necessary and sufficient, we use Fourier analytic tools to show that when $p$ is close to $q$ then any successful simulation is close to being scalar in the total variation sense.

• Publication . Article . Preprint . 2020

## Induced equators in flag spheres

Open Access English
Authors:
Maria Chudnovsky; Eran Nevo;
Project: EC | PROGEOCOM (320924), NSF | Forbidding Induced Subgra... (1763817)

We propose a combinatorial approach to the following strengthening of Gal's conjecture: $\gamma(\Delta)\ge \gamma(E)$ coefficientwise, where $\Delta$ is a flag homology sphere and $E\subseteq \Delta$ an induced homology sphere of codimension $1$. We provide partial evidence in favor of this approach, and prove a nontrivial nonlinear inequality that follows from the above conjecture, for boundary complexes of flag $d$-polytopes: $h_1(\Delta) h_i(\Delta) \ge (d-i+1)h_{i-1}(\Delta) + (i+1) h_{i+1}(\Delta)$ for all $0\le i\le d$. Comment: 12 pages

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