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- Publication . Preprint . Article . 2018Open Access EnglishAuthors:Ivano Baronchelli; G. Rodighiero; Harry I. Teplitz; Claudia Scarlata; Alberto Franceschini; S. Berta; Laia Barrufet; Mattia Vaccari; Matteo Bonato; Laure Ciesla; +15 moreIvano Baronchelli; G. Rodighiero; Harry I. Teplitz; Claudia Scarlata; Alberto Franceschini; S. Berta; Laia Barrufet; Mattia Vaccari; Matteo Bonato; Laure Ciesla; A. Zanella; R. Carraro; Chiara Mancini; A. Puglisi; M. A. Malkan; Simona Mei; Lucia Marchetti; James W. Colbert; Chris Sedgwick; Steve Serjeant; Chris Pearson; M. Radovich; A. Grado; L. Limatola; Giovanni Covone;Publisher: HAL CCSDCountries: France, Italy, United StatesProject: 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

Average popularityAverage popularity In bottom 99%Average influencePopularity: Citation-based measure reflecting the current impact.Average influence In bottom 99%Influence: Citation-based measure reflecting the total impact.add Add to ORCIDPlease grant OpenAIRE to access and update your ORCID works.This Research product is the result of merged Research products in OpenAIRE.

You have already added works in your ORCID record related to the merged Research product. - Publication . Article . Other literature type . Preprint . 2019Open AccessAuthors:Igarashi, Ayumi; Izsak, Rani; Elkind, Edith;Igarashi, Ayumi; Izsak, Rani; Elkind, Edith;Publisher: Association for the Advancement of Artificial Intelligence (AAAI)Country: United KingdomProject: 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

Average popularityAverage popularity In bottom 99%Average influencePopularity: Citation-based measure reflecting the current impact.Average influence In bottom 99%Influence: Citation-based measure reflecting the total impact.add Add to ORCIDPlease grant OpenAIRE to access and update your ORCID works.This Research product is the result of merged Research products in OpenAIRE.

You have already added works in your ORCID record related to the merged Research product. - Publication . Article . Preprint . 2017Open Access EnglishAuthors:Kyle Kawagoe; Greg Huber; Marc Pradas; Michael Wilkinson; Alain Pumir; Eli Ben-Naim;Kyle Kawagoe; Greg Huber; Marc Pradas; Michael Wilkinson; Alain Pumir; Eli Ben-Naim;
We investigate statistical properties of trails formed by a random process incorporating aggregation, fragmentation, and diffusion. In this stochastic process, which takes place in one spatial dimension, two neighboring trails may combine to form a larger one and also, one trail may split into two. In addition, trails move diffusively. The model is defined by two parameters which quantify the fragmentation rate and the fragment size. In the long-time limit, the system reaches a steady state, and our focus is the limiting distribution of trail weights. We find that the density of trail weight has power-law tail $P(w) \sim w^{-\gamma}$ for small weight $w$. We obtain the exponent $\gamma$ analytically, and find that it varies continuously with the two model parameters. The exponent $\gamma$ can be positive or negative, so that in one range of parameters small-weight tails are abundant, and in the complementary range, they are rare. Comment: 8 pages, 8 figures

Average popularityAverage popularity In bottom 99%Average influencePopularity: Citation-based measure reflecting the current impact.Average influence In bottom 99%Influence: Citation-based measure reflecting the total impact.add Add to ORCIDPlease grant OpenAIRE to access and update your ORCID works.This Research product is the result of merged Research products in OpenAIRE.

You have already added works in your ORCID record related to the merged Research product. - Publication . Article . Preprint . 2017Open Access EnglishAuthors:Rapaport, Ariel;Rapaport, Ariel;Project: EC | FRACTALSANDMETRICNT (306494)
We show there exists a constant $0

Average popularity In bottom 99%Average influencePopularity: Citation-based measure reflecting the current impact.Average influence In bottom 99%Influence: Citation-based measure reflecting the total impact.add Add to ORCIDPlease grant OpenAIRE to access and update your ORCID works.

You have already added works in your ORCID record related to the merged Research product. - Publication . Article . Preprint . 2013Open AccessAuthors:Gil Porat; Ady Arie;Gil Porat; Ady Arie;Publisher: The Optical Society
A comprehensive physical model of adiabatic three-wave mixing is developed for the fully nonlinear regime, i.e., without making the undepleted pump approximation. The conditions for adiabatic evolution are rigorously derived, together with an estimate of the bandwidth of the process. Furthermore, these processes are shown to be robust and efficient. Finally, numerical simulations demonstrate adiabatic frequency conversion in a wide variety of physically attainable configurations.

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You have already added works in your ORCID record related to the merged Research product. - Publication . Article . Preprint . 2019Open Access EnglishAuthors:Dekel Tsur;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.

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You have already added works in your ORCID record related to the merged Research product. - Publication . Article . Preprint . 2014 . Embargo End Date: 01 Jan 2014Open AccessAuthors:Alexander Shnirman; Yuval Gefen; Arijit Saha; I. S. Burmistrov; Mikhail N. Kiselev; Alexander Altland;Alexander Shnirman; Yuval Gefen; Arijit Saha; I. S. Burmistrov; Mikhail N. Kiselev; Alexander Altland;Publisher: arXiv
The presence of geometric phases is known to affect the dynamics of the systems involved. Here we consider a quantum degree of freedom, moving in a dissipative environment, whose dynamics is described by a Langevin equation with quantum noise. We show that geometric phases enter the stochastic noise terms. Specifically, we consider small ferromagnetic particles (nano-magnets) or quantum dots close to Stoner instability, and investigate the dynamics of the total magnetization in the presence of tunneling coupling to the metallic leads. We generalize the Ambegaokar-Eckern-Sch\"on (AES) effective action and the corresponding semiclassical equations of motion from the U(1) case of the charge degree of freedom to the SU(2) case of the magnetization. The Langevin forces (torques) in these equations are strongly influenced by the geometric phase. As a first but nontrivial application we predict low temperature quantum diffusion of the magnetization on the Bloch sphere, which is governed by the geometric phase. We propose a protocol for experimental observation of this phenomenon. Comment: 8 pages including Supplemental Material

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You have already added works in your ORCID record related to the merged Research product. - Publication . Preprint . Conference object . Article . 2020 . Embargo End Date: 01 Jan 2020Open AccessAuthors:Susanna F. de Rezende; Or Meir; Jakob Nordström; Toniann Pitassi; Robert Robere; Marc Vinyals;Susanna F. de Rezende; Or Meir; Jakob Nordström; Toniann Pitassi; Robert Robere; Marc Vinyals;Publisher: arXivProject: 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.

Average popularity In bottom 99%Average influencePopularity: Citation-based measure reflecting the current impact.Average influence In bottom 99%Influence: Citation-based measure reflecting the total impact.add Add to ORCIDPlease grant OpenAIRE to access and update your ORCID works.

You have already added works in your ORCID record related to the merged Research product. - Publication . Article . Preprint . 2021Open Access EnglishAuthors:Tomer Berg; Ofer Shayevitz; Young-Han Kim; Lele Wang;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.

Average popularity In bottom 99%Average influencePopularity: Citation-based measure reflecting the current impact.Average influence In bottom 99%Influence: Citation-based measure reflecting the total impact.add Add to ORCIDPlease grant OpenAIRE to access and update your ORCID works.

You have already added works in your ORCID record related to the merged Research product. - Publication . Article . Preprint . 2020Open Access EnglishAuthors:Maria Chudnovsky; Eran Nevo;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

Average popularity In bottom 99%Average influencePopularity: Citation-based measure reflecting the current impact.Average influence In bottom 99%Influence: Citation-based measure reflecting the total impact.add Add to ORCIDPlease grant OpenAIRE to access and update your ORCID works.

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###### 18,934 Research products, page 1 of 1,894

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- Publication . Preprint . Article . 2018Open Access EnglishAuthors:Ivano Baronchelli; G. Rodighiero; Harry I. Teplitz; Claudia Scarlata; Alberto Franceschini; S. Berta; Laia Barrufet; Mattia Vaccari; Matteo Bonato; Laure Ciesla; +15 moreIvano Baronchelli; G. Rodighiero; Harry I. Teplitz; Claudia Scarlata; Alberto Franceschini; S. Berta; Laia Barrufet; Mattia Vaccari; Matteo Bonato; Laure Ciesla; A. Zanella; R. Carraro; Chiara Mancini; A. Puglisi; M. A. Malkan; Simona Mei; Lucia Marchetti; James W. Colbert; Chris Sedgwick; Steve Serjeant; Chris Pearson; M. Radovich; A. Grado; L. Limatola; Giovanni Covone;Publisher: HAL CCSDCountries: France, Italy, United StatesProject: 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

Average popularity In bottom 99%Average influencePopularity: Citation-based measure reflecting the current impact.Average influence In bottom 99%Influence: Citation-based measure reflecting the total impact.add Add to ORCIDPlease grant OpenAIRE to access and update your ORCID works.

You have already added works in your ORCID record related to the merged Research product. - Publication . Article . Other literature type . Preprint . 2019Open AccessAuthors:Igarashi, Ayumi; Izsak, Rani; Elkind, Edith;Igarashi, Ayumi; Izsak, Rani; Elkind, Edith;Publisher: Association for the Advancement of Artificial Intelligence (AAAI)Country: United KingdomProject: 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

Average popularity In bottom 99%Average influencePopularity: Citation-based measure reflecting the current impact.Average influence In bottom 99%Influence: Citation-based measure reflecting the total impact.add Add to ORCIDPlease grant OpenAIRE to access and update your ORCID works.

You have already added works in your ORCID record related to the merged Research product. - Publication . Article . Preprint . 2017Open Access EnglishAuthors:Kyle Kawagoe; Greg Huber; Marc Pradas; Michael Wilkinson; Alain Pumir; Eli Ben-Naim;Kyle Kawagoe; Greg Huber; Marc Pradas; Michael Wilkinson; Alain Pumir; Eli Ben-Naim;
We investigate statistical properties of trails formed by a random process incorporating aggregation, fragmentation, and diffusion. In this stochastic process, which takes place in one spatial dimension, two neighboring trails may combine to form a larger one and also, one trail may split into two. In addition, trails move diffusively. The model is defined by two parameters which quantify the fragmentation rate and the fragment size. In the long-time limit, the system reaches a steady state, and our focus is the limiting distribution of trail weights. We find that the density of trail weight has power-law tail $P(w) \sim w^{-\gamma}$ for small weight $w$. We obtain the exponent $\gamma$ analytically, and find that it varies continuously with the two model parameters. The exponent $\gamma$ can be positive or negative, so that in one range of parameters small-weight tails are abundant, and in the complementary range, they are rare. Comment: 8 pages, 8 figures

Average popularity In bottom 99%Average influencePopularity: Citation-based measure reflecting the current impact.Average influence In bottom 99%Influence: Citation-based measure reflecting the total impact.add Add to ORCIDPlease grant OpenAIRE to access and update your ORCID works.

You have already added works in your ORCID record related to the merged Research product. - Publication . Article . Preprint . 2017Open Access EnglishAuthors:Rapaport, Ariel;Rapaport, Ariel;Project: EC | FRACTALSANDMETRICNT (306494)
We show there exists a constant $0

Average popularity In bottom 99%Average influencePopularity: Citation-based measure reflecting the current impact.Average influence In bottom 99%Influence: Citation-based measure reflecting the total impact.add Add to ORCIDPlease grant OpenAIRE to access and update your ORCID works.

You have already added works in your ORCID record related to the merged Research product. - Publication . Article . Preprint . 2013Open AccessAuthors:Gil Porat; Ady Arie;Gil Porat; Ady Arie;Publisher: The Optical Society
A comprehensive physical model of adiabatic three-wave mixing is developed for the fully nonlinear regime, i.e., without making the undepleted pump approximation. The conditions for adiabatic evolution are rigorously derived, together with an estimate of the bandwidth of the process. Furthermore, these processes are shown to be robust and efficient. Finally, numerical simulations demonstrate adiabatic frequency conversion in a wide variety of physically attainable configurations.

Average popularity In bottom 99%Average influencePopularity: Citation-based measure reflecting the current impact.Average influence In bottom 99%Influence: Citation-based measure reflecting the total impact.add Add to ORCIDPlease grant OpenAIRE to access and update your ORCID works.

You have already added works in your ORCID record related to the merged Research product. - Publication . Article . Preprint . 2019Open Access EnglishAuthors:Dekel Tsur;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.

Average popularity In bottom 99%Average influencePopularity: Citation-based measure reflecting the current impact.Average influence In bottom 99%Influence: Citation-based measure reflecting the total impact.add Add to ORCIDPlease grant OpenAIRE to access and update your ORCID works.

You have already added works in your ORCID record related to the merged Research product. - Publication . Article . Preprint . 2014 . Embargo End Date: 01 Jan 2014Open AccessAuthors:Alexander Shnirman; Yuval Gefen; Arijit Saha; I. S. Burmistrov; Mikhail N. Kiselev; Alexander Altland;Publisher: arXiv
The presence of geometric phases is known to affect the dynamics of the systems involved. Here we consider a quantum degree of freedom, moving in a dissipative environment, whose dynamics is described by a Langevin equation with quantum noise. We show that geometric phases enter the stochastic noise terms. Specifically, we consider small ferromagnetic particles (nano-magnets) or quantum dots close to Stoner instability, and investigate the dynamics of the total magnetization in the presence of tunneling coupling to the metallic leads. We generalize the Ambegaokar-Eckern-Sch\"on (AES) effective action and the corresponding semiclassical equations of motion from the U(1) case of the charge degree of freedom to the SU(2) case of the magnetization. The Langevin forces (torques) in these equations are strongly influenced by the geometric phase. As a first but nontrivial application we predict low temperature quantum diffusion of the magnetization on the Bloch sphere, which is governed by the geometric phase. We propose a protocol for experimental observation of this phenomenon. Comment: 8 pages including Supplemental Material

Average popularity In bottom 99%Average influencePopularity: Citation-based measure reflecting the current impact.Average influence In bottom 99%Influence: Citation-based measure reflecting the total impact.add Add to ORCIDPlease grant OpenAIRE to access and update your ORCID works.

You have already added works in your ORCID record related to the merged Research product. - Publication . Preprint . Conference object . Article . 2020 . Embargo End Date: 01 Jan 2020Open AccessAuthors:Susanna F. de Rezende; Or Meir; Jakob Nordström; Toniann Pitassi; Robert Robere; Marc Vinyals;Susanna F. de Rezende; Or Meir; Jakob Nordström; Toniann Pitassi; Robert Robere; Marc Vinyals;Publisher: arXivProject: 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.

Average popularity In bottom 99%Average influencePopularity: Citation-based measure reflecting the current impact.Average influence In bottom 99%Influence: Citation-based measure reflecting the total impact.add Add to ORCIDPlease grant OpenAIRE to access and update your ORCID works.

You have already added works in your ORCID record related to the merged Research product. - Publication . Article . Preprint . 2021Open Access EnglishAuthors:Tomer Berg; Ofer Shayevitz; Young-Han Kim; Lele Wang;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.

Average popularity In bottom 99%Average influencePopularity: Citation-based measure reflecting the current impact.Average influence In bottom 99%Influence: Citation-based measure reflecting the total impact.add Add to ORCIDPlease grant OpenAIRE to access and update your ORCID works.

You have already added works in your ORCID record related to the merged Research product. - Publication . Article . Preprint . 2020Open Access EnglishAuthors:Maria Chudnovsky; Eran Nevo;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

Average popularity In bottom 99%Average influencePopularity: Citation-based measure reflecting the current impact.Average influence In bottom 99%Influence: Citation-based measure reflecting the total impact.add Add to ORCIDPlease grant OpenAIRE to access and update your ORCID works.

You have already added works in your ORCID record related to the merged Research product.