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- Publication . Article . Preprint . 2021 . Embargo End Date: 01 Jan 2019Open AccessAuthors:Anat Ganor; C S Karthik; Dömötör Pálvölgyi;Anat Ganor; C S Karthik; Dömötör Pálvölgyi;Publisher: arXivProject: EC | COMPECON (740282)
Brouwer’s fixed point theorem states that any continuous function from a compact convex space to itself has a fixed point. Roughgarden and Weinstein (FOCS 2016) initiated the study of fixed point computation in the two-player communication model, where each player gets a function from [0,1]^n to [0,1]^n , and their goal is to find an approximate fixed point of the composition of the two functions. They left it as an open question to show a lower bound of 2^{\Omega (n)} for the (randomized) communication complexity of this problem, in the range of parameters which make it a total search problem. We answer this question affirmatively. Additionally, we introduce two natural fixed point problems in the two-player communication model. Each player is given a function from [0,1]^n to [0,1]^{n/2} , and their goal is to find an approximate fixed point of the concatenation of the functions. Each player is given a function from [0,1]^n to [0,1]^{n} , and their goal is to find an approximate fixed point of the mean of the functions. We show a randomized communication complexity lower bound of 2^{\Omega (n)} for these problems (for some constant approximation factor). Finally, we initiate the study of finding a panchromatic simplex in a Sperner-coloring of a triangulation (guaranteed by Sperner’s lemma) in the two-player communication model: A triangulation T of the d -simplex is publicly known and one player is given a set S_A\subset T and a coloring function from S_A to \lbrace 0,\ldots ,d/2\rbrace , and the other player is given a set S_B\subset T and a coloring function from S_B to \lbrace d/2+1,\ldots ,d\rbrace , such that S_A\dot{\cup }S_B=T , and their goal is to find a panchromatic simplex. We show a randomized communication complexity lower bound of |T|^{\Omega (1)} for the aforementioned problem as well (when d is large). On the positive side, we show that if d\le 4 then there is a deterministic protocol for the Sperner problem with O((\log |T|)^2) bits of communication.

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 . Preprint . Article . Other literature type . 2021Open Access EnglishAuthors:Daniel Nevo; Malka Gorfine;Daniel Nevo; Malka Gorfine;Project: NIH | Alzheimer's Disease Patie... (5U01AG006781-29)
An emerging challenge for time-to-event data is studying semi-competing risks, namely when two event times are of interest: a non-terminal event time (e.g. age at disease diagnosis), and a terminal event time (e.g. age at death). The non-terminal event is observed only if it precedes the terminal event, which may occur before or after the non-terminal event. Studying treatment or intervention effects on the dual event times is complicated because for some units, the non-terminal event may occur under one treatment value but not under the other. Until recently, existing approaches (e.g., the survivor average causal effect) generally disregarded the time-to-event nature of both outcomes. More recent research focused on principal strata effects within time-varying populations under Bayesian approaches. In this paper, we propose alternative non time-varying estimands, based on a single stratification of the population. We present a novel assumption utilizing the time-to-event nature of the data, which is weaker than the often-invoked monotonicity assumption. We derive results on partial identifiability, suggest a sensitivity analysis approach, and give conditions under which full identification is possible. Finally, we present non-parametric and semi-parametric estimation methods for right-censored data. 35 pages, 3 figure, 3 tables

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 . Preprint . Article . 2021Open AccessAuthors:Rusanovsky, Matan; Beeri, Ofer; Oren, Gal;Rusanovsky, Matan; Beeri, Ofer; Oren, Gal;Publisher: Springer Science and Business Media LLC
Metallography is crucial for a proper assessment of material's properties. It involves mainly the investigation of spatial distribution of grains and the occurrence and characteristics of inclusions or precipitates. This work presents an holistic artificial intelligence model for Anomaly Detection that automatically quantifies the degree of anomaly of impurities in alloys. We suggest the following examination process: (1) Deep semantic segmentation is performed on the inclusions (based on a suitable metallographic database of alloys and corresponding tags of inclusions), producing inclusions masks that are saved into a separated database. (2) Deep image inpainting is performed to fill the removed inclusions parts, resulting in 'clean' metallographic images, which contain the background of grains. (3) Grains' boundaries are marked using deep semantic segmentation (based on another metallographic database of alloys), producing boundaries that are ready for further inspection on the distribution of grains' size. (4) Deep anomaly detection and pattern recognition is performed on the inclusions masks to determine spatial, shape and area anomaly detection of the inclusions. Finally, the system recommends to an expert on areas of interests for further examination. The performance of the model is presented and analyzed based on few representative cases. Although the models presented here were developed for metallography analysis, most of them can be generalized to a wider set of problems in which anomaly detection of geometrical objects is desired. All models as well as the data-sets that were created for this work, are publicly available at https://github.com/Scientific-Computing-Lab-NRCN/MLography. Comment: arXiv admin note: substantial text overlap with arXiv:2003.04226 Same text as last submission, changed the author list to correspond to the pdf

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 . Presentation . Other literature type . Conference object . Preprint . 2021Open Access EnglishAuthors:Asif Katz; Shlomo Shamai Shitz; Michael Peleg;Asif Katz; Shlomo Shamai Shitz; Michael Peleg;Publisher: ZenodoProject: EC | CloudRadioNet (694630)
We investigate the special case of diamond relay comprising a Gaussian channel with identical frequency response from the user to the relays and fronthaul links with limited rate from the relays to the destination. We use the oblivious compress and forward (CF) with distributed compression and decode and forward (DF) where each relay decodes the whole message and sends half of its bits to the destination. We derive achievable rate by using time-sharing between DF and CF. It is proved that optimal CF-DF time sharing is advantageous over superposition of CF and DF. The optimal time sharing proportion between DF and CF and power and rate allocations are different at each frequency and are fully determined.

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 AccessAuthors:Novikov, Dmitry; Shapiro, Boris; Tahar, Guillaume;Novikov, Dmitry; Shapiro, Boris; Tahar, Guillaume;Publisher: Springer Science and Business Media LLCProject: EC | EffectiveTG (802107)
Meromorphic connections on Riemann surfaces originate and are closely related to the classical theory of linear ordinary differential equations with meromorphic coefficients. Limiting behaviour of geodesics of such connections has been studied by e.g. Abate, Bianchi and Tovena in relation with generalized Poincar\'{e}-Bendixson theorems. At present, it seems still to be unknown whether some of the theoretically possible asymptotic behaviours of such geodesics really exist. In order to fill the gap, we use the branched affine structure induced by a Fuchsian meromorphic connection to present several examples with geodesics having infinitely many self-intersections and quite peculiar omega-limit sets. Comment: 15 pages, 4 figures

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You have already added works in your ORCID record related to the merged Research product. - Publication . Article . Preprint . 2021 . Embargo End Date: 01 Jan 2021Open AccessAuthors:Miron Amusia; Arkadiy S. Baltenkov;Miron Amusia; Arkadiy S. Baltenkov;Publisher: arXiv
In this paper we calculate the elastic scattering cross sections of slow electron by carbon nanotubes. The corresponding electron-nanotube interaction is substituted by a zero-thickness cylindrical potential that neglects the atomic structure of real nanotubes, thus limiting the range of applicability of our approach to sufficiently low incoming electron energies. The strength of the potential is chosen the same that was used in describing scattering of electrons by fullerene C60. We present results for total and partial electron scattering cross sections as well as respective angular distributions, all with account of five lowest angular momenta contributions. In the calculations we assumed that the incoming electron moves perpendicular to the nanotube axis, since along the axis the incoming electron moves freely. Comment: 10 pages, 2 figures

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You have already added works in your ORCID record related to the merged Research product. - Publication . Article . Preprint . 2021 . Embargo End Date: 01 Jan 2018Open AccessAuthors:Itai Benjamini; David Ellis;Itai Benjamini; David Ellis;Publisher: arXivCountry: United Kingdom
We continue the study of the properties of graphs in which the ball of radius $r$ around each vertex induces a graph isomorphic to the ball of radius $r$ in some fixed vertex-transitive graph $F$, for various choices of $F$ and $r$. This is a natural extension of the study of regular graphs. More precisely, if $F$ is a vertex-transitive graph and $r \in \mathbb{N}$, we say a graph $G$ is {\em $r$-locally $F$} if the ball of radius $r$ around each vertex of $G$ induces a graph isomorphic to the graph induced by the ball of radius $r$ around any vertex of $F$. We consider the following random graph model: for each $n \in \mathbb{N}$, we let $G_n = G_n(F,r)$ be a graph chosen uniformly at random from the set of all unlabelled, $n$-vertex graphs that are $r$-locally $F$. We investigate the properties possessed by the random graph $G_n$ with high probability, for various natural choices of $F$ and $r$. We prove that if $F$ is a Cayley graph of a torsion-free group of polynomial growth, and $r$ is sufficiently large depending on $F$, then the random graph $G_n = G_n(F,r)$ has largest component of order at most $n^{5/6}$ with high probability, and has at least $\exp(n^{\delta})$ automorphisms with high probability, where $\delta>0$ depends upon $F$ alone. Both properties are in stark contrast to random $d$-regular graphs, which correspond to the case where $F$ is the infinite $d$-regular tree. We also show that, under the same hypotheses, the number of unlabelled, $n$-vertex graphs that are $r$-locally $F$ grows like a stretched exponential in $n$, again in contrast with $d$-regular graphs. In the case where $F$ is the standard Cayley graph of $\mathbb{Z}^d$, we obtain a much more precise enumeration result, and more precise results on the properties of the random graph $G_n(F,r)$. Our proofs use a mixture of results and techniques from geometry, group theory and combinatorics. Comment: Full proof of Theorem 7 added. Statement of Proposition 38 has been strengthened slightly. 61 pages

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You have already added works in your ORCID record related to the merged Research product. - Publication . Article . Preprint . 2021Open Access EnglishAuthors:Hagai Perets; Evgeni Grishin;Hagai Perets; Evgeni Grishin;Project: EC | SNeX (865932)
Recent surveys show that wide ($>10^4$ AU) binaries and triples are abundant in the field. We study the long-term evolution of wide hierarchical triple systems and the role played by the Galactic tidal (GT) field. We find that when the timescales of the secular von-Ziepel-Lidov-Kozai and the GT oscillations are comparable, triple evolution becomes chaotic which leads to extreme eccentricities. Consequently, the close pericentre approaches of the inner-binary components lead to strong interactions, mergers and collisions. We use a novel secular evolution code to quantify the key parameters and carry out a population-synthesis study of low and intermediate-mass wide-orbit triples. We find that in $\sim9\%$ of low-mass wide-triples the inner main-sequence binaries collide or tidally-inspiral within $10\ \rm Gyr$, with direct collisions are $6$ times more likely to occur. For the intermediate-mass sample, $\sim7.6\%$ of the systems merge or inspiral with roughly equal probabilities. We discuss the relative fractions of different stellar merger/inspiral outcomes as a function of their evolutionary stage (Main-Sequence, MS; Red-Giant, RG; or White-Dwarf, WD), their transient electromagnetic signatures and the final products of the merger/inspiral. In particular, the rate of WD-WD direct-collisions that lead to type-Ia Supernovae is comparable to other dynamical channels and accounts for at most $0.1\%$ of the observed rate. RG inspirals provide a novel channel for the formation of eccentric common-envelope-evolution binaries. The catalysis of mergers/collisions in triples due to GT could explain a significant fraction, or even the vast majority, of blue-stragglers in the field, produce progenitors for cataclysmic-variables, and give-rise to mergers/collisions of double-RG binaries. Accepted to MNRAS

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You have already added works in your ORCID record related to the merged Research product. - Publication . Article . Preprint . 2021 . Embargo End Date: 01 Jan 2021Open AccessAuthors:Yuval Scher; Shlomi Reuveni;Yuval Scher; Shlomi Reuveni;Publisher: arXiv
How much time does it take two molecules to react? If a reaction occurs upon contact, the answer to this question boils down to the classic first-passage time problem: find the time it takes the two molecules to meet. However, this is not always the case as molecules switch stochastically between reactive and non-reactive states. The reaction is then said to be ``gated' by the internal states of the molecules involved which could have a dramatic influence on kinetics. A unified, continuous-time, approach to gated reactions on networks was presented in [Phys. Rev. Lett. 127, 018301, 2021]. Here, we build on this recent advancement and develop an analogous discrete-time version of the theory. Similar to continuous-time, we employ a renewal approach to show that the gated reaction time can always be expressed in terms of the corresponding ungated first-passage and return times; which yields formulas for the generating function of the gated reaction-time distribution and its corresponding mean and variance. In cases where the mean reaction time diverges, we show that the long-time asymptotics of the gated problem is inherited from its ungated counterpart. However, when molecules spend most of their time non-reactive, an interim regime of slower power-law decay emerges prior to the terminal asymptotics. The discretization of time also gives rise to resonances and anti-resonances, which were absent from the continuous time picture. These features are illustrated using two case studies that also demonstrate how the general approach presented herein greatly simplifies the analysis of gated reactions.

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You have already added works in your ORCID record related to the merged Research product. - Publication . Article . Preprint . 2021Open AccessAuthors:Nikbakht, Homa; Wigger, Michele; Shamai Shitz, Shlomo;Nikbakht, Homa; Wigger, Michele; Shamai Shitz, Shlomo;Publisher: Institute of Electrical and Electronics Engineers (IEEE)Project: EC | CTO Com (715111), EC | CloudRadioNet (694630)
This paper analyzes the multiplexing gains (MG) for simultaneous transmission of delay-sensitive and delay-tolerant data over interference networks. In the considered model, only delay-tolerant data can profit from coordinated multipoint (CoMP) transmission or reception techniques, because delay-sensitive data has to be transmitted without further delay. Transmission of delay-tolerant data is also subject to a delay constraint, which is however less stringent than the one on delay-sensitive data. Different coding schemes are proposed, and the corresponding MG pairs for delay-sensitive and delay-tolerant data are characterized for Wyner's linear symmetric network and for Wyner's two-dimensional hexagonal network with and without sectorization. For Wyner's linear symmetric also an information-theoretic converse is established and shown to be exact whenever the cooperation rates are sufficiently large or the delay-sensitive MG is small or moderate. These results show that on Wyner's symmetric linear network and for sufficiently large cooperation rates, the largest MG for delay-sensitive data can be achieved without penalizing the maximum sum-MG of both delay-sensitive and delay-tolerant data. A similar conclusion holds for Wyner's hexagonal network only for the model with sectorization. In the model without sectorization, a penalty in sum-MG is incurred whenever one insists on a positive delay-sensitive MG. Comment: 41 pages, submitted to Transactions on Communications

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###### 12,153 Research products, page 1 of 1,216

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- Publication . Article . Preprint . 2021 . Embargo End Date: 01 Jan 2019Open AccessAuthors:Anat Ganor; C S Karthik; Dömötör Pálvölgyi;Anat Ganor; C S Karthik; Dömötör Pálvölgyi;Publisher: arXivProject: EC | COMPECON (740282)
Brouwer’s fixed point theorem states that any continuous function from a compact convex space to itself has a fixed point. Roughgarden and Weinstein (FOCS 2016) initiated the study of fixed point computation in the two-player communication model, where each player gets a function from [0,1]^n to [0,1]^n , and their goal is to find an approximate fixed point of the composition of the two functions. They left it as an open question to show a lower bound of 2^{\Omega (n)} for the (randomized) communication complexity of this problem, in the range of parameters which make it a total search problem. We answer this question affirmatively. Additionally, we introduce two natural fixed point problems in the two-player communication model. Each player is given a function from [0,1]^n to [0,1]^{n/2} , and their goal is to find an approximate fixed point of the concatenation of the functions. Each player is given a function from [0,1]^n to [0,1]^{n} , and their goal is to find an approximate fixed point of the mean of the functions. We show a randomized communication complexity lower bound of 2^{\Omega (n)} for these problems (for some constant approximation factor). Finally, we initiate the study of finding a panchromatic simplex in a Sperner-coloring of a triangulation (guaranteed by Sperner’s lemma) in the two-player communication model: A triangulation T of the d -simplex is publicly known and one player is given a set S_A\subset T and a coloring function from S_A to \lbrace 0,\ldots ,d/2\rbrace , and the other player is given a set S_B\subset T and a coloring function from S_B to \lbrace d/2+1,\ldots ,d\rbrace , such that S_A\dot{\cup }S_B=T , and their goal is to find a panchromatic simplex. We show a randomized communication complexity lower bound of |T|^{\Omega (1)} for the aforementioned problem as well (when d is large). On the positive side, we show that if d\le 4 then there is a deterministic protocol for the Sperner problem with O((\log |T|)^2) bits of communication.

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 . Article . Other literature type . 2021Open Access EnglishAuthors:Daniel Nevo; Malka Gorfine;Daniel Nevo; Malka Gorfine;Project: NIH | Alzheimer's Disease Patie... (5U01AG006781-29)
An emerging challenge for time-to-event data is studying semi-competing risks, namely when two event times are of interest: a non-terminal event time (e.g. age at disease diagnosis), and a terminal event time (e.g. age at death). The non-terminal event is observed only if it precedes the terminal event, which may occur before or after the non-terminal event. Studying treatment or intervention effects on the dual event times is complicated because for some units, the non-terminal event may occur under one treatment value but not under the other. Until recently, existing approaches (e.g., the survivor average causal effect) generally disregarded the time-to-event nature of both outcomes. More recent research focused on principal strata effects within time-varying populations under Bayesian approaches. In this paper, we propose alternative non time-varying estimands, based on a single stratification of the population. We present a novel assumption utilizing the time-to-event nature of the data, which is weaker than the often-invoked monotonicity assumption. We derive results on partial identifiability, suggest a sensitivity analysis approach, and give conditions under which full identification is possible. Finally, we present non-parametric and semi-parametric estimation methods for right-censored data. 35 pages, 3 figure, 3 tables

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 . Article . 2021Open AccessAuthors:Rusanovsky, Matan; Beeri, Ofer; Oren, Gal;Rusanovsky, Matan; Beeri, Ofer; Oren, Gal;Publisher: Springer Science and Business Media LLC
Metallography is crucial for a proper assessment of material's properties. It involves mainly the investigation of spatial distribution of grains and the occurrence and characteristics of inclusions or precipitates. This work presents an holistic artificial intelligence model for Anomaly Detection that automatically quantifies the degree of anomaly of impurities in alloys. We suggest the following examination process: (1) Deep semantic segmentation is performed on the inclusions (based on a suitable metallographic database of alloys and corresponding tags of inclusions), producing inclusions masks that are saved into a separated database. (2) Deep image inpainting is performed to fill the removed inclusions parts, resulting in 'clean' metallographic images, which contain the background of grains. (3) Grains' boundaries are marked using deep semantic segmentation (based on another metallographic database of alloys), producing boundaries that are ready for further inspection on the distribution of grains' size. (4) Deep anomaly detection and pattern recognition is performed on the inclusions masks to determine spatial, shape and area anomaly detection of the inclusions. Finally, the system recommends to an expert on areas of interests for further examination. The performance of the model is presented and analyzed based on few representative cases. Although the models presented here were developed for metallography analysis, most of them can be generalized to a wider set of problems in which anomaly detection of geometrical objects is desired. All models as well as the data-sets that were created for this work, are publicly available at https://github.com/Scientific-Computing-Lab-NRCN/MLography. Comment: arXiv admin note: substantial text overlap with arXiv:2003.04226 Same text as last submission, changed the author list to correspond to the pdf

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 . Presentation . Other literature type . Conference object . Preprint . 2021Open Access EnglishAuthors:Asif Katz; Shlomo Shamai Shitz; Michael Peleg;Asif Katz; Shlomo Shamai Shitz; Michael Peleg;Publisher: ZenodoProject: EC | CloudRadioNet (694630)
We investigate the special case of diamond relay comprising a Gaussian channel with identical frequency response from the user to the relays and fronthaul links with limited rate from the relays to the destination. We use the oblivious compress and forward (CF) with distributed compression and decode and forward (DF) where each relay decodes the whole message and sends half of its bits to the destination. We derive achievable rate by using time-sharing between DF and CF. It is proved that optimal CF-DF time sharing is advantageous over superposition of CF and DF. The optimal time sharing proportion between DF and CF and power and rate allocations are different at each frequency and are fully determined.

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 AccessAuthors:Novikov, Dmitry; Shapiro, Boris; Tahar, Guillaume;Novikov, Dmitry; Shapiro, Boris; Tahar, Guillaume;Publisher: Springer Science and Business Media LLCProject: EC | EffectiveTG (802107)
Meromorphic connections on Riemann surfaces originate and are closely related to the classical theory of linear ordinary differential equations with meromorphic coefficients. Limiting behaviour of geodesics of such connections has been studied by e.g. Abate, Bianchi and Tovena in relation with generalized Poincar\'{e}-Bendixson theorems. At present, it seems still to be unknown whether some of the theoretically possible asymptotic behaviours of such geodesics really exist. In order to fill the gap, we use the branched affine structure induced by a Fuchsian meromorphic connection to present several examples with geodesics having infinitely many self-intersections and quite peculiar omega-limit sets. Comment: 15 pages, 4 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 . 2021 . Embargo End Date: 01 Jan 2021Open AccessAuthors:Miron Amusia; Arkadiy S. Baltenkov;Miron Amusia; Arkadiy S. Baltenkov;Publisher: arXiv
In this paper we calculate the elastic scattering cross sections of slow electron by carbon nanotubes. The corresponding electron-nanotube interaction is substituted by a zero-thickness cylindrical potential that neglects the atomic structure of real nanotubes, thus limiting the range of applicability of our approach to sufficiently low incoming electron energies. The strength of the potential is chosen the same that was used in describing scattering of electrons by fullerene C60. We present results for total and partial electron scattering cross sections as well as respective angular distributions, all with account of five lowest angular momenta contributions. In the calculations we assumed that the incoming electron moves perpendicular to the nanotube axis, since along the axis the incoming electron moves freely. Comment: 10 pages, 2 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 . 2021 . Embargo End Date: 01 Jan 2018Open AccessAuthors:Itai Benjamini; David Ellis;Itai Benjamini; David Ellis;Publisher: arXivCountry: United Kingdom
We continue the study of the properties of graphs in which the ball of radius $r$ around each vertex induces a graph isomorphic to the ball of radius $r$ in some fixed vertex-transitive graph $F$, for various choices of $F$ and $r$. This is a natural extension of the study of regular graphs. More precisely, if $F$ is a vertex-transitive graph and $r \in \mathbb{N}$, we say a graph $G$ is {\em $r$-locally $F$} if the ball of radius $r$ around each vertex of $G$ induces a graph isomorphic to the graph induced by the ball of radius $r$ around any vertex of $F$. We consider the following random graph model: for each $n \in \mathbb{N}$, we let $G_n = G_n(F,r)$ be a graph chosen uniformly at random from the set of all unlabelled, $n$-vertex graphs that are $r$-locally $F$. We investigate the properties possessed by the random graph $G_n$ with high probability, for various natural choices of $F$ and $r$. We prove that if $F$ is a Cayley graph of a torsion-free group of polynomial growth, and $r$ is sufficiently large depending on $F$, then the random graph $G_n = G_n(F,r)$ has largest component of order at most $n^{5/6}$ with high probability, and has at least $\exp(n^{\delta})$ automorphisms with high probability, where $\delta>0$ depends upon $F$ alone. Both properties are in stark contrast to random $d$-regular graphs, which correspond to the case where $F$ is the infinite $d$-regular tree. We also show that, under the same hypotheses, the number of unlabelled, $n$-vertex graphs that are $r$-locally $F$ grows like a stretched exponential in $n$, again in contrast with $d$-regular graphs. In the case where $F$ is the standard Cayley graph of $\mathbb{Z}^d$, we obtain a much more precise enumeration result, and more precise results on the properties of the random graph $G_n(F,r)$. Our proofs use a mixture of results and techniques from geometry, group theory and combinatorics. Comment: Full proof of Theorem 7 added. Statement of Proposition 38 has been strengthened slightly. 61 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. - Publication . Article . Preprint . 2021Open Access EnglishAuthors:Hagai Perets; Evgeni Grishin;Hagai Perets; Evgeni Grishin;Project: EC | SNeX (865932)
Recent surveys show that wide ($>10^4$ AU) binaries and triples are abundant in the field. We study the long-term evolution of wide hierarchical triple systems and the role played by the Galactic tidal (GT) field. We find that when the timescales of the secular von-Ziepel-Lidov-Kozai and the GT oscillations are comparable, triple evolution becomes chaotic which leads to extreme eccentricities. Consequently, the close pericentre approaches of the inner-binary components lead to strong interactions, mergers and collisions. We use a novel secular evolution code to quantify the key parameters and carry out a population-synthesis study of low and intermediate-mass wide-orbit triples. We find that in $\sim9\%$ of low-mass wide-triples the inner main-sequence binaries collide or tidally-inspiral within $10\ \rm Gyr$, with direct collisions are $6$ times more likely to occur. For the intermediate-mass sample, $\sim7.6\%$ of the systems merge or inspiral with roughly equal probabilities. We discuss the relative fractions of different stellar merger/inspiral outcomes as a function of their evolutionary stage (Main-Sequence, MS; Red-Giant, RG; or White-Dwarf, WD), their transient electromagnetic signatures and the final products of the merger/inspiral. In particular, the rate of WD-WD direct-collisions that lead to type-Ia Supernovae is comparable to other dynamical channels and accounts for at most $0.1\%$ of the observed rate. RG inspirals provide a novel channel for the formation of eccentric common-envelope-evolution binaries. The catalysis of mergers/collisions in triples due to GT could explain a significant fraction, or even the vast majority, of blue-stragglers in the field, produce progenitors for cataclysmic-variables, and give-rise to mergers/collisions of double-RG binaries. Accepted to MNRAS

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 . 2021 . Embargo End Date: 01 Jan 2021Open AccessAuthors:Yuval Scher; Shlomi Reuveni;Yuval Scher; Shlomi Reuveni;Publisher: arXiv
How much time does it take two molecules to react? If a reaction occurs upon contact, the answer to this question boils down to the classic first-passage time problem: find the time it takes the two molecules to meet. However, this is not always the case as molecules switch stochastically between reactive and non-reactive states. The reaction is then said to be ``gated' by the internal states of the molecules involved which could have a dramatic influence on kinetics. A unified, continuous-time, approach to gated reactions on networks was presented in [Phys. Rev. Lett. 127, 018301, 2021]. Here, we build on this recent advancement and develop an analogous discrete-time version of the theory. Similar to continuous-time, we employ a renewal approach to show that the gated reaction time can always be expressed in terms of the corresponding ungated first-passage and return times; which yields formulas for the generating function of the gated reaction-time distribution and its corresponding mean and variance. In cases where the mean reaction time diverges, we show that the long-time asymptotics of the gated problem is inherited from its ungated counterpart. However, when molecules spend most of their time non-reactive, an interim regime of slower power-law decay emerges prior to the terminal asymptotics. The discretization of time also gives rise to resonances and anti-resonances, which were absent from the continuous time picture. These features are illustrated using two case studies that also demonstrate how the general approach presented herein greatly simplifies the analysis of gated reactions.

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 AccessAuthors:Nikbakht, Homa; Wigger, Michele; Shamai Shitz, Shlomo;Nikbakht, Homa; Wigger, Michele; Shamai Shitz, Shlomo;Publisher: Institute of Electrical and Electronics Engineers (IEEE)Project: EC | CTO Com (715111), EC | CloudRadioNet (694630)
This paper analyzes the multiplexing gains (MG) for simultaneous transmission of delay-sensitive and delay-tolerant data over interference networks. In the considered model, only delay-tolerant data can profit from coordinated multipoint (CoMP) transmission or reception techniques, because delay-sensitive data has to be transmitted without further delay. Transmission of delay-tolerant data is also subject to a delay constraint, which is however less stringent than the one on delay-sensitive data. Different coding schemes are proposed, and the corresponding MG pairs for delay-sensitive and delay-tolerant data are characterized for Wyner's linear symmetric network and for Wyner's two-dimensional hexagonal network with and without sectorization. For Wyner's linear symmetric also an information-theoretic converse is established and shown to be exact whenever the cooperation rates are sufficiently large or the delay-sensitive MG is small or moderate. These results show that on Wyner's symmetric linear network and for sufficiently large cooperation rates, the largest MG for delay-sensitive data can be achieved without penalizing the maximum sum-MG of both delay-sensitive and delay-tolerant data. A similar conclusion holds for Wyner's hexagonal network only for the model with sectorization. In the model without sectorization, a penalty in sum-MG is incurred whenever one insists on a positive delay-sensitive MG. Comment: 41 pages, submitted to Transactions on Communications

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.