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  • Publication . Article . Presentation . Conference object . Other literature type . Preprint . 2021
    Open Access English

    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.

  • Publication . Article . Preprint . 2021
    Open Access English
    Authors: 
    Dmitry Novikov; Boris Shapiro; Guillaume Tahar;
    Project: 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

  • Publication . Article . Preprint . 2021
    Open Access English
    Authors: 
    Ellis, David; Benjamini, Itai;
    Country: 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

  • Open Access English
    Authors: 
    Homa Nikbakht; Michele Wigger; Shlomo Shamai;
    Project: EC | CloudRadioNet (694630), EC | CTO Com (715111), EC | CloudRadioNet (694630), EC | CTO Com (715111)

    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. 41 pages, submitted to Transactions on Communications

  • Publication . Article . Preprint . 2021
    Open Access English
    Authors: 
    Andrea Guerrieri; Amit Sever;

    We consider a dual $S$-matrix Bootstrap approach in $d\geq 3$ space-time dimensions which relies solely on the rigorously proven analyticity, crossing, and unitarity properties of the scattering amplitudes. As a proof of principle, we provide rigorous upper and lower numerical bounds on the quartic coupling for the scattering of identical scalar particles in four dimensions. 5 + 10 pages, 3 + 6 figures, major revision in the appendices, improved numerics, typos corrected

  • Publication . Conference object . Preprint . Article . 2021
    Open Access English
    Authors: 
    Eyal Bar-Shalom; Michael Margaliot;

    The multiplicative and additive compounds of a matrix play an important role in several fields of mathematics including geometry, multi-linear algebra, combinatorics, and the analysis of nonlinear time-varying dynamical systems. There is a growing interest in applications of these compounds, and their generalizations, in systems and control theory. This tutorial paper provides a gentle introduction to these topics with an emphasis on the geometric interpretation of the compounds, and surveys some of their recent applications.

  • Open Access English
    Authors: 
    Giovanni Felder; David Kazhdan; Alexander Polishchuk;
    Project: EC | HAS (669655), NSF | Moduli of A-Infinity Stru... (1700642)

    The supermeasure whose integral is the genus $g$ vacuum amplitude of superstring theory is potentially singular on the locus in the moduli space of supercurves where the corresponding even theta-characteristic has nontrivial sections. We show that the supermeasure is actually regular for $g\leq 11$. The result relies on the study of the superperiod map. We also show that the minimal power of the classical Schottky ideal that annihilates the image of the superperiod map is equal to $g$ if $g$ is odd and is equal to $g$ or $g-1$ if $g$ is even. 41 pages

  • Publication . Article . Preprint . 2021
    Open Access English
    Authors: 
    Omri Lesser; Yuval Oreg;
    Project: EC | LEGOTOP (788715)

    Majorana zero modes in condensed matter systems have been the subject of much interest in recent years. Their non-Abelian exchange statistics, making them a unique state of matter, and their potential applications in topological quantum computation, earned them attention from both theorists and experimentalists. It is generally understood that in order to form Majorana zero modes in quasi-one-dimensional topological insulators, time-reversal symmetry must be broken. The straightforward mechanisms for doing so -- applying magnetic fields or coupling to ferromagnets -- turned out to have many unwanted side effects, such as degradation of superconductivity and the formation of sub-gap states, which is part of the reason Majorana zero modes have been eluding direct experimental detection for a long time. Here we review several proposal that rely on controlling the phase of the superconducting order parameter, either as the sole mechanism for time-reversal-symmetry breaking, or as an additional handy knob used to reduce the applied magnetic field. These proposals hold practical promise to improve Majorana formation, and they shed light on the physics underlying the formation of the topological superconducting state. 14 pages, 8 figures. Invited review for Journal of Physics D Special Issue on Topological Materials

  • Open Access English
    Authors: 
    Doruk Efe Gökmen; Zohar Ringel; Sebastian D. Huber; Maciej Koch-Janusz;
    Country: Switzerland
    Project: EC | TopMechMat (771503), EC | COMPLEX ML (896004)

    Identifying the relevant coarse-grained degrees of freedom in a complex physical system is a key stage in developing powerful effective theories in and out of equilibrium. The celebrated renormalization group provides a framework for this task, but its practical execution in unfamiliar systems is fraught with ad hoc choices, whereas machine learning approaches, though promising, often lack formal interpretability. Recently, the optimal coarse-graining in a statistical system was shown to exist, based on a universal, but computationally difficult information-theoretic variational principle. This limited its applicability to but the simplest systems; moreover, the relation to standard formalism of field theory was unclear. Here we present an algorithm employing state-of-art results in machine-learning-based estimation of information-theoretic quantities, overcoming these challenges. We use this advance to develop a new paradigm in identifying the most relevant field theory operators describing properties of the system, going beyond the existing approaches to real-space renormalization. We evidence its power on an interacting model, where the emergent degrees of freedom are qualitatively different from the microscopic building blocks of the theory. Our results push the boundary of formally interpretable applications of machine learning, conceptually paving the way towards automated theory building. Comment: Version accepted for publication in Physical Review Letters. See also the companion manuscript arXiv:2103.16887 "Symmetries and phase diagrams with real-space mutual estimation neural estimation"

  • Open Access English
    Authors: 
    Zixuan Ke; Hu Xu; Bing Liu;

    This paper studies continual learning (CL) of a sequence of aspect sentiment classification (ASC) tasks. Although some CL techniques have been proposed for document sentiment classification, we are not aware of any CL work on ASC. A CL system that incrementally learns a sequence of ASC tasks should address the following two issues: (1) transfer knowledge learned from previous tasks to the new task to help it learn a better model, and (2) maintain the performance of the models for previous tasks so that they are not forgotten. This paper proposes a novel capsule network based model called B-CL to address these issues. B-CL markedly improves the ASC performance on both the new task and the old tasks via forward and backward knowledge transfer. The effectiveness of B-CL is demonstrated through extensive experiments. arXiv admin note: text overlap with arXiv:2112.02714, arXiv:2112.02706

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