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  • Publication . Article . Preprint . 2022
    Open Access English
    Authors: 
    Edith Elkind; Erel Segal-Halevi; Warut Suksompong;
    Publisher: Elsevier
    Country: United Kingdom
    Project: EC | ACCORD (639945)

    We study the problem of fairly allocating a divisible resource, also known as cake cutting, with an additional requirement that the shares that different agents receive should be sufficiently separated from one another. This captures, for example, constraints arising from social distancing guidelines. While it is sometimes impossible to allocate a proportional share to every agent under the separation requirement, we show that the well-known criterion of maximin share fairness can always be attained. We then provide algorithmic analysis of maximin share fairness in this setting -- for instance, the maximin share of an agent cannot be computed exactly by any finite algorithm, but can be approximated with an arbitrarily small error. In addition, we consider the division of a pie (i.e., a circular cake) and show that an ordinal relaxation of maximin share fairness can be achieved. We also prove that an envy-free or equitable allocation that allocates the maximum amount of resource exists under separation. Appears in the 35th AAAI Conference on Artificial Intelligence (AAAI), 2021

  • Open Access English
    Authors: 
    Hengxin Tan; Daniel Kaplan; Binghai Yan;
    Project: EC | NonlinearTopo (815869)

    Magnetic topological insulators (MnBi$_2$Te$_4$)(Bi$_2$Te$_3$)$_n$ were anticipated to exhibit magnetic energy gaps while recent spectroscopic studies did not observe them. Thus, magnetism on the surface is under debate. In this work, we propose another symmetry criterion to probe the surface magnetism. Because of both time-reversal symmetry-breaking and inversion symmetry-breaking, we demonstrate that the surface band structure violates momentum-inversion symmetry and leads to a three-fold rather than six-fold rotational symmetry on the Fermi surface if corresponding surface states couple strongly to the surface magnetism. Such a momentum-inversion symmetry violation is significant along the $\Gamma-K$ direction for surface bands on the (0001) plane. Comment: 4 pages, 3 figures

  • Publication . Article . Preprint . 2022
    Open Access English
    Authors: 
    Adam Chapman; Solomon Vishkautsan;

    This paper is devoted to several new results concerning (standard) octonion polynomials. The first is the determination of the roots of all right scalar multiples of octonion polynomials. The roots of left multiples are also discussed, especially over fields of characteristic not 2. We then turn to study the dynamics of monic quadratic real octonion polynomials, classifying the fixed points into attracting, repelling and ambivalent, and concluding with a discussion on the behavior of pseudo-periodic points.

  • Publication . Preprint . Article . 2022
    Open Access English
    Authors: 
    Enrico Cannizzaro; Laura Sberna; Andrea Caputo; Paolo Pani;
    Publisher: APS
    Project: EC | DarkGRA (757480), EC | LDMThExp (682676)

    Black-hole superradiance has been used to place very strong bounds on a variety of models of ultralight bosons such as axions, new light scalars, and dark photons. It is common lore to believe that superradiance bounds are broadly model independent and therefore pretty robust. In this work we show however that superradiance bounds on dark photons can be challenged by simple, compelling extensions of the minimal model. In particular, if the dark photon populates a larger dark sector and couples to dark fermions playing the role of dark matter, then superradiance bounds can easily be circumvented, depending on the mass and (dark) charge of the dark matter. 10+3 pages, 4 figures

  • Open Access English
    Authors: 
    Dean P. Foster; Sergiu Hart;

    We propose to smooth out the calibration score, which measures how good a forecaster is, by combining nearby forecasts. While regular calibration can be guaranteed only by randomized forecasting procedures, we show that smooth calibration can be guaranteed by deterministic procedures. As a consequence, it does not matter if the forecasts are leaked, i.e., made known in advance: smooth calibration can nevertheless be guaranteed (while regular calibration cannot). Moreover, our procedure has finite recall, is stationary, and all forecasts lie on a finite grid. To construct the procedure, we deal also with the related setups of online linear regression and weak calibration. Finally, we show that smooth calibration yields uncoupled finite-memory dynamics in n-person games "smooth calibrated learning" in which the players play approximate Nash equilibria in almost all periods (by contrast, calibrated learning, which uses regular calibration, yields only that the time-averages of play are approximate correlated equilibria). http://www.ma.huji.ac.il/hart/publ.html#calib-eq

  • Open Access English
    Authors: 
    Tsevi Mazeh; Simchon Faigler; Dolev Bashi; Sahar Shahaf; Niv Davidson; Matthew Green; Roy Gomel; Dan Maoz; Amitay Sussholz; Subo Dong; +17 more
    Project: EC | EMERGE (833031)

    We have identified 2XMM J125556.57+565846.4, at a distance of 600 pc, as a binary system consisting of a normal star and a probable dormant neutron star. Optical spectra exhibit a slightly evolved F-type single star, displaying periodic Doppler shifts with a 2.76-day Keplerian circular orbit, with no indication of light from a secondary component. Optical and UV photometry reveal ellipsoidal variations with half the orbital period, due to the tidal deformation of the F star. The mass of the unseen companion is constrained to the range $1.1$--$2.1\,M_{\odot}$ at $3\sigma$ confidence, with the median of the mass distribution at $1.4\,M_{\odot}$, the typical mass of known neutron stars. A main-sequence star cannot masquerade as the dark companion. The distribution of possible companion masses still allows for the possibility of a very massive white dwarf. The companion itself could also be a close pair consisting of a white dwarf and an M star, or two white dwarfs, although the binary evolution that would lead to such a close triple system is unlikely. Similar ambiguities regarding the certain identification of a dormant neutron star are bound to affect most future discoveries of this type of non-interacting system. If the system indeed contains a dormant neutron star, it will become, in the future, a bright X-ray source and afterwards might even host a millisecond pulsar. Comment: 35 pages, 21 figures. accepted for publication in MNRAS

  • Open Access English
    Authors: 
    Rami Katz; Emilia Fridman;

    Finite-dimensional observer-based controller design for PDEs is a challenging problem. Recently, such controllers were introduced for the 1D heat equation, under the assumption that one of the observation or control operators is bounded. This paper suggests a constructive method for such controllers for 1D parabolic PDEs with both (observation and control) operators being unbounded. We consider the Kuramoto-Sivashinsky equation (KSE) under either boundary or in-domain point measurement and boundary actuation. We employ a modal decomposition approach via dynamic extension, using eigenfunctions of a Sturm-Liouville operator. The controller dimension is defined by the number of unstable modes, whereas the observer dimension $N$ may be larger than this number. We suggest a direct Lyapunov approach to the full-order closed-loop system, which results in an LMI whose elements and dimension depend on $N$. The value of $N$ and the decay rate are obtained from the LMI. We extend our approach to internal stabilization with guaranteed $L^2$-gain and input-to-state stabilization. We prove two crucial properties of the derived LMIs. First, We prove that the LMIs are always feasible provided $N$ and the $L^2$ or ISS gains are large enough, thereby obtaining guarantees for our approach. Moreover, for the case of stabilization, we show that feasibility of the LMI for some $N$ implies its feasibility for $N+1$ (i.e., enlarging $N$ in the LMI cannot deteriorate the resulting decay rate of the closed-loop system). Numerical examples demonstrate the efficiency of the method.

  • Open Access English
    Authors: 
    Yael Mathov; Tal Ben Senior; Asaf Shabtai; Yuval Elovici;

    Mass surveillance systems for voice over IP (VoIP) conversations pose a great risk to privacy. These automated systems use learning models to analyze conversations, and calls that involve specific topics are routed to a human agent for further examination. In this study, we present an adversarial-learning-based framework for privacy protection for VoIP conversations. We present a novel method that finds a universal adversarial perturbation (UAP), which, when added to the audio stream, prevents an eavesdropper from automatically detecting the conversation's topic. As shown in our experiments, the UAP is agnostic to the speaker or audio length, and its volume can be changed in real time, as needed. Our real-world solution uses a Teensy microcontroller that acts as an external microphone and adds the UAP to the audio in real time. We examine different speakers, VoIP applications (Skype, Zoom, Slack, and Google Meet), and audio lengths. Our results in the real world suggest that our approach is a feasible solution for privacy protection.

  • Publication . Article . Preprint . 2022
    Open Access English
    Authors: 
    Sergiu Hart; Yosef Rinott;

    Abstract The Bayesian posterior probability of the true state is stochastically dominated by that same posterior under the probability law of the true state. This generalizes to notions of “optimism” about posterior probabilities.

  • Publication . Preprint . Article . Conference object . 2022
    Open Access English
    Authors: 
    Sharir, Micha; Solomon, Noam;
    Publisher: Journal of Computational Geometry

    Let $L$ be a set of $n$ lines in $R^3$ that is contained, when represented as points in the four-dimensional Pl\"ucker space of lines in $R^3$, in an irreducible variety $T$ of constant degree which is \emph{non-degenerate} with respect to $L$ (see below). We show: \medskip \noindent{\bf (1)} If $T$ is two-dimensional, the number of $r$-rich points (points incident to at least $r$ lines of $L$) is $O(n^{4/3+\epsilon}/r^2)$, for $r \ge 3$ and for any $\epsilon>0$, and, if at most $n^{1/3}$ lines of $L$ lie on any common regulus, there are at most $O(n^{4/3+\epsilon})$ $2$-rich points. For $r$ larger than some sufficiently large constant, the number of $r$-rich points is also $O(n/r)$. As an application, we deduce (with an $\epsilon$-loss in the exponent) the bound obtained by Pach and de Zeeuw (2107) on the number of distinct distances determined by $n$ points on an irreducible algebraic curve of constant degree in the plane that is not a line nor a circle. \medskip \noindent{\bf (2)} If $T$ is two-dimensional, the number of incidences between $L$ and a set of $m$ points in $R^3$ is $O(m+n)$. \medskip \noindent{\bf (3)} If $T$ is three-dimensional and nonlinear, the number of incidences between $L$ and a set of $m$ points in $R^3$ is $O\left(m^{3/5}n^{3/5} + (m^{11/15}n^{2/5} + m^{1/3}n^{2/3})s^{1/3} + m + n \right)$, provided that no plane contains more than $s$ of the points. When $s = O(\min\{n^{3/5}/m^{2/5}, m^{1/2}\})$, the bound becomes $O(m^{3/5}n^{3/5}+m+n)$. As an application, we prove that the number of incidences between $m$ points and $n$ lines in $R^4$ contained in a quadratic hypersurface (which does not contain a hyperplane) is $O(m^{3/5}n^{3/5} + m + n)$. The proofs use, in addition to various tools from algebraic geometry, recent bounds on the number of incidences between points and algebraic curves in the plane. Comment: 21 pages, one figure

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