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  • image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
    Authors: Ghalme, Ganesh; Huang, Xin; Machino, Yuka; Rathi, Nidhi;

    We study the classic problem of \emph{fairly} dividing a heterogeneous and divisible resource -- modeled as a line segment $[0,1]$ and typically called as a \emph{cake} -- among $n$ agents. This work considers an interesting variant of the problem where agents are embedded on a graph. The graphical constraint entails that each agent evaluates her allocated share only against her neighbors' share. Given a graph, the goal is to efficiently find a \emph{locally envy-free} allocation where every agent values her share of the cake to be at least as much as that of any of her neighbors' share. The most significant contribution of this work is a bounded protocol that finds a locally envy-free allocation among $n$ agents on a tree graph using $n^{O(n)}$ queries under the standard Robertson-Webb (RW) query model. The query complexity of our proposed protocol, though exponential, significantly improves the currently best known hyper-exponential query complexity bound of Aziz and Mackenzie [AM16] for complete graphs. In particular, we also show that if the underlying tree graph has a depth of at most two, one can find a locally envy-free allocation with $O(n^4 \log n)$ RW queries. This is the first and the only known locally envy-free cake cutting protocol with polynomial query complexity for a non-trivial graph structure. Interestingly, our discrete protocols are simple and easy to understand, as opposed to highly involved protocol of [AM16]. This simplicity can be attributed to their recursive nature and the use of a single agent as a designated \emph{cutter}. We believe that these results will help us improve our algorithmic understanding of the arguably challenging problem of envy-free cake-cutting by uncovering the bottlenecks in its query complexity and its relation to the underlying graph structures. Comment: arXiv admin note: substantial text overlap with arXiv:2205.12559

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    arXiv.org e-Print Archive
    Other literature type . Preprint . 2022
    image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
    https://doi.org/10.1007/978-3-...
    Part of book or chapter of book . 2023 . Peer-reviewed
    License: Springer Nature TDM
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    https://doi.org/10.48550/arxiv...
    Article . 2022
    License: CC BY
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      image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/ arXiv.org e-Print Ar...arrow_drop_down
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      arXiv.org e-Print Archive
      Other literature type . Preprint . 2022
      image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
      https://doi.org/10.1007/978-3-...
      Part of book or chapter of book . 2023 . Peer-reviewed
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      https://doi.org/10.48550/arxiv...
      Article . 2022
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  • image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
    Authors: Jiaxu Tian; Dapeng Zhi; Si Liu; Peixin Wang; +2 Authors

    The intrinsic complexity of deep neural networks (DNNs) makes it challenging to verify not only the networks themselves but also the hosting DNN-controlled systems. Reachability analysis of these systems faces the same challenge. Existing approaches rely on over-approximating DNNs using simpler polynomial models. However, they suffer from low efficiency and large overestimation, and are restricted to specific types of DNNs. This paper presents a novel abstraction-based approach to bypass the crux of over-approximating DNNs in reachability analysis. Specifically, we extend conventional DNNs by inserting an additional abstraction layer, which abstracts a real number to an interval for training. The inserted abstraction layer ensures that the values represented by an interval are indistinguishable to the network for both training and decision-making. Leveraging this, we devise the first black-box reachability analysis approach for DNN-controlled systems, where trained DNNs are only queried as black-box oracles for the actions on abstract states. Our approach is sound, tight, efficient, and agnostic to any DNN type and size. The experimental results on a wide range of benchmarks show that the DNNs trained by using our approach exhibit comparable performance, while the reachability analysis of the corresponding systems becomes more amenable with significant tightness and efficiency improvement over the state-of-the-art white-box approaches.

    image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/ arXiv.org e-Print Ar...arrow_drop_down
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    arXiv.org e-Print Archive
    Other literature type . Preprint . 2022
    image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
    https://doi.org/10.1007/978-3-...
    Part of book or chapter of book . 2023 . Peer-reviewed
    License: Springer Nature TDM
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    https://doi.org/10.48550/arxiv...
    Article . 2022
    License: arXiv Non-Exclusive Distribution
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      arXiv.org e-Print Archive
      Other literature type . Preprint . 2022
      image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
      https://doi.org/10.1007/978-3-...
      Part of book or chapter of book . 2023 . Peer-reviewed
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      Article . 2022
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  • image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/

    We initiate a study of a new model of property testing that is a hybrid of testing properties of distributions and testing properties of strings. Specifically, the new model refers to testing properties of distributions, but these are distributions over huge objects (i.e., very long strings). Accordingly, the model accounts for the total number of local probes into these objects (resp., queries to the strings) as well as for the distance between objects (resp., strings). Specifically, the distance between distributions is defined as the earth mover’s distance with respect to the relative Hamming distance between strings. We study the query complexity of testing in this new model, focusing on three directions. First, we try to relate the query complexity of testing properties in the new model to the sample complexity of testing these properties in the standard distribution testing model. Second, we consider the complexity of testing properties that arise naturally in the new model (e.g., distributions that capture random variations of fixed strings). Third, we consider the complexity of testing properties that were extensively studied in the standard distribution testing model: Two such cases are uniform distributions and pairs of identical distributions, where we obtain the following results. - Testing whether a distribution over n-bit long strings is uniform on some set of size m can be done with query complexity Õ(m/ε³), where ε > (log₂m)/n is the proximity parameter. - Testing whether two distribution over n-bit long strings that have support size at most m are identical can be done with query complexity Õ(m^{2/3}/ε³). Both upper bounds are quite tight; that is, for ε = Ω(1), the first task requires Ω(m^c) queries for any c < 1 and n = ω(log m), whereas the second task requires Ω(m^{2/3}) queries. Note that the query complexity of the first task is higher than the sample complexity of the corresponding task in the standard distribution testing model, whereas in the case of the second task the bounds almost match.

    image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/ arXiv.org e-Print Ar...arrow_drop_down
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    arXiv.org e-Print Archive
    Other literature type . Preprint . 2022
    image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
    image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
    Episciences
    Article . 2023
    License: CC BY
    Data sources: Episciences
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    https://doaj.org/article/5247f...
    Article . 2023
    Data sources: DOAJ
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    https://doi.org/10.46298/theor...
    Article . 2023 . Peer-reviewed
    License: CC BY
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    https://doi.org/10.48550/arxiv...
    Article . 2022
    License: CC BY
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      Other literature type . Preprint . 2022
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      Episciences
      Article . 2023
      License: CC BY
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      https://doaj.org/article/5247f...
      Article . 2023
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      https://doi.org/10.46298/theor...
      Article . 2023 . Peer-reviewed
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  • image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/

    Heterostructures of layered transition metal dichalcogenides (TMDs) host long-lived, tunable excitons, making them intriguing candidates for material-based quantum information applications. Light absorption in these systems induces a plethora of optically excited states that hybridize both interlayer and intralayer characteristics, providing a distinctive starting point for their relaxation processes, in which the interplay between generated electron-hole pairs and their scattering with phonons play a key role. We present a first-principles theoretical approach to compute phonon-induced exciton decomposition due to rapid occupation of electron-hole pairs with finite momentum and opposite spin. Using the MoSe$_2$/WSe$_2$ heterostructure as a case study, we observe a reduction in the optical activity of bright states upon phonon scattering already in the first few femtoseconds proceeding the photoexcitation, driving exciton interlayer delocalization and subsequent variations in the exciton spin. Our results reveal an unexpected and previously unexplored starting point for exciton relaxation dynamics, suggesting increased availability for coherent interactions and non-radiative processes through ultrafast changes in exciton momentum, spatial, and spin properties upon light excitation.

    image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/ arXiv.org e-Print Ar...arrow_drop_down
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    arXiv.org e-Print Archive
    Other literature type . Preprint . 2023
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    https://doi.org/10.1103/physre...
    Article . 2023 . Peer-reviewed
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    Article . 2023
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      https://doi.org/10.1103/physre...
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    Authors: Taya Govreen-Segal; Noam Youngerman; Ishika Palit; Ehud Nakar; +2 Authors

    ABSTRACT We investigate the propagation of spherically symmetric shocks in relativistic homologously expanding media with density distributions following a power-law profile in their Lorentz factor. That is, $\rho _{_{\rm {ej}}} \propto t^{-3}\gamma _{_{\rm {ej}}}(r,t)^{-\alpha }$, where $\rho _{_{\rm {ej}}}$ is the medium proper density, $\gamma _{_{\rm {ej}}}$ is its Lorentz factor, α &gt; 0 is constant, and t, r are the time and radius from the centre. We find that the shocks behaviour can be characterized by their proper velocity, $U^{\prime }=\Gamma _s^{\prime }\beta _s^{\prime }$, where $\Gamma _s^{\prime }$ is the shock Lorentz factor as measured in the immediate upstream frame and $\beta _s^{\prime }$ is the corresponding three velocity. While generally, we do not expect the shock evolution to be self-similar, for every α &gt; 0 we find a critical value $U^{\prime }_c$ for which a self-similar solution with constant U′ exists. We then use numerical simulations to investigate the behaviour of general shocks. We find that shocks with $U^{\prime }\gt U^{\prime }_c$ have a monotonously growing U′, while those with $U^{\prime }\lt U^{\prime }_c$ have a decreasing U′ and will eventually die out. Finally, we present an analytic approximation, based on our numerical results, for the evolution of general shocks in the regime where U′ is ultrarelativistic.

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    arXiv.org e-Print Archive
    Other literature type . Preprint . 2023
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    Monthly Notices of the Royal Astronomical Society
    Article . 2023 . Peer-reviewed
    License: CC BY
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    Article . 2023
    License: arXiv Non-Exclusive Distribution
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      Monthly Notices of the Royal Astronomical Society
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    Authors: Solomon, Shay; Uzrad, Amitai;

    The minimum set cover (MSC) problem admits two classic algorithms: a greedy $\ln n$-approximation and a primal-dual $f$-approximation, where $n$ is the universe size and $f$ is the maximum frequency of an element. Both algorithms are simple and efficient, and remarkably -- one cannot improve these approximations under hardness results by more than a factor of $(1+\epsilon)$, for any constant $\epsilon > 0$. In their pioneering work, Gupta et al. [STOC'17] showed that the greedy algorithm can be dynamized to achieve $O(\log n)$-approximation with update time $O(f \log n)$. Building on this result, Hjuler et al. [STACS'18] dynamized the greedy minimum dominating set (MDS) algorithm, achieving a similar approximation with update time $O(\Delta \log n)$ (the analog of $O(f \log n)$), albeit for unweighted instances. The approximations of both algorithms, which are the state-of-the-art, exceed the static $\ln n$-approximation by a rather large constant factor. In sharp contrast, the current best dynamic primal-dual MSC algorithms achieve fast update times together with an approximation that exceeds the static $f$-approximation by a factor of (at most) $1+\epsilon$, for any $\epsilon > 0$. This paper aims to bridge the gap between the best approximation factor of the dynamic greedy MSC and MDS algorithms and the static $\ln n$ bound. We present dynamic algorithms for weighted greedy MSC and MDS with approximation $(1+\epsilon)\ln n$ for any $\epsilon > 0$, while achieving the same update time (ignoring dependencies on $\epsilon$) of the best previous algorithms (with approximation significantly larger than $\ln n$). Moreover, [...] Comment: Abstract truncated to fit arXiv limits; full version of a STOC'23 paper

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    Authors: Jonathan Nemirovsky; Rafi Weill; Ilan Meltzer; Yoav Sagi;

    Atomic interferometers measure forces and acceleration with exceptional precision. The conventional approach to atomic interferometry is to launch an atomic cloud into a ballistic trajectory and perform the wave-packet splitting in momentum space by Raman transitions. This places severe constraints on the possible atomic trajectory, positioning accuracy and probing duration. Here, we propose and analyze a novel atomic interferometer that uses micro-optical traps (optical tweezers) to manipulate and control the motion of atoms. The new interferometer allows long probing time, sub micrometer positioning accuracy, and utmost flexibility in shaping of the atomic trajectory. The cornerstone of the tweezer interferometer are the coherent atomic splitting and combining schemes. We present two adiabatic schemes with two or three tweezers that are robust to experimental imperfections and work simultaneously with many vibrational states. The latter property allows for multi-atom interferometry in a single run. We also highlight the advantage of using fermionic atoms to obtain single-atom occupation of vibrational states and to eliminate mean-field shifts. We examine the impact of tweezer intensity noise and demonstrate that, when constrained by shot noise, the interferometer can achieve a relative accuracy better than $10^{-11}$ in measuring Earth's gravitational acceleration. The sub-micrometer resolution and extended measurement duration offer promising opportunities for exploring fundamental physical laws in new regimes. We discuss two applications well-suited for the unique capabilities of the tweezer interferometer: the measurement of gravitational forces and the study of Casimir-Polder forces between atoms and surfaces. Crucially, our proposed tweezer interferometer is within the reach of current technological capabilities. 14 pages, 7 figures

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    Physical Review Research
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    Authors: Uzhansky, Michael; Rakshit, Abhishek; Kalcheim, Yoav; Koren, Elad;

    Pyroelectric and photovoltaic effects are vital in cutting-edge thermal imaging, infrared sensors, thermal and solar energy harvesting. Recent advances revealed the great potential of the bulk photovoltaic effect in two-dimensional (2D) semiconductor-ferroelectric materials to enable reconfigurable p-n junction operation with the potential to surpass the Shockley-Queiseer limit. Moreover, the extremely low thickness, high thermal conductivity, dangling bonds free interface, and room-temperature stable ferroelectricity down to a single monolayer endow 2D ferroelectrics with a superior pyroelectric figure of merit. Herein, we performed direct pyroelectric measurements of 2D $\alpha$-In$_2$Se$_3$ under dark and light conditions. The results reveal a gigantic pyroelectric coefficient of 30.7 mC/m$^2$K and a figure of merit of 135.9 m$^2$/C. In addition, we perform temperature-dependent short-circuit photovoltaic response measurements in which the excess photocurrent is modulated in proportion with the temperature variations due to the induced in-plane potential variations. Consequently, the discovered pyroelectric-photovoltaic effect allows the combination of direct temperature (photovoltaic) and temperature-derivative (pyroelectric) sensing. Finally, we utilized the intercoupled ferroelectricity of In$_2$Se$_3$ to realize a non-volatile, self-powered photovoltaic memory operation, demonstrating a stable short-circuit current switching with a decent 103 ON-OFF ratio. The coupled pyroelectric-photovoltaic effect, along with reconfigurable photocurrent, pave the way for a novel monolithic device technology with integrated thermal and optical response, in-memory logic and energy harvesting.

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    Authors: Hashim, Fatma A.; Mostafa, Reham R.; Khurma, Ruba Abu; Qaddoura, Raneem; +1 Authors

    Abstract Sea horse optimizer (SHO) is a noteworthy metaheuristic algorithm that emulates various intelligent behaviors exhibited by sea horses, encompassing feeding patterns, male reproductive strategies, and intricate movement patterns. To mimic the nuanced locomotion of sea horses, SHO integrates the logarithmic helical equation and Levy flight, effectively incorporating both random movements with substantial step sizes and refined local exploitation. Additionally, the utilization of Brownian motion facilitates a more comprehensive exploration of the search space. This study introduces a robust and high-performance variant of the SHO algorithm named modified sea horse optimizer (mSHO). The enhancement primarily focuses on bolstering SHO’s exploitation capabilities by replacing its original method with an innovative local search strategy encompassing three distinct steps: a neighborhood-based local search, a global non-neighbor-based search, and a method involving circumnavigation of the existing search region. These techniques improve mSHO algorithm’s search capabilities, allowing it to navigate the search space and converge toward optimal solutions efficiently. To evaluate the efficacy of the mSHO algorithm, comprehensive assessments are conducted across both the CEC2020 benchmark functions and nine distinct engineering problems. A meticulous comparison is drawn against nine metaheuristic algorithms to validate the achieved outcomes. Statistical tests, including Wilcoxon’s rank-sum and Friedman’s tests, are aptly applied to discern noteworthy differences among the compared algorithms. Empirical findings consistently underscore the exceptional performance of mSHO across diverse benchmark functions, reinforcing its prowess in solving complex optimization problems. Furthermore, the robustness of mSHO endures even as the dimensions of optimization challenges expand, signifying its unwavering efficacy in navigating complex search spaces. The comprehensive results distinctly establish the supremacy and efficiency of the mSHO method as an exemplary tool for tackling an array of optimization quandaries. The results show that the proposed mSHO algorithm has a total rank of 1 for CEC2020 test functions. In contrast, the mSHO achieved the best value for the engineering problems, recording a value of 0.012 665, 2993.634, 0.01 266, 1.724 967, 263.8915, 0.032 255, 58 507.14, 1.339 956, and 0.23 524 for the pressure vessel design, speed reducer design, tension/compression spring, welded beam design, three-bar truss engineering design, industrial refrigeration system, multi-product batch plant, cantilever beam problem, and multiple disc clutch brake problems, respectively. Source codes of mSHO are publicly available at https://www.mathworks.com/matlabcentral/fileexchange/135882-improved-sea-horse-algorithm.

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    Journal of Computational Design and Engineering
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    Authors: Shalev, Roy;

    Assuming an instance of the Brodsky-Rinot proxy principle holding at a regular uncountable cardinal $\kappa$, we construct $2^\kappa$-many pairwise non-embeddable minimal non-$\sigma$-scattered linear orders of size $\kappa$. In particular, in G\"odel's constructible universe $L$, these linear orders exist for any regular uncountable cardinal $\kappa$ that is not weakly compact. This extends a recent result of Cummings, Eisworth and Moore that takes care of all the successor cardinals of $L$. At the level of $\aleph_1$, their work answered an old question of Baumgartner by constructing from $\diamondsuit$ a minimal Aronszajn line that is not Souslin. Our use of the proxy principle yields the same conclusion from a weaker assumption which holds for instance in the generic extension after adding a single Cohen real to a model of $CH$. Comment: 22 pages, comments are welcome

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    Authors: Ghalme, Ganesh; Huang, Xin; Machino, Yuka; Rathi, Nidhi;

    We study the classic problem of \emph{fairly} dividing a heterogeneous and divisible resource -- modeled as a line segment $[0,1]$ and typically called as a \emph{cake} -- among $n$ agents. This work considers an interesting variant of the problem where agents are embedded on a graph. The graphical constraint entails that each agent evaluates her allocated share only against her neighbors' share. Given a graph, the goal is to efficiently find a \emph{locally envy-free} allocation where every agent values her share of the cake to be at least as much as that of any of her neighbors' share. The most significant contribution of this work is a bounded protocol that finds a locally envy-free allocation among $n$ agents on a tree graph using $n^{O(n)}$ queries under the standard Robertson-Webb (RW) query model. The query complexity of our proposed protocol, though exponential, significantly improves the currently best known hyper-exponential query complexity bound of Aziz and Mackenzie [AM16] for complete graphs. In particular, we also show that if the underlying tree graph has a depth of at most two, one can find a locally envy-free allocation with $O(n^4 \log n)$ RW queries. This is the first and the only known locally envy-free cake cutting protocol with polynomial query complexity for a non-trivial graph structure. Interestingly, our discrete protocols are simple and easy to understand, as opposed to highly involved protocol of [AM16]. This simplicity can be attributed to their recursive nature and the use of a single agent as a designated \emph{cutter}. We believe that these results will help us improve our algorithmic understanding of the arguably challenging problem of envy-free cake-cutting by uncovering the bottlenecks in its query complexity and its relation to the underlying graph structures. Comment: arXiv admin note: substantial text overlap with arXiv:2205.12559

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    https://doi.org/10.1007/978-3-...
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    Authors: Jiaxu Tian; Dapeng Zhi; Si Liu; Peixin Wang; +2 Authors

    The intrinsic complexity of deep neural networks (DNNs) makes it challenging to verify not only the networks themselves but also the hosting DNN-controlled systems. Reachability analysis of these systems faces the same challenge. Existing approaches rely on over-approximating DNNs using simpler polynomial models. However, they suffer from low efficiency and large overestimation, and are restricted to specific types of DNNs. This paper presents a novel abstraction-based approach to bypass the crux of over-approximating DNNs in reachability analysis. Specifically, we extend conventional DNNs by inserting an additional abstraction layer, which abstracts a real number to an interval for training. The inserted abstraction layer ensures that the values represented by an interval are indistinguishable to the network for both training and decision-making. Leveraging this, we devise the first black-box reachability analysis approach for DNN-controlled systems, where trained DNNs are only queried as black-box oracles for the actions on abstract states. Our approach is sound, tight, efficient, and agnostic to any DNN type and size. The experimental results on a wide range of benchmarks show that the DNNs trained by using our approach exhibit comparable performance, while the reachability analysis of the corresponding systems becomes more amenable with significant tightness and efficiency improvement over the state-of-the-art white-box approaches.

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    https://doi.org/10.1007/978-3-...
    Part of book or chapter of book . 2023 . Peer-reviewed
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      https://doi.org/10.1007/978-3-...
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    We initiate a study of a new model of property testing that is a hybrid of testing properties of distributions and testing properties of strings. Specifically, the new model refers to testing properties of distributions, but these are distributions over huge objects (i.e., very long strings). Accordingly, the model accounts for the total number of local probes into these objects (resp., queries to the strings) as well as for the distance between objects (resp., strings). Specifically, the distance between distributions is defined as the earth mover’s distance with respect to the relative Hamming distance between strings. We study the query complexity of testing in this new model, focusing on three directions. First, we try to relate the query complexity of testing properties in the new model to the sample complexity of testing these properties in the standard distribution testing model. Second, we consider the complexity of testing properties that arise naturally in the new model (e.g., distributions that capture random variations of fixed strings). Third, we consider the complexity of testing properties that were extensively studied in the standard distribution testing model: Two such cases are uniform distributions and pairs of identical distributions, where we obtain the following results. - Testing whether a distribution over n-bit long strings is uniform on some set of size m can be done with query complexity Õ(m/ε³), where ε > (log₂m)/n is the proximity parameter. - Testing whether two distribution over n-bit long strings that have support size at most m are identical can be done with query complexity Õ(m^{2/3}/ε³). Both upper bounds are quite tight; that is, for ε = Ω(1), the first task requires Ω(m^c) queries for any c < 1 and n = ω(log m), whereas the second task requires Ω(m^{2/3}) queries. Note that the query complexity of the first task is higher than the sample complexity of the corresponding task in the standard distribution testing model, whereas in the case of the second task the bounds almost match.

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    Episciences
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    https://doi.org/10.46298/theor...
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      https://doi.org/10.46298/theor...
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    Heterostructures of layered transition metal dichalcogenides (TMDs) host long-lived, tunable excitons, making them intriguing candidates for material-based quantum information applications. Light absorption in these systems induces a plethora of optically excited states that hybridize both interlayer and intralayer characteristics, providing a distinctive starting point for their relaxation processes, in which the interplay between generated electron-hole pairs and their scattering with phonons play a key role. We present a first-principles theoretical approach to compute phonon-induced exciton decomposition due to rapid occupation of electron-hole pairs with finite momentum and opposite spin. Using the MoSe$_2$/WSe$_2$ heterostructure as a case study, we observe a reduction in the optical activity of bright states upon phonon scattering already in the first few femtoseconds proceeding the photoexcitation, driving exciton interlayer delocalization and subsequent variations in the exciton spin. Our results reveal an unexpected and previously unexplored starting point for exciton relaxation dynamics, suggesting increased availability for coherent interactions and non-radiative processes through ultrafast changes in exciton momentum, spatial, and spin properties upon light excitation.

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    https://doi.org/10.1103/physre...
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