78 research outputs found

    Robust Communication Complexity of Matching: EDCS Achieves 5/6 Approximation

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    LIPIcs, Volume 261, ICALP 2023, Complete Volume

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    LIPIcs, Volume 261, ICALP 2023, Complete Volum

    Low-Depth Arithmetic Circuit Lower Bounds: Bypassing Set-Multilinearization

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    Robust Communication Complexity of Matching: EDCS Achieves 5/6 Approximation

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    We study the robust communication complexity of maximum matching. Edges of an arbitrary nn-vertex graph GG are randomly partitioned between Alice and Bob independently and uniformly. Alice has to send a single message to Bob such that Bob can find an (approximate) maximum matching of the whole graph GG. We specifically study the best approximation ratio achievable via protocols where Alice communicates only O~(n)\widetilde{O}(n) bits to Bob. There has been a growing interest on the robust communication model due to its connections to the random-order streaming model. An algorithm of Assadi and Behnezhad [ICALP'21] implies a (2/3+ϵ0.667)(2/3+\epsilon_0 \sim .667)-approximation for a small constant 0<ϵ0<10180 < \epsilon_0 < 10^{-18}, which remains the best-known approximation for general graphs. For bipartite graphs, Assadi and Behnezhad [Random'21] improved the approximation to .716 albeit with a computationally inefficient (i.e., exponential time) protocol. In this paper, we study a natural and efficient protocol implied by a random-order streaming algorithm of Bernstein [ICALP'20] which is based on edge-degree constrained subgraphs (EDCS) [Bernstein and Stein; ICALP'15]. The result of Bernstein immediately implies that this protocol achieves an (almost) (2/3.666)(2/3 \sim .666)-approximation in the robust communication model. We present a new analysis, proving that it achieves a much better (almost) (5/6.833)(5/6 \sim .833)-approximation. This significantly improves previous approximations both for general and bipartite graphs. We also prove that our analysis of Bernstein's protocol is tight

    An Improved Composition Theorem of a Universal Relation and Most Functions via Effective Restriction

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    Recently, Ivan Mihajlin and Alexander Smal proved a composition theorem of a universal relation and some function via so called xor composition, that is there exists some function f:{0,1}n{0,1}f:\{0,1\}^n \rightarrow \{0,1\} such that CC(UnKWf)1.5no(n)\textsf{CC}(\text{U}_n \diamond \text{KW}_f) \geq 1.5n-o(n) where CC\textsf{CC} denotes the communication complexity of the problem. In this paper, we significantly improve their result and present an asymptotically tight and much more general composition theorem of a universal relation and most functions, that is for most functions f:{0,1}n{0,1}f:\{0,1\}^n \rightarrow \{0,1\} we have CC(UmKWf)m+nO(m)\textsf{CC}(\text{U}_m \diamond \text{KW}_f) \geq m+ n -O(\sqrt{m}) when m=ω(log2n),n=ω(m)m=\omega(\log^2 n),n =\omega(\sqrt{m}). This is done by a direct proof of composition theorem of a universal relation and a multiplexor in the partially half-duplex model avoiding the xor composition. And the proof works even when the multiplexor only contains a few functions. One crucial ingredient in our proof involves a combinatorial problem of constructing a tree of many leaves and every leaf contains a non-overlapping set of functions. For each leaf, there is a set of inputs such that every function in the leaf takes the same value, that is all functions are restricted. We show how to choose a set of good inputs to effectively restrict these functions to force that the number of functions in each leaf is as small as possible while maintaining the total number of functions in all leaves. This results in a large number of leaves.Comment: change to previous version 1.fix typos and improve presentation of the paper 2.change all the letter Θ\Theta for trace to Ψ\Psi, to avoid confusion due to that the same letter Θ\Theta is used for the notation in asymtotics. 3.add more discussion in Section

    Review of Particle Physics

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    The Review summarizes much of particle physics and cosmology. Using data from previous editions, plus 2,143 new measurements from 709 papers, we list, evaluate, and average measured properties of gauge bosons and the recently discovered Higgs boson, leptons, quarks, mesons, and baryons. We summarize searches for hypothetical particles such as supersymmetric particles, heavy bosons, axions, dark photons, etc. Particle properties and search limits are listed in Summary Tables. We give numerous tables, figures, formulae, and reviews of topics such as Higgs Boson Physics, Supersymmetry, Grand Unified Theories, Neutrino Mixing, Dark Energy, Dark Matter, Cosmology, Particle Detectors, Colliders, Probability and Statistics. Among the 120 reviews are many that are new or heavily revised, including a new review on Machine Learning, and one on Spectroscopy of Light Meson Resonances. The Review is divided into two volumes. Volume 1 includes the Summary Tables and 97 review articles. Volume 2 consists of the Particle Listings and contains also 23 reviews that address specific aspects of the data presented in the Listings. The complete Review (both volumes) is published online on the website of the Particle Data Group (pdg.lbl.gov) and in a journal. Volume 1 is available in print as the PDG Book. A Particle Physics Booklet with the Summary Tables and essential tables, figures, and equations from selected review articles is available in print, as a web version optimized for use on phones, and as an Android app.United States Department of Energy (DOE) DE-AC02-05CH11231government of Japan (Ministry of Education, Culture, Sports, Science and Technology)Istituto Nazionale di Fisica Nucleare (INFN)Physical Society of Japan (JPS)European Laboratory for Particle Physics (CERN)United States Department of Energy (DOE

    Small Circuits Imply Efficient Arthur-Merlin Protocols

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    The inner product function ? x,y ? = ?_i x_i y_i mod 2 can be easily computed by a (linear-size) AC?(?) circuit: that is, a constant depth circuit with AND, OR and parity (XOR) gates. But what if we impose the restriction that the parity gates can only be on the bottom most layer (closest to the input)? Namely, can the inner product function be computed by an AC? circuit composed with a single layer of parity gates? This seemingly simple question is an important open question at the frontier of circuit lower bound research. In this work, we focus on a minimalistic version of the above question. Namely, whether the inner product function cannot be approximated by a small DNF augmented with a single layer of parity gates. Our main result shows that the existence of such a circuit would have unexpected implications for interactive proofs, or more specifically, for interactive variants of the Data Streaming and Communication Complexity models. In particular, we show that the existence of such a small (i.e., polynomial-size) circuit yields: 1) An O(d)-message protocol in the Arthur-Merlin Data Streaming model for every n-variate, degree d polynomial (over GF(2)), using only O?(d) ?log(n) communication and space complexity. In particular, this gives an AM[2] Data Streaming protocol for a variant of the well-studied triangle counting problem, with poly-logarithmic communication and space complexities. 2) A 2-message communication complexity protocol for any sparse (or low degree) polynomial, and for any function computable by an AC?(?) circuit. Specifically, for the latter, we obtain a protocol with communication complexity that is poly-logarithmic in the size of the AC?(?) circuit

    Using Active Learning to Teach Critical and Contextual Studies: One Teaching Plan, Two Experiments, Three Videos.

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    Since the 1970s, art and design education at UK universities has existedas a divided practice; on the one hand applying active learning in thestudio and on the other hand enforcing passive learning in the lecturetheatre. As a result, art and design students are in their vast majorityreluctant about modules that may require them to think, read and writecritically during their academic studies. This article describes, evaluatesand analyses two individual active learning experiments designed todetermine if it is possible to teach CCS modules in a manner thatencourages student participation. The results reveal that opting foractive learning methods improved academic achievement, encouragedcooperation, and enforced an inclusive classroom. Furthermore, andcontrary to wider perception, the article demonstrates that activelearning methods can be equally beneficial for small-size as well aslarge-size groups

    The 2nd International Electronic Conference on Applied Sciences

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    This book is focused on the works presented at the 2nd International Electronic Conference on Applied Sciences, organized by Applied Sciences from 15 to 31 October 2021 on the MDPI Sciforum platform. Two decades have passed since the start of the 21st century. The development of sciences and technologies is growing ever faster today than in the previous century. The field of science is expanding, and the structure of science is becoming ever richer. Because of this expansion and fine structure growth, researchers may lose themselves in the deep forest of the ever-increasing frontiers and sub-fields being created. This international conference on the Applied Sciences was started to help scientists conduct their own research into the growth of these frontiers by breaking down barriers and connecting the many sub-fields to cut through this vast forest. These functions will allow researchers to see these frontiers and their surrounding (or quite distant) fields and sub-fields, and give them the opportunity to incubate and develop their knowledge even further with the aid of this multi-dimensional network

    Practical approaches to delivering pandemic impacted laboratory teaching

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    #DryLabsRealScience is a community of practice established to support life science educators with the provision of laboratory-based classes in the face of the COVID-19 pandemic and restricted access to facilities. Four key approaches have emerged from the innovative work shared with the network: videos, simulations, virtual/augmented reality, and datasets, with each having strengths and weaknesses. Each strategy was used pre-COVID and has a sound theoretical underpinning; here, we explore how the pandemic has forced their adaptation and highlight novel utilisation to support student learning in the laboratory environment during the challenges faced by remote and blended teaching
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