Pub Date : 2023-01-20DOI: 10.1142/s2010324723400039
T. Nakai
{"title":"High frequency permeability of adjacent narrow strips having an inclined magnetic anisotropy","authors":"T. Nakai","doi":"10.1142/s2010324723400039","DOIUrl":"https://doi.org/10.1142/s2010324723400039","url":null,"abstract":"","PeriodicalId":54319,"journal":{"name":"Spin","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42534305","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-17DOI: 10.48550/arXiv.2301.07134
Xi Chen, Yaonan Jin, Tim Randolph, R. Servedio
A major goal in the area of exact exponential algorithms is to give an algorithm for the (worst-case) $n$-input Subset Sum problem that runs in time $2^{(1/2 - c)n}$ for some constant $c>0$. In this paper we give a Subset Sum algorithm with worst-case running time $O(2^{n/2} cdot n^{-gamma})$ for a constant $gamma>0.5023$ in standard word RAM or circuit RAM models. To the best of our knowledge, this is the first improvement on the classical ``meet-in-the-middle'' algorithm for worst-case Subset Sum, due to Horowitz and Sahni, which can be implemented in time $O(2^{n/2})$ in these memory models. Our algorithm combines a number of different techniques, including the ``representation method'' introduced by Howgrave-Graham and Joux and subsequent adaptations of the method in Austrin, Kaski, Koivisto, and Nederlof, and Nederlof and Wegrzycki, and ``bit-packing'' techniques used in the work of Baran, Demaine, and Patrascu on subquadratic algorithms for 3SUM.
{"title":"Subset Sum in Time 2n/2/poly(n)","authors":"Xi Chen, Yaonan Jin, Tim Randolph, R. Servedio","doi":"10.48550/arXiv.2301.07134","DOIUrl":"https://doi.org/10.48550/arXiv.2301.07134","url":null,"abstract":"A major goal in the area of exact exponential algorithms is to give an algorithm for the (worst-case) $n$-input Subset Sum problem that runs in time $2^{(1/2 - c)n}$ for some constant $c>0$. In this paper we give a Subset Sum algorithm with worst-case running time $O(2^{n/2} cdot n^{-gamma})$ for a constant $gamma>0.5023$ in standard word RAM or circuit RAM models. To the best of our knowledge, this is the first improvement on the classical ``meet-in-the-middle'' algorithm for worst-case Subset Sum, due to Horowitz and Sahni, which can be implemented in time $O(2^{n/2})$ in these memory models. Our algorithm combines a number of different techniques, including the ``representation method'' introduced by Howgrave-Graham and Joux and subsequent adaptations of the method in Austrin, Kaski, Koivisto, and Nederlof, and Nederlof and Wegrzycki, and ``bit-packing'' techniques used in the work of Baran, Demaine, and Patrascu on subquadratic algorithms for 3SUM.","PeriodicalId":54319,"journal":{"name":"Spin","volume":"3 1","pages":"39:1-39:18"},"PeriodicalIF":1.8,"publicationDate":"2023-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84346320","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-13DOI: 10.1142/s2010324723500066
A. V. Azovtsev, N. A. Pertsev
{"title":"Spin accumulation in acoustically excited Ni/GaAs/Ni trilayers","authors":"A. V. Azovtsev, N. A. Pertsev","doi":"10.1142/s2010324723500066","DOIUrl":"https://doi.org/10.1142/s2010324723500066","url":null,"abstract":"","PeriodicalId":54319,"journal":{"name":"Spin","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47554905","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-11DOI: 10.1142/s2010324723400027
O. Dinislamova, Ilya O. Yaryshev, A. V. Bugayova, T. Shklyar, A. Safronov, Z. Lotfollahi, F. Blyakhman
{"title":"Impact of magneto-deformation effect in ferrogels on the echogenicity of magnetic composites","authors":"O. Dinislamova, Ilya O. Yaryshev, A. V. Bugayova, T. Shklyar, A. Safronov, Z. Lotfollahi, F. Blyakhman","doi":"10.1142/s2010324723400027","DOIUrl":"https://doi.org/10.1142/s2010324723400027","url":null,"abstract":"","PeriodicalId":54319,"journal":{"name":"Spin","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47333088","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-11DOI: 10.1142/s2010324723500054
A. Benmansour, B. N. Brahmi, S. Bekhechi, A. Rachadi, H. Ez‐zahraouy
{"title":"Study of the critical behavior and the multi-layer transition in a spin-1 Ashkin Teller model under the effect of the RKKY interaction: Finite-size-scaling and Monte Carlo studies","authors":"A. Benmansour, B. N. Brahmi, S. Bekhechi, A. Rachadi, H. Ez‐zahraouy","doi":"10.1142/s2010324723500054","DOIUrl":"https://doi.org/10.1142/s2010324723500054","url":null,"abstract":"","PeriodicalId":54319,"journal":{"name":"Spin","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42636400","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.4230/LIPIcs.APPROX/RANDOM.2023.32
Meghal Gupta, R. Zhang
An interactive error correcting code ( iECC ) is an interactive protocol with the guarantee that the receiver can correctly determine the sender’s message, even in the presence of noise. It was shown in works by Gupta, Kalai, and Zhang (STOC 2022) and by Efremenko, Kol, Saxena, and Zhang (FOCS 2022) that there exist iECC ’s that are resilient to a larger fraction of errors than is possible in standard error-correcting codes without interaction. In this work, we improve upon these existing works in two ways: First, we improve upon the erasure iECC of Kalai, Gupta, and Zhang, which has communication complexity quadratic in the message size. In our work, we construct the first iECC resilient to > 12 adversarial erasures that is also positive rate. For any ϵ > 0, our iECC is resilient to 611 − ϵ adversarial erasures and has size O ϵ ( k ). Second, we prove a better upper bound on the maximal possible error resilience of any iECC in the case of bit flip errors. It is known that an iECC can achieve 14 + 10 − 5 error resilience (Efremenko, Kol, Saxena, and Zhang), while the best known upper bound was 27 ≈ 0 . 2857 (Gupta, Kalai, and Zhang). We improve upon the upper bound, showing that no iECC can be resilient to more than 1347 ≈ 0 . 2766 fraction of errors.
交互式纠错码(iECC)是一种交互式协议，它保证接收方即使在存在噪声的情况下也能正确地确定发送方的消息。Gupta、Kalai和Zhang (STOC 2022)以及Efremenko、Kol、Saxena和Zhang (FOCS 2022)的研究表明，与没有相互作用的标准纠错码相比，存在对更大比例错误具有弹性的iECC。在这项工作中，我们从两个方面改进了这些现有的工作:首先，我们改进了Kalai, Gupta和Zhang的擦除iECC，其通信复杂度为消息大小的二次元。在我们的工作中，我们构建了第一个对大于12个对抗性擦除具有弹性的iECC，这也是正速率。对于任何ε > 0，我们的iECC对611−ε对抗性擦除具有弹性，其大小为O ε (k)。其次，我们证明了在位翻转错误的情况下，任何iECC的最大可能错误恢复能力的上界。已知iECC可以达到14 + 10−5的错误弹性(Efremenko, Kol, Saxena, and Zhang)，而已知的上界是27≈0。2857 (Gupta, Kalai, and Zhang)。我们改进了上界，表明没有一个iECC可以弹性大于1347≈0。误差的2766分。
{"title":"Interactive Error Correcting Codes: New Constructions and Impossibility Bounds","authors":"Meghal Gupta, R. Zhang","doi":"10.4230/LIPIcs.APPROX/RANDOM.2023.32","DOIUrl":"https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2023.32","url":null,"abstract":"An interactive error correcting code ( iECC ) is an interactive protocol with the guarantee that the receiver can correctly determine the sender’s message, even in the presence of noise. It was shown in works by Gupta, Kalai, and Zhang (STOC 2022) and by Efremenko, Kol, Saxena, and Zhang (FOCS 2022) that there exist iECC ’s that are resilient to a larger fraction of errors than is possible in standard error-correcting codes without interaction. In this work, we improve upon these existing works in two ways: First, we improve upon the erasure iECC of Kalai, Gupta, and Zhang, which has communication complexity quadratic in the message size. In our work, we construct the first iECC resilient to > 12 adversarial erasures that is also positive rate. For any ϵ > 0, our iECC is resilient to 611 − ϵ adversarial erasures and has size O ϵ ( k ). Second, we prove a better upper bound on the maximal possible error resilience of any iECC in the case of bit flip errors. It is known that an iECC can achieve 14 + 10 − 5 error resilience (Efremenko, Kol, Saxena, and Zhang), while the best known upper bound was 27 ≈ 0 . 2857 (Gupta, Kalai, and Zhang). We improve upon the upper bound, showing that no iECC can be resilient to more than 1347 ≈ 0 . 2766 fraction of errors.","PeriodicalId":54319,"journal":{"name":"Spin","volume":"1 1","pages":"32:1-32:14"},"PeriodicalIF":1.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79838994","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.1007/978-3-031-32157-3_6
Roi Fogler, Itay Cohen, D. Peled
{"title":"Accelerating Black Box Testing with Light-Weight Learning","authors":"Roi Fogler, Itay Cohen, D. Peled","doi":"10.1007/978-3-031-32157-3_6","DOIUrl":"https://doi.org/10.1007/978-3-031-32157-3_6","url":null,"abstract":"","PeriodicalId":54319,"journal":{"name":"Spin","volume":"85 1","pages":"103-120"},"PeriodicalIF":1.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87496953","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.4230/LIPIcs.APPROX/RANDOM.2023.60
F. G. Jeronimo
Good codes over an alphabet of constant size q can approach but not surpass distance 1 − 1 /q . This makes the use of q -ary codes a necessity in some applications, and much work has been devoted to the case of constant alphabet q . In the large distance regime, namely, distance 1 − 1 /q − ε for small ε > 0, the Gilbert–Varshamov (GV) bound asserts that rate Ω q ( ε 2 ) is achievable whereas the q -ary MRRW bound gives a rate upper bound of O q ( ε 2 log(1 /ε )). In this sense, the GV bound is almost optimal in this regime. Prior to this work there was no known explicit and efficiently decodable q -ary codes near the GV bound, in this large distance regime, for any constant q ≥ 3. We design an e O ε,q ( N ) time decoder for explicit (expander based) families of linear codes C N,q,ε ⊆ F Nq of distance (1 − 1 /q )(1 − ε ) and rate Ω q ( ε 2+ o (1) ), for any desired ε > 0 and any constant prime q , namely, almost optimal in this regime. These codes are ε -balanced,i.e., for every non-zero codeword, the frequency of each symbol lies in the interval [1 /q − ε, 1 /q + ε ]. A key ingredient of the q -ary decoder is a new near-linear time approximation algorithm for linear equations ( k -LIN) over Z q on expanding hypergraphs, in particular, those naturally arising in the decoding of these codes. We also investigate k -CSPs on expanding hypergraphs in more generality. We show that special trade-offs available for k -LIN over Z q hold for linear equations over a finite group. To handle general finite groups, we design a new matrix version of weak regularity for expanding hypergraphs. We also obtain a near-linear time approximation algorithm for general expanding k -CSPs over q -ary alphabet. This later algorithm runs in time e O k,q ( m + n ), where m is the number of constraints and n is the number of variables. This improves the previous best running time of O ( n Θ k,q (1) ) by a Sum-of-Squares based algorithm of [AJT, 2019] (in the expanding regular case). We obtain our results by generalizing the framework of [JST, 2021] based on weak regularity decomposition for expanding hypergraphs. This framework was originally designed for binary k -XOR with the goal of providing near-linear time decoder for explicit binary codes, near the GV bound, from the breakthrough work of Ta-Shma [STOC, 2017]. The explicit families of codes over prime F q are based on suitable instatiations of the Jalan–Moshkovitz (Abelian) generalization of Ta-Shma’s distance amplification procedure.
{"title":"Fast Decoding of Explicit Almost Optimal ε-Balanced q-Ary Codes And Fast Approximation of Expanding k-CSPs","authors":"F. G. Jeronimo","doi":"10.4230/LIPIcs.APPROX/RANDOM.2023.60","DOIUrl":"https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2023.60","url":null,"abstract":"Good codes over an alphabet of constant size q can approach but not surpass distance 1 − 1 /q . This makes the use of q -ary codes a necessity in some applications, and much work has been devoted to the case of constant alphabet q . In the large distance regime, namely, distance 1 − 1 /q − ε for small ε > 0, the Gilbert–Varshamov (GV) bound asserts that rate Ω q ( ε 2 ) is achievable whereas the q -ary MRRW bound gives a rate upper bound of O q ( ε 2 log(1 /ε )). In this sense, the GV bound is almost optimal in this regime. Prior to this work there was no known explicit and efficiently decodable q -ary codes near the GV bound, in this large distance regime, for any constant q ≥ 3. We design an e O ε,q ( N ) time decoder for explicit (expander based) families of linear codes C N,q,ε ⊆ F Nq of distance (1 − 1 /q )(1 − ε ) and rate Ω q ( ε 2+ o (1) ), for any desired ε > 0 and any constant prime q , namely, almost optimal in this regime. These codes are ε -balanced,i.e., for every non-zero codeword, the frequency of each symbol lies in the interval [1 /q − ε, 1 /q + ε ]. A key ingredient of the q -ary decoder is a new near-linear time approximation algorithm for linear equations ( k -LIN) over Z q on expanding hypergraphs, in particular, those naturally arising in the decoding of these codes. We also investigate k -CSPs on expanding hypergraphs in more generality. We show that special trade-offs available for k -LIN over Z q hold for linear equations over a finite group. To handle general finite groups, we design a new matrix version of weak regularity for expanding hypergraphs. We also obtain a near-linear time approximation algorithm for general expanding k -CSPs over q -ary alphabet. This later algorithm runs in time e O k,q ( m + n ), where m is the number of constraints and n is the number of variables. This improves the previous best running time of O ( n Θ k,q (1) ) by a Sum-of-Squares based algorithm of [AJT, 2019] (in the expanding regular case). We obtain our results by generalizing the framework of [JST, 2021] based on weak regularity decomposition for expanding hypergraphs. This framework was originally designed for binary k -XOR with the goal of providing near-linear time decoder for explicit binary codes, near the GV bound, from the breakthrough work of Ta-Shma [STOC, 2017]. The explicit families of codes over prime F q are based on suitable instatiations of the Jalan–Moshkovitz (Abelian) generalization of Ta-Shma’s distance amplification procedure.","PeriodicalId":54319,"journal":{"name":"Spin","volume":"7 1","pages":"60:1-60:16"},"PeriodicalIF":1.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86890770","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.4230/LIPIcs.APPROX/RANDOM.2023.27
Mark de Berg, Arpan Sadhukhan, F. Spieksma
We study Dominating Set and Independent Set for dynamic graphs in the vertex-arrival model. We say that a dynamic algorithm for one of these problems is k -stable when it makes at most k changes to its output independent set or dominating set upon the arrival of each vertex. We study trade-offs between the stability parameter k of the algorithm and the approximation ratio it achieves. We obtain the following results. We show that there is a constant ε ∗ > 0 such that any dynamic (1+ ε ∗ )-approximation algorithm for Dominating Set has stability parameter Ω( n ), even for bipartite graphs of maximum degree 4. We present algorithms with very small stability parameters for Dominating Set in the setting where the arrival degree of each vertex is upper bounded by d . In particular, we give a 1-stable ( d + 1) 2 -approximation, and a 3-stable (9 d/ 2)-approximation algorithm. We show that there is a constant ε ∗ > 0 such that any dynamic (1+ ε ∗ )-approximation algorithm for Independent Set has stability parameter Ω( n ), even for bipartite graphs of maximum degree 3. Finally, we present a 2-stable O ( d )-approximation algorithm for Independent Set , in the setting where the average degree of the graph is upper bounded by some constant d at all times.
{"title":"Stable Approximation Algorithms for Dominating Set and Independent Set","authors":"Mark de Berg, Arpan Sadhukhan, F. Spieksma","doi":"10.4230/LIPIcs.APPROX/RANDOM.2023.27","DOIUrl":"https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2023.27","url":null,"abstract":"We study Dominating Set and Independent Set for dynamic graphs in the vertex-arrival model. We say that a dynamic algorithm for one of these problems is k -stable when it makes at most k changes to its output independent set or dominating set upon the arrival of each vertex. We study trade-offs between the stability parameter k of the algorithm and the approximation ratio it achieves. We obtain the following results. We show that there is a constant ε ∗ > 0 such that any dynamic (1+ ε ∗ )-approximation algorithm for Dominating Set has stability parameter Ω( n ), even for bipartite graphs of maximum degree 4. We present algorithms with very small stability parameters for Dominating Set in the setting where the arrival degree of each vertex is upper bounded by d . In particular, we give a 1-stable ( d + 1) 2 -approximation, and a 3-stable (9 d/ 2)-approximation algorithm. We show that there is a constant ε ∗ > 0 such that any dynamic (1+ ε ∗ )-approximation algorithm for Independent Set has stability parameter Ω( n ), even for bipartite graphs of maximum degree 3. Finally, we present a 2-stable O ( d )-approximation algorithm for Independent Set , in the setting where the average degree of the graph is upper bounded by some constant d at all times.","PeriodicalId":54319,"journal":{"name":"Spin","volume":"80 1","pages":"27:1-27:19"},"PeriodicalIF":1.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72683253","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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