Pub Date : 2026-01-29DOI: 10.48550/arxiv.2601.22344
Marc Aurèle Gilles, Heather Wilber
The low-rank approximation properties of Randomly Pivoted LU (RPLU), a variant of Gaussian elimination where pivots are sampled proportional to the squared entries of the Schur complement, are analyzed. It is shown that the RPLU iterates converge geometrically in expectation for matrices with rapidly decaying singular values. RPLU outperforms existing low-rank approximation algorithms in two settings: first, when memory is limited, RPLU can be implemented with $mathcal{O}(k^2 + m + n)$ storage and $mathcal{O}( k(m + n)+ kmathcal{M}(mat{A}) + k^3)$ operations, where $mathcal{M}(mat{A})$ is the cost of a matvec with $mat{A}inmathbb{C}^{ntimes m}$ or its adjoint, for a rank-$k$ approximation. Second, when the matrix and its Schur complements share exploitable structure, such as for Cauchy-like matrices. The efficacy of RPLU is illustrated with several examples, including applications in rational approximation and solving large linear systems on GPUs.
{"title":"Low-Rank Approximation by Randomly Pivoted LU","authors":"Marc Aurèle Gilles, Heather Wilber","doi":"10.48550/arxiv.2601.22344","DOIUrl":"https://doi.org/10.48550/arxiv.2601.22344","url":null,"abstract":"The low-rank approximation properties of Randomly Pivoted LU (RPLU), a variant of Gaussian elimination where pivots are sampled proportional to the squared entries of the Schur complement, are analyzed. It is shown that the RPLU iterates converge geometrically in expectation for matrices with rapidly decaying singular values. RPLU outperforms existing low-rank approximation algorithms in two settings: first, when memory is limited, RPLU can be implemented with $mathcal{O}(k^2 + m + n)$ storage and $mathcal{O}( k(m + n)+ kmathcal{M}(mat{A}) + k^3)$ operations, where $mathcal{M}(mat{A})$ is the cost of a matvec with $mat{A}inmathbb{C}^{ntimes m}$ or its adjoint, for a rank-$k$ approximation. Second, when the matrix and its Schur complements share exploitable structure, such as for Cauchy-like matrices. The efficacy of RPLU is illustrated with several examples, including applications in rational approximation and solving large linear systems on GPUs.","PeriodicalId":496270,"journal":{"name":"arXiv (Cornell University)","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147382012","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-13DOI: 10.48550/arxiv.2311.07133
Johnson, Joseph, Liu, Ricky Ini
We define a birational map between labelings of a rectangular poset and its associated trapezoidal poset. This map tropicalizes to a bijection between the plane partitions of these posets of fixed height, giving a new bijective proof of a result by Proctor. We also show that this map is equivariant with respect to birational rowmotion, resolving a conjecture of Williams and implying that birational rowmotion on trapezoidal posets has finite order.
{"title":"Plane partitions and rowmotion on rectangular and trapezoidal posets","authors":"Johnson, Joseph, Liu, Ricky Ini","doi":"10.48550/arxiv.2311.07133","DOIUrl":"https://doi.org/10.48550/arxiv.2311.07133","url":null,"abstract":"We define a birational map between labelings of a rectangular poset and its associated trapezoidal poset. This map tropicalizes to a bijection between the plane partitions of these posets of fixed height, giving a new bijective proof of a result by Proctor. We also show that this map is equivariant with respect to birational rowmotion, resolving a conjecture of Williams and implying that birational rowmotion on trapezoidal posets has finite order.","PeriodicalId":496270,"journal":{"name":"arXiv (Cornell University)","volume":"119 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136352295","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
To mitigate the potential misuse of large language models (LLMs), recent research has developed watermarking algorithms, which restrict the generation process to leave an invisible trace for watermark detection. Due to the two-stage nature of the task, most studies evaluate the generation and detection separately, thereby presenting a challenge in unbiased, thorough, and applicable evaluations. In this paper, we introduce WaterBench, the first comprehensive benchmark for LLM watermarks, in which we design three crucial factors: (1) For textbf{benchmarking procedure}, to ensure an apples-to-apples comparison, we first adjust each watermarking method's hyper-parameter to reach the same watermarking strength, then jointly evaluate their generation and detection performance. (2) For textbf{task selection}, we diversify the input and output length to form a five-category taxonomy, covering $9$ tasks. (3) For textbf{evaluation metric}, we adopt the GPT4-Judge for automatically evaluating the decline of instruction-following abilities after watermarking. We evaluate $4$ open-source watermarks on $2$ LLMs under $2$ watermarking strengths and observe the common struggles for current methods on maintaining the generation quality. The code and data are available at url{https://github.com/THU-KEG/WaterBench}.
{"title":"WaterBench: Towards Holistic Evaluation of Watermarks for Large Language\u0000 Models","authors":"Tu, Shangqing, Sun, Yuliang, Bai, Yushi, Yu, Jifan, Hou, Lei, Li, Juanzi","doi":"10.48550/arxiv.2311.07138","DOIUrl":"https://doi.org/10.48550/arxiv.2311.07138","url":null,"abstract":"To mitigate the potential misuse of large language models (LLMs), recent research has developed watermarking algorithms, which restrict the generation process to leave an invisible trace for watermark detection. Due to the two-stage nature of the task, most studies evaluate the generation and detection separately, thereby presenting a challenge in unbiased, thorough, and applicable evaluations. In this paper, we introduce WaterBench, the first comprehensive benchmark for LLM watermarks, in which we design three crucial factors: (1) For textbf{benchmarking procedure}, to ensure an apples-to-apples comparison, we first adjust each watermarking method's hyper-parameter to reach the same watermarking strength, then jointly evaluate their generation and detection performance. (2) For textbf{task selection}, we diversify the input and output length to form a five-category taxonomy, covering $9$ tasks. (3) For textbf{evaluation metric}, we adopt the GPT4-Judge for automatically evaluating the decline of instruction-following abilities after watermarking. We evaluate $4$ open-source watermarks on $2$ LLMs under $2$ watermarking strengths and observe the common struggles for current methods on maintaining the generation quality. The code and data are available at url{https://github.com/THU-KEG/WaterBench}.","PeriodicalId":496270,"journal":{"name":"arXiv (Cornell University)","volume":"118 51","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136352299","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Mobile health programs are becoming an increasingly popular medium for dissemination of health information among beneficiaries in less privileged communities. Kilkari is one of the world's largest mobile health programs which delivers time sensitive audio-messages to pregnant women and new mothers. We have been collaborating with ARMMAN, a non-profit in India which operates the Kilkari program, to identify bottlenecks to improve the efficiency of the program. In particular, we provide an initial analysis of the trajectories of beneficiaries' interaction with the mHealth program and examine elements of the program that can be potentially enhanced to boost its success. We cluster the cohort into different buckets based on listenership so as to analyze listenership patterns for each group that could help boost program success. We also demonstrate preliminary results on using historical data in a time-series prediction to identify beneficiary dropouts and enable NGOs in devising timely interventions to strengthen beneficiary retention.
{"title":"Analyzing and Predicting Low-Listenership Trends in a Large-Scale Mobile\u0000 Health Program: A Preliminary Investigation","authors":"Lalan, Arshika, Verma, Shresth, Sudan, Kumar Madhu, Mahale, Amrita, Hegde, Aparna, Tambe, Milind, Taneja, Aparna","doi":"10.48550/arxiv.2311.07139","DOIUrl":"https://doi.org/10.48550/arxiv.2311.07139","url":null,"abstract":"Mobile health programs are becoming an increasingly popular medium for dissemination of health information among beneficiaries in less privileged communities. Kilkari is one of the world's largest mobile health programs which delivers time sensitive audio-messages to pregnant women and new mothers. We have been collaborating with ARMMAN, a non-profit in India which operates the Kilkari program, to identify bottlenecks to improve the efficiency of the program. In particular, we provide an initial analysis of the trajectories of beneficiaries' interaction with the mHealth program and examine elements of the program that can be potentially enhanced to boost its success. We cluster the cohort into different buckets based on listenership so as to analyze listenership patterns for each group that could help boost program success. We also demonstrate preliminary results on using historical data in a time-series prediction to identify beneficiary dropouts and enable NGOs in devising timely interventions to strengthen beneficiary retention.","PeriodicalId":496270,"journal":{"name":"arXiv (Cornell University)","volume":"118 48","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136352302","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Fluid antenna multiple access (FAMA) is capable of exploiting the high spatial diversity of wireless channels to mitigate multi-user interference via flexible port switching, which achieves a better performance than traditional multi-input-multi-output (MIMO) systems. Moreover, integrated data and energy transfer (IDET) is able to provide both the wireless data transfer (WDT) and wireless energy transfer (WET) services towards low-power devices. In this paper, a FAMA assisted IDET system is studied, where $N$ access points (APs) provide dedicated IDET services towards $N$ user equipments (UEs). Each UE is equipped with a single fluid antenna. The performance of WDT and WET , textit{i.e.}, the WDT outage probability, the WET outage probability, the reliable throughput and the average energy harvesting amount, are analysed theoretically by using time switching (TS) between WDT and WET. Numerical results validate our theoretical analysis, which reveals that the number of UEs and TS ratio should be optimized to achieve a trade-off between the WDT and WET performance. Moreover, FAMA assisted IDET achieves a better performance in terms of both WDT and WET than traditional MIMO with the same antenna size.
{"title":"Performance Analysis of Integrated Data and Energy Transfer Assisted by\u0000 Fluid Antenna Systems","authors":"Lin, Xiao, Yang, Halvin, Zhao, Yizhe, Hu, Jie, Wong, Kai-Kit","doi":"10.48550/arxiv.2311.07134","DOIUrl":"https://doi.org/10.48550/arxiv.2311.07134","url":null,"abstract":"Fluid antenna multiple access (FAMA) is capable of exploiting the high spatial diversity of wireless channels to mitigate multi-user interference via flexible port switching, which achieves a better performance than traditional multi-input-multi-output (MIMO) systems. Moreover, integrated data and energy transfer (IDET) is able to provide both the wireless data transfer (WDT) and wireless energy transfer (WET) services towards low-power devices. In this paper, a FAMA assisted IDET system is studied, where $N$ access points (APs) provide dedicated IDET services towards $N$ user equipments (UEs). Each UE is equipped with a single fluid antenna. The performance of WDT and WET , textit{i.e.}, the WDT outage probability, the WET outage probability, the reliable throughput and the average energy harvesting amount, are analysed theoretically by using time switching (TS) between WDT and WET. Numerical results validate our theoretical analysis, which reveals that the number of UEs and TS ratio should be optimized to achieve a trade-off between the WDT and WET performance. Moreover, FAMA assisted IDET achieves a better performance in terms of both WDT and WET than traditional MIMO with the same antenna size.","PeriodicalId":496270,"journal":{"name":"arXiv (Cornell University)","volume":"118 47","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136352303","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-13DOI: 10.48550/arxiv.2311.07269
Ruscitti, Francesco, Dubey, Ram Sewak, Laguzzi, Giorgio
Motivated by the analysis of a general optimal portfolio selection problem, which encompasses as special cases an optimal consumption and an optimal debt-arrangement problem, we are concerned with the questions of how a personality trait like risk-perception can be formalized and whether the two objectives of utility-maximization and risk-minimization can be both achieved simultaneously. We address these questions by developing an axiomatic foundation of preferences for which utility-maximization is equivalent to minimizing a utility-based shortfall risk measure. Our axiomatization hinges on a novel axiom in decision theory, namely the risk-perception axiom.
{"title":"Decision-making under risk: when is utility maximization equivalent to\u0000 risk minimization?","authors":"Ruscitti, Francesco, Dubey, Ram Sewak, Laguzzi, Giorgio","doi":"10.48550/arxiv.2311.07269","DOIUrl":"https://doi.org/10.48550/arxiv.2311.07269","url":null,"abstract":"Motivated by the analysis of a general optimal portfolio selection problem, which encompasses as special cases an optimal consumption and an optimal debt-arrangement problem, we are concerned with the questions of how a personality trait like risk-perception can be formalized and whether the two objectives of utility-maximization and risk-minimization can be both achieved simultaneously. We address these questions by developing an axiomatic foundation of preferences for which utility-maximization is equivalent to minimizing a utility-based shortfall risk measure. Our axiomatization hinges on a novel axiom in decision theory, namely the risk-perception axiom.","PeriodicalId":496270,"journal":{"name":"arXiv (Cornell University)","volume":"115 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136352313","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-13DOI: 10.48550/arxiv.2311.07310
Nenno, Dennis Michael, Caspari, Adrian
The quest for real-time dynamic optimization solutions in the process industry represents a formidable computational challenge, particularly within the realm of applications like model predictive control where rapid and reliable computations are critical. Conventional methods can struggle to surmount the complexities of such tasks. Quantum computing and quantum annealing emerge as avant-garde contenders to transcend conventional computational constraints. We convert a dynamic optimization problem, characterized by a system of differential equations, into a Quadratic Unconstrained Binary Optimization problem, enabling quantum computational approaches. The empirical findings synthesized from classical methods, simulated annealing, quantum annealing via D-Wave's quantum annealer, and hybrid solver methodologies, illuminate the intricate landscape of computational prowess essential for tackling complex and high-dimensional dynamic optimization problems. Our findings suggest that while quantum annealing is a maturing technology that currently does not outperform state-of-the-art classical solvers, continuous improvements could eventually aid in increasing efficiency within the chemical process industry.
{"title":"Dynamic Optimization on Quantum Hardware: Feasibility for a Process\u0000 Industry Use Case","authors":"Nenno, Dennis Michael, Caspari, Adrian","doi":"10.48550/arxiv.2311.07310","DOIUrl":"https://doi.org/10.48550/arxiv.2311.07310","url":null,"abstract":"The quest for real-time dynamic optimization solutions in the process industry represents a formidable computational challenge, particularly within the realm of applications like model predictive control where rapid and reliable computations are critical. Conventional methods can struggle to surmount the complexities of such tasks. Quantum computing and quantum annealing emerge as avant-garde contenders to transcend conventional computational constraints. We convert a dynamic optimization problem, characterized by a system of differential equations, into a Quadratic Unconstrained Binary Optimization problem, enabling quantum computational approaches. The empirical findings synthesized from classical methods, simulated annealing, quantum annealing via D-Wave's quantum annealer, and hybrid solver methodologies, illuminate the intricate landscape of computational prowess essential for tackling complex and high-dimensional dynamic optimization problems. Our findings suggest that while quantum annealing is a maturing technology that currently does not outperform state-of-the-art classical solvers, continuous improvements could eventually aid in increasing efficiency within the chemical process industry.","PeriodicalId":496270,"journal":{"name":"arXiv (Cornell University)","volume":"114 25","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136352320","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-13DOI: 10.48550/arxiv.2311.07455
Holloway, Philip, Marshall, Philip J., Verma, Aprajita, More, Anupreeta, Cañameras, Raoul, Jaelani, Anton T., Ishida, Yuichiro, Wong, Kenneth C.
The arrival of the Vera C. Rubin Observatory's Legacy Survey of Space and Time (LSST), Euclid-Wide and Roman wide area sensitive surveys will herald a new era in strong lens science in which the number of strong lenses known is expected to rise from $mathcal{O}(10^3)$ to $mathcal{O}(10^5)$. However, current lens-finding methods still require time-consuming follow-up visual inspection by strong-lens experts to remove false positives which is only set to increase with these surveys. In this work we demonstrate a range of methods to produce calibrated probabilities to help determine the veracity of any given lens candidate. To do this we use the classifications from citizen science and multiple neural networks for galaxies selected from the Hyper Suprime-Cam (HSC) survey. Our methodology is not restricted to particular classifier types and could be applied to any strong lens classifier which produces quantitative scores. Using these calibrated probabilities, we generate an ensemble classifier, combining citizen science and neural network lens finders. We find such an ensemble can provide improved classification over the individual classifiers. We find a false positive rate of $10^{-3}$ can be achieved with a completeness of $46%$, compared to $34%$ for the best individual classifier. Given the large number of galaxy-galaxy strong lenses anticipated in LSST, such improvement would still produce significant numbers of false positives, in which case using calibrated probabilities will be essential for population analysis of large populations of lenses.
Vera C. Rubin天文台的时空遗产巡天(LSST)，欧几里得宽和罗马广域敏感巡天的到来，将宣告强透镜科学的新时代，其中已知的强透镜数量预计将从$mathcal{O}(10^3)$增加到$mathcal{O}(10^5)$。然而，目前的透镜寻找方法仍然需要由强透镜专家进行耗时的后续目视检查，以消除假阳性，而假阳性只会随着这些调查而增加。在这项工作中，我们展示了一系列方法来产生校准概率，以帮助确定任何给定候选透镜的准确性。为了做到这一点，我们使用了来自公民科学和多个神经网络的分类，这些分类是从超级超级相机(HSC)调查中选择的星系。我们的方法不局限于特定的分类器类型，可以应用于任何产生定量分数的强透镜分类器。使用这些校准的概率，我们生成了一个集成分类器，结合了公民科学和神经网络寻镜器。我们发现这样的集成可以提供比单个分类器更好的分类。我们发现假阳性率为$10^{-3}$，完备性为$46%$，而最佳单个分类器的完备性为$34%$。考虑到LSST中预期的大量星系-星系强透镜，这种改进仍然会产生大量的假阳性，在这种情况下，使用校准的概率对于大量透镜的种群分析是必不可少的。
{"title":"A Bayesian Approach to Strong Lens Finding in the Era of Wide-area\u0000 Surveys","authors":"Holloway, Philip, Marshall, Philip J., Verma, Aprajita, More, Anupreeta, Cañameras, Raoul, Jaelani, Anton T., Ishida, Yuichiro, Wong, Kenneth C.","doi":"10.48550/arxiv.2311.07455","DOIUrl":"https://doi.org/10.48550/arxiv.2311.07455","url":null,"abstract":"The arrival of the Vera C. Rubin Observatory's Legacy Survey of Space and Time (LSST), Euclid-Wide and Roman wide area sensitive surveys will herald a new era in strong lens science in which the number of strong lenses known is expected to rise from $mathcal{O}(10^3)$ to $mathcal{O}(10^5)$. However, current lens-finding methods still require time-consuming follow-up visual inspection by strong-lens experts to remove false positives which is only set to increase with these surveys. In this work we demonstrate a range of methods to produce calibrated probabilities to help determine the veracity of any given lens candidate. To do this we use the classifications from citizen science and multiple neural networks for galaxies selected from the Hyper Suprime-Cam (HSC) survey. Our methodology is not restricted to particular classifier types and could be applied to any strong lens classifier which produces quantitative scores. Using these calibrated probabilities, we generate an ensemble classifier, combining citizen science and neural network lens finders. We find such an ensemble can provide improved classification over the individual classifiers. We find a false positive rate of $10^{-3}$ can be achieved with a completeness of $46%$, compared to $34%$ for the best individual classifier. Given the large number of galaxy-galaxy strong lenses anticipated in LSST, such improvement would still produce significant numbers of false positives, in which case using calibrated probabilities will be essential for population analysis of large populations of lenses.","PeriodicalId":496270,"journal":{"name":"arXiv (Cornell University)","volume":"108 26","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136352341","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We investigate the S=1 antiferromagnetic quantum spin chain with the exchange and single-ion anisotropies in a magnetic field, using the numerical exact diagonalization of finite-size clusters, the level spectroscopy analysis, and the density matrix renormalization group (DMRG) method. It is found that a translational symmetry broken magnetization plateau possibly appears at the half of the saturation magnetization, when the anisotropies compete with each other. The level spectroscopy analysis gives the phase diagram at half the saturation magnetization. The DMRG calculation presents the magnetization curves for some typical parameters and clarifies the spin structure in the plateau phase.
{"title":"Translational symmetry broken magnetization plateau of the S=1\u0000 antiferromagnetic Heisenberg chain with competing anisotropies","authors":"Sakai, Tôru, Okamoto, Kiyomi, Okunishi, Kouichi, Hashimoto, Masaru, Houda, Tomoki, Furuchi, Rito, Nakano, Hiroki","doi":"10.48550/arxiv.2311.07123","DOIUrl":"https://doi.org/10.48550/arxiv.2311.07123","url":null,"abstract":"We investigate the S=1 antiferromagnetic quantum spin chain with the exchange and single-ion anisotropies in a magnetic field, using the numerical exact diagonalization of finite-size clusters, the level spectroscopy analysis, and the density matrix renormalization group (DMRG) method. It is found that a translational symmetry broken magnetization plateau possibly appears at the half of the saturation magnetization, when the anisotropies compete with each other. The level spectroscopy analysis gives the phase diagram at half the saturation magnetization. The DMRG calculation presents the magnetization curves for some typical parameters and clarifies the spin structure in the plateau phase.","PeriodicalId":496270,"journal":{"name":"arXiv (Cornell University)","volume":"119 29","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136352459","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-13DOI: 10.48550/arxiv.2311.07130
Bérczi, Kristóf, Mátravölgyi, Bence, Schwarcz, Tamás
In recent years, combinatorial reconfiguration problems have attracted great attention due to their connection to various topics such as optimization, counting, enumeration, or sampling. One of the most intriguing open questions concerns the exchange distance of two matroid basis sequences, a problem that appears in several areas of computer science and mathematics. In 1980, White proposed a conjecture for the characterization of two basis sequences being reachable from each other by symmetric exchanges, which received a significant interest also in algebra due to its connection to toric ideals and Gr"obner bases. In this work, we verify White's conjecture for basis sequences of length two in regular matroids, a problem that was formulated as a separate question by Farber, Richter, and Shan and Andres, Hochst"attler, and Merkel. Most of previous work on White's conjecture has not considered the question from an algorithmic perspective. We study the problem from an optimization point of view: our proof implies a polynomial algorithm for determining a sequence of symmetric exchanges that transforms a basis pair into another, thus providing the first polynomial upper bound on the exchange distance of basis pairs in regular matroids. As a byproduct, we verify a conjecture of Gabow from 1976 on the serial symmetric exchange property of matroids for the regular case.
{"title":"Reconfiguration of basis pairs in regular matroids","authors":"Bérczi, Kristóf, Mátravölgyi, Bence, Schwarcz, Tamás","doi":"10.48550/arxiv.2311.07130","DOIUrl":"https://doi.org/10.48550/arxiv.2311.07130","url":null,"abstract":"In recent years, combinatorial reconfiguration problems have attracted great attention due to their connection to various topics such as optimization, counting, enumeration, or sampling. One of the most intriguing open questions concerns the exchange distance of two matroid basis sequences, a problem that appears in several areas of computer science and mathematics. In 1980, White proposed a conjecture for the characterization of two basis sequences being reachable from each other by symmetric exchanges, which received a significant interest also in algebra due to its connection to toric ideals and Gr\"obner bases. In this work, we verify White's conjecture for basis sequences of length two in regular matroids, a problem that was formulated as a separate question by Farber, Richter, and Shan and Andres, Hochst\"attler, and Merkel. Most of previous work on White's conjecture has not considered the question from an algorithmic perspective. We study the problem from an optimization point of view: our proof implies a polynomial algorithm for determining a sequence of symmetric exchanges that transforms a basis pair into another, thus providing the first polynomial upper bound on the exchange distance of basis pairs in regular matroids. As a byproduct, we verify a conjecture of Gabow from 1976 on the serial symmetric exchange property of matroids for the regular case.","PeriodicalId":496270,"journal":{"name":"arXiv (Cornell University)","volume":"119 24","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136352464","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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