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arXiv 2025年

作者： Matson, Raymond Alexander Dzintars Graduate Program in Mathematics University of California Riverside United States

In this thesis, we explore the representation theory of double affine Hecke algebras (DAHAs) through the lens of stated skein theory. Over the past decade, there have been several works establishing robust connections between skein algebras and DAHAs. Particularly, Samuelson proved that a spherical subalgebra of the type A1 DAHA can be realized as a quotient of the Kauffman bracket skein algebra of the torus with boundary, Kq(T 2 \ D2). Since the A1 double affine Hecke algebra is Morita equivalent to its spherical subalgebra, discovering modules for Kq(T 2 \ D2) immediately provides us with modules for the A1 DAHA. Stated skein theory enhances traditional Kauffman bracket skein theory by incorporating the boundary components of manifolds, thereby offering additional properties such as excision that enrich the algebraic structure. Furthermore, Kauffman bracket skein algebras embed into their stated counterparts, showing that stated skein algebras are extensions of Kauffman bracket skein algebras. We use this extended framework to further develop the representation theory of the A1 DAHA. After identifying generators for the stated skein algebra of T 2 \ D2, we embed this algebra into a quantum 6-torus and leverage the nice representation-theoretic properties of quantum tori to construct a module of Laurent polynomials. Additionally, as T 2 is the boundary of any knot complement, we discuss how to construct a more topologically-defined module from various knots and provide an explicit example for the unknot. This approach builds upon the ideas of Berest and Samuelson, who showed that there exists a natural DAHA action on the Kauffman bracket skein module of knot complements. © 2025, CC BY.

关键词： Topology

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Heterogeneous catalytic oxidative desulfurization of dibenzothiophene of metal oxide–Mg/Al layered double hydroxide

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Environmental Science and Pollution Research 2025年第13期32卷 8555-8563页

作者： Ahmad, Nur Hanifah, Yulizah Arsyad, Fitri Suryani Lesbani, Aldes Graduate School of Mathematics and Natural Sciences Faculty of Mathematics and Natural Sciences Universitas Sriwijaya Sumatera Selatan Palembang30139 Indonesia Research Center of Inorganic Materials and Coordination Complexes Universitas Sriwijaya Sumatera Selatan Palembang30139 Indonesia Research Center for Chemistry National Research and Innovation Agency Building 452 KST BJ Habibie Banten Serpong Tangerang Selatan15311 Indonesia Master Program of Material Science Graduate School Universitas Sriwijaya Sumatera Selatan Palembang30139 Indonesia

Mg/Al-TiO2 and Mg/Al-ZnO were successfully prepared for dibenzothiophene catalytic oxidative desulfurization. XRD, FTIR, TEM, and BET analyses were utilized to characterize the catalyst. In composites, the distinctive XRD patterns of precursors are still observable. FTIR spectra of the absorption bands were at 3448, 1627, 1381, 601, and 547 cm−1. The TEM pictures of the sample also revealed the almost spherical and hexagonal platelets of Mg/Al-LDH and its composite. Mg/Al LDH, Mg/Al-TiO2, and Mg/Al-ZnO had typical pore sizes of 35.78 nm, 52.81 nm, and 38.37 nm, respectively. The graph of nitrogen isotherms Mg/Al LDH, Mg/Al-TiO2, and Mg/Al-ZnO followed type IV isotherms. In addition, the conversion rates on Mg/Al-ZnO, Mg/Al-TiO2, ZnO, Mg/Al-LDH, and TiO2 were 99.34%, 99.50%, 91.20%, 96.29%, and 88.06%, respectively. This work presents alternative materials for the oxidative desulfurization of dibenzothiophene in practical applications. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2025.

关键词： Zinc oxide

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MURMURATIONS AND SATO-TATE CONJECTURES FOR HIGH RANK ZETAS OF ELLIPTIC CURVES II: BEYOND RIEMANN HYPOTHESIS

arXiv

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arXiv 2025年

作者： Shi, Zhan Weng, Lin Graduate Program of Mathematics for Innovation Kyushu University Fukuoka Japan Faculty of Mathematics Kyushu University Fukuoka Japan

As a continuation of our earlier paper [6], we offer a new approach to murmurations and Sato-Tate laws for higher rank zetas of elliptic curves. Our approach here does not depend on the Riemann hypothesis for the so-called a-invariant aE{Fp;n in rank npě 3q even for the Sato-Tate law, rather, on a much refined structure, a similar version of which was already observed earlier by Zagier and the senior author of this paper in [12] when the rank n Riemann hypothesis was established. Namely, instead of the rank n Riemann hypothesis bounds ´1 ď a2E?{Fppn;n ď 1 on which our first paper is based, we use the asymptotic bounds ´1 ď aE{Fp;n2`ppnn´´1q1 ? qpp`pn´5q ď 1. Accordingly, rank n Sato-Tate law can be established and rank n murmurations can be formulated equally well, similar to the corresponding structures in the abelian framework for Artin zetas of elliptic curves. © 2025, CC BY.

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Sampling Decisions

arXiv

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arXiv 2025年

作者： Chertkov, Michael Ahn, Sungsoo Behjoo, Hamidreza Program in Applied Mathematics Department of Mathematics University of Arizona TucsonAZ United States Graduate School of AI KAIST Korea Republic of

In this manuscript, we introduce a novel Decision Flow (DF) framework for sampling decisions from a target distribution while incorporating additional guidance from a prior sampler. DF can be viewed as an AI-driven algorithmic reincarnation of the Markov Decision Process (MDP) approach in Stochastic Optimal Control. It extends the continuous-space, continuous-time Path Integral Diffusion sampling technique of [1] to discrete time and space, while also generalizing the Generative Flow Network framework of [2]. In its most basic form – an explicit, Neural Network (NN)-free formulation – DF leverages the linear solvability of the underlying MDP [3] to adjust the transition probabilities of the prior sampler. The resulting Markov process is expressed as a convolution of the reverse-time Green’s function of the prior sampling with the target distribution. We illustrate the DF framework through an example of sampling from the Ising model, discuss potential NN-based extensions, and outline how DF can enhance guided sampling across various applications. Copyright © 2025, The Authors. All rights reserved.

关键词： Stochastic systems

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The Effect of Na2O/Ho2O3 Substitution on absorption spectra of Ho-Tm codoped Boro-Tellurite Glass 12

The Effect of Na2O/Ho2O3 Substitution on absorption spectra ...

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12th International Conference on Physics and Its Applications, ICOPIA 2024

作者： Marzuki, A. Djeksadipura, W.M.S. Ramelan, A.H. Fausta, D.E. Harjana Sutomo, A.D. Physics Department Faculty of Mathematics and Natural Science Universitas Sebelas Maret Surakarta. Jl. Ir. Sutami No. 36 Surakarta57126 Indonesia Graduate Physics Program Faculty of Mathematics and Natural Science Universitas Sebelas Maret Surakarta. Jl. Ir. Sutami No. 36 Surakarta57126 Indonesia

Boro-tellurite glasses composed of 57B2O3– (4-y)Na2O-–15Bi2O3-20TeO2–3TiO2–1Tm2O3-yHo2O3 (y = 0, 0.5, 1.0, 1.5, 2.0, and 2.5 mol%) were succesfully synthesised and the change in their absorption spectra in wavelength range 300-1100 nm were studied. All glasses were fabricated at the same melting temperature 1000oC and subsequenlty qunched and annnealled in the same manner. It can be seen that glass dopped with only Tm3+ ions (y = 0) shows three absorption peaks, i.e., 471, 686, and 792 nm. As Ho3+ ions were added, there were additional six new peaks appear, i.e., peaks located around 417, 450, 485, 538, and 642 nm. The study reveals that different peaks show difference of sensitivity to the additional Ho3+ ions concentration with peaks around 450 nm shows the most sensitive. © 2025 Institute of Physics Publishing. All rights reserved.

关键词： Glass

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Assessment of rhizosphere microbial activity using optimized RNA extraction coupled with universal ribosomal RNA depletion techniques

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BMC Methods 2025年第1期2卷 1-10页

作者： Tamrakar, Kipa Miller, P. Winston Dolan, Maureen C. Wijeratne, Asela J. Molecular Biosciences Graduate Program Arkansas State University Jonesboro USA Arkansas Biosciences Institute Jonesboro USA Department of Biological Sciences Beck College of Sciences and Mathematics Arkansas State University Jonesboro USA

Metatranscriptomics, which analyzes gene expression patterns in a heterogeneous community, is a powerful tool to evaluate microbial functional activity. A key challenge in this process is obtaining high-quality RNA, which is complicated by the composition and ecosystem complexity of the soil matrix. Another crucial step involves the removal of highly abundant ribosomal RNA (rRNA), as its presence can dominate sequencing results and obscure the detection of messenger RNA (mRNA) expression. Conventional library preparation methods often struggle to efficiently remove rRNA from a complex mix of prokaryotic and eukaryotic organisms, further complicating mRNA isolation. To overcome these limitations, we have developed an optimized method for extracting RNA from soybean rhizosphere microbes, followed by universal rRNA depletion to create rRNA-free samples for sequencing. These samples were sequenced using an Illumina high-throughput sequencer. Our optimized cetyltrimethylammonium bromide (CTAB) phenol–chloroform extraction protocol significantly improved RNA yield and quality from clay-rich soils, outperforming previously published methods and commercial kits. Illumina sequencing data revealed minimal rRNA contamination, and the resulting short reads could be successfully assembled into transcripts. These findings also demonstrate that using the Zymo-Seq RiboFree Total RNA Library Kit effectively enabled library preparation from complex environmental samples for Illumina sequencing. This RNA sample preparation method, combined with our optimized extraction technique, provides a valuable approach for studying rhizosphere microbes that hold exciting potential for advancing soil health assessments and understanding plant–microbe-pathogen interactions.

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Efficient Maximum Euclidean Distance Transform Computation in Component Trees Using the Differential Image Foresting Transform

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Journal of Mathematical Imaging and Vision 2025年第3期67卷 1-23页

作者： Silva, Dennis J. Miranda, Paulo A. V. Alves, Wonder A. L. Hashimoto, Ronaldo F. Kosinka, Jiří Roerdink, Jos B. T. M. Institute of Mathematics and Statistics University of São Paulo São Paulo Brazil Bernoulli Institute for Mathematics Computer Science and Artificial Intelligence University of Groningen Groningen The Netherlands Informatics and Knowledge Management Graduate Program Nove de Julho University São Paulo Brazil

The distance transform is a crucial technique in binary image processing, assigning the distance to the nearest contour to each foreground pixel. In this extended version of our previous work, we enhance our method for computing the maximum distance transform (DT) value, now utilizing the optimized differential image foresting transform (DIFT) and improved contour extraction processes. These advancements enable more efficient computation of the maximum DT value across all connected components of a grayscale image, significantly reducing computational time by intelligently reusing DIFT trees rooted at contour points (DIFT seeds). Our optimized algorithm now achieves processing speeds that are twice as fast as our previous differential method. The proposed attribute, maximum distance, which measures the thickness of objects within the image, has proven pivotal in different image processing approaches. We showcase this through detailed illustrations of attribute opening, extinction value filters, watershed, and ultimate attribute openings.

关键词： Binary images

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Biomarkers of heavy metals pollution in mangrove ecosystems: Comparative assessment in industrial impact and conservation zones

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Toxicology Reports 2025年 14卷 102011页

作者： Rozirwan Khotimah, Nadila Nur Putri, Wike Ayu Eka Fauziyah Aryawati, Riris Diansyah, Gusti Nugroho, Redho Yoga Department of Marine Science Faculty of Mathematics and Natural Sciences Universitas Sriwijaya South Sumatra Indralaya 30862 Indonesia Environmental Management Study Program Graduate Program Universitas Sriwijaya Palembang 30139 Indonesia

Heavy metal contamination from industrial activities in coastal regions can lead to pollution in mangrove ecosystems. Mangroves produce antioxidant compounds to mitigate the impact of free radicals. This study aimed to analyze the correlation between the concentration of heavy metals Pb and Cu and antioxidant activity in Avicennia alba and Excoecaria agallocha mangroves from areas affected by industrial activities and conservation areas, Banyuasin, South Sumatra, Indonesia. This study was conducted in September 2023 with sampling locations in the Payung Island area and the Barong River conservation area, Berbak Sembilang National Park. The samples taken included sediment and mangrove leaves. The concentration of heavy metals Pb and Cu was measured by atomic absorption spectrometry. Antioxidant activity test using the DPPH test, total phenol using the Folin-Ciocalteu method, and phytochemical profile screening using GCMS. Statistical analysis of the correlation between antioxidant activity and heavy metal concentration using the Pearson correlation. The results showed that the highest concentration of heavy metals in sediment and mangrove leaves was found in the area affected by industrial activity, with a range of Pb values of 0.67 ± 0.16–18.70 ± 0.48 mg/kg and Cu values of 3.39 ± 0.20–6.07 ± 0.37 mg / kg. The results of sediment pollution assessment for heavy metals Pb and Cu at Igeo < 0 indicates uncontaminated, 1 < Cf < 3 indicates low contamination, and PLI 0–2 indicates not polluted. While the results of heavy metal bioaccumulation in leaves were BCF < 1, indicates low bioaccumulation. E. agallocha leaves from the Pulau Payung area showed very strong antioxidant activity of 21.63 μg/ml, and the highest total phenol content reached 398.80 mg GAE/g. Analysis of compounds with the highest antioxidant activity identified the presence of esters, aldehydes, alcohols, fatty acids, glycosides, flavonoids, terpenoids, and steroids. Correlation analysis shows that higher

关键词： Biomarkers Conservation zones Heavy metals Industrial activities Mangrove

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Machine learning of microstructure–property relationships in materials with robust features from foundational vision transformers

arXiv

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arXiv 2025年

作者： Whitman, Sheila E. Latypov, Marat I. Graduate Interdisciplinary Program in Applied Mathematics University of Arizona TucsonAZ85721 United States Department of Materials Science and Engineering University of Arizona TucsonAZ85721 United States

Machine learning of microstructure–property relationships from data is an emerging approach in computational materials science. Most existing machine learning efforts focus on the development of task-specific models for each microstructure–property relationship. We propose utilizing pre-trained foundational vision transformers for the extraction of task-agnostic microstructure features and subsequent light-weight machine learning of a microstructure-dependent property. We demonstrate our approach with pre-trained state-of-the-art vision transformers (CLIP, DINOV2, SAM) in two case studies on machine-learning: (i) elastic modulus of two-phase microstructures based on simulations data;and (ii) Vicker’s hardness of Ni-base and Co-base superalloys based on experimental data published in literature. Our results show the potential of foundational vision transformers for robust microstructure representation and efficient machine learning of microstructure–property relationships without the need for expensive task-specific training or fine-tuning of bespoke deep learning models. © 2025, CC BY.

关键词： Elastic moduli

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Fixed-parameter algorithms for cardinality-constrained graph partitioning problems on sparse graphs

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Discrete Applied mathematics 2025年 373卷 343-354页

作者： Yamada, Suguru Hanaka, Tesshu Graduate Program of Mathematics for Innovation Kyushu University 744 Motooka Nishi-ku Fukuoka Fukuoka 819-0395 Japan Faculty of Information Science and Electrical Engineering Kyushu University 744 Motooka Nishi-ku Fukuoka Fukuoka 819-0395 Japan

For an undirected and edge-weighted graph G=(V,E) and a vertex subset S⊆V, we define a function φG(S)≔(1−α)⋅w(S)+α⋅w(S,V∖S), where α∈[0,1] is a real number, w(S) is the sum of the weights of edges having two endp... 详细信息

For an undirected and edge-weighted graph G=(V,E) and a vertex subset S⊆V, we define a function φ_G(S)≔(1−α)⋅w(S)+α⋅w(S,V∖S), where α∈[0,1] is a real number, w(S) is the sum of the weights of edges having two endpoints in S, and w(S,V∖S) is the sum of the weights of edges having one endpoint in S and the other in V∖S. Then, given an undirected and edge-weighted graph G=(V,E) and a positive integer k, MAX (MIN)α-FIXED CARDINALITY GRAPH PARTITIONING (MAX (MIN)α-FCGP) is the problem to find a vertex subset S⊆V of size k that maximizes (minimizes) φ_G(S). In this paper, we first show that MAXα-FCGP with α∈[1/3,1] and MINα-FCGP with α∈[0,1/3] can be solved in time 2^o(kd+k)(e+ed)^kn^O(1) where k is the solution size, d is the degeneracy of an input graph, and e is Napier's constant. Then we consider MAX (MIN) CONNECTEDα-FCGP, which additionally requires the connectivity of a solution. We show that if MAX (MIN)α-FCGP is W[1]-hard parameterized by k, so is MAX (MIN) CONNECTEDα-FCGP. Then, we give a 2^O(klogn^O(1)-time randomized algorithm on apex-minor-free graphs. Moreover, for MAX CONNECTEDα-FCGP with α∈[1/3,1] and MIN CONNECTEDα-FCGP with α∈[0,1/3], we propose a (1+d)^k2^o(kd)+O(k)n^O(1)-time algorithm. Finally, we show that they admit FPT-ASs parameterized by k when edge weights are constant. © 2025 Elsevier B.V.

关键词： Degeneracy Fixed-parameter tractability Graph partitioning Parameterized approximation

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