IA Scholar Query: Embedding Linkages on an Integer Lattice.
https://scholar.archive.org/
Internet Archive Scholar query results feedeninfo@archive.orgWed, 28 Sep 2022 00:00:00 GMTfatcat-scholarhttps://scholar.archive.org/help1440TEI2022 Conference Book
https://scholar.archive.org/work/fo5eliwof5bnnn3ms3vetgbpoi
A Book of Abstracts and more for the TEI2022 Conference!James Cummingswork_fo5eliwof5bnnn3ms3vetgbpoiWed, 28 Sep 2022 00:00:00 GMTCanonical diagonal liftings I: Dormant PGL(n)-opers on algebraic curves
https://scholar.archive.org/work/q4vjgcew4bdrdkpifpc3j7md3q
The present paper forms the first part of a series in which we treat some topics on dormant opers and Frobenius-Ehresmann structures from an arithmetic point of view. In the present paper, motivated by the issue of lifting homogeneous linear differential equations in prime characteristic p, we generalize the moduli theory of dormant PGL_n-opers on pointed stable curves. One of the main results is the construction of a compactified moduli space classifying dormant PGL_n-opers of level N >0. We also examine its geometric structure, including a factorization property according to clutching morphisms. Furthermore, the generic étaleness of the moduli space for n=2 is proved by obtaining a detailed understanding of the deformation space in terms of cohomology groups. As a consequence, we give a certain unique lifting of any dormant PGL_2-oper of level N on a general curve to characteristic p^N; this lifting is called the canonical diagonal lifting. Canonical diagonal liftings enable us to establish an equivalence between the counting problems of related objects in characteristic p and p^N.Yasuhiro Wakabayashiwork_q4vjgcew4bdrdkpifpc3j7md3qSun, 18 Sep 2022 00:00:00 GMTMachine Learning for Property Prediction and Optimization of Polymeric Nanocomposites: A State-of-the-Art
https://scholar.archive.org/work/ynu4jrigorg5jcigxk4dynau6e
Recently, the field of polymer nanocomposites has been an area of high scientific and industrial attention due to noteworthy improvements attained in these materials, arising from the synergetic combination of properties of a polymeric matrix and an organic or inorganic nanomaterial. The enhanced performance of those materials typically involves superior mechanical strength, toughness and stiffness, electrical and thermal conductivity, better flame retardancy and a higher barrier to moisture and gases. Nanocomposites can also display unique design possibilities, which provide exceptional advantages in developing multifunctional materials with desired properties for specific applications. On the other hand, machine learning (ML) has been recognized as a powerful predictive tool for data-driven multi-physical modelling, leading to unprecedented insights and an exploration of the system's properties beyond the capability of traditional computational and experimental analyses. This article aims to provide a brief overview of the most important findings related to the application of ML for the rational design of polymeric nanocomposites. Prediction, optimization, feature identification and uncertainty quantification are presented along with different ML algorithms used in the field of polymeric nanocomposites for property prediction, and selected examples are discussed. Finally, conclusions and future perspectives are highlighted.Elizabeth Champa-Bujaico, Pilar García-Díaz, Ana M. Díez-Pascualwork_ynu4jrigorg5jcigxk4dynau6eWed, 14 Sep 2022 00:00:00 GMTTEI2022 Conference Book
https://scholar.archive.org/work/mmxyz3rs75gwzgkh3nzevfbdfa
A Book of Abstracts and more for the TEI2022 Conference!James Cummingswork_mmxyz3rs75gwzgkh3nzevfbdfaMon, 12 Sep 2022 00:00:00 GMTVariational methods and its applications to computer vision
https://scholar.archive.org/work/dtthbdie4vf7nc4nxvyanwq7rq
Many computer vision applications such as image segmentation can be formulated in a "variational" way as energy minimization problems. Unfortunately, the computational task of minimizing these energies is usually difficult as it generally involves non convex functions in a space with thousands of dimensions and often the associated combinatorial problems are NP-hard to solve. Furthermore, they are ill-posed inverse problems and therefore are extremely sensitive to perturbations (e.g. noise). For this reason in order to compute a physically reliable approximation from given noisy data, it is necessary to incorporate into the mathematical model appropriate regularizations that require complex computations. The main aim of this work is to describe variational segmentation methods that are particularly effective for curvilinear structures. Due to their complex geometry, classical regularization techniques cannot be adopted because they lead to the loss of most of low contrasted details. In contrast, the proposed method not only better preserves curvilinear structures, but also reconnects some parts that may have been disconnected by noise. Moreover, it can be easily extensible to graphs and successfully applied to different types of data such as medical imagery (i.e. vessels, hearth coronaries etc), material samples (i.e. concrete) and satellite signals (i.e. streets, rivers etc.). In particular, we will show results and performances about an implementation targeting new generation of High Performance Computing (HPC) architectures where different types of coprocessors cooperate. The involved dataset consists of approximately 200 images of cracks, captured in three different tunnels by a robotic machine designed for the European ROBO-SPECT project.Erika Pellegrino, Panagiota Stathakiwork_dtthbdie4vf7nc4nxvyanwq7rqWed, 07 Sep 2022 00:00:00 GMTTemporal structure of the world
https://scholar.archive.org/work/it2xnhklsnd7dlwa2hgzlrk67m
The thesis starts from the position of Ontic Structural Realism, which holds that the world just is structure, and from the ontology of Rainforest Realism in which the only things that exist are (Dennettian) real patterns. I argue that the temporal structure of the world emerges from the temporal aspect of spacetime and consists in real patterns of time existing at different ontological scales. Such scale relativity of ontology allows the temporal structure of the world to display very different features. At the scale of instants and of extremely small duration, I argue that there is non-dynamic, tenseless structure to which the earlier than relation may be applied. At the scale of larger duration, I argue that there occurs robust objective becoming that just is dynamic composition of larger-scale material structure (as real patterns) – initiating a real, tensed, passage of time. Thus, something akin to a Block Universe can be found at the very small scales of time, from which emerges the dynamic world of our experience.Keith Heard, University Of Edinburgh, Alasdair Richmond, Elinor Masonwork_it2xnhklsnd7dlwa2hgzlrk67mTue, 06 Sep 2022 00:00:00 GMTDecomposition of Frobenius pushforwards of line bundles on wonderful compactifications
https://scholar.archive.org/work/gjk4lfhw3nhelnjo7pb7q3smbe
De Concini-Procesi introduced varieties known as wonderful compactifications, which are smooth projective compactifications of semisimple adjoint groups G. We study the Frobenius pushforwards of invertible sheaves on the wonderful compactifications, and in particular its decomposition into locally free subsheaves. We give necessary and sufficient conditions for a specific line bundle to be a direct summand of the Frobenius pushforward of another line bundle, formulated in terms of the weight lattice of G, the universal cover of G (identified with the Picard group of the wonderful compactification). In the case of G=𝖯𝖲𝖫_n, we offer lower bounds on the multiplicities (as direct summands) for those line bundles satisfying the sufficient conditions. We also decompose Frobenius pushforwards of line bundles into a direct sum of vector subbundles, whose ranks are determined by invariants on the weight lattice of G. We study a particular block which decomposes as a direct sum of line bundles, and identify the line bundles which appear in this block. Finally, we present two approaches to compute the class of the Frobenius pushforward of line bundles on wonderful compactifications in the rational Grothendieck group and in the rational Chow group.Merrick Cai, Vasily Krylovwork_gjk4lfhw3nhelnjo7pb7q3smbeSat, 03 Sep 2022 00:00:00 GMTWeak quasi-Hopf algebras, C*-tensor categories and conformal field theory, and the Kazhdan-Lusztig-Finkelberg theorem
https://scholar.archive.org/work/sfhf6c3i6zeh5mvtv5r2bcxsdq
We discuss tensor categories motivated by CFT, their unitarizability and applications to various models including the affine VOAs. We discuss classification of type A Verlinde fusion categories. We propose an approach to Kazhdan-Lusztig-Finkelberg theorem. This theorem gives a ribbon equivalence between the fusion category associated to a quantum group at a certain root of unity and that associated to a corresponding affine vertex operator algebra at a suitable positive integer level. We develop ideas by Wenzl. Our results rely on the notion of weak-quasi-Hopf algebra of Drinfeld-Mack-Schomerus. We were also guided by Drinfeld original proof, by Bakalov and Kirillov and Neshveyev and Tuset work for a generic parameter. Wenzl described a fusion tensor product in quantum group fusion categories, and related it to the unitary structure. Given two irreducible objects, the inner product of the fusion tensor product is induced by the braiding of U_q(g), with q a suitable root of 1. Moreover, the paper suggests a suitable untwisting procedure to make the unitary structure trivial. Then it also describes a continuous path that intuitively connects objects of the quantum group fusion category to representations of the simple Lie group defining the affine Lie algebra. We study this procedure. One of our main results is the construction of a Hopf algebra in a weak sense associated to quantum group fusion category and of a twist of it giving a wqh structure on the Zhu algebra and a unitary modular fusion category structure on the representation category of the affine Lie algebra, confirming an early view by Frenkel and Zhu. We show that this modular fusion category structure is equivalent to that obtained via the tensor product theory of VOAs by Huang and Lepowsky. This gives a direct proof of FKL theorem.Sebastiano Carpi, Sergio Ciamprone, Marco Valerio Giannone, Claudia Pinzariwork_sfhf6c3i6zeh5mvtv5r2bcxsdqWed, 31 Aug 2022 00:00:00 GMTNew compressed cover tree for k-nearest neighbor search
https://scholar.archive.org/work/ydsvaevkcvcddmcnwqxbwuv6am
This thesis consists of two topics related to computational geometry and one topic related to topological data analysis (TDA), which combines fields of computational geometry and algebraic topology for analyzing data. The first part studies the classical problem of finding k nearest neighbors to m query points in a larger set of n reference points in any metric space. The second part is about the construction of a Minimum Spanning Tree (MST) on any finite metric space. The third part extends the key concept of persistence within Topological Data Analysis in a new direction.Yury Elkinwork_ydsvaevkcvcddmcnwqxbwuv6amWed, 24 Aug 2022 00:00:00 GMTEvaluating the Feasibility of a Provably Secure Privacy-Preserving Entity Resolution Adaptation of PPJoin using Homomorphic Encryption
https://scholar.archive.org/work/oruxqvwyfjcwli4vnfve4cxn6i
Entity resolution is the task of disambiguating records that refer to the same entity in the real world. In this work, we explore adapting one of the most efficient and accurate Jaccard-based entity resolution algorithms - PPJoin, to the private domain via homomorphic encryption. Towards this, we present our precise adaptation of PPJoin (HE-PPJoin) that details certain subtle data structure modifications and algorithmic additions needed for correctness and privacy. We implement HE-PPJoin by extending the PALISADE homomorphic encryption library and evaluate over it for accuracy and incurred overhead. Furthermore, we directly compare HE-PPJoin against P4Join, an existing privacy-preserving variant of PPJoin which uses fingerprinting for raw content obfuscation, by demonstrating a rigorous analysis of the efficiency, accuracy, and privacy properties achieved by our adaptation as well as a characterization of those same attributes in P4Join.Tanmay Ghai, Yixiang Yao, Srivatsan Ravi, Pedro Szekelywork_oruxqvwyfjcwli4vnfve4cxn6iWed, 17 Aug 2022 00:00:00 GMT3d spectral networks and classical Chern-Simons theory
https://scholar.archive.org/work/a3nz4hnfr5cfnngrxz6zwnmbda
We define the notion of spectral network on manifolds of dimension ≤ 3. For a manifold X equipped with a spectral network, we construct equivalences between Chern-Simons invariants of flat SL(2,ℂ)-bundles over X and Chern-Simons invariants of flat ℂ^×-bundles over ramified double covers X. Applications include a new viewpoint on dilogarithmic formulas for Chern-Simons invariants of flat SL(2,ℂ)-bundles over triangulated 3-manifolds, and an explicit description of Chern-Simons lines of flat SL(2,ℂ)-bundles over triangulated surfaces. Our constructions heavily exploit the locality of Chern-Simons invariants, expressed in the language of extended (invertible) topological field theory.Daniel S. Freed, Andrew Neitzkework_a3nz4hnfr5cfnngrxz6zwnmbdaMon, 15 Aug 2022 00:00:00 GMTBeamline simulations using monochromators with high d-spacing crystals
https://scholar.archive.org/work/siu4a7y4zfexleaxd3o52c43ci
Monochromators for synchrotron radiation beamlines typically use perfect crystals for the hard X-ray regime and gratings for soft X-rays. There is an intermediate range, typically 1–3 keV (tender X-rays), which common perfect crystals have difficulties covering and gratings have low efficiency, although some less common crystals with high d-spacing could be suitable. To evaluate the suitability of these crystals for a particular beamline, it is useful to evaluate the crystals' performance using tools such as ray-tracing. However, simulations for double-crystal monochromators are only available for the most used crystals such as Si, Ge or diamond. Here, an upgrade of the SHADOW ray-tracing code and complementary tools in the OASYS suite are presented to simulate high d-spacing crystals with arbitrary, and sometimes complex, structures such as beryl, YB66, muscovite, etc. Isotropic and anisotropic temperature factors are also considered. The YB66 crystal with 1936 atomic sites in the unit cell is simulated, and its applicability for tender X-ray monochromators is discussed in the context of new low-emittance storage rings.X. J. Yu, X. Chi, T. Smulders, A. T. S. Wee, A. Rusydi, M. Sanchez del Rio, M. B. H. Breesework_siu4a7y4zfexleaxd3o52c43ciFri, 12 Aug 2022 00:00:00 GMTClassification of Unitary RCFTs with Two Primaries and Central Charge Less Than 25
https://scholar.archive.org/work/owumdr5kvnhtjkkcxyo6at57be
We classify all unitary, rational conformal field theories with two primaries, central charge c<25, and arbitrary Wronskian index. We find that any such theory is either a Mathur–Mukhi–Sen (MMS) theory with two primaries, or a coset of a chiral algebra with one primary operator by such an MMS theory. By leveraging the existing classification of chiral algebras with one primary operator, central charge c≤ 24, and a non-zero number of dimension-one currents, we are able to explicitly enumerate all of the aforementioned cosets and compute their characters. This leads to 123 theories, most of which are new. We emphasize that our work is a bona fide classification of RCFTs, not just of characters. Our techniques are general, and we argue that they offer a promising strategy for classifying chiral algebras with low central charge beyond two primaries.Sunil Mukhi, Brandon C. Rayhaunwork_owumdr5kvnhtjkkcxyo6at57beWed, 10 Aug 2022 00:00:00 GMTCalogero-Moser spaces vs unipotent representations
https://scholar.archive.org/work/jmtyfwgcknd6ph3ms2ljroatdy
Lusztig's classification of unipotent representations of finite reductive groups depends only on the associated Weyl group W (endowed with its Frobenius automorphism). All the structural questions (families, Harish-Chandra series, partition into blocks...) have an answer in a combinatorics that can be entirely built directly from W. Over the years, we have noticed that the same combinatorics seems to be encoded in the Poisson geometry of a Calogero-Moser space associated with W (roughly speaking, families correspond to ℂ^×-fixed points, Harish-Chandra series correspond to symplectic leaves, blocks correspond to symplectic leaves in the fixed point subvariety under the action of a root of unity). The aim of this survey is to gather all these observations, state precise conjectures and provide general facts and examples supporting these conjectures.Cédric Bonnaféwork_jmtyfwgcknd6ph3ms2ljroatdyThu, 04 Aug 2022 00:00:00 GMTData Fusion: Theory, Methods, and Applications
https://scholar.archive.org/work/ntcpnuxe4zd3do75kjdnhn6j6a
A proper fusion of complex data is of interest to many researchers in diverse fields, including computational statistics, computational geometry, bioinformatics, machine learning, pattern recognition, quality management, engineering, statistics, finance, economics, etc. It plays a crucial role in: synthetic description of data processes or whole domains, creation of rule bases for approximate reasoning tasks, reaching consensus and selection of the optimal strategy in decision support systems, imputation of missing values, data deduplication and consolidation, record linkage across heterogeneous databases, and clustering. This open-access research monograph integrates the spread-out results from different domains using the methodology of the well-established classical aggregation framework, introduces researchers and practitioners to Aggregation 2.0, as well as points out the challenges and interesting directions for further research.Marek Gagolewskiwork_ntcpnuxe4zd3do75kjdnhn6j6aTue, 02 Aug 2022 00:00:00 GMTOn minimal tilting complexes in highest weight categories
https://scholar.archive.org/work/6wql43voy5ck5bzuam6jrtw2ee
We explain the construction of minimal tilting complexes for objects of highest weight categories and we study in detail the minimal tilting complexes for standard objects and simple objects. For certain categories of representations of complex simple Lie algebras, affine Kac-Moody algebras and quantum groups at roots of unity, we relate the multiplicities of indecomposable tilting objects appearing in the terms of these complexes to the coefficients of Kazhdan-Lusztig polynomials. We also prove that the minimal tilting complexes of Weyl modules and simple modules of p-regular highest weight over a simply-connected simple algebraic group over an algebraically closed field of characteristic p>0 have some properties in common with minimal tilting complexes of Weyl modules and simple modules over the corresponding quantum group at a p-th root of unity.Jonathan Gruberwork_6wql43voy5ck5bzuam6jrtw2eeMon, 25 Jul 2022 00:00:00 GMTInterleaving by Parts: Join Decompositions of Interleavings and Join-Assemblage of Geodesics
https://scholar.archive.org/work/t54uueibingdpdknjvlgvnng4i
Metrics of interest in topological data analysis (TDA) are often explicitly or implicitly in the form of an interleaving distance d_I between poset maps (i.e. order-preserving maps), e.g. the Gromov-Hausdorff distance between metric spaces can be reformulated in this way. We propose a representation of a poset map 𝐅:𝒫→𝒬 as a join (i.e. supremum) ⋁_b∈ B𝐅_b of simpler poset maps 𝐅_b (for a join dense subset B⊂𝒬) which in turn yields a decomposition of d_I into a product metric. The decomposition of d_I is simple, but its ramifications are manifold: (1) We can construct a geodesic path between any poset maps 𝐅 and 𝐆 with d_I(𝐅,𝐆)<∞ by assembling geodesics between all 𝐅_bs and 𝐆_bs via the join operation. This construction generalizes at least three constructions of geodesic paths that have appeared in the literature. (2) We can extend the Gromov-Hausdorff distance to a distance between simplicial filtrations over an arbitrary poset with a flow, preserving its universality and geodesicity. (3) We can clarify equivalence between several known metrics on multiparameter hierarchical clusterings. (4) We can illuminate the relationship between the erosion distance by Patel and the graded rank function by Betthauser, Bubenik, and Edwards, which in turn takes us to an interpretation on the representation ⋁_b 𝐅_b as a generalization of persistence landscapes and graded rank functions.Woojin Kim, Facundo Mémoli, Anastasios Stefanouwork_t54uueibingdpdknjvlgvnng4iTue, 19 Jul 2022 00:00:00 GMTAn investigation of computer integrated batch manufacturing processes in small and medium-sized enterprises (SMEs)
https://scholar.archive.org/work/xwizl7y7mjgxlkzw2sytqffzbm
Global competition and improved manufacturing technologies have resulted in shorter product life cycles and smaller batch production with increasing product variations. Traditional batch manufacturing can never cater efficiently and effectively to the needs of ever changing markets. These changes and problems force small and medium-sized enterprises (SMEs) to look for adaptations and improvements in their manufacturing processes. Larger companies have resources to adapt to these changes, however SMEs face major obstacles such as a lack of finance, technology know-how and expertise. These difficulties are heightened by the fact that current technologies and research are tailored towards larger companies and pay little attention to the demands of SMEs. This research presents an integrated methodology intended specifically to assist SMEs in the design and selection of the most viable batch manufacturing system. The motivation for the research was twofold, firstly there was a need to transfer the advanced batch manufacturing technologies to SMEs through the applications of analytical hierarchy technique (AHP) and computer simulation which are generally used in larger companies, and utilise them effectively in their manufacturing processes. Secondly, the lack of a comprehensive and integrated methodology to deal with the major concerns faced by SMEs in adopting these technologies needed to be addressed. Unlike previous investigations, this study uses an approach which considers all facets of an SME including organisational, tactical, operational and financial issues. It attempts to address the complex problems of manufacturing system design by integrating a decision framework with the group technology concept and powerful computer tools. This is accomplished by the use of multi-criteria decision making, Group Technology, computer simulation and costs modelling tools and techniques. To validate the suitability of the methodology, an industrial case study with an SME engaged in discrete batch manufacturing was used. The [...]Thu Siwork_xwizl7y7mjgxlkzw2sytqffzbmTue, 19 Jul 2022 00:00:00 GMTTate cohomology of Whittaker lattices and Base change of cuspidal representations of GL_n
https://scholar.archive.org/work/6yzyhtprmnhffaf4r2lbqgbnna
Let p and l be distinct primes and let n be a positive integer. Let E be a finite Galois extension of degree l of a p-adic field F. Let π and ρ be two l-adic integral smooth cuspidal representations of GL_n(E) and GL_n(F) respectively such that π is obtained as base change of ρ. Then the Tate cohomology Ĥ^0(π), as an l-modular representation of GL_n(F), is well defined. In this article, we show that Ĥ^0(π) is isomorphic to the Frobenius twist of the reduction mod-l of the representation ρ. We assume that l, p n and l is banal for GL_n-1(F).Sabyasachi Dhar, Santosh Nadimpalliwork_6yzyhtprmnhffaf4r2lbqgbnnaSun, 17 Jul 2022 00:00:00 GMTBlock decomposition via the geometric Satake equivalence
https://scholar.archive.org/work/wb2lve6mbraifb7gjns6fqia2q
We give a new proof for the description of the blocks in the category of representations of a reductive algebraic group 𝐆 over a field of positive characteristic ℓ (originally due to Donkin), by working in the Satake category of the Langlands dual group and applying Smith-Treumann theory as developed by Riche and Williamson. On the representation theoretic side, our methods enable us to give a bound for the length of a minimum chain linking two weights in the same block, and to give a new proof for the block decomposition of a quantum group at an ℓ-th root of unity.Emilien Zabethwork_wb2lve6mbraifb7gjns6fqia2qWed, 13 Jul 2022 00:00:00 GMT