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CONSTRUCTION OF BRAUER-SEVERI VARIETIES

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arXiv 2017年

作者： García, Elisa Lorenzo Laboratoire IRMAR Université de Rennes 1 Campus de Beaulieu bât. 22-23 Rennes Cédex35042 France

In this paper we give an algorithm for computing equations of Brauer-Severi varieties over fields of characteristic 0. As an example we show the equations of all Brauer-Severi surfaces defined over Q. Copyright ©... 详细信息

关键词： computation theory

What will computational modelling approaches have to say in the era of atomistic cryo-EM data?

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arXiv 2020年

作者： Fraser, James S. Lindorff-Larsen, Kresten Bonomi, Massimiliano Department of Bioengineering and Therapeutic Sciences University of California San Francisco San FranciscoCA United States Structural Biology and NMR Laboratory Linderstrom-Lang Centre for Protein Science Department of Biology University of Copenhagen Copenhagen Denmark Structural Bioinformatics Unit Department of Structural Biology and Chemistry CNRS UMR 3528 C3BI CNRS USR 3756 Institut Pasteur Paris France

The focus of this viewpoint is to identify, in the era of atomistic resolution cryo-electron microscopy data, the areas in which computational modelling and molecular simulations will bring valuable contributions to structural biologists and to give an overview of some of the existing efforts in this direction. Copyright © 2020, The Authors. All rights reserved.

关键词： computation theory

computational model to quantify object innovativeness

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arXiv 2021年

作者： Ivanov, Vladimir K. Centre of New Information Technologies Tver State Technical University Afanasy Nikitin emb. 22 Tver Russia

The article considers the quantitative assessment approach to the innovativeness of different objects. The proposed assessment model is based on the object data retrieval from various databases including the Internet. We present an object linguistic model, the processing technique for the measurement results including the results retrieved from the different search engines, and the evaluating technique of the source credibility. Empirical research of the computational model adequacy includes the acquisition and preprocessing of patent data from different databases and the computation of invention innovativeness values: Their novelty and relevance. The experiment results, namely the comparative assessments of innovativeness values and major trends, show the models developed are sufficiently adequate and can be used in further research. © 2021, CC BY-NC-ND.

关键词： computation theory

The Motivic Mahowald Invariant

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arXiv 2018年

作者： Quigley, J.D.

The classical Mahowald invariant is a method for producing nonzero classes in the stable homotopy groups of spheres from classes in lower stems. We study the Mahowald invariant in the setting of motivic stable homotopy theory over Spec(C). We compute a motivic version of the C2-Tate construction for various motivic spectra, and show that this construction produces "blueshift" in these cases. We use these computations to show that the Mahowald invariant of ηi, i ≥ 1, is the first element in Adams filtration i of the w1-periodic families constructed by Andrews [4]. This provides an exotic periodic analog of Mahowald and Ravenel’s computation [26] that the classical Mahowald invariant of 2i, i ≥ 1, is the first element in Adams filtration i of the v1-periodic families constructed by Adams [2].MSC Codes SSP42 Copyright © 2018, The Authors. All rights reserved.

关键词： computation theory

Brain connectomes come of age

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arXiv 2020年

作者： Wang, Xiao-Jing Pereira, Ulises Rosa, Marcello G.P. Kennedy, Henry Center for Neural Science New York University 4 Washington Place New YorkNY10003 United States Biomedicine Discovery Institute Australian Research Council Centre of Excellence for Integrative Brain Function Monash University ClaytonVIC3800 Australia Stem Cell and Brain Research Institute INSERM U846 Bron69500 France

Databases of directed- and weighted- connectivity for mouse, macaque and marmoset monkeys, have recently become available and begun to be used to build dynamical models. A hierarchical organization can be defined based on laminar patterns of cortical connections, possibly improved by thalamocortical projections. A large-scale model of the macaque cortex endowed with a laminar structure accounts for layer-dependent and frequency-modulated interplays between bottom-up and top-down processes. Signal propagation in a version of the model with spiking neurons displays a threshold of stimulus amplitude for the activity to gain access to the prefrontal cortex, reminiscent of the ignition phenomenon associated with conscious perception. These two examples illustrate how connectomics may inform theory leading to discoveries. computational modeling raises open questions for future empirical research, in a back-and-forth collaboration of experimentalists and theorists. Copyright © 2020, The Authors. All rights reserved.

关键词： computation theory

The Potential of the Confluence of Theoretical and Algorithmic Modeling in Music Recommendation

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arXiv 2019年

作者： Bauer, Christine Johannes Kepler University Linz Linz Austria

The task of a music recommender system is to predict what music item a particular user would like to listen to next. This position paper discusses the main challenges of the music preference prediction task: the lack of information on the many contextual factors influencing a user’s music preferences in existing open datasets, the lack of clarity of what the right choice of music is and whether a right choice exists at all;the multitude of criteria (beyond accuracy) that have to be met for a "good" music item recommendation;and the need for explanations on relationships to identify (and potentially counteract) unwanted biases in recommendation approaches. The paper substantiates the position that the confluence of theoretical modeling (which seeks to explain behaviors) and algorithmic modeling (which seeks to predict behaviors) seems to be an effective avenue to take in computational modeling for music recommender systems. Copyright © 2019, The Authors. All rights reserved.

关键词： computation theory

SUBREGULAR NILPOTENT ORBITS AND EXPLICIT CHARACTER FORMULAS FOR MODULES OVER AFFINE LIE ALGEBRAS

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arXiv 2022年

作者： Bezrukavnikov, Roman Kac, Victor Krylov, Vasily Department of Mathematics Massachusetts Institute of Technology 77 Massachusetts Avenue CambridgeMA02139 United States National Research University Higher School of Economics Department of Mathematics 6 Usacheva st. Moscow119048 Russia

Let g be a simple finite dimensional complex Lie algebra and let bg be the corresponding affine Lie algebra. Kac and Wakimoto observed that in some cases the coefficients in the character formula for a simple highest weight bg-module are either bounded or are given by a linear function of the weight. We explain and generalize this observation using Kazhdan-Lusztig theory, by computing values at q = 1 of certain (parabolic) affine inverse Kazhdan-Lusztig polynomials. In particular, we obtain explicit character formulas for some bg-modules of negative integer level k when g is of type Dn, E6, E7, E8 and k > −2, −3, −4, −6 respectively, as conjectured by Kac and Wakimoto. The calculation relies on the explicit description of the canonical basis in the cell quotient of the anti-spherical module over the affine Hecke algebra corresponding to the subregular cell. We also present an explicit description of the corresponding objects in the derived category of equivariant coherent sheaves on the Springer resolution, they correspond to irreducible objects in the heart of a certain t-structure related to the so called non-commutative Springer resolution. Copyright © 2022, The Authors. All rights reserved.

关键词： computation theory

Efficient enumeration of subgraphs and induced subgraphs with bounded girth

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arXiv 2018年

作者： Kurita, Kazuhiro Wasa, Kunihiro Conte, Alessio Arimura, Hiroki Uno, Takeaki IST Hokkaido University Sapporo Japan National Institute of Informatics Tokyo Japan

The girth of a graph is the length of its shortest cycle. Due to its relevance in graph theory, network analysis and practical fields such as dis- tributed computing, girth-related problems have been object of attention in both past and recent literature. In this paper, we consider the problem of listing connected subgraphs with bounded girth. As a large girth is index of sparsity, this allows to extract sparse structures from the input graph. We propose two algorithms, for enumerating respectively vertex induced subgraphs and edge induced subgraphs with bounded girth, both running in O(n) amortized time per solution and using O(n3) space. Furthermore, the algorithms can be easily adapted to relax the connectivity requirement and to deal with weighted graphs. As a byproduct, the second algorithm can be used to answer the well known question of finding the densest n-vertex graph(s) of girth k. Copyright © 2018, The Authors. All rights reserved.

关键词： computation theory

MENP: An open-source MATLAB implementation of multipole expansion for applications in nanophotonics

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arXiv 2020年

作者： Hinamoto, Tatsuki Fujii, Minoru Department of Electrical and Electronic Engineering Graduate School of Engineering Kobe University Kobe657-8501 Japan

In modern nanophotonics, multipolar interference plays an indispensable role to realize novel optical devices represented by metasurfaces with unprecedented functionalities. Not only to engineer subwavelength structures that constitute such devices but also to realize and interpret unnatural phenomena in nanophotonics, a program that efficiently carries out multipole expansion is highly demanded. MENP is a MATLAB program for computation of multipole contributions to light scattering from current density distributions induced in nanophotonic resonators. The main purpose of MENP is to carry out post-processing of a rigid multipole expansion for full-field simulations which in principle provide the information of all near- and far-field interactions (e.g. as a total scattering cross section). MENP decomposes total scattering cross sections into partial ones due to electric and magnetic dipoles and higher-order terms based on recently developed exact multipole expansion formulas. We validate the program by comparing results for ideal and realistic nanospheres with those obtained with the Mie theory. We also demonstrate the potential of MENP for analysis of anapole states by calculating the multipole expansion under the long-wavelength approximation which enables us to introduce toroidal dipole moments. © 2020, CC BY.

关键词： computation theory