Institute of Mathematics AS CR, v. v. i.
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Vertex transitive graphs obtained by generalizing a left loop construction of the Hoffman-Singleton graph
No full textsummary:We construct a family of vertex transitive graphs on a left loop structure of order where is a power of a prime such that . The graphs are of diameter 2. The smallest of these graphs is isomorphic to the Hoffman--Singleton graph
A new uncertainty-aware similarity for user-based collaborative filtering
Get PDFsummary:User-based Collaborative Filtering (UBCF) is a common approach in Recommender Systems (RS). Essentially, UBCF predicts unprovided entries for the target user by selecting similar neighbors. The effectiveness of UBCF greatly depends on the selected similarity measure and the subsequent choice of neighbors. This paper presents a new Uncertainty-Aware Similarity measure "UASim" which enhances CF by accurately calculating how similar, dissimilar, and uncertain users' preferences are. Uncertainty is a key factor of "UASim" that is managed in the neighborhood selection step of CF. Extensive experimental evaluation, conducted on Flixter, Movielens-100K, and Movielens-1M datasets, indicates that "UASim" shows better performance compared to many representative predefined similarity measures. The proposed measure demonstrates enhancements across various performance indicators, namely: Mean Absolute Error (MAE), Root Mean Square Error (RMSE), coverage, and the F-score
Error estimation for finite element solutions on meshes that contain thin elements
No full textsummary:In an error estimation of finite element solutions to the Poisson equation, we usually impose the shape regularity assumption on the meshes to be used. In this paper, we show that even if the shape regularity condition is violated, the standard error estimation can be obtained if ``bad'' elements that violate the shape regularity or maximum angle condition are covered virtually by simplices that satisfy the minimum angle condition. A numerical experiment illustrates the theoretical result
Stability analysis for acoustic waveguides. Part 3: impedance boundary conditions
No full textsummary:A model two-dimensional acoustic waveguide with lateral impedance boundary conditions (and outgoing boundary conditions at the waveguide outlet) is considered. The governing operator is proved to be bounded below with a stability constant inversely proportional to the length of the waveguide. The presence of impedance boundary conditions leads to a non self-adjoint operator which considerably complicates the analysis. The goal of this paper is to elucidate these complications and tools that are applicable, as simply as possible. This work is a continuation of prior waveguide studies (where self-adjoint operators arose) by J. M. Melenk et al. (2023), and L. Demkowicz et al. (2024)
Lie algebra structure in the model of 3-link snake robot
Get PDFsummary:In this paper, we study a 5 dimensional configuration space of a 3-link snake robot model moving in a plane. We will derive two vector fields generating a distribution which represents a space of the robot’s allowable movement directions. An arbitrary choice of such generators generates the entire tangent space of the configuration space, i.e. the distribution is bracket-generating, but our choice additionally generates a finite dimensional Lie algebra over real numbers. This allows us to extend our model to a model with local Lie group structure, which may have interesting consequences for our original model
Braided coproduct, antipode and adjoint action for
Get PDFsummary:Motivated by our attempts to construct an analogue of the Dirac operator in the setting of , we write down explicitly the braided coproduct, antipode, and adjoint action for quantum algebra . The braided adjoint action is seen to coincide with the ordinary quantum adjoint action, which also follows from the general results of S. Majid
Report on the conference Paths to Mathematics
No full textsummary:Příspěvek obsahuje stručnou informaci o konání a programu konference Cesty k matematice
Adjustment of the scaling parameter of Dai-Kou type conjugate gradient methods with application to motion control
No full textsummary:We introduce a new scaling parameter for the Dai-Kou family of conjugate gradient algorithms (2013), which is one of the most numerically efficient methods for unconstrained optimization. The suggested parameter is based on eigenvalue analysis of the search direction matrix and minimizing the measure function defined by Dennis and Wolkowicz (1993). The corresponding search direction of conjugate gradient method has the sufficient descent property and the extended conjugacy condition. The global convergence of the proposed algorithm is given for both uniformly convex and general nonlinear objective functions. Also, numerical experiments on a set of test functions of the CUTER collections and the practical problem of the manipulator of robot movement control show that the proposed method is effective