IA Scholar Query: Equicardinality on Linear Orders.
https://scholar.archive.org/
Internet Archive Scholar query results feedeninfo@archive.orgThu, 25 Aug 2022 00:00:00 GMTfatcat-scholarhttps://scholar.archive.org/help1440Approximation of Images via Generalized Higher Order Singular Value Decomposition over Finite-dimensional Commutative Semisimple Algebra
https://scholar.archive.org/work/xmdmzp6lhbd5hi6o3yfj72cyla
Low-rank approximation of images via singular value decomposition is well-received in the era of big data. However, singular value decomposition (SVD) is only for order-two data, i.e., matrices. It is necessary to flatten a higher order input into a matrix or break it into a series of order-two slices to tackle higher order data such as multispectral images and videos with the SVD. Higher order singular value decomposition (HOSVD) extends the SVD and can approximate higher order data using sums of a few rank-one components. We consider the problem of generalizing HOSVD over a finite dimensional commutative algebra. This algebra, referred to as a t-algebra, generalizes the field of complex numbers. The elements of the algebra, called t-scalars, are fix-sized arrays of complex numbers. One can generalize matrices and tensors over t-scalars and then extend many canonical matrix and tensor algorithms, including HOSVD, to obtain higher-performance versions. The generalization of HOSVD is called THOSVD. Its performance of approximating multi-way data can be further improved by an alternating algorithm. THOSVD also unifies a wide range of principal component analysis algorithms. To exploit the potential of generalized algorithms using t-scalars for approximating images, we use a pixel neighborhood strategy to convert each pixel to "deeper-order" t-scalar. Experiments on publicly available images show that the generalized algorithm over t-scalars, namely THOSVD, compares favorably with its canonical counterparts.Liang Liao, Sen Lin, Lun Li, Xiuwei Zhang, Song Zhao, Yan Wang, Xinqiang Wang, Qi Gao, Jingyu Wangwork_xmdmzp6lhbd5hi6o3yfj72cylaThu, 25 Aug 2022 00:00:00 GMTGeneralized permutahedra and positive flag Dressians
https://scholar.archive.org/work/xgzqlczjrjhmho5oevr5foprkq
We study valuated matroids, their tropical incidence relations, flag matroids and total positivity. This leads to a characterization of permutahedral subdivisions, namely subdivisions of regular permutahedra into generalized permutahedra. Further, we get a characterization of those subdivisions arising from positive valuated flag matroids.Michael Joswig, Georg Loho, Dante Luber, Jorge Alberto Olartework_xgzqlczjrjhmho5oevr5foprkqTue, 07 Jun 2022 00:00:00 GMTA Note on the Critical Groups of Strongly Regular Graphs and Their Generalizations
https://scholar.archive.org/work/jxe3sv36gbf2jje343bqt2xnke
We determine the maximum order of an element in the critical group of a strongly regular graph, and show that it achieves the spectral bound due to Lorenzini. We extend the result to all graphs with exactly two non-zero Laplacian eigenvalues, and study the signed graph version of the problem. We also study the monodromy pairing on the critical groups, and suggest an approach to study the structure of these groups using the pairing.Kenneth Hung, Chi Ho Yuenwork_jxe3sv36gbf2jje343bqt2xnkeWed, 25 May 2022 00:00:00 GMTQuality versus speed in energy demand prediction for district heating systems
https://scholar.archive.org/work/a2chwufxovfnzorhwqm4icwmgi
In this paper, we consider energy demand prediction in district heating systems. Effective energy demand prediction is essential in combined heat power systems when offering electrical energy in competitive electricity markets. To address this problem, we propose two sets of algorithms: (1) a novel extension to the algorithm proposed by E. Dotzauer and (2) an autoregressive predictor based on hour-of-week adjusted linear regression on moving averages of energy consumption. These two methods are compared against state-of-the-art artificial neural networks. Energy demand predictor algorithms have various computational costs and prediction quality. While prediction quality is a widely used measure of predictor superiority, computational costs are less frequently analyzed and their impact is not so extensively studied. When predictor algorithms are constantly updated using new data, some computationally expensive forecasting methods may become inapplicable. The computational costs can be split into training and execution parts. The execution part is the cost paid when the already trained algorithm is applied to predict something. In this paper, we evaluate the above methods with respect to the quality and computational costs, both in the training and in the execution. The comparison is conducted on a real-world dataset from a district heating system in the northwest part of Poland.Witold Andrzejewski and Jedrzej Potoniec and Maciej Drozdowski and Jerzy Stefanowski and Robert Wrembel and Paweł Stapfwork_a2chwufxovfnzorhwqm4icwmgiTue, 10 May 2022 00:00:00 GMTGraphs with $G^p$-connected medians
https://scholar.archive.org/work/lbmthrl36vcytkfokbaitlgtry
The median of a graph $G$ with weighted vertices is the set of all vertices $x$ minimizing the sum of weighted distances from $x$ to the vertices of $G$. For any integer $p\ge 2$, we characterize the graphs in which, with respect to any non-negative weights, median sets always induce connected subgraphs in the $p$th power $G^p$ of $G$. This extends some characterizations of graphs with connected medians (case $p=1$) provided by Bandelt and Chepoi (2002). The characteristic conditions can be tested in polynomial time for any $p$. We also show that several important classes of graphs in metric graph theory, including bridged graphs (and thus chordal graphs), graphs with convex balls, bucolic graphs, and bipartite absolute retracts, have $G^2$-connected medians. Extending the result of Bandelt and Chepoi that basis graphs of matroids are graphs with connected medians, we characterize the isometric subgraphs of Johnson graphs and of halved-cubes with connected medians.Laurine Bénéteau, Jérémie Chalopin, Victor Chepoi, Yann Vaxèswork_lbmthrl36vcytkfokbaitlgtrySat, 01 Jan 2022 00:00:00 GMTCycle structure and colorings of directed graphs
https://scholar.archive.org/work/4oljppo7pnh3vlrxkkkho6zd4m
This thesis deals with problems from the theory of finite directed graphs. A directed graph (digraph for short) is a binary relation whose domain has finite size. With that digraphs can be seen as a very general way of representing (possibly asymmetric) relations between pairs from a finite set of objects. Undoubtedly, such a generality allows to encode many structures by digraphs. This works particularly well if important properties of the structure at hand can be expressed as relations or connections between objects. To give some selected examples, let us mention road networks, electricity networks, radio networks, the world wide web, circuits in electronic devices, or neural networks. A main focus of the thesis at hand is the investigation of properties of one of the most fundamental objects all over graph theory, the so-called cycle (sometimes also called circuit). A cycle in a graph is determined by a closed alternating sequence of cyclically connected vertices and edges. In a graph of finite size one will typically see loads of distinct cycles of various types. Therefore cycles constitute an important and recurring motive in almost all branches of graph theory, for instance, they play important roles in structural graph theory, in the theory of flows on directed networks, in theoretical characterizations of graph classes, as well as in the theory of graph colorings. Additionally, cycles play a decisive role in numerous algorithmic problems and their solutions, such as in the Traveling Salesman Problem, algorithms for finding a largest matching in a given graph, in the max-flow problem, and also in subprocedures such as Kruskal's algorithm for finding a minimum weight spanning tree. For those reasons, a substantial amount of research in graph theory has specialised on the structure of cycles in graphs. In the first major part of this thesis we deal with cycles which occur in directed graphs, and prove several necessary and sufficient theoretical conditions for the existence of cycles of certain types. Additi [...]Raphael Mario Steiner, Technische Universität Berlin, Stefan Felsnerwork_4oljppo7pnh3vlrxkkkho6zd4mThu, 30 Dec 2021 00:00:00 GMT