Fugledge-Kadison-determinant entropy formulas and isomorphisms of lattice models

Diese Diplomarbeit behandelt die Entropien der folgenden Modelle im thermodynamischen Limes: Spanning Trees und der damit verbundene Essential Spanning Forest Prozess, Dimer Überdeckungen, das Abelsche Sandhäufchen Modell und das Harmonische Modell. Diese Modelle aus verschiedenen Disziplinen der Mathematik können als dynamische Systeme oder als Beispiele aus der statistischen Mechanik interpretiert werden. Methoden aus der Operatoren Theorie und der harmonischen Analysis werden zur Darstellung der Entropie als Logarithmus der Fuglede-Kadison Determinante verwendet, wobei die Fuglede-Kadison Determinante ursprünglich für Operatoren in einem Faktor vom Typ II_1 eingeführt wurde. Ähnliche Methoden werden zur Berechnung der Entropie von expansiven Wirkungen von diskreten, residuell-endlichen, mittelbaren Gruppen durch Automorphismen von kompakten, abelschen Gruppen verwendet; wobei diese Wirkungen auch in einem eigenen Kapitel beschrieben werden.This thesis studies entropies of the following models in the thermodynamic limit: spanning trees and the associated essential spanning forest process, dimer covers, the abelian sandpile model and the harmonic model. These models arise from various fields in mathematics, but all of them can be interpreted as dynamical systems in higher dimensions and as examples from statistical mechanics. Tools of operator theory and harmonic analysis will be used to express entropy as logarithm of the Fuglede-Kadison determinant, which was originally defined on operators in a factor of type II_1. Similar methods (although in a more algebraic setting) will be used to calculate the entropy of expansive actions of discrete residually finite amenable groups by automorphisms of compact abelian groups

Self-Evaluation Applied Mathematics 2003-2008 University of Twente

This report contains the self-study for the research assessment of the Department of Applied Mathematics (AM) of the Faculty of Electrical Engineering, Mathematics and Computer Science (EEMCS) at the University of Twente (UT). The report provides the information for the Research Assessment Committee for Applied Mathematics, dealing with mathematical sciences at the three universities of technology in the Netherlands. It describes the state of affairs pertaining to the period 1 January 2003 to 31 December 2008

Foundations of Software Science and Computation Structures

This open access book constitutes the proceedings of the 22nd International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2019, which took place in Prague, Czech Republic, in April 2019, held as part of the European Joint Conference on Theory and Practice of Software, ETAPS 2019. The 29 papers presented in this volume were carefully reviewed and selected from 85 submissions. They deal with foundational research with a clear significance for software science

Similarity, Retrieval, and Classification of Motion Capture Data

Three-dimensional motion capture data is a digital representation of the complex spatio-temporal structure of human motion. Mocap data is widely used for the synthesis of realistic computer-generated characters in data-driven computer animation and also plays an important role in motion analysis tasks such as activity recognition. Both for efficiency and cost reasons, methods for the reuse of large collections of motion clips are gaining in importance in the field of computer animation. Here, an active field of research is the application of morphing and blending techniques for the creation of new, realistic motions from prerecorded motion clips. This requires the identification and extraction of logically related motions scattered within some data set. Such content-based retrieval of motion capture data, which is a central topic of this thesis, constitutes a difficult problem due to possible spatio-temporal deformations between logically related motions. Recent approaches to motion retrieval apply techniques such as dynamic time warping, which, however, are not applicable to large data sets due to their quadratic space and time complexity. In our approach, we introduce various kinds of relational features describing boolean geometric relations between specified body points and show how these features induce a temporal segmentation of motion capture data streams. By incorporating spatio-temporal invariance into the relational features and induced segments, we are able to adopt indexing methods allowing for flexible and efficient content-based retrieval in large motion capture databases. As a further application of relational motion features, a new method for fully automatic motion classification and retrieval is presented. We introduce the concept of motion templates (MTs), by which the spatio-temporal characteristics of an entire motion class can be learned from training data, yielding an explicit, compact matrix representation. The resulting class MT has a direct, semantic interpretation, and it can be manually edited, mixed, combined with other MTs, extended, and restricted. Furthermore, a class MT exhibits the characteristic as well as the variational aspects of the underlying motion class at a semantically high level. Classification is then performed by comparing a set of precomputed class MTs with unknown motion data and labeling matching portions with the respective motion class label. Here, the crucial point is that the variational (hence uncharacteristic) motion aspects encoded in the class MT are automatically masked out in the comparison, which can be thought of as locally adaptive feature selection

Collected Papers (on various scientific topics), Volume XIII

This thirteenth volume of Collected Papers is an eclectic tome of 88 papers in various fields of sciences, such as astronomy, biology, calculus, economics, education and administration, game theory, geometry, graph theory, information fusion, decision making, instantaneous physics, quantum physics, neutrosophic logic and set, non-Euclidean geometry, number theory, paradoxes, philosophy of science, scientific research methods, statistics, and others, structured in 17 chapters (Neutrosophic Theory and Applications; Neutrosophic Algebra; Fuzzy Soft Sets; Neutrosophic Sets; Hypersoft Sets; Neutrosophic Semigroups; Neutrosophic Graphs; Superhypergraphs; Plithogeny; Information Fusion; Statistics; Decision Making; Extenics; Instantaneous Physics; Paradoxism; Mathematica; Miscellanea), comprising 965 pages, published between 2005-2022 in different scientific journals, by the author alone or in collaboration with the following 110 co-authors (alphabetically ordered) from 26 countries: Abduallah Gamal, Sania Afzal, Firoz Ahmad, Muhammad Akram, Sheriful Alam, Ali Hamza, Ali H. M. Al-Obaidi, Madeleine Al-Tahan, Assia Bakali, Atiqe Ur Rahman, Sukanto Bhattacharya, Bilal Hadjadji, Robert N. Boyd, Willem K.M. Brauers, Umit Cali, Youcef Chibani, Victor Christianto, Chunxin Bo, Shyamal Dalapati, Mario Dalcín, Arup Kumar Das, Elham Davneshvar, Bijan Davvaz, Irfan Deli, Muhammet Deveci, Mamouni Dhar, R. Dhavaseelan, Balasubramanian Elavarasan, Sara Farooq, Haipeng Wang, Ugur Halden, Le Hoang Son, Hongnian Yu, Qays Hatem Imran, Mayas Ismail, Saeid Jafari, Jun Ye, Ilanthenral Kandasamy, W.B. Vasantha Kandasamy, Darjan Karabašević, Abdullah Kargın, Vasilios N. Katsikis, Nour Eldeen M. Khalifa, Madad Khan, M. Khoshnevisan, Tapan Kumar Roy, Pinaki Majumdar, Sreepurna Malakar, Masoud Ghods, Minghao Hu, Mingming Chen, Mohamed Abdel-Basset, Mohamed Talea, Mohammad Hamidi, Mohamed Loey, Mihnea Alexandru Moisescu, Muhammad Ihsan, Muhammad Saeed, Muhammad Shabir, Mumtaz Ali, Muzzamal Sitara, Nassim Abbas, Munazza Naz, Giorgio Nordo, Mani Parimala, Ion Pătrașcu, Gabrijela Popović, K. Porselvi, Surapati Pramanik, D. Preethi, Qiang Guo, Riad K. Al-Hamido, Zahra Rostami, Said Broumi, Saima Anis, Muzafer Saračević, Ganeshsree Selvachandran, Selvaraj Ganesan, Shammya Shananda Saha, Marayanagaraj Shanmugapriya, Songtao Shao, Sori Tjandrah Simbolon, Florentin Smarandache, Predrag S. Stanimirović, Dragiša Stanujkić, Raman Sundareswaran, Mehmet Șahin, Ovidiu-Ilie Șandru, Abdulkadir Șengür, Mohamed Talea, Ferhat Taș, Selçuk Topal, Alptekin Ulutaș, Ramalingam Udhayakumar, Yunita Umniyati, J. Vimala, Luige Vlădăreanu, Ştefan Vlăduţescu, Yaman Akbulut, Yanhui Guo, Yong Deng, You He, Young Bae Jun, Wangtao Yuan, Rong Xia, Xiaohong Zhang, Edmundas Kazimieras Zavadskas, Zayen Azzouz Omar, Xiaohong Zhang, Zhirou Ma.‬‬‬‬‬‬‬