Efficient reconfiguration algorithms of de Bruijn and Kautz networks into linear arrays

AbstractIn this paper, we prove the existence of ranking and unranking algorithms on d-ary de Bruijn and Kautz graphs. A ranking algorithm takes as input the label of a node and returns the rank r of that node in a hamiltonian path (0⩽r⩽N−1, where N is the order of the considered graph). An unranking algorithm takes as input an integer r (0⩽r⩽N−1) and returns the label of the rth ranked node in a hamiltonian path. Our results generalize results given by Annexstein for binary de Bruijn graphs. The key of our framework is based on a recursive construction of hamiltonian paths in de Bruijn and Kautz graphs. The construction uses suitable uniform homomorphisms of de Bruijn and Kautz graphs of diameter D on de Bruijn graphs of diameter D−1. Our ranking and unranking algorithms have sequential time complexity in O(D2), where D is the length of node labels

Approximate inference on graphical models: message-passing, loop-corrected methods and applications

L'abstract è presente nell'allegato / the abstract is in the attachmen

Aspects of practical implementations of PRAM algorithms

The PRAM is a shared memory model of parallel computation which abstracts away from inessential engineering details. It provides a very simple architecture independent model and provides a good programming environment. Theoreticians of the computer science community have proved that it is possible to emulate the theoretical PRAM model using current technology. Solutions have been found for effectively interconnecting processing elements, for routing data on these networks and for distributing the data among memory modules without hotspots. This thesis reviews this emulation and the possibilities it provides for large scale general purpose parallel computation. The emulation employs a bridging model which acts as an interface between the actual hardware and the PRAM model. We review the evidence that such a scheme crn achieve scalable parallel performance and portable parallel software and that PRAM algorithms can be optimally implemented on such practical models. In the course of this review we presented the following new results: 1. Concerning parallel approximation algorithms, we describe an NC algorithm for finding an approximation to a minimum weight perfect matching in a complete weighted graph. The algorithm is conceptually very simple and it is also the first NC-approximation algorithm for the task with a sub-linear performance ratio. 2. Concerning graph embedding, we describe dense edge-disjoint embeddings of the complete binary tree with n leaves in the following n-node communication networks: the hypercube, the de Bruijn and shuffle-exchange networks and the 2-dimcnsional mesh. In the embeddings the maximum distance from a leaf to the root of the tree is asymptotically optimally short. The embeddings facilitate efficient implementation of many PRAM algorithms on networks employing these graphs as interconnection networks. 3. Concerning bulk synchronous algorithmics, we describe scalable transportable algorithms for the following three commonly required types of computation; balanced tree computations. Fast Fourier Transforms and matrix multiplications

Field theoretic formulation and empirical tracking of spatial processes

Spatial processes are attacked on two fronts. On the one hand, tools from theoretical and statistical physics can be used to understand behaviour in complex, spatially-extended multi-body systems. On the other hand, computer vision and statistical analysis can be used to study 4D microscopy data to observe and understand real spatial processes in vivo. On the rst of these fronts, analytical models are developed for abstract processes, which can be simulated on graphs and lattices before considering real-world applications in elds such as biology, epidemiology or ecology. In the eld theoretic formulation of spatial processes, techniques originating in quantum eld theory such as canonical quantisation and the renormalization group are applied to reaction-di usion processes by analogy. These techniques are combined in the study of critical phenomena or critical dynamics. At this level, one is often interested in the scaling behaviour; how the correlation functions scale for di erent dimensions in geometric space. This can lead to a better understanding of how macroscopic patterns relate to microscopic interactions. In this vein, the trace of a branching random walk on various graphs is studied. In the thesis, a distinctly abstract approach is emphasised in order to support an algorithmic approach to parts of the formalism. A model of self-organised criticality, the Abelian sandpile model, is also considered. By exploiting a bijection between recurrent con gurations and spanning trees, an e cient Monte Carlo algorithm is developed to simulate sandpile processes on large lattices. On the second front, two case studies are considered; migratory patterns of leukaemia cells and mitotic events in Arabidopsis roots. In the rst case, tools from statistical physics are used to study the spatial dynamics of di erent leukaemia cell lineages before and after a treatment. One key result is that we can discriminate between migratory patterns in response to treatment, classifying cell motility in terms of sup/super/di usive regimes. For the second case study, a novel algorithm is developed to processes a 4D light-sheet microscopy dataset. The combination of transient uorescent markers and a poorly localised specimen in the eld of view leads to a challenging tracking problem. A fuzzy registration-tracking algorithm is developed to track mitotic events so as to understand their spatiotemporal dynamics under normal conditions and after tissue damage.Open Acces

組合せ最適化問題のための測定フィードバック型コヒーレント・イジングマシンの実現と評価

学位の種別: 課程博士審査委員会委員 : （主査）東京大学教授 合原 一幸, 東京大学教授 岩田 覚, 東京大学准教授 平田 祥人, 東京大学准教授 大西 立顕, 東京大学准教授 鈴木 大慈University of Tokyo(東京大学

Report / Institute für Physik

The 2014 Report of the Physics Institutes of the Universität Leipzig presents a hopefully interesting overview of our research activities in the past year. It is also testimony of our scientific interaction with colleagues and partners worldwide. We are grateful to our guests for enriching our academic year with their contributions in the colloquium and within the work groups. The open full professorship in the Institute for Experimental Physics I has been filled with an outstanding candidate. We could attract Prof. Ralf Seidel from the University of Münster. He is an expert in molecular biophysics that complements the existing strength in cellular biophysics. Prof. Hollands could fill all positions of his ERC Starting Grant, so that the work on the project \"Quantum Fields and Curvature – Novel Constructive Approach via Operator Product Expansion\" is now running at full pace. Within the Horizon 2020 project LOMID \"Large Cost-effective OLED Microdisplays and their Applications\" (2015-2017) with eight European partners including industry the semiconductor physics group contributes with transparent oxide devices. A joint laboratory for single ion implantation was established between the Leibniz-Institute for Surface Modification (IOM) and the university under the guidance of Profs. Rauschenbach and Meijer. The EU IRSES Network DIONICOS \"Dynamics of and in Complex Systems\", a consortium of 6 European and 12 non-European partners, including sites in England, France and Germany as well as in Russia, Ukraine, India, the United States and Venezuela, started in February 2014. In the next four years the Leipzig node headed by Prof. Janke will profit from the numerous international contacts this network provides. With a joint project, Prof. Kroy and Prof. Cichos participate in the newly established priority research programme SPP 1726 \"Microswimmers\", which started with a kick-off workshop in October 2014. In 2014 the International Graduate College \"Statistical Physics of Complex Systems\" run by the computational physics group has commenced its third 3-years granting period funded by Deutsch-Französische Hochschule (DFH-UFA). Besides the main partner Université de Lorraine in Nancy, France, now also Coventry University, UK, and the Institute for Condensed Matter Physis of the National Academy of Sciences of Ukraine in Lviv, Ukraine, participate as associated partners. During the last week of September the TCO2014 conference \"Transparent Conductive Oxides – Fundamentals and Applications\" took place in honor of the 100th anniversary of the death of Prof. Dr. KarlW. Bädeker. In 1907 Karl Bädeker had discovered transparent conductive materials and oxides in Leipzig. About a hundred participants joined for many invited talks from international experts, intense discussion and new cooperations. At the end of November the by now traditional 15th nternational Workshop on Recent Developments in Computational Physics \"CompPhys14\" organized by Prof. Janke took place in Leipzig. Around 60 scientists from over 10 different countries exchanged ideas and discussed recent progress in several fields of computational physics. Work has successfully continued in the Centers of Excellence (Sonderforschungsbereiche) SFB 762 \"Functionality ofOxide Interfaces\" and SFB TRR 102 \"Polymers under Multiple Constraints: Restricted and Controlled Molecular Order and Mobility\" (just renewed for 2015-2019). Our activities and success are only possible with the generous support fromvarious funding agencies for which we are very grateful and which is individually acknowledged in the brief reports

LIPIcs, Volume 251, ITCS 2023, Complete Volume

LIPIcs, Volume 251, ITCS 2023, Complete Volum

Report / Institute für Physik

The 2014 Report of the Physics Institutes of the Universität Leipzig presents a hopefully interesting overview of our research activities in the past year. It is also testimony of our scientific interaction with colleagues and partners worldwide. We are grateful to our guests for enriching our academic year with their contributions in the colloquium and within the work groups. The open full professorship in the Institute for Experimental Physics I has been filled with an outstanding candidate. We could attract Prof. Ralf Seidel from the University of Münster. He is an expert in molecular biophysics that complements the existing strength in cellular biophysics. Prof. Hollands could fill all positions of his ERC Starting Grant, so that the work on the project \"Quantum Fields and Curvature – Novel Constructive Approach via Operator Product Expansion\" is now running at full pace. Within the Horizon 2020 project LOMID \"Large Cost-effective OLED Microdisplays and their Applications\" (2015-2017) with eight European partners including industry the semiconductor physics group contributes with transparent oxide devices. A joint laboratory for single ion implantation was established between the Leibniz-Institute for Surface Modification (IOM) and the university under the guidance of Profs. Rauschenbach and Meijer. The EU IRSES Network DIONICOS \"Dynamics of and in Complex Systems\", a consortium of 6 European and 12 non-European partners, including sites in England, France and Germany as well as in Russia, Ukraine, India, the United States and Venezuela, started in February 2014. In the next four years the Leipzig node headed by Prof. Janke will profit from the numerous international contacts this network provides. With a joint project, Prof. Kroy and Prof. Cichos participate in the newly established priority research programme SPP 1726 \"Microswimmers\", which started with a kick-off workshop in October 2014. In 2014 the International Graduate College \"Statistical Physics of Complex Systems\" run by the computational physics group has commenced its third 3-years granting period funded by Deutsch-Französische Hochschule (DFH-UFA). Besides the main partner Université de Lorraine in Nancy, France, now also Coventry University, UK, and the Institute for Condensed Matter Physis of the National Academy of Sciences of Ukraine in Lviv, Ukraine, participate as associated partners. During the last week of September the TCO2014 conference \"Transparent Conductive Oxides – Fundamentals and Applications\" took place in honor of the 100th anniversary of the death of Prof. Dr. KarlW. Bädeker. In 1907 Karl Bädeker had discovered transparent conductive materials and oxides in Leipzig. About a hundred participants joined for many invited talks from international experts, intense discussion and new cooperations. At the end of November the by now traditional 15th nternational Workshop on Recent Developments in Computational Physics \"CompPhys14\" organized by Prof. Janke took place in Leipzig. Around 60 scientists from over 10 different countries exchanged ideas and discussed recent progress in several fields of computational physics. Work has successfully continued in the Centers of Excellence (Sonderforschungsbereiche) SFB 762 \"Functionality ofOxide Interfaces\" and SFB TRR 102 \"Polymers under Multiple Constraints: Restricted and Controlled Molecular Order and Mobility\" (just renewed for 2015-2019). Our activities and success are only possible with the generous support fromvarious funding agencies for which we are very grateful and which is individually acknowledged in the brief reports