On Derandomizing Local Distributed Algorithms

The gap between the known randomized and deterministic local distributed algorithms underlies arguably the most fundamental and central open question in distributed graph algorithms. In this paper, we develop a generic and clean recipe for derandomizing LOCAL algorithms. We also exhibit how this simple recipe leads to significant improvements on a number of problem. Two main results are: - An improved distributed hypergraph maximal matching algorithm, improving on Fischer, Ghaffari, and Kuhn [FOCS'17], and giving improved algorithms for edge-coloring, maximum matching approximation, and low out-degree edge orientation. The first gives an improved algorithm for Open Problem 11.4 of the book of Barenboim and Elkin, and the last gives the first positive resolution of their Open Problem 11.10. - An improved distributed algorithm for the Lov\'{a}sz Local Lemma, which gets closer to a conjecture of Chang and Pettie [FOCS'17], and moreover leads to improved distributed algorithms for problems such as defective coloring and $k$-SAT.Comment: 37 page

Coherent multi-dimensional segmentation of multiview images using a variational framework and applications to image based rendering

Image Based Rendering (IBR) and in particular light field rendering has attracted a lot of attention for interpolating new viewpoints from a set of multiview images. New images of a scene are interpolated directly from nearby available ones, thus enabling a photorealistic rendering. Sampling theory for light fields has shown that exact geometric information in the scene is often unnecessary for rendering new views. Indeed, the band of the function is approximately limited and new views can be rendered using classical interpolation methods. However, IBR using undersampled light fields suffers from aliasing effects and is difficult particularly when the scene has large depth variations and occlusions. In order to deal with these cases, we study two approaches: New sampling schemes have recently emerged that are able to perfectly reconstruct certain classes of parametric signals that are not bandlimited but characterized by a finite number of parameters. In this context, we derive novel sampling schemes for piecewise sinusoidal and polynomial signals. In particular, we show that a piecewise sinusoidal signal with arbitrarily high frequencies can be exactly recovered given certain conditions. These results are applied to parametric multiview data that are not bandlimited. We also focus on the problem of extracting regions (or layers) in multiview images that can be individually rendered free of aliasing. The problem is posed in a multidimensional variational framework using region competition. In extension to previous methods, layers are considered as multi-dimensional hypervolumes. Therefore the segmentation is done jointly over all the images and coherence is imposed throughout the data. However, instead of propagating active hypersurfaces, we derive a semi-parametric methodology that takes into account the constraints imposed by the camera setup and the occlusion ordering. The resulting framework is a global multi-dimensional region competition that is consistent in all the images and efficiently handles occlusions. We show the validity of the approach with captured light fields. Other special effects such as augmented reality and disocclusion of hidden objects are also demonstrated

Trocq: Proof Transfer for Free, With or Without Univalence

Libraries of formalized mathematics use a possibly broad range of different representations for a same mathematical concept. Yet light to major manual input from users remains most often required for obtaining the corresponding variants of theorems, when such obvious replacements are typically left implicit on paper. This article presents Trocq, a new proof transfer framework for dependent type theory. Trocq is based on a novel formulation of type equivalence, used to generalize the univalent parametricity translation. This framework takes care of avoiding dependency on the axiom of univalence when possible, and may be used with more relations than just equivalences. We have implemented a corresponding plugin for the Coq proof assistant, in the CoqElpi meta-language. We use this plugin on a gallery of representative examples of proof transfer issues in interactive theorem proving, and illustrate how Trocq covers the spectrum of several existing tools, used in program verification as well as in formalized mathematics in the broad sense

Grid generation for the solution of partial differential equations

A general survey of grid generators is presented with a concern for understanding why grids are necessary, how they are applied, and how they are generated. After an examination of the need for meshes, the overall applications setting is established with a categorization of the various connectivity patterns. This is split between structured grids and unstructured meshes. Altogether, the categorization establishes the foundation upon which grid generation techniques are developed. The two primary categories are algebraic techniques and partial differential equation techniques. These are each split into basic parts, and accordingly are individually examined in some detail. In the process, the interrelations between the various parts are accented. From the established background in the primary techniques, consideration is shifted to the topic of interactive grid generation and then to adaptive meshes. The setting for adaptivity is established with a suitable means to monitor severe solution behavior. Adaptive grids are considered first and are followed by adaptive triangular meshes. Then the consideration shifts to the temporal coupling between grid generators and PDE-solvers. To conclude, a reflection upon the discussion, herein, is given

Machine Tool Communication (MTComm) Method and Its Applications in a Cyber-Physical Manufacturing Cloud

The integration of cyber-physical systems and cloud manufacturing has the potential to revolutionize existing manufacturing systems by enabling better accessibility, agility, and efficiency. To achieve this, it is necessary to establish a communication method of manufacturing services over the Internet to access and manage physical machines from cloud applications. Most of the existing industrial automation protocols utilize Ethernet based Local Area Network (LAN) and are not designed specifically for Internet enabled data transmission. Recently MTConnect has been gaining popularity as a standard for monitoring status of machine tools through RESTful web services and an XML based messaging structure, but it is only designed for data collection and interpretation and lacks remote operation capability. This dissertation presents the design, development, optimization, and applications of a service-oriented Internet-scale communication method named Machine Tool Communication (MTComm) for exchanging manufacturing services in a Cyber-Physical Manufacturing Cloud (CPMC) to enable manufacturing with heterogeneous physically connected machine tools from geographically distributed locations over the Internet. MTComm uses an agent-adapter based architecture and a semantic ontology to provide both remote monitoring and operation capabilities through RESTful services and XML messages. MTComm was successfully used to develop and implement multi-purpose applications in in a CPMC including remote and collaborative manufacturing, active testing-based and edge-based fault diagnosis and maintenance of machine tools, cross-domain interoperability between Internet-of-things (IoT) devices and supply chain robots etc. To improve MTComm’s overall performance, efficiency, and acceptability in cyber manufacturing, the concept of MTComm’s edge-based middleware was introduced and three optimization strategies for data catching, transmission, and operation execution were developed and adopted at the edge. Finally, a hardware prototype of the middleware was implemented on a System-On-Chip based FPGA device to reduce computational and transmission latency. At every stage of its development, MTComm’s performance and feasibility were evaluated with experiments in a CPMC testbed with three different types of manufacturing machine tools. Experimental results demonstrated MTComm’s excellent feasibility for scalable cyber-physical manufacturing and superior performance over other existing approaches

Machine Tool Communication (MTComm) Method and Its Applications in a Cyber-Physical Manufacturing Cloud

The integration of cyber-physical systems and cloud manufacturing has the potential to revolutionize existing manufacturing systems by enabling better accessibility, agility, and efficiency. To achieve this, it is necessary to establish a communication method of manufacturing services over the Internet to access and manage physical machines from cloud applications. Most of the existing industrial automation protocols utilize Ethernet based Local Area Network (LAN) and are not designed specifically for Internet enabled data transmission. Recently MTConnect has been gaining popularity as a standard for monitoring status of machine tools through RESTful web services and an XML based messaging structure, but it is only designed for data collection and interpretation and lacks remote operation capability. This dissertation presents the design, development, optimization, and applications of a service-oriented Internet-scale communication method named Machine Tool Communication (MTComm) for exchanging manufacturing services in a Cyber-Physical Manufacturing Cloud (CPMC) to enable manufacturing with heterogeneous physically connected machine tools from geographically distributed locations over the Internet. MTComm uses an agent-adapter based architecture and a semantic ontology to provide both remote monitoring and operation capabilities through RESTful services and XML messages. MTComm was successfully used to develop and implement multi-purpose applications in in a CPMC including remote and collaborative manufacturing, active testing-based and edge-based fault diagnosis and maintenance of machine tools, cross-domain interoperability between Internet-of-things (IoT) devices and supply chain robots etc. To improve MTComm’s overall performance, efficiency, and acceptability in cyber manufacturing, the concept of MTComm’s edge-based middleware was introduced and three optimization strategies for data catching, transmission, and operation execution were developed and adopted at the edge. Finally, a hardware prototype of the middleware was implemented on a System-On-Chip based FPGA device to reduce computational and transmission latency. At every stage of its development, MTComm’s performance and feasibility were evaluated with experiments in a CPMC testbed with three different types of manufacturing machine tools. Experimental results demonstrated MTComm’s excellent feasibility for scalable cyber-physical manufacturing and superior performance over other existing approaches

The Caesar Problem in its Historical Context: Mathematical Background

The issues surrounding the Caesar problem are assumed to be inert as far as ongoing mathematics is concerned. This paper aims to correct this impression by spelling out the ways that, in their historical context, Frege's remarks would have had considerable resonance with work that other mathematicians such as Riemann and Dedekind were doing. The search for presentation-independent characterizations of objects and global definitions was seen as bound up with fundamental methodological questions in complex analysis and number theory.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/72188/1/j.1746-8361.2005.01029.x.pd

Multilingual representations and models for improved low-resource language processing

Word representations are the cornerstone of modern NLP. Representing words or characters using real-valued vectors as static representations that can capture the Semantics and encode the meaning has been popular among researchers. In more recent years, Pretrained Language Models using large amounts of data and creating contextualized representations achieved great performance in various tasks such as Semantic Role Labeling. These large pretrained language models are capable of storing and generalizing information and can be used as knowledge bases. Language models can produce multilingual representations while only using monolingual data during training. These multilingual representations can be beneficial in many tasks such as Machine Translation. Further, knowledge extraction models that only relied on information extracted from English resources, can now benefit from extra resources in other languages. Although these results were achieved for high-resource languages, there are thousands of languages that do not have large corpora. Moreover, for other tasks such as machine translation, if large monolingual data is not available, the models need parallel data, which is scarce for most languages. Further, many languages lack tokenization models, and splitting the text into meaningful segments such as words is not trivial. Although using subwords helps the models to have better coverage over unseen data and new words in the vocabulary, generalizing over low-resource languages with different alphabets and grammars is still a challenge. This thesis investigates methods to overcome these issues for low-resource languages. In the first publication, we explore the degree of multilinguality in multilingual pretrained language models. We demonstrate that these language models can produce high-quality word alignments without using parallel training data, which is not available for many languages. In the second paper, we extract word alignments for all available language pairs in the public bible corpus (PBC). Further, we created a tool for exploring these alignments which are especially helpful in studying low-resource languages. The third paper investigates word alignment in multiparallel corpora and exploits graph algorithms for extracting new alignment edges. In the fourth publication, we propose a new model to iteratively generate cross-lingual word embeddings and extract word alignments when only small parallel corpora are available. Lastly, the fifth paper finds that aggregation of different granularities of text can improve word alignment quality. We propose using subword sampling to produce such granularities

Quantum annealing for vehicle routing and scheduling problems

Metaheuristic approaches to solving combinatorial optimization problems have many attractions. They sidestep the issue of combinatorial explosion; they return good results; they are often conceptually simple and straight forward to implement. There are also shortcomings. Optimal solutions are not guaranteed; choosing the metaheuristic which best fits a problem is a matter of experimentation; and conceptual differences between metaheuristics make absolute comparisons of performance difficult. There is also the difficulty of configuration of the algorithm - the process of identifying precise values for the parameters which control the optimization process. Quantum annealing is a metaheuristic which is the quantum counterpart of the well known classical Simulated Annealing algorithm for combinatorial optimization problems. This research investigates the application of quantum annealing to the Vehicle Routing Problem, a difficult problem of practical significance within industries such as logistics and workforce scheduling. The work devises spin encoding schemes for routing and scheduling problem domains, enabling an effective quantum annealing algorithm which locates new solutions to widely used benchmarks. The performance of the metaheuristic is further improved by the development of an enhanced tuning approach using fitness clouds as behaviour models. The algorithm is shown to be further enhanced by taking advantage of multiprocessor environments, using threading techniques to parallelize the optimization workload. The work also shows quantum annealing applied successfully in an industrial setting to generate solutions to complex scheduling problems, results which created extra savings over an incumbent optimization technique. Components of the intellectual property rendered in this latter effort went on to secure a patent-protected status