3,103 research outputs found

    Undergraduate Catalog of Studies, 2023-2024

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    Undergraduate Catalog of Studies, 2023-2024

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    UMSL Bulletin 2023-2024

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    The 2023-2024 Bulletin and Course Catalog for the University of Missouri St. Louis.https://irl.umsl.edu/bulletin/1088/thumbnail.jp

    Algorithms and complexity for approximately counting hypergraph colourings and related problems

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    The past decade has witnessed advancements in designing efficient algorithms for approximating the number of solutions to constraint satisfaction problems (CSPs), especially in the local lemma regime. However, the phase transition for the computational tractability is not known. This thesis is dedicated to the prototypical problem of this kind of CSPs, the hypergraph colouring. Parameterised by the number of colours q, the arity of each hyperedge k, and the vertex maximum degree Ī”, this problem falls into the regime of LovĆ”sz local lemma when Ī” ā‰² qįµ. In prior, however, fast approximate counting algorithms exist when Ī” ā‰² qįµ/Ā³, and there is no known inapproximability result. In pursuit of this, our contribution is two-folded, stated as follows. ā€¢ When q, k ā‰„ 4 are evens and Ī” ā‰„ 5Ā·qįµ/Ā², approximating the number of hypergraph colourings is NP-hard. ā€¢ When the input hypergraph is linear and Ī” ā‰² qįµ/Ā², a fast approximate counting algorithm does exist

    LIPIcs, Volume 251, ITCS 2023, Complete Volume

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    LIPIcs, Volume 251, ITCS 2023, Complete Volum

    UMSL Bulletin 2022-2023

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    The 2022-2023 Bulletin and Course Catalog for the University of Missouri St. Louis.https://irl.umsl.edu/bulletin/1087/thumbnail.jp

    On the path integration system of insects: there and back again

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    Navigation is an essential capability of animate organisms and robots. Among animate organisms of particular interest are insects because they are capable of a variety of navigation competencies solving challenging problems with limited resources, thereby providing inspiration for robot navigation. Ants, bees and other insects are able to return to their nest using a navigation strategy known as path integration. During path integration, the animal maintains a running estimate of the distance and direction to its nest as it travels. This estimate, known as the `home vector', enables the animal to return to its nest. Path integration was the technique used by sea navigators to cross the open seas in the past. To perform path integration, both sailors and insects need access to two pieces of information, their direction and their speed of motion over time. Neurons encoding the heading and speed have been found to converge on a highly conserved region of the insect brain, the central complex. It is, therefore, believed that the central complex is key to the computations pertaining to path integration. However, several questions remain about the exact structure of the neuronal circuit that tracks the animal's heading, how it differs between insect species, and how the speed and direction are integrated into a home vector and maintained in memory. In this thesis, I have combined behavioural, anatomical, and physiological data with computational modelling and agent simulations to tackle these questions. Analysis of the internal compass circuit of two insect species with highly divergent ecologies, the fruit fly Drosophila melanogaster and the desert locust Schistocerca gregaria, revealed that despite 400 million years of evolutionary divergence, both species share a fundamentally common internal compass circuit that keeps track of the animal's heading. However, subtle differences in the neuronal morphologies result in distinct circuit dynamics adapted to the ecology of each species, thereby providing insights into how neural circuits evolved to accommodate species-specific behaviours. The fast-moving insects need to update their home vector memory continuously as they move, yet they can remember it for several hours. This conjunction of fast updating and long persistence of the home vector does not directly map to current short, mid, and long-term memory accounts. An extensive literature review revealed a lack of available memory models that could support the home vector memory requirements. A comparison of existing behavioural data with the homing behaviour of simulated robot agents illustrated that the prevalent hypothesis, which posits that the neural substrate of the path integration memory is a bump attractor network, is contradicted by behavioural evidence. An investigation of the type of memory utilised during path integration revealed that cold-induced anaesthesia disrupts the ability of ants to return to their nest, but it does not eliminate their ability to move in the correct homing direction. Using computational modelling and simulated agents, I argue that the best explanation for this phenomenon is not two separate memories differently affected by temperature but a shared memory that encodes both the direction and distance. The results presented in this thesis shed some more light on the labyrinth that researchers of animal navigation have been exploring in their attempts to unravel a few more rounds of Ariadne's thread back to its origin. The findings provide valuable insights into the path integration system of insects and inspiration for future memory research, advancing path integration techniques in robotics, and developing novel neuromorphic solutions to computational problems

    The success probability in Levine's hat problem, and independent sets in graphs

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    Lionel Levine's hat challenge has tt players, each with a (very large, or infinite) stack of hats on their head, each hat independently colored at random black or white. The players are allowed to coordinate before the random colors are chosen, but not after. Each player sees all hats except for those on her own head. They then proceed to simultaneously try and each pick a black hat from their respective stacks. They are proclaimed successful only if they are all correct. Levine's conjecture is that the success probability tends to zero when the number of players grows. We prove that this success probability is strictly decreasing in the number of players, and present some connections to problems in graph theory: relating the size of the largest independent set in a graph and in a random induced subgraph of it, and bounding the size of a set of vertices intersecting every maximum-size independent set in a graph.Comment: arXiv admin note: substantial text overlap with arXiv:2103.01541, arXiv:2103.0599

    Undergraduate Catalog of Studies, 2022-2023

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    Precision Studies of QCD in the Low Energy Domain of the EIC

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    The manuscript focuses on the high impact science of the EIC with objective to identify a portion of the science program for QCD precision studies that requires or greatly benefits from high luminosity and low center-of-mass energies. The science topics include (1) Generalized Parton Distributions, 3D imagining and mechanical properties of the nucleon (2) mass and spin of the nucleon (3) Momentum dependence of the nucleon in semi-inclusive deep inelastic scattering (4) Exotic meson spectroscopy (5) Science highlights of nuclei (6) Precision studies of Lattice QCD in the EIC era (7) Science of far-forward particle detection (8) Radiative effects and corrections (9) Artificial Intelligence (10) EIC interaction regions for high impact science program with discovery potential. This paper documents the scientific basis for supporting such a program and helps to define the path toward the realization of the second EIC interaction region.Comment: 103 pages,47 figure
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