6,339 research outputs found

    Symmetries of Riemann surfaces and magnetic monopoles

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    This thesis studies, broadly, the role of symmetry in elucidating structure. In particular, I investigate the role that automorphisms of algebraic curves play in three specific contexts; determining the orbits of theta characteristics, influencing the geometry of the highly-symmetric Bring’s curve, and in constructing magnetic monopole solutions. On theta characteristics, I show how to turn questions on the existence of invariant characteristics into questions of group cohomology, compute comprehensive tables of orbit decompositions for curves of genus 9 or less, and prove results on the existence of infinite families of curves with invariant characteristics. On Bring’s curve, I identify key points with geometric significance on the curve, completely determine the structure of the quotients by subgroups of automorphisms, finding new elliptic curves in the process, and identify the unique invariant theta characteristic on the curve. With respect to monopoles, I elucidate the role that the Hitchin conditions play in determining monopole spectral curves, the relation between these conditions and the automorphism group of the curve, and I develop the theory of computing Nahm data of symmetric monopoles. As such I classify all 3-monopoles whose Nahm data may be solved for in terms of elliptic functions

    Composition and Cobordism Maps

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    We study the relationship between the algebra of module homomorphisms under composition and 4-dimensional cobordisms in the context of bordered Heegaard Floer homology. In particular, we prove that composition of module homomorphisms of type-DD structures induces the pair of pants cobordism map on Heegaard Floer homology in the morphism spaces formulation of the latter, due to Lipshitz--Ozsv\'{a}th--Thurston. Along the way, we prove a gluing result for cornered 4-manifolds constructed from bordered Heegaard triples. As applications, we present a new algorithm for computing arbitrary cobordism maps on Heegaard Floer homology and construct new nontrivial AA_\infty-deformations of Khovanov's arc algebras. Motivated by this last result and a K\"{u}nneth theorem for Heegaard Floer complexes of connected sums, we also prove the existence of a tensor product decomposition for arc algebras in characteristic 2 and show that there cannot be such a splitting over Z\Z

    Exact steady states of minimal models of nonequilibrium statistical mechanics

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    Systems out of equilibrium with their environment are ubiquitous in nature. Of particular relevance to biological applications are models in which each microscopic component spontaneously generates its own motion. Known collectively as active matter, such models are natural effective descriptions of many biological systems, from subcellular motors to flocks of birds. One would like to understand such phenomena using the tools of statistical mechanics, yet the inherent nonequilibrium setting means that the most powerful classical results of that field cannot be applied. This circumstance has fuelled interest in exactly solvable models of active matter. The aim in studying such models is twofold. Firstly, as exactly solvable model are often minimal, it makes them good candidates as generic coarse-grained descriptions of real-world processes. Secondly, even if the model in question does not correspond directly to some situation realizable in experiment, its exact solution may suggest some general principles, which could also apply to more complex phenomena. A typical tool to investigate the properties of a large system is to study the behaviour of a probe particle placed in such an environment. In this context, cases of interest are both an active particle in a passive environment or an active particle in an active environment. One model that has attracted much attention in this regard is the asymmetric simple exclusion process (ASEP), which is a prototypical minimal model of driven diffusive transport. In this thesis, I consider two variations of the ASEP on a ring geometry. The first is a system of symmetrically diffusing particles with one totally asymmetric (driven) defect particle. The second is a system of partially asymmetric particles, with one defect that may overtake the other particles. I analyze the steady states of these systems using two exact methods: the matrix product ansatz, and, for the second model the Bethe ansatz. This allows me to derive the exact density profiles and mean currents for these models, and, for the second model, the diffusion constant. Moreover, I use the Yang-Baxter formalism to study the general class of two-species partially asymmetric processes with overtaking. This allows me to determine conditions under which such models can be solved using the Bethe ansatz

    Authentication enhancement in command and control networks: (a study in Vehicular Ad-Hoc Networks)

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    Intelligent transportation systems contribute to improved traffic safety by facilitating real time communication between vehicles. By using wireless channels for communication, vehicular networks are susceptible to a wide range of attacks, such as impersonation, modification, and replay. In this context, securing data exchange between intercommunicating terminals, e.g., vehicle-to-everything (V2X) communication, constitutes a technological challenge that needs to be addressed. Hence, message authentication is crucial to safeguard vehicular ad-hoc networks (VANETs) from malicious attacks. The current state-of-the-art for authentication in VANETs relies on conventional cryptographic primitives, introducing significant computation and communication overheads. In this challenging scenario, physical (PHY)-layer authentication has gained popularity, which involves leveraging the inherent characteristics of wireless channels and the hardware imperfections to discriminate between wireless devices. However, PHY-layerbased authentication cannot be an alternative to crypto-based methods as the initial legitimacy detection must be conducted using cryptographic methods to extract the communicating terminal secret features. Nevertheless, it can be a promising complementary solution for the reauthentication problem in VANETs, introducing what is known as “cross-layer authentication.” This thesis focuses on designing efficient cross-layer authentication schemes for VANETs, reducing the communication and computation overheads associated with transmitting and verifying a crypto-based signature for each transmission. The following provides an overview of the proposed methodologies employed in various contributions presented in this thesis. 1. The first cross-layer authentication scheme: A four-step process represents this approach: initial crypto-based authentication, shared key extraction, re-authentication via a PHY challenge-response algorithm, and adaptive adjustments based on channel conditions. Simulation results validate its efficacy, especially in low signal-to-noise ratio (SNR) scenarios while proving its resilience against active and passive attacks. 2. The second cross-layer authentication scheme: Leveraging the spatially and temporally correlated wireless channel features, this scheme extracts high entropy shared keys that can be used to create dynamic PHY-layer signatures for authentication. A 3-Dimensional (3D) scattering Doppler emulator is designed to investigate the scheme’s performance at different speeds of a moving vehicle and SNRs. Theoretical and hardware implementation analyses prove the scheme’s capability to support high detection probability for an acceptable false alarm value ≤ 0.1 at SNR ≥ 0 dB and speed ≤ 45 m/s. 3. The third proposal: Reconfigurable intelligent surfaces (RIS) integration for improved authentication: Focusing on enhancing PHY-layer re-authentication, this proposal explores integrating RIS technology to improve SNR directed at designated vehicles. Theoretical analysis and practical implementation of the proposed scheme are conducted using a 1-bit RIS, consisting of 64 × 64 reflective units. Experimental results show a significant improvement in the Pd, increasing from 0.82 to 0.96 at SNR = − 6 dB for multicarrier communications. 4. The fourth proposal: RIS-enhanced vehicular communication security: Tailored for challenging SNR in non-line-of-sight (NLoS) scenarios, this proposal optimises key extraction and defends against denial-of-service (DoS) attacks through selective signal strengthening. Hardware implementation studies prove its effectiveness, showcasing improved key extraction performance and resilience against potential threats. 5. The fifth cross-layer authentication scheme: Integrating PKI-based initial legitimacy detection and blockchain-based reconciliation techniques, this scheme ensures secure data exchange. Rigorous security analyses and performance evaluations using network simulators and computation metrics showcase its effectiveness, ensuring its resistance against common attacks and time efficiency in message verification. 6. The final proposal: Group key distribution: Employing smart contract-based blockchain technology alongside PKI-based authentication, this proposal distributes group session keys securely. Its lightweight symmetric key cryptography-based method maintains privacy in VANETs, validated via Ethereum’s main network (MainNet) and comprehensive computation and communication evaluations. The analysis shows that the proposed methods yield a noteworthy reduction, approximately ranging from 70% to 99%, in both computation and communication overheads, as compared to the conventional approaches. This reduction pertains to the verification and transmission of 1000 messages in total

    The infrared structure of perturbative gauge theories

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    Infrared divergences in the perturbative expansion of gauge theory amplitudes and cross sections have been a focus of theoretical investigations for almost a century. New insights still continue to emerge, as higher perturbative orders are explored, and high-precision phenomenological applications demand an ever more refined understanding. This review aims to provide a pedagogical overview of the subject. We briefly cover some of the early historical results, we provide some simple examples of low-order applications in the context of perturbative QCD, and discuss the necessary tools to extend these results to all perturbative orders. Finally, we describe recent developments concerning the calculation of soft anomalous dimensions in multi-particle scattering amplitudes at high orders, and we provide a brief introduction to the very active field of infrared subtraction for the calculation of differential distributions at colliders. © 2022 Elsevier B.V

    LIPIcs, Volume 251, ITCS 2023, Complete Volume

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    LIPIcs, Volume 251, ITCS 2023, Complete Volum

    Revisiting the capitalization of public transport accessibility into residential land value: an empirical analysis drawing on Open Science

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    Background: The delivery and effective operation of public transport is fundamental for a for a transition to low-carbon emission transport systems’. However, many cities face budgetary challenges in providing and operating this type of infrastructure. Land value capture (LVC) instruments, aimed at recovering all or part of the land value uplifts triggered by actions other than the landowner, can alleviate some of this pressure. A key element of LVC lies in the increment in land value associated with a particular public action. Urban economic theory supports this idea and considers accessibility to be a core element for determining residential land value. Although the empirical literature assessing the relationship between land value increments and public transport infrastructure is vast, it often assumes homogeneous benefits and, therefore, overlooks relevant elements of accessibility. Advancements in the accessibility concept in the context of Open Science can ease the relaxation of such assumptions. Methods: This thesis draws on the case of Greater Mexico City between 2009 and 2019. It focuses on the effects of the main public transport network (MPTN) which is organised in seven temporal stages according to its expansion phases. The analysis incorporates location based accessibility measures to employment opportunities in order to assess the benefits of public transport infrastructure. It does so by making extensive use of the open-source software OpenTripPlanner for public transport route modelling (≈ 2.1 billion origin-destination routes). Potential capitalizations are assessed according to the hedonic framework. The property value data includes individual administrative mortgage records collected by the Federal Mortgage Society (≈ 800,000). The hedonic function is estimated using a variety of approaches, i.e. linear models, nonlinear models, multilevel models, and spatial multilevel models. These are estimated by the maximum likelihood and Bayesian methods. The study also examines possible spatial aggregation bias using alternative spatial aggregation schemes according to the modifiable areal unit problem (MAUP) literature. Results: The accessibility models across the various temporal stages evidence the spatial heterogeneity shaped by the MPTN in combination with land use and the individual perception of residents. This highlights the need to transition from measures that focus on the characteristics of transport infrastructure to comprehensive accessibility measures which reflect such heterogeneity. The estimated hedonic function suggests a robust, positive, and significant relationship between MPTN accessibility and residential land value in all the modelling frameworks in the presence of a variety of controls. The residential land value increases between 3.6% and 5.7% for one additional standard deviation in MPTN accessibility to employment in the final set of models. The total willingness to pay (TWTP) is considerable, ranging from 0.7 to 1.5 times the equivalent of the capital costs of the bus rapid transit Line-7 of the Metrobús system. A sensitivity analysis shows that the hedonic model estimation is sensitive to the MAUP. In addition, the use of a post code zoning scheme produces the closest results compared to the smallest spatial analytical scheme (0.5 km hexagonal grid). Conclusion: The present thesis advances the discussion on the capitalization of public transport on residential land value by adopting recent contributions from the Open Science framework. Empirically, it fills a knowledge gap given the lack of literature around this topic in this area of study. In terms of policy, the findings support LVC as a mechanism of considerable potential. Regarding fee-based LVC instruments, there are fairness issues in relation to the distribution of charges or exactions to households that could be addressed using location based measures. Furthermore, the approach developed for this analysis serves as valuable guidance for identifying sites with large potential for the implementation of development based instruments, for instance land readjustments or the sale/lease of additional development rights

    2023-2024 Catalog

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    The 2023-2024 Governors State University Undergraduate and Graduate Catalog is a comprehensive listing of current information regarding:Degree RequirementsCourse OfferingsUndergraduate and Graduate Rules and Regulation
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