8,357 research outputs found
Cyclic proof systems for modal fixpoint logics
This thesis is about cyclic and ill-founded proof systems for modal fixpoint logics, with and without explicit fixpoint quantifiers.Cyclic and ill-founded proof-theory allow proofs with infinite branches or paths, as long as they satisfy some correctness conditions ensuring the validity of the conclusion. In this dissertation we design a few cyclic and ill-founded systems: a cyclic one for the weak Grzegorczyk modal logic K4Grz, based on our explanation of the phenomenon of cyclic companionship; and ill-founded and cyclic ones for the full computation tree logic CTL* and the intuitionistic linear-time temporal logic iLTL. All systems are cut-free, and the cyclic ones for K4Grz and iLTL have fully finitary correctness conditions.Lastly, we use a cyclic system for the modal mu-calculus to obtain a proof of the uniform interpolation property for the logic which differs from the original, automata-based one
Techniques for high-multiplicity scattering amplitudes and applications to precision collider physics
In this thesis, we present state-of-the-art techniques for the computation of scattering amplitudes in Quantum Field Theories. Following an introduction to the topic, we describe a robust framework that enables the calculation of multi-scale two-loop amplitudes directly relevant to modern particle physics phenomenology at the Large Hadron Collider and beyond. We discuss in detail the use of finite fields to bypass the algebraic complexity of such computations, as well as the method of integration-by-parts relations and differential equations. We apply our framework to calculate the two-loop amplitudes contributing to three process: Higgs boson production in association with a bottom-quark pair, W boson production with a photon and a jet, as well as lepton-pair scattering with an off-shell and an on-shell photon. Finally, we draw our conclusions and discuss directions for future progress of amplitude computations
Southern Adventist University Undergraduate Catalog 2023-2024
Southern Adventist University\u27s undergraduate catalog for the academic year 2023-2024.https://knowledge.e.southern.edu/undergrad_catalog/1123/thumbnail.jp
Fragments and frame classes:Towards a uniform proof theory for modal fixed point logics
This thesis studies the proof theory of modal fixed point logics. In particular, we construct proof systems for various fragments of the modal mu-calculus, interpreted over various classes of frames. With an emphasis on uniform constructions and general results, we aim to bring the relatively underdeveloped proof theory of modal fixed point logics closer to the well-established proof theory of basic modal logic. We employ two main approaches. First, we seek to generalise existing methods for basic modal logic to accommodate fragments of the modal mu-calculus. We use this approach for obtaining Hilbert-style proof systems. Secondly, we adapt existing proof systems for the modal mu-calculus to various classes of frames. This approach yields proof systems which are non-well-founded, or cyclic.The thesis starts with an introduction and some mathematical preliminaries. In Chapter 3 we give hypersequent calculi for modal logic with the master modality, building on work by Ori Lahav. This is followed by an Intermezzo, where we present an abstract framework for cyclic proofs, in which we give sufficient conditions for establishing the bounded proof property. In Chapter 4 we generalise existing work on Hilbert-style proof systems for PDL to the level of the continuous modal mu-calculus. Chapter 5 contains a novel cyclic proof system for the alternation-free two-way modal mu-calculus. Finally, in Chapter 6, we present a cyclic proof system for Guarded Kleene Algebra with Tests and take a first step towards using it to establish the completeness of an algebraic counterpart
LIPIcs, Volume 251, ITCS 2023, Complete Volume
LIPIcs, Volume 251, ITCS 2023, Complete Volum
Algebraic solutions of linear differential equations: an arithmetic approach
Given a linear differential equation with coefficients in , an
important question is to know whether its full space of solutions consists of
algebraic functions, or at least if one of its specific solutions is algebraic.
After presenting motivating examples coming from various branches of
mathematics, we advertise in an elementary way a beautiful local-global
arithmetic approach to these questions, initiated by Grothendieck in the late
sixties. This approach has deep ramifications and leads to the still unsolved
Grothendieck-Katz -curvature conjecture.Comment: 47 page
Direct measurement of coating thermal noise in the AEI 10m prototype
A thermal noise interferometer for the characterization of thermal noise in high reflectivity mirrors has been commissioned and first direct measurements of coating thermal noise have been performed. This serves as an important step in the improvement of current and future gravitational wave detectors
A Multi-level Analysis on Implementation of Low-Cost IVF in Sub-Saharan Africa: A Case Study of Uganda.
Introduction: Globally, infertility is a major reproductive disease that affects an estimated 186 million people worldwide. In Sub-Saharan Africa, the burden of infertility is considerably high, affecting one in every four couples of reproductive age. Furthermore, infertility in this context has severe psychosocial, emotional, economic and health consequences. Absence of affordable fertility services in Sub-Saharan Africa has been justified by overpopulation and limited resources, resulting in inequitable access to infertility treatment compared to developed countries. Therefore, low-cost IVF (LCIVF) initiatives have been developed to simplify IVF-related treatment, reduce costs, and improve access to treatment for individuals in low-resource contexts. However, there is a gap between the development of LCIVF initiatives and their implementation in Sub-Saharan Africa. Uganda is the first country in East and Central Africa to undergo implementation of LCIVF initiatives within its public health system at Mulago Women’s Hospital.
Methods: This was an exploratory, qualitative, single, case study conducted at Mulago Women’s Hospital in Kampala, Uganda. The objective of this study was to explore how LCIVF initiatives have been implemented within the public health system of Uganda at the macro-, meso- and micro-level. Primary qualitative data was collected using semi-structured interviews, hospital observations informal conversations, and document review. Using purposive and snowball sampling, a total of twenty-three key informants were interviewed including government officials, clinicians (doctors, nurses, technicians), hospital management, implementers, patient advocacy representatives, private sector practitioners, international organizational representatives, educational institution, and professional medical associations. Sources of secondary data included government and non-government reports, hospital records, organizational briefs, and press outputs. Using a multi-level data analysis approach, this study undertook a hybrid inductive/deductive thematic analysis, with the deductive analysis guided by the Consolidated Framework for Implementation Research (CFIR).
Findings: Factors facilitating implementation included international recognition of infertility as a reproductive disease, strong political advocacy and oversight, patient needs & advocacy, government funding, inter-organizational collaboration, tension to change, competition in the private sector, intervention adaptability & trialability, relative priority, motivation &advocacy of fertility providers and specialist training. While barriers included scarcity of embryologists, intervention complexity, insufficient knowledge, evidence strength & quality of intervention, inadequate leadership engagement & hospital autonomy, poor public knowledge, limited engagement with traditional, cultural, and religious leaders, lack of salary incentives and concerns of revenue loss associated with low-cost options.
Research contributions: This study contributes to knowledge of factors salient to implementation of LCIVF initiatives in a Sub-Saharan context. Effective implementation of these initiatives requires (1) sustained political support and favourable policy & legislation, (2) public sensitization and engagement of traditional, cultural, and religious leaders (3) strengthening local innovation and capacity building of fertility health workers, in particular embryologists (4) sustained implementor leadership engagement and inter-organizational collaboration and (5) proven clinical evidence and utilization of LCIVF initiatives in innovator countries. It also adds to the literature on the applicability of the CFIR framework in explaining factors that influence successful implementation in developing countries and offer opportunities for comparisons across studies
Holonomic Bessel modules and generating functions
We have solved a number of holonomic PDEs derived from the Bessel modules
which are related to the generating functions of classical Bessel functions and
the difference Bessel functions recently discovered by Bohner and Cuchta. This
-module approach both unifies and extends generating functions of the
classical and the difference Bessel functions. It shows that the algebraic
structures of the Bessel modules and related modules determine the possible
formats of Bessel's generating functions studied in this article. As a
consequence of these -modules structures, a number of new recursion
formulae, integral representations and new difference Bessel polynomials have
been discovered. The key ingredients of our argument involve new transmutation
formulae related to the Bessel modules and the construction of -linear maps
between different appropriately constructed submodules. This work can be viewed
as -module approach to Truesdell's -equation theory specialised to Bessel
functions. The framework presented in this article can be applied to other
special functions.Comment: 97 pages including one blank pag
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