5,558 research outputs found
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
UMSL Bulletin 2023-2024
The 2023-2024 Bulletin and Course Catalog for the University of Missouri St. Louis.https://irl.umsl.edu/bulletin/1088/thumbnail.jp
Fuzzy Natural Logic in IFSA-EUSFLAT 2021
The present book contains five papers accepted and published in the Special Issue, “Fuzzy Natural Logic in IFSA-EUSFLAT 2021”, of the journal Mathematics (MDPI). These papers are extended versions of the contributions presented in the conference “The 19th World Congress of the International Fuzzy Systems Association and the 12th Conference of the European Society for Fuzzy Logic and Technology jointly with the AGOP, IJCRS, and FQAS conferences”, which took place in Bratislava (Slovakia) from September 19 to September 24, 2021. Fuzzy Natural Logic (FNL) is a system of mathematical fuzzy logic theories that enables us to model natural language terms and rules while accounting for their inherent vagueness and allows us to reason and argue using the tools developed in them. FNL includes, among others, the theory of evaluative linguistic expressions (e.g., small, very large, etc.), the theory of fuzzy and intermediate quantifiers (e.g., most, few, many, etc.), and the theory of fuzzy/linguistic IF–THEN rules and logical inference. The papers in this Special Issue use the various aspects and concepts of FNL mentioned above and apply them to a wide range of problems both theoretically and practically oriented. This book will be of interest for researchers working in the areas of fuzzy logic, applied linguistics, generalized quantifiers, and their applications
T-spherical linear Diophantine fuzzy aggregation operators for multiple attribute decision-making
This paper aims to amalgamate the notion of a T-spherical fuzzy set (T-SFS) and a linear Diophantine fuzzy set (LDFS) to elaborate on the notion of the T-spherical linear Diophantine fuzzy set (T-SLDFS). The new concept is very effective and is more dominant as compared to T-SFS and LDFS. Then, we advance the basic operations of T-SLDFS and examine their properties. To effectively aggregate the T-spherical linear Diophantine fuzzy data, a T-spherical linear Diophantine fuzzy weighted averaging (T-SLDFWA) operator and a T-spherical linear Diophantine fuzzy weighted geometric (T-SLDFWG) operator are proposed. Then, the properties of these operators are also provided. Furthermore, the notions of the T-spherical linear Diophantine fuzzy-ordered weighted averaging (T-SLDFOWA) operator; T-spherical linear Diophantine fuzzy hybrid weighted averaging (T-SLDFHWA) operator; T-spherical linear Diophantine fuzzy-ordered weighted geometric (T-SLDFOWG) operator; and T-spherical linear Diophantine fuzzy hybrid weighted geometric (T-SLDFHWG) operator are proposed. To compare T-spherical linear Diophantine fuzzy numbers (T-SLDFNs), different types of score and accuracy functions are defined. On the basis of the T-SLDFWA and T-SLDFWG operators, a multiple attribute decision-making (MADM) method within the framework of T-SLDFNs is designed, and the ranking results are examined by different types of score functions. A numerical example is provided to depict the practicality and ascendancy of the proposed method. Finally, to demonstrate the excellence and accessibility of the proposed method, a comparison analysis with other methods is conducted
Computing a partition function of a generalized pattern-based energy over a semiring
Valued constraint satisfaction problems with ordered variables (VCSPO) are a
special case of Valued CSPs in which variables are totally ordered and soft
constraints are imposed on tuples of variables that do not violate the order.
We study a restriction of VCSPO, in which soft constraints are imposed on a
segment of adjacent variables and a constraint language consists of
-valued characteristic functions of predicates. This kind of
potentials generalizes the so-called pattern-based potentials, which were
applied in many tasks of structured prediction.
For a constraint language we introduce a closure operator, , and give examples of constraint
languages for which is small. If all predicates in
are cartesian products, we show that the minimization of a generalized
pattern-based potential (or, the computation of its partition function) can be
made in
time, where is a set of variables, is a domain set. If, additionally,
only non-positive weights of constraints are allowed, the complexity of the
minimization task drops to where is the
arity of . For a general language and non-positive
weights, the minimization task can be carried out in time.
We argue that in many natural cases is of moderate
size, though in the worst case can blow up and
depend exponentially on
"Le present est plein de l’avenir, et chargé du passé" : Vorträge des XI. Internationalen Leibniz-Kongresses, 31. Juli – 4. August 2023, Leibniz Universität Hannover, Deutschland. Band 3
[No abstract available]Deutschen Forschungsgemeinschaft (DFG)/Projektnr. 517991912VGH VersicherungNiedersächsisches Ministerium für Wissenschaft und Kultur (MWK
Distributionally Robust Model Predictive Control: Closed-loop Guarantees and Scalable Algorithms
We establish a collection of closed-loop guarantees and propose a scalable,
Newton-type optimization algorithm for distributionally robust model predictive
control (DRMPC) applied to linear systems, zero-mean disturbances, convex
constraints, and quadratic costs. Via standard assumptions for the terminal
cost and constraint, we establish distribtionally robust long-term and
stage-wise performance guarantees for the closed-loop system. We further
demonstrate that a common choice of the terminal cost, i.e., as the solution to
the discrete-algebraic Riccati equation, renders the origin input-to-state
stable for the closed-loop system. This choice of the terminal cost also
ensures that the exact long-term performance of the closed-loop system is
independent of the choice of ambiguity set the for DRMPC formulation. Thus, we
establish conditions under which DRMPC does not provide a long-term performance
benefit relative to stochastic MPC (SMPC). To solve the proposed DRMPC
optimization problem, we propose a Newton-type algorithm that empirically
achieves superlinear convergence by solving a quadratic program at each
iteration and guarantees the feasibility of each iterate. We demonstrate the
implications of the closed-loop guarantees and the scalability of the proposed
algorithm via two examples.Comment: 34 pages, 6 figure
Formation of quiescent big bang singularities
Hawking's singularity theorem says that cosmological solutions arising from
initial data with positive mean curvature have a past singularity. However, the
nature of the singularity remains unclear. We therefore ask: If the initial
hypersurface has sufficiently large mean curvature, does the curvature
necessarily blow up towards the singularity?
In case the eigenvalues of the expansion-normalized Weingarten map are
everywhere distinct and satisfy a certain algebraic condition (which in 3+1
dimensions is equivalent to them being positive), we prove that this is the
case in the CMC Einstein-non-linear scalar field setting. More specifically, we
associate a set of geometric expansion-normalized quantities to any initial
data set with positive mean curvature. These quantities are expected to
converge, in the quiescent setting, in the direction of crushing big bang
singularities. Our main result says that if the mean curvature is large enough,
relative to an appropriate Sobolev norm of these geometric quantities, and if
the algebraic condition is satisfied, then a quiescent (as opposed to
oscillatory) big bang singularity with curvature blow-up forms. This provides a
stable regime of big bang formation without requiring proximity to any
particular class of background solutions.
An important recent result by Fournodavlos, Rodnianski and Speck demonstrates
stable big bang formation for all the spatially flat and spatially homogeneous
solutions to the Einstein-scalar field equations satisfying the algebraic
condition. Here we obtain analogous stability results for any solution inducing
data at the singularity, in the sense introduced by the third author, in
particular generalizing the aforementioned result. Moreover, we are able to
prove both future and past global non-linear stability of a large class of
spatially locally homogeneous solutions.Comment: 77 page
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