9,320 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
Optimization of Beyond 5G Network Slicing for Smart City Applications
Transitioning from the current fifth-generation (5G) wireless technology, the advent of beyond 5G (B5G) signifies a pivotal stride toward sixth generation (6G) communication technology. B5G, at its essence, harnesses end-to-end (E2E) network slicing (NS) technology, enabling the simultaneous accommodation of multiple logical networks with distinct performance requirements on a shared physical infrastructure. At the forefront of this implementation lies the critical process of network slice design, a phase central to the realization of efficient smart city networks. This thesis assumes a key role in the network slicing life cycle, emphasizing the analysis and formulation of optimal procedures for configuring, customizing, and allocating E2E network slices. The focus extends to catering to the unique demands of smart city applications, encompassing critical areas such as emergency response, smart buildings, and video surveillance. By addressing the intricacies of network slice design, the study navigates through the complexities of tailoring slices to meet specific application needs, thereby contributing to the seamless integration of diverse services within the smart city framework. Addressing the core challenge of NS, which involves the allocation of virtual networks on the physical topology with optimal resource allocation, the thesis introduces a dual integer linear programming (ILP) optimization problem. This problem is formulated to jointly minimize the embedding cost and latency. However, given the NP-hard nature of this ILP, finding an efficient alternative becomes a significant hurdle. In response, this thesis introduces a novel heuristic approach the matroid-based modified greedy breadth-first search (MGBFS) algorithm. This pioneering algorithm leverages matroid properties to navigate the process of virtual network embedding and resource allocation. By introducing this novel heuristic approach, the research aims to provide near-optimal solutions, overcoming the computational complexities associated with the dual integer linear programming problem. The proposed MGBFS algorithm not only addresses the connectivity, cost, and latency constraints but also outperforms the benchmark model delivering solutions remarkably close to optimal. This innovative approach represents a substantial advancement in the optimization of smart city applications, promising heightened connectivity, efficiency, and resource utilization within the evolving landscape of B5G-enabled communication technology
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
Classical and quantum algorithms for scaling problems
This thesis is concerned with scaling problems, which have a plethora of connections to different areas of mathematics, physics and computer science. Although many structural aspects of these problems are understood by now, we only know how to solve them efficiently in special cases.We give new algorithms for non-commutative scaling problems with complexity guarantees that match the prior state of the art. To this end, we extend the well-known (self-concordance based) interior-point method (IPM) framework to Riemannian manifolds, motivated by its success in the commutative setting. Moreover, the IPM framework does not obviously suffer from the same obstructions to efficiency as previous methods. It also yields the first high-precision algorithms for other natural geometric problems in non-positive curvature.For the (commutative) problems of matrix scaling and balancing, we show that quantum algorithms can outperform the (already very efficient) state-of-the-art classical algorithms. Their time complexity can be sublinear in the input size; in certain parameter regimes they are also optimal, whereas in others we show no quantum speedup over the classical methods is possible. Along the way, we provide improvements over the long-standing state of the art for searching for all marked elements in a list, and computing the sum of a list of numbers.We identify a new application in the context of tensor networks for quantum many-body physics. We define a computable canonical form for uniform projected entangled pair states (as the solution to a scaling problem), circumventing previously known undecidability results. We also show, by characterizing the invariant polynomials, that the canonical form is determined by evaluating the tensor network contractions on networks of bounded size
Fairness-aware Machine Learning in Educational Data Mining
Fairness is an essential requirement of every educational system, which is reflected in a variety of educational activities. With the extensive use of Artificial Intelligence (AI) and Machine Learning (ML) techniques in education, researchers and educators can analyze educational (big) data and propose new (technical) methods in order to support teachers, students, or administrators of (online) learning systems in the organization of teaching and learning. Educational data mining (EDM) is the result of the application and development of data mining (DM), and ML techniques to deal with educational problems, such as student performance prediction and student grouping. However, ML-based decisions in education can be based on protected attributes, such as race or gender, leading to discrimination of individual students or subgroups of students. Therefore, ensuring fairness in ML models also contributes to equity in educational systems. On the other hand, bias can also appear in the data obtained from learning environments. Hence, bias-aware exploratory educational data analysis is important to support unbiased decision-making in EDM.
In this thesis, we address the aforementioned issues and propose methods that mitigate discriminatory outcomes of ML algorithms in EDM tasks. Specifically, we make the following contributions:
We perform bias-aware exploratory analysis of educational datasets using Bayesian networks to identify the relationships among attributes in order to understand bias in the datasets. We focus the exploratory data analysis on features having a direct or indirect relationship with the protected attributes w.r.t. prediction outcomes.
We perform a comprehensive evaluation of the sufficiency of various group fairness measures in predictive models for student performance prediction problems. A variety of experiments on various educational datasets with different fairness measures are performed to provide users with a broad view of unfairness from diverse aspects.
We deal with the student grouping problem in collaborative learning. We introduce the fair-capacitated clustering problem that takes into account cluster fairness and cluster cardinalities. We propose two approaches, namely hierarchical clustering and partitioning-based clustering, to obtain fair-capacitated clustering.
We introduce the multi-fair capacitated (MFC) students-topics grouping problem that satisfies students' preferences while ensuring balanced group cardinalities and maximizing the diversity of members regarding the protected attribute. We propose three approaches: a greedy heuristic approach, a knapsack-based approach using vanilla maximal 0-1 knapsack formulation, and an MFC knapsack approach based on group fairness knapsack formulation.
In short, the findings described in this thesis demonstrate the importance of fairness-aware ML in educational settings. We show that bias-aware data analysis, fairness measures, and fairness-aware ML models are essential aspects to ensure fairness in EDM and the educational environment.Ministry of Science and Culture of Lower Saxony/LernMINT/51410078/E
LIPIcs, Volume 251, ITCS 2023, Complete Volume
LIPIcs, Volume 251, ITCS 2023, Complete Volum
UMSL Bulletin 2022-2023
The 2022-2023 Bulletin and Course Catalog for the University of Missouri St. Louis.https://irl.umsl.edu/bulletin/1087/thumbnail.jp
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