280 research outputs found
Archives of the Social Sciences (Complete First Issue, 2023)
The issue comprises 5 scholarly publications
Numerical aspects of black hole superradiance
In this work we explore a numerical technique, based on the spherical harmonic decomposition and the discretization of the radial coordinate through Čebyšëv polynomial interpolation, for the computation of quasi-bound states of linear massive scalar and vector perturbations in spinning black hole spacetimes in General Relativity. The aim is studying black hole superradiant instabilities, an energy-extraction mechanism triggered by the presence of massive bosonic fields near black holes, which finds wide applications in constraining scenarios beyond Standard Model and General Relativity. This method does not rely on any separation ansätze, thus it can have wide applications. Consequently we extend the technique so that it can be applied also to the computation of massive tensor quasi-bound states in spinning black holes in General Relativity, whose separability ansatz is currently unknown. We also apply it to spinning black holes in scalar-tensor theory non-linearly interacting with plasma, wherein the massless scalar perturbations acquires an effective mass, finding a novel way for constraining scalar-tensor theories
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Improved Asymptotics for Multi-armed Bandit Experiments under Optimism-based Policies: Theory and Applications
The classical multi-armed bandit paradigm is a foundational framework for online decision making underlying a wide variety of important applications, e.g., clinical trials, advertising, sequential assignments, assortment optimization, etc. This work will examine two salient aspects of decision making that arise naturally in settings with large action spaces.
The first issue pertains to the division of samples across arms at the level of a trajectory (or sample-path). Traditional bounds at the ensemble-level (or in expectation) only translate to meaningful pathwise guarantees (high probability bounds) when the separation between mean rewards is ``large,'' commonly referred to as the ``well-separated'' regime in the literature. On the other hand, applications with a large action space are intrinsically endowed with smaller separations between arm-means (e.g., multiple products of similar quality in e-retail). As a result, classical ensemble-level guarantees for such problems become vacuous at the sample-path level in several settings. This theoretical gap in the understanding of bandit algorithms in the ``small gap'' regime can be of significant consequence in applications where considerations such as fairness and post hoc inference play an important role. Our work provides the first systematic treatment and analysis of this aspect under the celebrated UCB class of optimism-based bandit algorithms, including a complete diffusion-limit characterization of its regret. The diffusion-scale lens also reveals profound insights and highlights distinctions between UCB and the popular posterior sampling-based method, Thompson Sampling, such as an ``incomplete learning'' phenomenon that is characteristic of the latter.
The second research question studied in this work concerns the complexity of decision making in problems where the action space is endowed with a large number of substitutable alternatives. For example, it is common in e-retail for multiple brands to offer similar products (in terms of quality-of-service) that compete for revenue within a given product segment. We model the platform's decision problem in this example as a bandit with countably many arms, and investigate limits of achievable performance under canonical bandit algorithms adapted to this setting. We also propose novel rate-optimal algorithms that leverage results for the ``small gap'' regime alluded to earlier, and show that these outperform aforementioned conventional adaptations. We extend the countable-armed bandit paradigm to also serve as a basal motif in sequential assignment and dynamic matching problems typical of settings such as online labor markets.
The last chapter of this thesis investigates achievable performance in the countable-armed bandit problem under non-stationarity that is attributable to vanishing arms. This characteristic abstracts away certain attrition and churn processes observable in online markets, e.g., a popular brand may retract its product from a platform owing to under-exposure within its category -- a potential negative externality of the exploration carried out by the platform's policy
The Self The Soul and The World: Affect Reason and Complexity
This book looks at the affective-cognitive roots of how the human mind inquires into the workings of nature and, more generally, how the mind confronts reality. Reality is an infinitely complex system, in virtue of which the mind can comprehend it only in bits and pieces, by making up interpretations of the myriads of signals received from the world by way of integrating those with information stored from the past. This constitutes a piecemeal interpretation by which we assemble our phenomenal reality. In perceiving the complex world and responding to it, the mind invokes the logic of affect and the logic of reason, the former mostly innate and implicit, and the latter generated consciously in explicit terms with reference to mind-independent relations between entities in nature. It is a strange combination of affect and reason that enables us to make decisions and inferences, --- the latter mostly of the inductive type --- thereby making possible the development of theories. Theories are our tool-kits for explaining and predicting phenomena, guiding us along in our journey in life. Theories, however, are defeasible, and need to be constantly updated, at times even radically. In this, the self and the soul are of enormous relevance. The former is the affect-based psychological engine driving all our mental processes, while the latter is the capacity of the conscious mind to examine and reconstruct the self by modulating repressed conflicts. If the soul remains inoperative, all our theories become misdirected and a rot spreads inexorably all around us
LIPIcs, Volume 261, ICALP 2023, Complete Volume
LIPIcs, Volume 261, ICALP 2023, Complete Volum
Operational Research: methods and applications
This is the final version. Available on open access from Taylor & Francis via the DOI in this recordThroughout its history, Operational Research has evolved to include methods, models and algorithms that have been applied to a wide range of contexts. This encyclopedic article consists of two main sections: methods and applications. The first summarises the up-to-date knowledge and provides an overview of the state-of-the-art methods and key developments in the various subdomains of the field. The second offers a wide-ranging list of areas where Operational Research has been applied. The article is meant to be read in a nonlinear fashion and used as a point of reference by a diverse pool of readers: academics, researchers, students, and practitioners. The entries within the methods and applications sections are presented in alphabetical order. The authors dedicate this paper to the 2023 Turkey/Syria earthquake victims. We sincerely hope that advances in OR will play a role towards minimising the pain and suffering caused by this and future catastrophes
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