Yes / The set of subsystems Sigma(m) of a finite quantum system Sigma(n) with variables in Z(n) together with logical connectives, is a Heyting algebra. The probabilities tau(m vertical bar rho(n)) Tr vertical bar B(m)rho(n)] (where B(m) is the projector to Sigma(m)) are compatible with associativity of the join in the Heyting algebra, only if the variables belong to the same chain. Consequently, contextuality in the present formalism, has the chains as contexts. Various Bell-like inequalities are discussed. They are violated, and this proves that quantum mechanics is a contextual theory.

Thesis advisor: Elisenda Grigsby / The space of parameter vectors for a feedforward ReLU neural networks with any fixed architecture is a high dimensional Euclidean space being used to represent the associated class of functions. However, there exist well-known global symmetries and extra poorly-understood hidden symmetries which do not change the neural network function computed by network with different parameter settings. This makes the true dimension of the space of function to be less than the number of parameters. In this thesis, we are interested in the structure of hidden symmetries for neural networks with various parameter settings, and particular neural networks with architecture \((1,n,1)\). For this class of architectures, we fully categorize the insufficiency of local functional dimension coming from activation patterns and give a complete list of combinatorial criteria guaranteeing a parameter setting admits no hidden symmetries coming from slopes of piecewise linear functions in the parameter space. Furthermore, we compute the probability that these hidden symmetries arise, which is rather small compared to the difference between functional dimension and number of parameters. This suggests the existence of other hidden symmetries. We investigate two mechanisms to explain this phenomenon better. Moreover, we motivate and define the notion of \(\varepsilon\)-effective activation regions and \(\varepsilon\)-effective functional dimension. We also experimentally estimate the difference between \(\varepsilon\)-effective functional dimension and true functional dimension for various parameter settings and different \(\varepsilon\). / Thesis (PhD) — Boston College, 2024. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Mathematics.

No description available.

In this thesis, we study how the efficiency of competitive equilibrium in a pure exchange economy with hidden action depends on the market structure. We consider both competitive anonymous markets, where consumers make their choices taking as given some relevant economic parameters, and competitive strategic markets, where consumers interact with financial intermediaries who explicitly take into account the choices of other economic agents. In the first chapter, we review some known results on the efficiency of competitive equilibrium under different market structures. In the second chapter, we assume that there are multiple consumption goods and that the level of action affects the marginal benefit consumers get from consumption. We consider two different market structures: a complete set of contingent-commodity markets, and a complete set of financial markets, together with spot markets for consumption goods. The main result we provide in this chapter is that under more general hypothesis than those usually considered in the literature, the equilibrium with financial markets is not efficient. In the third chapter, we assume that consumers can insure themselves by voluntarily committing to deliver part of their endowment to a common pool in exchange for a sure return from the pool itself. We show that an equilibrium with pool of promises exists, and we characterize it.

In this thesis, we study how the efficiency of competitive equilibrium in a pure exchange economy with hidden action depends on the market structure. We consider both competitive anonymous markets, where consumers make their choices taking as given some relevant economic parameters, and competitive strategic markets, where consumers interact with financial intermediaries who explicitly take into account the choices of other economic agents. In the first chapter, we review some known results on the efficiency of competitive equilibrium under different market structures. In the second chapter, we assume that there are multiple consumption goods and that the level of action affects the marginal benefit consumers get from consumption. We consider two different market structures: a complete set of contingent-commodity markets, and a complete set of financial markets, together with spot markets for consumption goods. The main result we provide in this chapter is that under more general hypothesis than those usually considered in the literature, the equilibrium with financial markets is not efficient. In the third chapter, we assume that consumers can insure themselves by voluntarily committing to deliver part of their endowment to a common pool in exchange for a sure return from the pool itself. We show that an equilibrium with pool of promises exists, and we characterize it.

Precipitation is an important element in the hydrological cycle. To predict and simulate large-scale precipitation, Global Circulation Models (GCMs) are widely used. However, their grid scale is too big to apply to local hydrologic fields. In this study, non-homogenous hidden Markov models (NHMM) are explored as a means of generating the probability of precipitation occurrence in small scale given large-scaled weather patterns. Three different spatial models: (1) independent (2) auto-logistic (3) Chow-Liu tree, are also explored, along with methods and steps for parameter estimation. From this exploration, independent models with NHMM are recommended for very small precipitation networks, and the maximum likelihood method is found to be the most practical fitting method. If there are many points for downscaling, Chow-Liu tree models with the Expectation-Maximization (EM) algorithm are recommended. If more exact solutions are needed, auto-logistic models can be employed. If many points are considered in auto-logistic models, the (EM) algorithm should be used to estimate parameters separately and global optimization methods should be used for emission matrix. The major problem found with the NHMM model in this study is matching the rainfall amount for each year or month. This problem can be addressed by whether combining occurrence models with amount modes or by improving only occurrence models.

Medical students need to acquire not only biomedical knowledge and clinical skills, but also a professional identity to become future qualified physicians. However, much of the professionalization of medical students comes not from the formal curriculum, but the implicit hidden curriculum. This thesis is based on a content and discourse analysis of 75 articles that employ the term “hidden curriculum” or “hidden curricula” in the article title or abstract in two medical education journals Medical Education and Academic Medicine. The study tries to answer two main research questions: what the components of hidden curriculum are, and why hidden curriculum is becoming a popular discourse in medical education. The purpose of this research is to use the key concepts informed by theories developed by Bourdieu and Goffman to build a theoretical framework to understand the usage and interpretation of hidden curriculum from the medical educators’ perspective. I conclude that hidden curriculum is used in a distinct and ambiguous way in medical education literature, emphasizing institutional culture, role modeling, and socialization process. A discrepancy between the usage of hidden curriculum in medical education literature and sociological study is found. Though many innovations have been initiated in both practical pedagogy and the model of medical education, there has been little change in the legitimate knowledge in medicine, the ways in which medical education is organized, the underlying institutional hierarchy, and medical students’ learning experiences.

The Baum-Welch algorithm for training hidden Markov models (HMMs) requires model topology and initial parameters to be specifed, and iteratively improves the model parameters. Sometimes prior knowledge of the process being modeled allows such specifcation, but often this knowledge is unavailable. Experimentation and guessing are resorted to. Techniques for discovering the model structure from observation data exist but their use is not commonplace. We propose a state split-ting approach to structure discovery, where states are split based on two heuristics: within-state autocorrelation and a measure of Markov violation in the state path. Statistical hypothesis testing is used to decide which states to split, providing a natural termination criterion and taking into account the number of observations assigned to each state, splitting states only when the data demands it. / Thesis (M.A.)-University of KwaZulu-Natal, Durban, 2009.

Thesis (Ph. D.)--University of Aarhus, 2004. / Title from PDF title page (viewed on Jan 3, 2007). Includes articles and manuscripts co-authored with others. Includes bibliographical references. Also available in PostScript format.

This thesis is the synthesis of theoretical and experimental works performed in the area of quantum foundations, particularly on quantum correlations and experimental tests of multiplicative Bell inequalities. First we begin with a comprehensive theoretical work performed on the foundations of quantum mechanics, focusing on the puzzling concepts of quantum entanglement, and hidden variable theories. Specifically, we present a broad overview of different classes of hidden variable theories such as local, crypto-nonlocal, contextual and non-local theories, along with several Bell like inequalities for these theories, providing theoretical proofs based on quantum mechanics for the falsification of some of these theories. Second we present a body of experimental, and theoretical works performed on a new class of Bell inequalities, i.e., the multiplicative Bell inequalities. We experimentally report the observation of the Bell parameters close to the Tsirelson (quantum) limit, upto a large number of measurement devices $(n)$, and compare the results with a particular deterministic strategy. We also obtain classical bounds for some $n$, and report the experimental violation of these classical limits. We theoretically derive new richer bounds on the CHSH inequality (named after John Clauser, Michael Horne, Abnor Shimony and Richard Holt) and the multiplicative Bell parameter for $n=2$, based on the principle of ``relativistic independence'', and experimentally observe the distribution of Bell parameters as predicted by these bounds.