In 2003 the Belle collaboration announced the discovery of the X(3872) particle. This was confirmed shortly thereafter by the CDF, D0 and BaBar collaborations, and later by the LHCb collaboration. Based on the decay modes that have been observed to date, it is clear that this particle is a hadron, that is, a composite particle that experiences the strong nuclear force. The X(3872) was found within a family of well understood hadrons called charmonia. Interestingly, it is quite difficult to interpret the X(3872) as a charmonium state. For this reason it has been widely speculated that the X(3872) cannot be understood in terms of the quark model, unlike the vast majority of hadrons observed to date. Such hitherto unobserved particles are called exotic hadrons. Since the discovery of the X(3872), many similarly anomalous charmonium-like particles have been discovered. As would be expected, some unanticipated hadrons have also been found in the closely related bottomonium spectrum. These particles are collectively referred to as heavy quarkonium-like. Evidence is growing that at least some of these particles are exotic hadrons. If confirmed, this would have dramatic implications for our understanding of the strong nuclear force. A major experimental and theoretical effort is now underway in the field of hadron spectroscopy to determine the identities of the heavy quarkonium-like states. In order to investigate the possibility that some of these states could be exotic hadrons, theoretical calculations are needed to firmly establish their properties. One of the main arguments for the existence of exotic hadrons is that they are predicted by the fundamental theory of the strong interaction, Quantum Chromodynamics (QCD). Therefore it is desirable to predict the properties of exotic hadrons using a theoretical approach that is firmly based in QCD. One such method is QCD sum rules (QSR). The research presented here uses the QSR technique to study exotic hadrons. There are several themes in this work. First is the use of QSR to predict the masses of exotic hadrons that may exist among the heavy quarkonium-like states. The second theme is the application of sophisticated loop integration methods in order to obtain more complete theoretical results. These in turn can be extended to higher orders in the perturbative expansion in order to predict the properties of exotic hadrons more accurately. The third theme involves developing a renormalization methodology for these higher order calculations. This research has implications for the Y(3940), X(3872), Zc(3895), Yb(10890), Zb(10610) and Zb(10650) particles, thereby contributing to the ongoing effort to understand these and other heavy quarkonium-like states.

We demonstrate new results in additive combinatorics, including a proof of a conjecture by J. Solymosi: for every epsilon > 0, there exists delta > 0 such that, given n² points in a grid formation in R², if L is a set of lines in general position such that each line intersects at least n^{1-delta} points of the grid, then |L| < n^epsilon. This result implies a conjecture of Gy. Elekes regarding a uniform statistical version of Freiman's theorem for linear functions with small image sets.

Thesis (M.S. in Operations Research)--Naval Postgraduate School, Dec. 2004. / Thesis Advisor(s): James N. Eagle, W. Matthew Carlyle. Includes bibliographical references (p. 35). Also available online.

Probabilistic graphical models have been successfully applied to a wide variety of fields such as computer vision, natural language processing, robotics, and many more. However, for large scale problems represented using unrestricted probabilistic graphical models, exact inference is often intractable, which means that the model cannot compute the correct value of a joint probability query in a reasonable time. In general, approximate inference has been used to address this intractability, in which the exact joint probability is approximated. An increasingly popular alternative is tractable models. These models are constrained such that exact inference is efficient. To offer efficient exact inference, tractable models either benefit from graph-theoretic properties, such as bounded treewidth, or structural properties such as local structures, determinism, or symmetry. An appealing group of probabilistic models that capture local structures and determinism includes arithmetic circuits (ACs) and sum-product networks (SPNs), in which marginal and conditional queries can be answered efficiently. In this dissertation, we describe ID-SPN, a state-of-the-art SPN learner as well as novel methods for learning tractable graphical models in a discriminative setting, in particular through introducing Generalized ACs, which combines ACs and neural networks. Using extensive experiments, we show that the proposed methods often achieves better performance comparing to selected baselines. This dissertation includes previously published and unpublished co-authored material. / 10000-01-01

In 1986, Boguslaw Tomaszewski asked the following question: Consider n real numbers a1, . . . , an such that the sum of their squares is 1. Of the 2n expressions |ε1a1 + · · · + εnan| with εi = ±1, can there be more with value > 1 than with value ≤ 1? Apart from being of intrinsic interest in probability, an answer to this conjecture would also have applications in quadratic programming. However, even after more than thirty years the conjecture is still unsolved. In this thesis we settle a special case of the conjecture - we prove that the conjecture holds for vectors of the form (α, δ, . . . , δ) of sufficiently large dimension. This generalizes earlier result which showed that the conjecture holds for vectors of the form (δ, . . . , δ). 1

Optimal control design and implementation for nonlinear systems is a topic of much interest. However, unlike for linear systems, for nonlinear systems explicit analytical solution for optimal feedback control is not available. Numerical techniques, on the other hand, can be used to approximate the solution of the HJB equation to find the optimal control. In this research, a computational approach is developed for finding the optimal control for nonlinear systems with polynomial vector fields based on sum of squares technique. In this research, a numerical technique is developed for optimal control of polynomial nonlinear systems. The approach follows a four-step procedure to obtain both local and approximate global optimality. In the first step, local optimal control is found by using the linearization method and solving the Algebraic Riccati equation with respect to the quadratic part of a given performance index. Next, we utilize the density function method to find a globally stabilizing polynomial nonlinear control for the nonlinear system. In the third step, we find a corresponding Lyapunov function for the designed control in the previous steps based on the Hamilton Jacobi inequality by using semidefinite programming. Finally, to achieve global optimality, we iteratively update the pair of nonlinear control and Lyapunov function based on a state-dependent polynomial matrix inequality. Numerical examples illustrate the effectiveness of the design approach.

Syftet med undersökningen var att, ur ett elevperspektiv, öka kunskapen om vad elever i åk 2 anser om studieron under matematiklektionerna och med ett särskilt fokus på elever i SUM(särskilda undervisningsbehov i matematik). Genom en replikationsstudie genomfördes en filmbaserad enkätundersökning med 82 elever i åk 2, varav 9 elever i SUM. Resultatet visade på brister i studieron redan i åk 2. Efter analysen framkom fem faktorer som skiljer mellan de elever som svarade att de får studiero på matematiklektionerna och dem som inte får studiero. De fem faktorerna var; matematik är tråkigt, matematik är svårt, tar inte hjälp från kompisar, inte tillräckligt med utmaningar och får inte vara med och bestämma. I studien framkom också att elever i SUM påverkas i större omfattning av att inte få studiero vilket gör att dessa faktorer är något som bör beaktas redan i lågstadiet.

<p> A definition of polynomial differentiability of an arc in the real affine plane at a point is given. The differentiable points are classified with respect to the intersection and support properties of certain families of osculating polynomials. For a given point of an arc, these properties are used to define a certain n-tuple of integers, the characteristic of that point. It is shown that the polynomial order of polynomially differentiable interior point of an arc is at least as great as the sum of the digits of its characteristic.</p> / Thesis / Doctor of Philosophy (PhD)

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Studier visar att taluppfattningen hör samman med att utveckla en inre representation av tallinjen, men hur detta ska gå till är inte helt klarlagt.  Syftet med denna studie är att undersöka i vilken utsträckning riktade klassrumsaktiviteter kan påverka elevers förmåga att placera naturliga tal 0–10 på tallinjen, med extra fokus på elever med särskilda undervisningsbehov i matematik, samt hur inkluderingen i klassrummet kan bli tydlig under dessa aktiviteter. Studien omfattar ett förtest, interventioner där övningar med tallinjen genomförts och observeras samt ett eftertest med samma utformning som förtestet. Resultatet visar att interventionerna har en positiv påverkan på elevers förmåga att placera naturliga tal 0–10 på tallinjen. Observationsresultatet visar tydliga tecken på flera inkluderingsbegrepp i matematik där alla elever samarbetade i ett tillåtande klassrumsklimat.