Li¡VTsai, is a important person of the rationalism in the Middle and late Ming Dynasty. After middle Ming Dynasty, conscience lost the practice of the early aims. People to save the drawback of the Wang's descendants, have filed a new theory to correct the decadent atmosphere, one of the governance drawback of the descendants is the Substance of Nature to be raised. They not only integrate of both Chu's and Wang's though, also according to personal thinking of moral theories to breakthrough the new and review Wang's criterion, also to breakthrough Chu's doctrine system of limitations. Transfer of the Substance of Nature ideologue on the moral principles to chien¡V lo establishing leave Wang's category, appear to the moral theories by the Substance of Mind were turned to Substance of Nature of the rationalism in the late Ming Dynasty, and reflect the complex intertwined politics and society of the current situation and academic thought depravity seeking new response of Late Ming Dynasty. chien¡V lo according to Great Learning propose the doctrine of chih ¡V hsiu, mind¡Bconscience of Wang's though are classified as acquired,and classified the mind as Substance of Nature headed by the system. Unlike Wang's study of mind, is the ontological basis and cause Tong¡VLin resonance for the rescue Wang's correction movement in the positive direction of the late Ming Dynasty.The scholar of Substance of Nature headed are integrate of both Chu's and Wang's though , relies their own thinking of the founding the current situation and academic atmosphere to a new way, and, indirectly, reflect the pulse of the academic atmosphere of the Late Ming Dynasty. Li chien¡V lo stand in it , the chih¡Vhsiu theory has its leading role in the academic trend of the late Ming.

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Any Riemannian manifold possesses a minimal solution of the heat equation for the Dirichlet Laplacian, called the heat kernel. During the last decades many authors investigated geometric properties of the manifold such that its heat kernel fulfills a so-called Gaussian upper bound. Especially compact and non-compact manifolds with lower bounded Ricci curvature have been examined and provide such Gaussian estimates. In the compact case it ended even with integral Ricci curvature assumptions. The important techniques to obtain Gaussian bounds are the symmetrization procedure for compact manifolds and relative Faber-Krahn estimates or gradient estimates for the heat equation, where the first two base on isoperimetric properties of certain sets. In this thesis, we generalize the existing results to the following. Locally uniform integral bounds on the negative part of Ricci curvature lead to Gaussian upper bounds for the heat kernel, no matter whether the manifold is compact or not. Therefore, we show local isoperimetric inequalities under this condition and use relative Faber-Krahn estimates to derive explicit Gaussian upper bounds. If the manifold is compact, we can even generalize the integral curvature condition to the case that the negative part of Ricci curvature is in the so-called Kato class. We even obtain uniform Gaussian upper bounds using gradient estimate techniques. Apart from the geometric generalizations for obtaining Gaussian upper bounds we use those estimates to generalize Bochner’s theorem. More precisely, the estimates for the heat kernel obtained above lead to ultracontractive estimates for the heat semigroup and the semigroup generated by the Hodge Laplacian. In turn, we can formulate rigidity results for the triviality of the first cohomology group if the amount of curvature going below a certain positive threshold is small in a suitable sense. If we can only assume such smallness of the negative part of the Ricci curvature, we can bound the Betti number by explicit terms depending on the generalized curvature assumptions in a uniform manner, generalizing certain existing results from the cited literature. / Jede Riemannsche Mannigfaltigkeit besitzt eine minimale Lösung für die Wärmeleitungsgleichung des zur Mannigfaltigkeit gehörigen Dirichlet-Laplaceoperators, den Wärmeleitungskern. Während der letzten Jahrzehnte fanden viele Autoren geometrische Eigenschaften der Mannigfaltigkeiten unter welchen der Wärmeleitungskern eine sogenannte Gaußsche obere Abschätzung besitzt. Insbesondere bestizen sowohl kompakte als auch nichtkompakte Mannigfaltigkeiten mit nach unten beschränkter Ricci-Krümmung solche Gaußschen Abschätzungen. Im kompakten Fall reichten bisher sogar Integralbedingungen an die Ricci-Krümmung aus. Die wichtigen Techniken, um Gaußsche Abschätzungen zu erhalten, sind die Symmetrisierung für kompakte Mannigfaltigkeiten und relative Faber-Krahn- und Gradientenabschätzungen für die Wärmeleitungsgleichung, wobei die ersten beiden auf isoperimetrischen Eigenschaften gewisser Mengen beruhen. In dieser Arbeit verallgemeinern wir die bestehenden Resultate im folgenden Sinne. Lokal gleichmäßig beschränkte Integralschranken an den Negativteil der Ricci-Krümmung ergeben Gaußsche obere Abschätzungen sowohl im kompakten als auch nichtkompakten Fall. Dafür zeigen wir lokale isoperimetrische Ungleichungen unter dieser Voraussetzung und nutzen die relativen Faber-Krahn-Abschätzungen für eine explizite Gaußsche Schranke. Für kompakte Mannigfaltigkeiten können wir sogar die Integralschranken an den Negativteil der Ricci-Krümmung durch die sogenannte Kato-Bedingung ersetzen. In diesem Fall erhalten wir gleichmäßige Gaußsche Abschätzungen mit einer Gradientenabschätzung. Neben den geometrischen Verallgemeinerungen für Gaußsche Schranken nutzen wir unsere Ergebnisse, um Bochners Theorem zu verallgemeinern. Wärmeleitungskernabschätzungen ergeben ultrakontraktive Schranken für die Wärmeleitungshalbgruppe und die Halbgruppe, die durch den Hodge-Operator erzeugt wird. Damit können wir Starrheitseigenschaften für die erste Kohomologiegruppe zeigen, wenn der Teil der Ricci-Krümmung, welcher unter einem positiven Level liegt, in einem bestimmten Sinne klein genug ist. Wenn der Negativteil der Ricci-Krümmung nicht zu groß ist, können wir die erste Betti-Zahl noch immer explizit uniform abschätzen.

Solving real world problems with mixed integer programming (MIP) involves efforts in modeling and efficient algorithms. To solve a minimization MIP problem, a lower bound is needed in a branch-and-bound algorithm to evaluate the quality of a feasible solution and to improve the efficiency of the algorithm. This thesis develops a new MIP model and studies algorithms for obtaining lower bounds for MIP. The first part of the thesis is dedicated to a new production planning model with pricing decisions. To increase profit, a company can use pricing to influence its demand to increase revenue, decrease cost, or both. We present a model that uses pricing discounts to increase production and delivery flexibility, which helps to decrease costs. Although the revenue can be hurt by introducing pricing discounts, the total profit can be increased by properly choosing the discounts and production and delivery decisions. We further explore the idea with variations of the model and present the advantages of using flexibility to increase profit. The second part of the thesis focuses on solving integer programming(IP) problems by improving lower bounds. Specifically, we consider obtaining lower bounds for the multi- dimensional knapsack problem (MKP). Because MKP lacks special structures, it allows us to consider general methods for obtaining lower bounds for IP, which includes various relaxation algorithms. A problem relaxation is achieved by either enlarging the feasible region, or decreasing the value of the objective function on the feasible region. In addition, dual algorithms can also be used to obtain lower bounds, which work directly on solving the dual problems. We first present some characteristics of the value function of MKP and extend some properties from the knapsack problem to MKP. The properties of MKP allow some large scale problems to be reduced to smaller ones. In addition, the quality of corner relaxation bounds of MKP is considered. We explore conditions under which the corner relaxation is tight for MKP, such that relaxing some of the constraints does not affect the quality of the lower bounds. To evaluate the overall tightness of the corner relaxation, we also show the worst-case gap of the corner relaxation for MKP. To identify parameters that contribute the most to the hardness of MKP and further evaluate the quality of lower bounds obtained from various algorithms, we analyze the characteristics that impact the hardness of MKP with a series of computational tests and establish a testbed of instances for computational experiments in the thesis. Next, we examine the lower bounds obtained from various relaxation algorithms com- putationally. We study methods of choosing constraints for relaxations that produce high- quality lower bounds. We use information obtained from linear relaxations to choose con- straints to relax. However, for many hard instances, choosing the right constraints can be challenging, due to the inaccuracy of the LP information. We thus develop a dual heuristic algorithm that explores various constraints to be used in relaxations in the Branch-and- Bound algorithm. The algorithm uses lower bounds obtained from surrogate relaxations to improve the LP bounds, where the relaxed constraints may vary for different nodes. We also examine adaptively controlling the parameters of the algorithm to improve the performance. Finally, the thesis presents two problem-specific algorithms to obtain lower bounds for MKP: A subadditive lifting method is developed to construct subadditive dual solutions, which always provide valid lower bounds. In addition, since MKP can be reformulated as a shortest path problem, we present a shortest path algorithm that uses estimated distances by solving relaxations problems. The recursive structure of the graph is used to accelerate the algorithm. Computational results of the shortest path algorithm are given on the testbed instances.

Pattern theory, a mathematical framework for representing knowledge of complex patterns developed by applied mathematician Ulf Grenander, has been shown to have potential uses in automatic target recognition (ATR). Prior research performed in the mid-1990s at Washington University in St. Louis resulted in ATR algorithms based on concepts in pattern theory for forward-looking infrared (FLIR) and laser radar (LADAR) imagery, but additional work was needed to create algorithms that could be implemented in real ATR systems. This was due to performance barriers and a lack of calibration between target models and real data. This work addresses some of these issues by exploring techniques that can be used to create practical pattern-theoretic ATR algorithms. This dissertation starts by reviewing the previous pattern-theoretic ATR research described above and discussing new results involving the unification of two previously separate outcomes of that research: multi-target detection/recognition and thermal state estimation in FLIR imagery. To improve the overall utility of pattern-theoretic ATR, the following areas are re-examined: 1) generalized diffusion processes to update target pose estimates and 2) the calibration of thermal models with FLIR target data. The final section of this dissertation analyzes the fundamental accuracy limits of target pose estimation under different sensor conditions, independent of the target detection/recognition algorithm employed. The Cramér-Rao lower bound (CRLB) is used to determine these accuracy limits.

Diagonally dominant matrices arise in many applications. In this work, we exploit the structure of diagonally dominant matrices to provide sharp entrywise relative perturbation bounds. We first generalize the results of Dopico and Koev to provide relative perturbation bounds for the LDU factorization with a well conditioned L factor. We then establish relative perturbation bounds for the inverse that are entrywise and independent of the condition number. This allows us to also present relative perturbation bounds for the linear system Ax=b that are independent of the condition number. Lastly, we continue the work of Ye to provide relative perturbation bounds for the eigenvalues of symmetric indefinite matrices and non-symmetric matrices.

Uppsatsen syftar till att utvärdera effekten av Förberedande och orienterande utbildning, vilket är en insats som ges till arbetssökande för att gynna framtida aktivitet inom arbetskraften. Insatsen är en av Arbetsförmedlingens största, och bedöms öka ytterligare framöver. En kombination av coarsened exact matchning samt propensity score matchning används för att försöka fastställa kausala effekter på individnivå med mikrodata från Arbetsförmedlingen och SCB. Deltagare som skrevs in hos Arbetsförmedlingen 2008 studeras och utfallen som tillämpas är inkomster och socialbidragstagande, vilka mäts 2010, 2011, 2012 respektive 2013. Resultaten visar att deltagare i insatsen generellt har sämre arbetsmarknadsutfall än jämförelsegruppen som består av öppet arbetslösa. Känslighetsanalysen visar att det kan finnas vissa problem med selektion, men dessa bedöms inte omkullkasta resultaten. Vidare fastställs att de skattade effekterna avtar med uppföljningstiden, vilket tyder på att det kan finnas inlåsningseffekter. En annan förklaring till att negativa effekter av deltagande kan uppstå är enligt den nationalekonomiska litteraturen att deltagande i insatsen signalerar något negativt till potentiella arbetsgivare, snarare än att insatsen bidrar med en produktivitetsökning för den arbetssökande individen.

We investigate the unprovability of NP$\not\subseteq$P/poly in various fragments of arithmetic. The unprovability is usually obtained by showing hardness of propositional formulas encoding superpolynomial circuit lower bounds. Firstly, we discuss few relevant techniques and known theorems. Namely, natural proofs, feasible interpolation, KPT theorem, iterability, gadget generators etc. Then we prove some original results. We show the unprovability of superpolynomial circuit lower bounds for systems admitting certain forms of feasible interpolation (modulo a hardness assumption) and for systems roughly described as tree-like Frege systems working with formulas using only a small fraction of variables of the statement that is supposed to be proved. These results are obtained by proving the hardness of the Nisan-Wigderson generators in corresponding proof systems.

Title: Optimization and stress tests Author: Diana Fašungová Department: Department of Probability and Mathematical Statistics Supervisor: Prof. RNDr. Jitka Dupačová, DrSc., Department of Probability and Mathematical Statistics Abstract: In the thesis we apply contamination technique on a portfolio optimiza- tion problem using minimization of risk measure CVaR. The problem is considered from a risk manager point of view. We stress correlation structure of data and of revenues using appropriately chosen data for this kind of problem and for ge- nerated stress scenarios. From behaviour of CVaR with regard to contamination bounds, we formulate recommendations for the risk manager optimizing his port- folio. The recommendations are interpreted for both types of stress scenarios. In the end, limitations of the model and possible ways of improvement are discussed. Keywords: contamination bounds, stress tests, portfolio optimization, risk mana- gement

(please take a look at the pdf)