Nearly all imaginable human activities rest on a context-appropriate dynamic control of the flow of retinal data into the nervous system via eye movements. The brain’s task is to move the eyes so as to exert intelligent predictive control over the informational content of the retinal data stream. An intelligent oculomotor controller would first model future contingent upon each possible next action in the oculomotor repertoire, then rank-order the repertoire by assigning a value v(a,t) to each possible action a at each time t, and execute the oculomotor action with the highest predicted value each time. We present a striking evidence of such an intelligent neural control of human eyes in a laboratory task of visual search for a small target camouflaged by a natural-like stochastic texture, a task in which the value of fixating a given location naturally corresponds to the expected information gain about the unknown location of the target. Human searchers behave as if maintaining a map of beliefs (represented as probabilities) about the target location, updating their beliefs with visual data obtained on each fixation optimally using the Bayes Rule. On average, human eye movement patterns appear remarkably consistent with an intelligent strategy of moving eyes to maximize the expected information gain, but inconsistent with the strategy of always foveating the currently most likely location of the target (a prevalent intuition in the existing theories). We derive principled, simple, accurate, and robust mathematical formulas to compute belief and information value maps across the search area on each fixation (or time step). The formulas are exact expressions in the limiting cases of small amount of information extracted, which occurs when the number of potential target locations is infinite, or when the time step is vanishingly small (used for online control of fixation duration). Under these circumstances, the computation of information value map reduces to a linear filtering of beliefs on each time step, and beliefs can be maintained simply as running weighted averages. A model algorithm employing these simple computations captures many statistical properties of human eye movements in our search task. / text

Formal models, those which explicitly specify the postulates on which they are based, the development of their 'predictions' from those postulates, and the boundary conditions under which they apply, have the potential to be useful tools in archaeological inference and explanation. Detailed examination of one such model, the mathematical model commonly referred to as the diet breadth or prey choice model, shows that its archaeological application is severely complicated by two factors that are difficult or impossible to specify for prehistoric cases: 1) limits on the amount of meat consumable by a food-sharing group before spoilage or loss to scavengers and 2) hunting failure rates. The former introduce significant uncertainties into the food yield or energetic return term of resource rankings, while the latter affect both resource rankings and the resouce encounter rates leading to prey inclusion or exclusion from the diet. Together, these factors make rigorous diet breadth / prey choice model-based inferences from ungulate archaeofaunas impractical, especially in Paleolithic cases. Following success in recent years in making diet breadth model-based inferences about Paleolithic demography from small game analyses that involved computer simulation modeling of prey species' resilience to hunting pressure, the development and employment of a similar model applied to ungulate species reveals that, in general, the differences in the abilty of populations of different ungulate species to sustain harvest rates are not sufficient to allow the relative representation of ungulate remains in archaeological sites to be a viable basis for human demographic inferences. However, in cases where ungulate remains allow the determination of both prey age structure and sex ratio, it is possible to distinguish low exploitation rates, high exploitation rates, and overhunting. In some cases, the sex ratio data may also alter relative hunting resilience levels in such a way that it may be possible to infer that one species was capable of supporting a larger human population than another.

In racing, it is useful to analyze vehicle performance and driving strategies to achieve the best result possible in competitions. This is often done by simulations and test driving. In this thesis optimal control is used to examine how a racing car should be driven to minimize the lap time. This is achieved by calculating the optimal racing line at various tracks. The tracks can have arbitrary layout and consist of corners with non-constant radius. The road can have variable width. A four wheel vehicle model with lateral and longitudinal weight transfer is used. To increase the performance of the optimization algorithm, a set of additional techniques are used. The most important one is to divide tracks into smaller overlapping segments and find the optimal line for each segment independently. This turned out to be useful when the track is long. The optimal racing line is found for various tracks and cars. The solutions have several similarities to real driving techniques. The result is presented as driving instructions in Racer, a car simulator.

More strict control quality requirements are raised to the synthesis of modern algorithmic control systems which can not be satisfied by using classical methods of systems synthesis. Also, the usage of them sometimes becomes impossible, e.g. in cases when a mathematical model of the control object is described by means of complex differential equations or in cases when the model itself is unknown. By applying the suggested synthesis methods of quasi-optimal and variable structure systems as well as algorithms, it is possible to avoid disadvantages common with classical synthesis methods.

Magistro darbe plačiai nagrinėjami H. Markowitz (1952), J. Tobin (1958), W. Sharpe (1964), S. Ross (1976), G. Fama ir K. French (1993) ir kitų autorių darbai, kuriuose akcentuojami portfelio formavimo kriterijai bei optimalaus portfelio sudarymo problemos. Darbas apima modernios portfelio teorijos praktinio pritaikymo aspektus, įvertinant vertybinių popierių atrankos į portfelį ir jų įkainojimo ypatumus bei portfelio vertę įtakojančius veiksnius, ieškant būdų jiems kiekybiškai išreikšti. Atlikta SEB VB Investicijų valdymas valdomų ir platinamų investicinių fondų pelningumo ir rizikos analizė 2005-2007m. bei atliktos analizės rezultatų pagrindu suformuoti investicinių fondų portfeliai skirti konservatyviam, racionaliam bei agresyviam investuotojui. Darbe parodyta, kaip ant kapitalo paskirstymo tiesės rasti optimalius liestinės su naudingumo abejingumo kreivėmis portfelius. Beto, magistro darbe buvo sprendžiami portfelių optimizavimo uždaviniai bei atliktas suformuotų portfelių maksimalių finansinių nuostolių įvertinimas, naudojant imitacinį rizikos vertės metodą. Gauti tyrimo rezultatai gali būti reikšmingi kiekvienam investuotojui, siekiant rasti sau priimtiną portfelį, esant optimaliam rizikos ir pelno santykiui. / This master’s final paper analyzes H. Markowitz (1952), J. Tobin (1958), W. Sharpe (1964), S. Ross (1976), G. Fama ir K. French (1993) theories, emphasizing the portfolio construction criteria and its optimization problems. The paper includes the practical aspects of the the modern portfolio theory application, estimating the portfolio selection and selected securities pricing points. It also analyzes the factors that influence the portfolio value, while searching for the ways to give them the quantitative repersenation.The paper estimates the risk and the return of the mutual funds managed and distributed by SEB VB Investment Management in 2005-2007m. and the fund portfolios are constructed for the conservative, rational and aggressive investors on the basis of the estimate results. The research enables to find the tangency portfolio on the capital allocation line, estimating the investors’ preferences. Furthermore, the paper solves the portfolio optimization task and it also gives the estimate of the maximum portfolio losses, using Monte Carlo simulation. The research results are important to every investor, contructing the portfolio with optimal risk/return trade-off.

This dissertation addresses the causes of and policy responses to the 1990s current account crises. The first chapter explores the relative importance of external shocks as key determinants of the significant increase of foreign reserves accumulated in many emerging market economies, and provides a comprehensive framework to assess the adequacy of reserve holdings. Using the case of Mexico, I find that more than two thirds of the increase in international reserves can be replicated by a linear combination of external shocks, without an abrupt regime shift after the Tequila crisis. I also find that Mexico has historically adopted an appropriate reserves policy, with 1994 being an exception. However, under the current reserves policy, there is a positive probability of a current account crisis in the near future. In chapter Two, I investigate the optimal reserves policy. The analysis predicts an optimal level of reserves in Mexico that is considerably higher than the actual level. When I account for the possibility of a bailout by the outside world in case of a crisis, Mexico's current reserves policy is in the range of my model's predictions. The final chapter proposes a new explanation for the existence and nature of sudden stops. In my model, a sudden stop forms a necessary solution to the moral hazard problem in investment and can be rationalized as part of an optimal lending strategy in the face of asymmetric information. / Thesis (Ph.D, Economics) -- Queen's University, 2009-08-13 22:52:26.219

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In this thesis we study three different problems: convex ancient solutions to the power-of-mean curvature flow; Sharp inequalities; regularity results in some applications of optimal transportation. The second chapter is devoted to the power-of-mean curvature flow; We prove some estimates for convex ancient solutions (the existence time for the solution starts from -\infty) to the power-of-mean curvature flow, when the power is strictly greater than \frac{1}{2}. As an application, we prove that in two dimension, the blow-down of an entire convex translating solution, namely u_{h}=\frac{1}{h}u(h^{\frac{1}{1+\alpha}}x), locally uniformly converges to \frac{1}{1+\alpha}|x|^{1+\alpha} as h\rightarrow\infty. The second application is that for generalized curve shortening flow (convex curve evolving in its normal direction with speed equal to a power of its curvature), if the convex compact ancient solution sweeps the whole space \mathbb{R}^{2}, it must be a shrinking circle. Otherwise the solution must be defined in a strip region. In the first section of the third chapter, we prove a one-parameter family of sharp conformally invariant integral inequalities for functions on the $n$-dimensional unit ball. As a limiting case, we obtain an inequality that generalizes Carleman's inequality for harmonic functions in the plane to poly-harmonic functions in higher dimensions. The second section represents joint work with Tobias Weth and Rupert Frank; the main result is that, one can always put a sharp remainder term on the righthand side of the sharp fractional sobolev inequality. In the first section of the final chapter, under some suitable condition, we prove that the solution to the principal-agent problem must be C^{1}. The proof is based on a perturbation argument. The second section represents joint work with Emanuel Indrei; the main result is that, under (A3S) condition on the cost and c-convexity condition on the domains, the free boundary in the optimal partial transport problem is C^{1,\alpha}.