Computational methods for tactical simulations

Tämä taktiikan tutkimus keskittyy tietokoneavusteisen simuloinnin laskennallisiin menetelmiin, joita voidaan käyttää taktisen tason sotapeleissä. Työn tärkeimmät tuotokset ovat laskennalliset mallit todennäköisyyspohjaisen analyysin mahdollistaviin taktisen tason taistelusimulaattoreihin, joita voidaan käyttää vertailevaan analyysiin joukkue-prikaatitason tarkastelutilanteissa. Laskentamallit keskittyvät vaikuttamiseen. Mallit liittyvät vahingoittavan osuman todennäköisyyteen, jonka perusteella vaikutus joukossa on mallinnettu tilakoneina ja Markovin ketjuina. Edelleen näiden tulokset siirretään tapahtumapuuanalyysiin operaation onnistumisen todennäköisyyden osalta. Pienimmän laskentayksikön mallinnustaso on joukkue- tai ryhmätasolla, jotta laskenta-aika prikaatitason sotapelitarkasteluissa pysyisi riittävän lyhyenä samalla, kun tulokset ovat riittävän tarkkoja suomalaiseen maastoon. Joukkueiden mies- ja asejärjestelmävahvuudet ovat jakaumamuodossa, eivätkä yksittäisiä lukuja. Simuloinnin integroinnissa voidaan käyttää asejärjestelmäkohtaisia predictor corrector –parametreja, mikä mahdollistaa aika-askelta lyhytaikaisempien taistelukentän ilmiöiden mallintamisen. Asemallien pohjana ovat aiemmat tutkimukset ja kenttäkokeet, joista osa kuuluu tähän väitöstutkimukseen. Laskentamallien ohjelmoitavuus ja käytettävyys osana simulointityökalua on osoitettu tekijän johtaman tutkijaryhmän ohjelmoiman ”Sandis”- taistelusimulointiohjelmiston avulla, jota on kehitetty ja käytetty Puolustusvoimien Teknillisessä Tutkimuslaitoksessa. Sandikseen on ohjelmoitu karttakäyttöliittymä ja taistelun kulkua simuloivia laskennallisia malleja. Käyttäjä tai käyttäjäryhmä tekee taktiset päätökset ja syöttää nämä karttakäyttöliittymän avulla simulointiin, jonka tuloksena saadaan kunkin joukkuetason peliyksikön tappioiden jakauma, keskimääräisten tappioiden osalta kunkin asejärjestelmän aiheuttamat tappiot kuhunkin maaliin, ammuskulutus ja radioyhteydet ja niiden tila sekä haavoittuneiden evakuointi-tilanne joukkuetasolta evakuointisairaalaan asti. Tutkimuksen keskeisiä tuloksia (kontribuutio) ovat 1) uusi prikaatitason sotapelitilanteiden laskentamalli, jonka pienin yksikkö on joukkue tai ryhmä; 2) joukon murtumispisteen määritys tappioiden ja haavoittuneiden evakuointiin sitoutuvien taistelijoiden avulla; 3) todennäköisyyspohjaisen riskianalyysin käyttömahdollisuus vertailevassa tutkimuksessa sekä 4) kokeellisesti testatut tulen vaikutusmallit ja 5) toimivat integrointiratkaisut. Työ rajataan maavoimien taistelun joukkuetason todennäköisyysjakaumat luovaan laskentamalliin, kenttälääkinnän malliin ja epäsuoran tulen malliin integrointimenetelmineen sekä niiden antamien tulosten sovellettavuuteen. Ilmasta ja mereltä maahan -asevaikutusta voidaan tarkastella, mutta ei ilma- ja meritaistelua. Menetelmiä soveltavan Sandis -ohjelmiston malleja, käyttötapaa ja ohjelmistotekniikkaa kehitetään edelleen. Merkittäviä jatkotutkimuskohteita mallinnukseen osalta ovat muun muassa kaupunkitaistelu, vaunujen kaksintaistelu ja maaston vaikutus tykistön tuleen sekä materiaalikulutuksen arviointi.

Investigations on Stochastic Storage Systems with Positive Service Time

In this thesis the queueing-inventory models considered are analyzed as continuous time Markov chains in which we use the tools such as matrix analytic methods. We obtain the steady-state distributions of various queueing-inventory models in product form under the assumption that no customer joins the system when the inventory level is zero. This is despite the strong correlation between the number of customers joining the system and the inventory level during lead time. The resulting quasi-birth-anddeath (QBD) processes are solved explicitly by matrix geometric methods

Variable parameter and double sampling (X)over-bar charts in the presence of correlation: The Markov chain approach

The general assumption under which the (X) over bar chart is designed is that the process mean has a constant in-control value. However, there are situations in which the process mean wanders. When it wanders according to a first-order autoregressive (AR (1)) model, a complex approach involving Markov chains and integral equation methods is used to evaluate the properties of the (X) over bar chart. In this paper, we propose the use of a pure Markov chain approach to study the performance of the (X) over bar chart. The performance of the chat (X) over bar with variable parameters and the (X) over bar with double sampling are compared. (C) 2011 Elsevier B.V. All rights reserved.

Evolução das disparidades da extração vegetal e da silvicultura na Amazônia Legal: uma aplicação da cadeia de Markov

O artigo analisa a convergência municipal da produtividade vegetal (extração vegetal e silvicultura) na região da Amazônia Legal entre os anos de 1996 e 2006. Para analisar a convergência, optou-se pela metodologia da matriz de transição de Markov (Processo Estacionário de Primeira Ordem de Markov). Os resultados mostram a existência de 13 classes de convergência da produtividade vegetal. No longo prazo, a hipótese de convergência absoluta não se mantém, visto que 68,23% dos municípios encontram-se numa classe inferior à média municipal, 33,54% em uma classe intermediária acima da média e 13,41% em uma classe superior acima da média.

Aplicações das Cadeias de Markov para o Ensino Médio

Pós-graduação em Matemática em Rede Nacional - IBILCE

Geometric and Combinatorial Aspects of NonEquilibrium Statistical Mechanics

Non-Equilibrium Statistical Mechanics is a broad subject. Grossly speaking, it deals with systems which have not yet relaxed to an equilibrium state, or else with systems which are in a steady non-equilibrium state, or with more general situations. They are characterized by external forcing and internal fluxes, resulting in a net production of entropy which quantifies dissipation and the extent by which, by the Second Law of Thermodynamics, time-reversal invariance is broken. In this thesis we discuss some of the mathematical structures involved with generic discrete-state-space non-equilibrium systems, that we depict with networks in all analogous to electrical networks. We define suitable observables and derive their linear regime relationships, we discuss a duality between external and internal observables that reverses the role of the system and of the environment, we show that network observables serve as constraints for a derivation of the minimum entropy production principle. We dwell on deep combinatorial aspects regarding linear response determinants, which are related to spanning tree polynomials in graph theory, and we give a geometrical interpretation of observables in terms of Wilson loops of a connection and gauge degrees of freedom. We specialize the formalism to continuous-time Markov chains, we give a physical interpretation for observables in terms of locally detailed balanced rates, we prove many variants of the fluctuation theorem, and show that a well-known expression for the entropy production due to Schnakenberg descends from considerations of gauge invariance, where the gauge symmetry is related to the freedom in the choice of a prior probability distribution. As an additional topic of geometrical flavor related to continuous-time Markov chains, we discuss the Fisher-Rao geometry of nonequilibrium decay modes, showing that the Fisher matrix contains information about many aspects of non-equilibrium behavior, including non-equilibrium phase transitions and superposition of modes. We establish a sort of statistical equivalence principle and discuss the behavior of the Fisher matrix under time-reversal. To conclude, we propose that geometry and combinatorics might greatly increase our understanding of nonequilibrium phenomena.

Evaluating statistical methods used to estimate the number of postsynaptic receptors.

Calcium levels in spines play a significant role in determining the sign and magnitude of synaptic plasticity. The magnitude of calcium influx into spines is highly dependent on influx through N-methyl D-aspartate (NMDA) receptors, and therefore depends on the number of postsynaptic NMDA receptors in each spine. We have calculated previously how the number of postsynaptic NMDA receptors determines the mean and variance of calcium transients in the postsynaptic density, and how this alters the shape of plasticity curves. However, the number of postsynaptic NMDA receptors in the postsynaptic density is not well known. Anatomical methods for estimating the number of NMDA receptors produce estimates that are very different than those produced by physiological techniques. The physiological techniques are based on the statistics of synaptic transmission and it is difficult to experimentally estimate their precision. In this paper we use stochastic simulations in order to test the validity of a physiological estimation technique based on failure analysis. We find that the method is likely to underestimate the number of postsynaptic NMDA receptors, explain the source of the error, and re-derive a more precise estimation technique. We also show that the original failure analysis as well as our improved formulas are not robust to small estimation errors in key parameters.

Searching for convergence in phylogenetic Markov chain Monte Carlo

Markov chain Monte Carlo (MCMC) is a methodology that is gaining widespread use in the phylogenetics community and is central to phylogenetic software packages such as MrBayes. An important issue for users of MCMC methods is how to select appropriate values for adjustable parameters such as the length of the Markov chain or chains, the sampling density, the proposal mechanism, and, if Metropolis-coupled MCMC is being used, the number of heated chains and their temperatures. Although some parameter settings have been examined in detail in the literature, others are frequently chosen with more regard to computational time or personal experience with other data sets. Such choices may lead to inadequate sampling of tree space or an inefficient use of computational resources. We performed a detailed study of convergence and mixing for 70 randomly selected, putatively orthologous protein sets with different sizes and taxonomic compositions. Replicated runs from multiple random starting points permit a more rigorous assessment of convergence, and we developed two novel statistics, delta and epsilon, for this purpose. Although likelihood values invariably stabilized quickly, adequate sampling of the posterior distribution of tree topologies took considerably longer. Our results suggest that multimodality is common for data sets with 30 or more taxa and that this results in slow convergence and mixing. However, we also found that the pragmatic approach of combining data from several short, replicated runs into a metachain to estimate bipartition posterior probabilities provided good approximations, and that such estimates were no worse in approximating a reference posterior distribution than those obtained using a single long run of the same length as the metachain. Precision appears to be best when heated Markov chains have low temperatures, whereas chains with high temperatures appear to sample trees with high posterior probabilities only rarely. [Bayesian phylogenetic inference; heating parameter; Markov chain Monte Carlo; replicated chains.]

Evaluating New Matrix Pooled Testing Methods for Detecting HIV Treatment Failure with and without Covariate Information

Thesis (Master's)--University of Washington, 2016-08

Likelihood-Based Inference for Partially Observed Multi-Type Markov Branching Processes

Thesis (Ph.D.)--University of Washington, 2016-08

Stability and ergodicity of piecewise deterministic Markov processes

The main goal of this paper is to establish some equivalence results on stability, recurrence, and ergodicity between a piecewise deterministic Markov process ( PDMP) {X( t)} and an embedded discrete-time Markov chain {Theta(n)} generated by a Markov kernel G that can be explicitly characterized in terms of the three local characteristics of the PDMP, leading to tractable criterion results. First we establish some important results characterizing {Theta(n)} as a sampling of the PDMP {X( t)} and deriving a connection between the probability of the first return time to a set for the discrete-time Markov chains generated by G and the resolvent kernel R of the PDMP. From these results we obtain equivalence results regarding irreducibility, existence of sigma-finite invariant measures, and ( positive) recurrence and ( positive) Harris recurrence between {X( t)} and {Theta(n)}, generalizing the results of [ F. Dufour and O. L. V. Costa, SIAM J. Control Optim., 37 ( 1999), pp. 1483-1502] in several directions. Sufficient conditions in terms of a modified Foster-Lyapunov criterion are also presented to ensure positive Harris recurrence and ergodicity of the PDMP. We illustrate the use of these conditions by showing the ergodicity of a capacity expansion model.

Singular Perturbation for the Discounted Continuous Control of Piecewise Deterministic Markov Processes

This paper deals with the expected discounted continuous control of piecewise deterministic Markov processes (PDMP`s) using a singular perturbation approach for dealing with rapidly oscillating parameters. The state space of the PDMP is written as the product of a finite set and a subset of the Euclidean space a""e (n) . The discrete part of the state, called the regime, characterizes the mode of operation of the physical system under consideration, and is supposed to have a fast (associated to a small parameter epsilon > 0) and a slow behavior. By using a similar approach as developed in Yin and Zhang (Continuous-Time Markov Chains and Applications: A Singular Perturbation Approach, Applications of Mathematics, vol. 37, Springer, New York, 1998, Chaps. 1 and 3) the idea in this paper is to reduce the number of regimes by considering an averaged model in which the regimes within the same class are aggregated through the quasi-stationary distribution so that the different states in this class are replaced by a single one. The main goal is to show that the value function of the control problem for the system driven by the perturbed Markov chain converges to the value function of this limit control problem as epsilon goes to zero. This convergence is obtained by, roughly speaking, showing that the infimum and supremum limits of the value functions satisfy two optimality inequalities as epsilon goes to zero. This enables us to show the result by invoking a uniqueness argument, without needing any kind of Lipschitz continuity condition.

Jordan-Wigner fermionization of the one-dimensional Bariev model of three coupled XY chains

The Jordan-Wigner fermionization for the one-dimensional Bariev model of three coupled XY chains is formulated. The L-matrix in terms of fermion operators and the R-matrix are presented explicitly. Furthermore, the graded reflection equations and their solutions are discussed.

Neighborhood and Efficiency in Manufacturing in Brazilian Regions: A Spatial Markov Chain Analysis

This paper analyzes the geography of regional competitiveness in manufacturing in Brazil. The authors estimate stochastic frontiers to calculate regional efficiency of representative firms in 137 regions in the period 2000-2006, in four sectors defined by technological intensity. The efficiency results are analyzed using Markov Spatial Transition Matrices to provide insights into the transition of regions between efficiency levels, considering their local spatial context. The results indicate that geography plays an important role in manufacturing competitiveness. In particular, regions with more competitive neighbors are more likely to improve their relative efficiency (pull effect) over time, and regions with less competitive neighbors are more likely to lose relative efficiency (drag effect). The authors find that the pull effect is stronger than the drag effect.

Enamel matrix derivative induces matrix synthesis by cultured human periodontal fibroblast cells

Background: Periodontal wound healing and regeneration require that new matrix be synthesized, creating an environment into which cells can migrate. One agent which has been described as promoting periodontal regeneration is an enamel matrix protein derivative (EMD). Since no specific growth factors have been identified in EMD preparations, it is postulated that EMD acts as a matrix enhancement factor. This study was designed to investigate the effect of EMD in vitro on matrix synthesis by cultured periodontal fibroblasts. Methods: The matrix response of the cells was evaluated by determination of the total proteoglycan synthesis, glycosaminoglycan profile, and hyaluronan synthesis by the uptake of radiolabeled precursors. The response of the individual proteoglycans, versican, decorin, and biglycan were examined at the mRNA level by Northern blot analysis. Hyaluronan synthesis was probed by identifying the isotypes of hyaluronan synthase (HAS) expressed in periodontal fibroblasts as HAS-2 and HAS-3 and the effect of EMD on the levels of mRNA for each enzyme was monitored by reverse transcription polymerase chain reaction (RTPCR). Comparisons were made between gingival fibroblast (GF) cells and periodontal ligament (PDLF) cells. Results: EMD was found to significantly affect the synthesis of the mRNAs for the matrix proteoglycans versican, biglycan, and decorin, producing a response similar to, but potentially greater than, mitogenic cytokines. EMD also stimulated hyaluronan synthesis in both GF and PDLF cells. Although mRNA for HAS-2 was elevated in GF after exposure to EMD, the PDLF did not show a similar response. Therefore, the point at which the stimulation of hyaluronan becomes effective may not be at the level of stimulation of the mRNA for hyaluronan synthase, but, rather, at a later point in the pathway of regulation of hyaluronan synthesis. In all cases, GF cells appeared to be more responsive to EMD than PDLF cells in vitro. Conclusions: EMD has the potential to significantly modulate matrix synthesis in a manner consistent with early regenerative events.