Analysis of some Stochastic models in inventories and Queues

The thesis entitled Analysis of Some Stochastic Models in Inventories and Queues. This thesis is devoted to the study of some stochastic models in Inventories and Queues which are physically realizable, though complex. It contains a detailed analysis of the basic stochastic processes underlying these models. In this thesis, (s,S) inventory systems with nonidentically distributed interarrival demand times and random lead times, state dependent demands, varying ordering levels and perishable commodities with exponential life times have been studied. The queueing system of the type Ek/Ga,b/l with server vacations, service systems with single and batch services, queueing system with phase type arrival and service processes and finite capacity M/G/l queue when server going for vacation after serving a random number of customers are also analysed. The analogy between the queueing systems and inventory systems could be exploited in solving certain models. In vacation models, one important result is the stochastic decomposition property of the system size or waiting time. One can think of extending this to the transient case. In inventory theory, one can extend the present study to the case of multi-item, multi-echelon problems. The study of perishable inventory problem when the commodities have a general life time distribution would be a quite interesting problem. The analogy between the queueing systems and inventory systems could be exploited in solving certain models.

Input constraints handling in an MPC/feedback linearization scheme

The combination of model predictive control based on linear models (MPC) with feedback linearization (FL) has attracted interest for a number of years, giving rise to MPC+FL control schemes. An important advantage of such schemes is that feedback linearizable plants can be controlled with a linear predictive controller with a fixed model. Handling input constraints within such schemes is difficult since simple bound contraints on the input become state dependent because of the nonlinear transformation introduced by feedback linearization. This paper introduces a technique for handling input constraints within a real time MPC/FL scheme, where the plant model employed is a class of dynamic neural networks. The technique is based on a simple affine transformation of the feasible area. A simulated case study is presented to illustrate the use and benefits of the technique.

Critical slip and time dependence in sea ice friction

Recent research into sea ice friction has focussed on ways to provide a model which maintains much of the clarity and simplicity of Amonton's law, yet also accounts for memory effects. One promising avenue of research has been to adapt the rate- and state- dependent models which are prevalent in rock friction. In such models it is assumed that there is some fixed critical slip displacement, which is effectively a measure of the displacement over which memory effects might be considered important. Here we show experimentally that a fixed critical slip displacement is not a valid assumption in ice friction, whereas a constant critical slip time appears to hold across a range of parameters and scales. As a simple rule of thumb, memory effects persist to a significant level for 10 s. We then discuss the implications of this finding for modelling sea ice friction and for our understanding of friction in general.

Flexibility of representational states in working memory

The relationship between working memory (WM) and attention is a highly interdependent one, with evidence that attention determines the state in which items in WM are retained. Through focusing of attention, an item might be held in a more prioritized state, commonly termed as the focus of attention (FOA). The remaining items, although still retrievable, are considered to be in a different representational state. One means to bring an item into the FOA is to use retrospective cues (‘retro-cues’) which direct attention to one of the objects retained in WM. Alternatively, an item can enter a privileged state once attention is directed towards it through bottom-up influences (e.g. recency effect) or by performing an action on one of the retained items (‘incidental’ cueing). In all these cases, the item in the FOA is recalled with better accuracy compared to the other items in WM. Far less is known about the nature of the other items in WM and whether they can be flexibly manipulated in and out of the FOA. We present data from three types of experiments as well as transcranial magnetic stimulation to early visual cortex to manipulate the item inside FOA. Taken together, our results suggest that the context in which items are retained in WM matters. When an item remains behaviourally relevant, despite not being inside the FOA, re-focusing attention upon it can increase its recall precision. This suggests that a non-FOA item can be held in a state in which it can be later retrieved. However, if an item is rendered behaviourally unimportant because it is very unlikely to be probed, it cannot be brought back into the FOA, nor recalled with high precision. Under such conditions, some information appears to be irretrievably lost from WM. These findings, obtained from several different methods, demonstrate quite considerable flexibility with which items in WM can be represented depending upon context. They have important consequences for emerging state-dependent models of WM.

Enhanced long-range forecast skill in boreal winter following stratospheric strong vortex conditions

There has been a great deal of recent interest in producing weather forecasts on the 2–6 week sub-seasonal timescale, which bridges the gap between medium-range (0–10 day) and seasonal (3–6 month) forecasts. While much of this interest is focused on the potential applications of skilful forecasts on the sub-seasonal range, understanding the potential sources of sub-seasonal forecast skill is a challenging and interesting problem, particularly because of the likely state-dependence of this skill (Hudson et al 2011). One such potential source of state-dependent skill for the Northern Hemisphere in winter is the occurrence of stratospheric sudden warming (SSW) events (Sigmond et al 2013). Here we show, by analysing a set of sub-seasonal hindcasts, that there is enhanced predictability of surface circulation not only when the stratospheric vortex is anomalously weak following SSWs but also when the vortex is extremely strong. Sub-seasonal forecasts initialized during strong vortex events are able to successfully capture the associated surface temperature and circulation anomalies. This results in an enhancement of Northern annular mode forecast skill compared to forecasts initialized during the cases when the stratospheric state is close to climatology. We demonstrate that the enhancement of skill for forecasts initialized during periods of strong vortex conditions is comparable to that achieved for forecasts initialized during weak events. This result indicates that additional confidence can be placed in sub-seasonal forecasts when the stratospheric polar vortex is significantly disturbed from its normal state.

Approach to Equilibrium for a Class of Random Quantum Models of Infinite Range

We consider random generalizations of a quantum model of infinite range introduced by Emch and Radin. The generalizations allow a neat extension from the class l (1) of absolutely summable lattice potentials to the optimal class l (2) of square summable potentials first considered by Khanin and Sinai and generalised by van Enter and van Hemmen. The approach to equilibrium in the case of a Gaussian distribution is proved to be faster than for a Bernoulli distribution for both short-range and long-range lattice potentials. While exponential decay to equilibrium is excluded in the nonrandom l (1) case, it is proved to occur for both short and long range potentials for Gaussian distributions, and for potentials of class l (2) in the Bernoulli case. Open problems are discussed.

Education, preferences for leisure, and the optimal income tax schedule

Recent advances in dynamic Mirrlees economies have incorporated the treatment of human capital investments as an important dimension of government policy. This paper adds to this literature by considering a two period economy where agents are di erentiated by their preferences for leisure and their productivity, both private information. The fact that productivity is only learnt later in an agent's life introduces uncertainty to agent's savings and human capital choices and makes optimal the use of multi-period tie-ins in the mechanism that characterizes the government policy. We show that optimal policies are often interim ine cient and that the introduction of these ine ciencies may take the form of marginal tax rates on labor income of varying sign and educational policies that include the discouragement of human capital acquisition. With regards to implementation, state-dependent linear taxes implement optimal savings, while human capital policies may require labor income taxes that depend directly on agents' schooling.

Ensaios sobre o fator estocástico de descontos

Este trabalho propõe maneiras alternativas para a estimação consistente de uma medida abstrata, crucial para o estudo de decisões intertemporais, o qual é central a grande parte dos estudos em macroeconomia e finanças: o Fator Estocástico de Descontos (SDF, sigla em Inglês). Pelo emprego da Equação de Apreçamento constrói-se um inédito estimador consistente do SDF que depende do fato de que seu logaritmo é comum a todos os ativos de uma economia. O estimador resultante é muito simples de se calcular, não depende de fortes hipóteses econômicas, é adequado ao teste de diversas especificações de preferência e para a investigação de paradoxos de substituição intertemporal, e pode ser usado como base para a construção de um estimador para a taxa livre de risco. Alternativas para a estratégia de identificação são aplicadas e um paralelo entre elas e estratégias de outras metodologias é traçado. Adicionando estrutura ao ambiente inicial, são apresentadas duas situações onde a distribuição assintótica pode ser derivada. Finalmente, as metodologias propostas são aplicadas a conjuntos de dados dos EUA e do Brasil. Especificações de preferência usualmente empregadas na literatura, bem como uma classe de preferências dependentes do estado, são testadas. Os resultados são particularmente interessantes para a economia americana. A aplicação de teste formais não rejeita especificações de preferências comuns na literatura e estimativas para o coeficiente relativo de aversão ao risco se encontram entre 1 e 2, e são estatisticamente indistinguíveis de 1. Adicionalmente, para a classe de preferência s dependentes do estado, trajetórias altamente dinâmicas são estimadas para a tal coeficiente, as trajetórias são confinadas ao intervalo [1,15, 2,05] e se rejeita a hipótese de uma trajetória constante.

The macroeconomic effects of infrequent information with adjustment costs

We extend the macroeconomic literature on Sstype rules by introducing infrequent information in a kinked ad justment cost model. We first show that optimal individual decision rules are both state-and -time dependent. We then develop an aggregation framework to study the macroeconomic implications of such optimal individual decision rules. In our model, a vast number of agents act together, and more so when uncertainty is large.The average effect of an aggregate shock is inversely related to its size and to aggregate uncertainty. These results are in contrast with those obtained with full information ad justment cost models.

Demand-pull stagflation

This paper explores the possibility of stagflation emanating exc1usively from monetaJy sbocks, without concurrent supply shocks or shifts in potential output. This arises in connection with a tight money paradox. in the context of a fiscal theory of the price leveI. The paper exhibits perfect foresight equilibria with output and inflation fluctuating in opposite direetions as a consequence of small monetary shocks, and also following changes in monetaJy policy regime that launch the economy into hyperinflation or that produce dramatic stabilization of already high inflation. For that purpose, an analytically convenient dynamic general equilibrium macro model is deve10ped wbere nominal rigidities are represented by a cross between staggered two-period contracts and state dependent price adjustment in the presence of menu costs.

Does liquidity constraints matter for Ricardian equivalence?

The paper analysis a general equilibrium model with two periods, several households and a government that has to finance some expenditures in the first period. Households may have some private information either about their type (adverse selection) or about some action levei chosen in the first period that affects the probability of certain states of nature in the second period (moral hazard). Trade of financiai assets are intermediated by a finite collection of banks. Banks objective functions are determined in equilibrium by shareholders. Due to private information it may be optimal for the banks to introduce constraints in the set of available portfolios for each household as wellas household specific asset prices. In particular, households may face distinct interest rates for holding the risk-free asset. The government finances its expenditures either by taxing households in the first period or by issuing bonds in the first period and taxing households in the second period. Taxes may be state-dependent. Suppose government policies are neutml: i) government policies do not affect the distribution of wealth across households; and ii) if the government decides to tax a household in the second period there is a portfolio available for the banks that generates the Mme payoff in each state of nature as the household taxes. Tben, Ricardian equivalence holds if and only if an appropriate boundary condition is satisfied. Moreover, at every free-entry equilibrium the boundary condition is satisfied and thus Ricardian equivalence holds. These results do not require any particular assumption on the banks' objective function. In particular, we do not assume banks to be risk neutral.

Selective Coupling between Theta Phase and Neocortical Fast Gamma Oscillations during REM-Sleep in Mice

TORT, A. B. L. ; SCHEFFER-TEIXEIRA, R ; Souza, B.C. ; DRAGUHN, A. ; BRANKACK, J. . Theta-associated high-frequency oscillations (110-160 Hz) in the hippocampus and neocortex. Progress in Neurobiology , v. 100, p. 1-14, 2013.

Effects of inhibition gastric acid secretion on arterial acid-base status during digestion in the toad Bufo marinus

Digestion affects acid-base status, because the net transfer of HCl from the blood to the stomach lumen leads to an increase in HCO3- levels in both extra- and intracellular compartments. The increase in plasma [HCO3-], the alkaline tide, is particularly pronounced in amphibians and reptiles, but is not associated with an increased arterial pH, because of a concomitant rise in arterial Pco(2) caused by a relative hypoventilation. In this study, we investigate whether the postprandial increase in Paco(2) of the toad Bufo marinus represents a compensatory response to the increased plasma [HCO3-] or a state-dependent change in the control of pulmonary ventilation. To this end, we successfully prevented the alkaline tide, by inhibiting gastric acid secretion with omeprazole, and compared the response to that of untreated toads determined in our laboratory during the same period. In addition, we used vascular infusions of bicarbonate to mimic the alkaline tide in fasting animals. Omeprazole did not affect blood gases, acid-base and haematological parameters in fasting toads, but abolished the postprandial increase in plasma [HCO3-] and the rise in arterial Pco(2) that normally peaks 48 h into the digestive period. Vascular infusion of HCO3-, that mimicked the postprandial rise in plasma [HCO3-], led to a progressive respiratory compensation of arterial pH through increased arterial Pco(2) Thus, irrespective of whether the metabolic alkalosis is caused by gastric acid secretion in response to a meal or experimental infusion of bicarbonate, arterial pH is being maintained by an increased arterial Pco(2). It seems, therefore, that the elevated Pco(2), occuring during the postprandial period, constitutes of a regulated response to maintain pH rather than a state-dependent change in ventilatory control. (C) 2003 Elsevier B.V. All rights reserved.

Variational supersymmetric approach to evaluate Fokker-Planck probability

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Statements on chaos control designs, including a fractional order dynamical system, applied to a MEMS comb-drive actuator

In this work, we deal with a micro electromechanical system (MEMS), represented by a micro-accelerometer. Through numerical simulations, it was found that for certain parameters, the system has a chaotic behavior. The chaotic behaviors in a fractional order are also studied numerically, by historical time and phase portraits, and the results are validated by the existence of positive maximal Lyapunov exponent. Three control strategies are used for controlling the trajectory of the system: State Dependent Riccati Equation (SDRE) Control, Optimal Linear Feedback Control, and Fuzzy Sliding Mode Control. The controls proved effective in controlling the trajectory of the system studied and robust in the presence of parametric errors.