The B-Terminal Busy Probability Prediction

In the teletraffic engineering of all the telecommunication networks, parameters characterizing the terminal traffic are used. One of the most important of them is the probability of finding the called (B-terminal) busy. This parameter is studied in some of the first and last papers in Teletraffic Theory. We propose a solution in this topic in the case of (virtual) channel systems, such as PSTN and GSM. We propose a detailed conceptual traffic model and, based on it, an analytical macro-state model of the system in stationary state, with: Bernoulli– Poisson–Pascal input flow; repeated calls; limited number of homogeneous terminals; losses due to abandoned and interrupted dialling, blocked and interrupted switching, not available intent terminal, blocked and abandoned ringing and abandoned conversation. Proposed in this paper approach may help in determination of many network traffic characteristics at session level, in performance evaluation of the next generation mobile networks.

Conditional probability calculations for the nonlinear Schrödinger equation with additive noise

The method for the computation of the conditional probability density function for the nonlinear Schrödinger equation with additive noise is developed. We present in a constructive form the conditional probability density function in the limit of small noise and analytically derive it in a weakly nonlinear case. The general theory results are illustrated using fiber-optic communications as a particular, albeit practically very important, example.

Credibility theory-based available transfer capability assessment

Since the development of large scale power grid interconnections and power markets, research on available transfer capability (ATC) has attracted great attention. The challenges for accurate assessment of ATC originate from the numerous uncertainties in electricity generation, transmission, distribution and utilization sectors. Power system uncertainties can be mainly described as two types: randomness and fuzziness. However, the traditional transmission reliability margin (TRM) approach only considers randomness. Based on credibility theory, this paper firstly built models of generators, transmission lines and loads according to their features of both randomness and fuzziness. Then a random fuzzy simulation is applied, along with a novel method proposed for ATC assessment, in which both randomness and fuzziness are considered. The bootstrap method and multi-core parallel computing technique are introduced to enhance the processing speed. By implementing simulation for the IEEE-30-bus system and a real-life system located in Northwest China, the viability of the models and the proposed method is verified.

Conditional Confidence Interval for the Scale Parameter of a Weibull Distribution

2000 Mathematics Subject Classification: 62F25, 62F03.

Mixed Negative Binomial Distribution by Weighted Gamma Mixing Distribution

Павел Т. Стойнов - В тази работа се разглежда отрицателно биномното разпределение, известно още като разпределение на Пойа. Предполагаме, че смесващото разпределение е претеглено гама разпределение. Изведени са вероятностите в някои частни случаи. Дадени са рекурентните формули на Панжер.

An Estimate of the Probability Pr(X

2000 Mathematics Subject Classification: 33C90, 62E99

Efficient computation of decoherent quantum walks through eigenvalue perturbation

A number of recent studies have investigated the introduction of decoherence in quantum walks and the resulting transition to classical random walks. Interestingly,it has been shown that algorithmic properties of quantum walks with decoherence such as the spreading rate are sometimes better than their purely quantum counterparts. Not only quantum walks with decoherence provide a generalization of quantum walks that naturally encompasses both the quantum and classical case, but they also give rise to new and different probability distribution. The application of quantum walks with decoherence to large graphs is limited by the necessity of evolving state vector whose sizes quadratic in the number of nodes of the graph, as opposed to the linear state vector of the purely quantum (or classical) case. In this technical report,we show how to use perturbation theory to reduce the computational complexity of evolving a continuous-time quantum walk subject to decoherence. More specifically, given a graph over n nodes, we show how to approximate the eigendecomposition of the n2×n2 Lindblad super-operator from the eigendecomposition of the n×n graph Hamiltonian.

Hybrid sampling on mutual information entropy-based clustering ensembles for optimizations

In this paper, we focus on the design of bivariate EDAs for discrete optimization problems and propose a new approach named HSMIEC. While the current EDAs require much time in the statistical learning process as the relationships among the variables are too complicated, we employ the Selfish gene theory (SG) in this approach, as well as a Mutual Information and Entropy based Cluster (MIEC) model is also set to optimize the probability distribution of the virtual population. This model uses a hybrid sampling method by considering both the clustering accuracy and clustering diversity and an incremental learning and resample scheme is also set to optimize the parameters of the correlations of the variables. Compared with several benchmark problems, our experimental results demonstrate that HSMIEC often performs better than some other EDAs, such as BMDA, COMIT, MIMIC and ECGA. © 2009 Elsevier B.V. All rights reserved.

One-dimensional optical wave turbulence:experiment and theory

We present a review of the latest developments in one-dimensional (1D) optical wave turbulence (OWT). Based on an original experimental setup that allows for the implementation of 1D OWT, we are able to show that an inverse cascade occurs through the spontaneous evolution of the nonlinear field up to the point when modulational instability leads to soliton formation. After solitons are formed, further interaction of the solitons among themselves and with incoherent waves leads to a final condensate state dominated by a single strong soliton. Motivated by the observations, we develop a theoretical description, showing that the inverse cascade develops through six-wave interaction, and that this is the basic mechanism of nonlinear wave coupling for 1D OWT. We describe theory, numerics and experimental observations while trying to incorporate all the different aspects into a consistent context. The experimental system is described by two coupled nonlinear equations, which we explore within two wave limits allowing for the expression of the evolution of the complex amplitude in a single dynamical equation. The long-wave limit corresponds to waves with wave numbers smaller than the electrical coherence length of the liquid crystal, and the opposite limit, when wave numbers are larger. We show that both of these systems are of a dual cascade type, analogous to two-dimensional (2D) turbulence, which can be described by wave turbulence (WT) theory, and conclude that the cascades are induced by a six-wave resonant interaction process. WT theory predicts several stationary solutions (non-equilibrium and thermodynamic) to both the long- and short-wave systems, and we investigate the necessary conditions required for their realization. Interestingly, the long-wave system is close to the integrable 1D nonlinear Schrödinger equation (NLSE) (which contains exact nonlinear soliton solutions), and as a result during the inverse cascade, nonlinearity of the system at low wave numbers becomes strong. Subsequently, due to the focusing nature of the nonlinearity, this leads to modulational instability (MI) of the condensate and the formation of solitons. Finally, with the aid of the probability density function (PDF) description of WT theory, we explain the coexistence and mutual interactions between solitons and the weakly nonlinear random wave background in the form of a wave turbulence life cycle (WTLC).

Why (and When) are Preferences Convex? Threshold Effects and Uncertain Quality

It is often assumed (for analytical convenience, but also in accordance with common intuition) that consumer preferences are convex. In this paper, we consider circumstances under which such preferences are (or are not) optimal. In particular, we investigate a setting in which goods possess some hidden quality with known distribution, and the consumer chooses a bundle of goods that maximizes the probability that he receives some threshold level of this quality. We show that if the threshold is small relative to consumption levels, preferences will tend to be convex; whereas the opposite holds if the threshold is large. Our theory helps explain a broad spectrum of economic behavior (including, in particular, certain common commercial advertising strategies), suggesting that sensitivity to information about thresholds is deeply rooted in human psychology.

Climate change in game theory

The study provides an overview of the application possibilities of game theory to climate change. The characteristics of games are adapted to the topics of climate and carbon. The importance of uncertainty, probability, marginal value of adaptation, common pool resources, etc. are tailored to the context of international relations and the challenge of global warming.

A bizonyosságfüggvények elméletének alkalmazása a pénzügyi kimutatások ellenőrzésében (The application of the theory of belief functions in the audit of financial statements)

A könyvvizsgálati kockázat a téves auditjelentés kiadásának kockázata olyan esetekben, amikor a beszámoló lényeges hibás állítást tartalmaz. Ez a kockázat indirekt módon a hitelintézetek és pénzügyi vállalkozások működésében is megjelenik azokban az esetekben, amikor a lényeges hibás állítást a finanszírozott vállalkozás auditált beszámolója tartalmazza, amelynek az alapján finanszírozási döntést hoznak, vagy a finanszírozás folytatásáról a beszámolóban szereplő, hibás információkból számított hitelkovenánsok alapján döntenek. A könyvvizsgálat kockázatában a vizsgált gazdálkodó üzleti kockázatai tükröződnek vissza, ezért a kockázat felmérése és az ellenőrzés ennek alapján való megtervezése, majd végrehajtása kulcsfontosságú. Jelen tanulmány – kapcsolódva a Hitelintézeti Szemle 2011. évi 4. számához – szintén a kockázat és bizonytalanság témakörét tárgyalja, pontosabban ennek egy gyakorlati vetületét: a bizonyosságfüggvények (belief functions) alkalmazását a könyvvizsgálatban; mindezt a teljesség és a tankönyvszerű rendszerfelépítés igénye nélkül. A módszer ugyanis hazánkban szinte ismeretlen, nemzetközi viszonylatban viszont empirikus kutatásban is rámutattak már az alkalmazás lehetséges előnyeire a hagyományos valószínűségelméleten alapuló számszerű kockázatbecslésekkel szemben. Eszerint a bizonyosságfüggvények jobban reprezentálják a könyvvizsgálóknak a kockázatról alkotott képét, mint a valószínűségek, mert – szemben a hagyományos modellel – nem két, hanem három állapotot kezelnek: a pozitív bizonyíték létezését, a negatív bizonyíték létezését és a bizonyíték hiányának esetét. _______ Audit risk is the risk that the auditor expresses an inappropriate audit opinion when the fi nancial statements are materially misstated. This kind of risk indirectly appears in the fi nancial statements of fi nancial institutions, when the material misstatement is in the fi nanced entity’s statements that serve as a basis for lending decisions or when the decision is made based upon credit covenants calculated from misstated information. The risks of the audit process refl ect the business risks of the auditee, so the assessment of risks, and further the planning and performance of the audit based on it is of key importance. The current study – connecting to No 4 2011 of Hitelintézeti Szemle – also discusses the topic of risk and uncertainty, or to be more precise a practical implementation of the aforementioned: the application of belief functions in the fi eld of external audit. All this without the aim of achieving completeness or textbook-like scrutiny in building up the theory. While the formalism is virtually unknown in Hungary, on the international scene empirical studies pointed out the possible advantages of the application of the method in contrast to risk assessments based on the traditional theory of probability. Accordingly, belief functions provide a better representation of auditors’ perception of risk, as in contrast to the traditional model, belief functions deal with three rather than two states: the existence of supportive evidence, that of negative evidence and the lack of evidence.

Essays on investment, growth and income distribution

In this dissertation, I examine both theoretically and empirically the relationship between stock prices and income distribution using an endogenous growth model with social status impatience.^ The theoretical part looks into how status impatience and current economic status jointly determine time preference, savings, future economic status, stock prices, growth and wealth distribution in the steady state. This work builds on Burgstaller and Karayalcin (1996).^ More specifically, I look at (i) the effects of the distribution of status impatience levels on the distribution of steady state assets, incomes and consumption and (ii) the effects of changes in relative levels of status impatience on stock prices. Therefore, from (i) and (ii), I derive the correlation between stock prices, incomes and asset distribution. Also, the analysis of the stack market is undertaken in the presence of adjustment costs to investments.^ The empirical chapter looks at (i) the correlation between income inequality and long run economic growth on the one hand and (ii) the correlation between stock market prices and income inequality on the other. The role of stock prices and social status is examined to better understand the forces that enable a country to grow overtime and to determine why output per capita varies across countries. The data are from Summers and Heston (1988), Barro and Wolf (1989), Alesina and Rodrik (1994), Global financial Database (1997) and the World Bank. Data for social status are collected through a primary sample survey on the internet. Twenty-five developed and developing countries are included in the sample.^ The model developed in this study was specified as a system of simultaneous equations, in which per capita growth rate and income inequality were endogenous variables. Additionally, stock price index and social status measures were also incorporated. The results indicate that income inequality is inversely related to economic growth. In addition, increase in income inequality arising from higher stock prices constrains growth. Moreover, where social status is determined by income levels, it influences long run growth. Therefore, these results support findings of Persson and Tabellini (1994) and Alesina and Rodrik (1994). ^

Using extreme value theory to value stock market returns

Extreme stock price movements are of great concern to both investors and the entire economy. For investors, a single negative return, or a combination of several smaller returns, can possible wipe out so much capital that the firm or portfolio becomes illiquid or insolvent. If enough investors experience this loss, it could shock the entire economy. An example of such a case is the stock market crash of 1987. Furthermore, there has been a lot of recent interest regarding the increasing volatility of stock prices. ^ This study presents an analysis of extreme stock price movements. The data utilized was the daily returns for the Standard and Poor's 500 index from January 3, 1978 to May 31, 2001. Research questions were analyzed using the statistical models provided by extreme value theory. One of the difficulties in examining stock price data is that there is no consensus regarding the correct shape of the distribution function generating the data. An advantage with extreme value theory is that no detailed knowledge of this distribution function is required to apply the asymptotic theory. We focus on the tail of the distribution. ^ Extreme value theory allows us to estimate a tail index, which we use to derive bounds on the returns for very low probabilities on an excess. Such information is useful in evaluating the volatility of stock prices. There are three possible limit laws for the maximum: Gumbel (thick-tailed), Fréchet (thin-tailed) or Weibull (no tail). Results indicated that extreme returns during the time period studied follow a Fréchet distribution. Thus, this study finds that extreme value analysis is a valuable tool for examining stock price movements and can be more efficient than the usual variance in measuring risk. ^

Distribution and ecology of amphibians and reptiles in a fragmented landscape, northeastern Bolivia

Habitat loss and fragmentation have been implicated as driving forces behind recent waves of extinction. The regional landscape where this study occurred is a mosaic of forest and grassland, and therefore provides an ideal system with which to investigate the implications of habitat patchiness for the distribution and ecology of organisms. Here I describe patterns of amphibian and reptile distribution among and within habitats at the study site, investigate associations between habitat and community structure, describe nested subset patterns on forest islands, and quantify the relationship between body size and density across ecological scales and taxonomic groups. ^ Species richness did not vary across habitats, between forest island isolation classes or between island edges and cores. In contrast, species composition varied at all three ecological scales, reflecting differences in the distribution of both forest and open-habitat affiliated species. Species composition was associated with multivariate habitat profiles, with differences occurring along the isolation gradient of forest islands rather than the area gradient. The relationship between species composition and habitat was stronger for amphibians than for reptiles, a pattern that may be ascribed to physiological differences between the two groups. Analysis of nested subset pattern of community structure indicated that species composition of islands is nested as a function of isolation. Four species whose distribution on forest islands seems to be dispersal-limited drive the relationship between nestedness and isolation. Although there were several examples of shifts in body size across spatial scales and taxonomic groups, body size was not associated with density as predicted by theory, which may reflect differences between real and habitat islands, or differential responses of poikilothermic vertebrates to changes in density relative to homeotherms. ^ Taken together, the strongest result to emerge from this research is the importance of isolation, rather than area, on community structure in this system. Much evidence suggested that different ecological groups of species show distinct patterns of distribution both within and among habitat types. This suggests that species distributions at this site are not the result of 'neutral' processes at the community level, but rather reflect fundamental differences in the ecology of component species. ^