Graph Constructions for the Contact Process with a Prescribed Critical Rate

We construct graphs (trees of bounded degree) on which the contact process has critical rate (which will be the same for both global and local survival) equal to any prescribed value between zero and λc(Z), the critical rate of the one-dimensional contact process. We exhibit both graphs in which the process at this target critical value survives (locally) and graphs where it dies out (globally).publishedVersio

Graph constructions for the contact process with a prescribed critical rate

We construct graphs (trees of bounded degree) on which the contact process has critical rate (which will be the same for both global and local survival) equal to any prescribed value between zero and $\lambda_c(\mathbb{Z})$, the critical rate of the one-dimensional contact process. We exhibit both graphs in which the process at this target critical value survives (locally) and graphs where it dies out (globally).Comment: 31 pages, 1 figur

Multiple time scales and the empirical models for stochastic volatility

The most common stochastic volatility models such as the Ornstein-Uhlenbeck (OU), the Heston, the exponential OU (ExpOU) and Hull-White models define volatility as a Markovian process. In this work we check of the applicability of the Markovian approximation at separate times scales and will try to answer the question which of the stochastic volatility models indicated above is the most realistic. To this end we consider the volatility at both short (a few days) and long (a few months)time scales as a Markovian process and estimate for it the coefficients of the Kramers-Moyal expansion using the data for Dow-Jones Index. It has been found that the empirical data allow to take only the first two coefficients of expansion to be non zero that define form of the volatility stochastic differential equation of Ito. It proved to be that for the long time scale the empirical data support the ExpOU model. At the short time scale the empirical model coincides with ExpOU model for the small volatility quantities only.Comment: 19 pages, 6 figure

Underlying Dynamics of Typical Fluctuations of an Emerging Market Price Index: The Heston Model from Minutes to Months

We investigate the Heston model with stochastic volatility and exponential tails as a model for the typical price fluctuations of the Brazilian S\~ao Paulo Stock Exchange Index (IBOVESPA). Raw prices are first corrected for inflation and a period spanning 15 years characterized by memoryless returns is chosen for the analysis. Model parameters are estimated by observing volatility scaling and correlation properties. We show that the Heston model with at least two time scales for the volatility mean reverting dynamics satisfactorily describes price fluctuations ranging from time scales larger than 20 minutes to 160 days. At time scales shorter than 20 minutes we observe autocorrelated returns and power law tails incompatible with the Heston model. Despite major regulatory changes, hyperinflation and currency crises experienced by the Brazilian market in the period studied, the general success of the description provided may be regarded as an evidence for a general underlying dynamics of price fluctuations at intermediate mesoeconomic time scales well approximated by the Heston model. We also notice that the connection between the Heston model and Ehrenfest urn models could be exploited for bringing new insights into the microeconomic market mechanics.Comment: 20 pages, 9 figures, to appear in Physica

Structure of Extreme Correlated Equilibria: a Zero-Sum Example and its Implications

We exhibit the rich structure of the set of correlated equilibria by analyzing the simplest of polynomial games: the mixed extension of matching pennies. We show that while the correlated equilibrium set is convex and compact, the structure of its extreme points can be quite complicated. In finite games the ratio of extreme correlated to extreme Nash equilibria can be greater than exponential in the size of the strategy spaces. In polynomial games there can exist extreme correlated equilibria which are not finitely supported; we construct a large family of examples using techniques from ergodic theory. We show that in general the set of correlated equilibrium distributions of a polynomial game cannot be described by conditions on finitely many moments (means, covariances, etc.), in marked contrast to the set of Nash equilibria which is always expressible in terms of finitely many moments

Megacities and High Speed Rail systems: which comes first?

A megacity is usually defined as a metropolitan area with a total population in excess of 10 million people. The number of megacities is increasing worldwide. In most agglomerations and megacities, urban planning and public infrastructure can guide the urban development in order to achieve a proper sustainable structure only partially. The extension of cities is in most cases in advance of urban development work and the provision of public facilities (Kotter, 2004). In Europe, apart from London and Paris, megacities are rarer. However, due to the general high density of population in Europe and the short distance between medium and large cities there is the possibility of High Speed Rail (HSR) enables the emergence of groups of cities that will be linked together and thus reap the economic benefits associated with megacities, namely economies of scale, economies of agglomeration and bigger labour markets. In this contribution the authors argue that in some cases, specific facilities can foster the formation of megacities; in fact, this is the case of HSR systems. Specifically, High-Speed trains can be used to solve two different accessibility problems. In the first case, where a point-to-point link is dominant, each train is a potential substitute for an air connection between two cities, i.e. it connects cities (or rather CBDs) at long distance with a direct train connection (Blum et al., 1997).The HSR links between Paris and Lyon, Paris and London and, Tokyo and Osaka, could be seen as examples of this first type of train connection. In the second case, where a HSR network is dominant, the rail system links together many cities and CBDs and, hence, creates a new type of region with a high intra-regional accessibility sharing a common labour market and a common market for household and business services. In this case the HSR binds together cities in a band, where each pair of cities is at a time distance of between 20 minutes and 1 hour, allowing daily commuting. In the U.S., HSR projects are very recent and they will have the role of connecting already formed megacities. An example is the state of California, which is planning an 800-mile HSR service connecting Los Angeles and San Francisco into a two and a half hour trip. On the other hand, Europe, together with Asia, is the leader in HSR systems; in fact the development of HSR has been one of the central features of recent European Union transport infrastructure policy. The proposals for a European HSR network emerged in a report of the 1990 Community of European Railways and this was essentially adopted as the base for what became the European Community’s proposed Trans-European Network for HSR (Vickerman, 1997). In this paper the case studies of Portugal, where the HSR is a work in progress and of Italy, in which some lines have already been built, will be described in detail from the viewpoint of the various kinds of development described above

Papel dos receptores histaminérgicos da medula espinhal na inflamação articular de ratos e sua possível contribuição como adjuvante para os efeitos da morfina

Dissertação (mestrado) - Universidade Federal de Santa Catarina, Centro de Ciências Biológicas. Programa de Pós-Graduação em FarmacologiaA medula espinhal é conhecida por ser um centro de controle ortodrômico (nocicepção), bem como antidrômico (vasodilatação) na via nociceptiva. Os receptores de histamina participam da transmissão nociceptiva na medula espinhal, assim, é concebível que a histamina possa também desempenhar um papel no controle medular da vasodilatação periférica. O objetivo deste estudo foi avaliar o papel da via histaminérgica medular na incapacitação, no edema articular e na migração celular induzida pela injeção da carragenina na articulação do joelhos de ratos. Os animais receberam todos os fármacos por via intratecal 20 min antes da injeção intraarticular de carragenina (50 mg). A incapacitação articular foi medida pela contagem do tempo de elevação da pata (TEP), durante 1 min de caminhada forçada a cada hora, num total de 6 horas. O edema foi avaliado pela mensuração do diâmetro articular (DA). Após 6 h, o líquido sinovial foi coletado para a avaliação do infiltrado de leucócitos. A histamina foi hiponociceptiva e pró-edematogenica, diminuindo dessa forma o TEP (20 nmol) e aumentando o DA (0,002 nmol). Da mesma forma, 2-PEA diminuiu o TEP (1 nmol), e aumentou o DA (0,001 nmol). Cetirizina aumentou o TEP (0,126 pmol), e diminuiu do edema (12,6 nmol). O dimaprit diminuiu incapacitação, mas aumentou edema (18 pmol). Da mesma forma, ranitidina aumentou a incapacitação e diminuiu o edema (38 pmol). Immepip diminuiu a incapacitação (8 nmol), mas aumentou o edema (32 nmol). A tioperamida foi hipernociceptiva (4 nmol), e pró-edematogenica (0,04 nmol). A morfina inibiu incapacitação e edema (5, 45 nmol). A co-administração de morfina (0,5 nmol) com cetirizina (12,6 nmol) e immepip (16 pmol) causou hiponocicepção. Cetirizina e thioperamide aumentou o conteúdo sinovial leucócitos. A histamina pode atuar na medula espinhal por receptores H1 e H3 causando hiponocicepção, mas sua ação também pode aumentar a inflamação periférica.Spinal cord is known to be a center that controls ortodromic (nociception) as well as antidromic traffic (vasodilation) in the nociceptive pathway. Histamine receptors are known to participate in the spinal cord nociceptive transmission, thus it is conceivable that histamine may also play a role in the spinal cord control on the peripheral vasodilation. The aim of this study was evaluate the role of spinal cord histamine in the articular incapacitation, edema and cell migration induced by carrageenan injection into rat knee-joints. The animals received intrathecal injection with drugs 20 min before knee-joint carrageenan injection (50 ìg). Articular incapacitation was measured by counting the paw elevation time, during 1-min periods of forced walk hourly. Edema was accessed by the metering of the articular diameter. After 6 h, synovial fluid was collected for the evaluation of leukocyte infiltration. Histamine decreased the incapacitation (20 nmol), while increased the edema (0.002 nmol). Similarly, 2-PEA decreased the incapacitation (1 nmol), and increased the edema (0.001 nmol). Cetirizine increased the incapacitation (0.126 pmol), and decreased edema (12,6 nmol). Dimaprit decreased incapacitation, but increased edema (18 pmol). Similarly, Ranitidine increased incapacitation and decreased edema (38 pmol). Immepip decreased the incapacitation (8 nmol), but increased the edema (32 nmol). Thioperamide increased the incapacitation (4 nmol), and the edema (0.04 nmol). Morphine inhibited incapacitation and edema (5; 45 nmol). The coadministration of morphine (0.5 nmol) with cetirizine (12,6 nmol) and immepip (16 pmol) decreased incapacitation. Cetirizine and thioperamide increased the synovial leukocyte content. Histamine may act in the spinal cord by H1 and H3 receptors to cause hyponociception, but this action may also increase peripheral inflammation