On Equilibrium Distribution of a Reversible Growth Model

We study a probabilistic model of interacting spins indexed by elements of a finite subset of the d-dimensional integer lattice, da parts per thousand yen1. Conditions of time reversibility are examined. It is shown that the model equilibrium distribution converges to a limit distribution as the indexing set expands to the whole lattice. The occupied site percolation problem is solved for the limit distribution. Two models with similar dynamics are also discussed.

Non-Equilibrium Reaction Rates in the Macroscopic Chemistry Method for DSMC Calculations

The Direct Simulation Monte Carlo (DSMC) method is used to simulate the flow of rarefied gases. In the Macroscopic Chemistry Method (MCM) for DSMC, chemical reaction rates calculated from local macroscopic flow properties are enforced in each cell. Unlike the standard total collision energy (TCE) chemistry model for DSMC, the new method is not restricted to an Arrhenius form of the reaction rate coefficient, nor is it restricted to a collision cross-section which yields a simple power-law viscosity. For reaction rates of interest in aerospace applications, chemically reacting collisions are generally infrequent events and, as such, local equilibrium conditions are established before a significant number of chemical reactions occur. Hence, the reaction rates which have been used in MCM have been calculated from the reaction rate data which are expected to be correct only for conditions of thermal equilibrium. Here we consider artificially high reaction rates so that the fraction of reacting collisions is not small and propose a simple method of estimating the rates of chemical reactions which can be used in the Macroscopic Chemistry Method in both equilibrium and non-equilibrium conditions. Two tests are presented: (1) The dissociation rates under conditions of thermal non-equilibrium are determined from a zero-dimensional Monte-Carlo sampling procedure which simulates ‘intra-modal’ non-equilibrium; that is, equilibrium distributions in each of the translational, rotational and vibrational modes but with different temperatures for each mode; (2) The 2-D hypersonic flow of molecular oxygen over a vertical plate at Mach 30 is calculated. In both cases the new method produces results in close agreement with those given by the standard TCE model in the same highly nonequilibrium conditions. We conclude that the general method of estimating the non-equilibrium reaction rate is a simple means by which information contained within non-equilibrium distribution functions predicted by the DSMC method can be included in the Macroscopic Chemistry Method.

Equilibrium distributions of discrete non-autonomous graphs

We introduce the notions of equilibrium distribution and time of convergence in discrete non-autonomous graphs. Under some conditions we give an estimate to the convergence time to the equilibrium distribution using the second largest eigenvalue of some matrices associated with the system.

Equilibrium distributions of topological states in circular DNA: Interplay of supercoiling and knotting

Two variables define the topological state of closed double-stranded DNA: the knot type, K, and ΔLk, the linking number difference from relaxed DNA. The equilibrium distribution of probabilities of these states, P(ΔLk, K), is related to two conditional distributions: P(ΔLk|K), the distribution of ΔLk for a particular K, and P(K|ΔLk) and also to two simple distributions: P(ΔLk), the distribution of ΔLk irrespective of K, and P(K). We explored the relationships between these distributions. P(ΔLk, K), P(ΔLk), and P(K|ΔLk) were calculated from the simulated distributions of P(ΔLk|K) and of P(K). The calculated distributions agreed with previous experimental and theoretical results and greatly advanced on them. Our major focus was on P(K|ΔLk), the distribution of knot types for a particular value of ΔLk, which had not been evaluated previously. We found that unknotted circular DNA is not the most probable state beyond small values of ΔLk. Highly chiral knotted DNA has a lower free energy because it has less torsional deformation. Surprisingly, even at |ΔLk| > 12, only one or two knot types dominate the P(K|ΔLk) distribution despite the huge number of knots of comparable complexity. A large fraction of the knots found belong to the small family of torus knots. The relationship between supercoiling and knotting in vivo is discussed.

Convergence time to equilibrium distributions of autonomous and periodic non-autonomous graphs

We present some estimates of the time of convergence to the equilibrium distribution in autonomous and periodic non-autonomous graphs, with ergodic stochastic adjacency matrices, using the eigenvalues of these matrices. On this way we generalize previous results from several authors, that only considered reversible matrices.

Role of phosphorylation in the conformation of tau peptides implicated in Alzheimer's disease

A series of peptides corresponding to isolated regions of Tau (tau) protein have been synthesized and their conformations determined by H-1 NMR spectroscopy. Immunodominant peptides corresponding to tau(224-240) and a bisphosphorylated derivative in which a single Thr and a single Ser are phosphorylated at positions 231 and 235 respectively, and which are recognized by an Alzheimer's disease-specific monoclonal antibody, were the main focus of the study. The nonphosphorylated peptide adopts essentially a random coil conformation in aqueous solution, but becomes slightly more ordered into P-type structure as the hydrophobicity of the solvent is increased by adding up to 50% trifluoroethanol (TFE). Similar trends are observed for the bisphosphorylated peptide, with a somewhat stronger tendency to form an extended structure, There is tentative NMR evidence for a small population of species containing a turn at residues 229-231 in the phosphorylated peptide, and this is strongly supported by CD spectroscopy. A proposal that the selection of a bioactive conformation from a disordered solution ensemble may be an important step (in either tubulin binding or in the formation of PHF) is supported by kinetic data on Pro isomerization. A recent study showed that Thr231 phosphorylation affected the rate of prolyl isomerization and abolished tubulin binding. This binding was restored by the action of the prolyl isomerase Pin1. In the current study, we find evidence for the existence of both trans and cis forms of tau peptides in solution but no difference in the equilibrium distribution of cis-trans isomers upon phosphorylation. Increasing hydrophobicity decreases the prevalence of cis forms and increases the major trans conformation of each of the prolines present in these molecules. We also synthesized mutant peptides containing Tyr substitutions preceding the Pro residues and found that phosphorylation of Tyr appears to have an effect on the equilibrium ratio of cis-trans isomerization and decreases the cis content.

Microscopic origin of non-Gaussian distributions of financial returns

In this paper we study the possible microscopic origin of heavy-tailed probability density distributions for the price variation of financial instruments. We extend the standard log-normal process to include another random component in the so-called stochastic volatility models. We study these models under an assumption, akin to the Born-Oppenheimer approximation, in which the volatility has already relaxed to its equilibrium distribution and acts as a background to the evolution of the price process. In this approximation, we show that all models of stochastic volatility should exhibit a scaling relation in the time lag of zero-drift modified log-returns. We verify that the Dow-Jones Industrial Average index indeed follows this scaling. We then focus on two popular stochastic volatility models, the Heston and Hull-White models. In particular, we show that in the Hull-White model the resulting probability distribution of log-returns in this approximation corresponds to the Tsallis (t-Student) distribution. The Tsallis parameters are given in terms of the microscopic stochastic volatility model. Finally, we show that the log-returns for 30 years Dow Jones index data is well fitted by a Tsallis distribution, obtaining the relevant parameters. (c) 2007 Elsevier B.V. All rights reserved.

FDI, Trade Costs and Regional Asymmetries

We set up a trade model where three countries compete for an exogenous number of firms. Our innovation lies in the geography of the model. Of the three countries, one is the hub through which all trade takes place. First, we establish the natural geography of the region, which is given by the equilibrium distribution of industrial activity in the absence of taxes or subsidies. We then examine the implications for corporate taxes when the countries compete with each other to attract firms. We find that, even when all countries are the same size, the centrality of the hub gives it an advantage in tax setting, such that its equilibrium tax can be larger than that of the spokes and yet it still attracts a disproportionate share of industry. Thus geographic advantage in tax competition has a second dimension, centrality in addition to size.

Matching stages of heavy-ion collision models

Heavy-ion reactions and other collective dynamical processes are frequently described by different theoretical approaches for the different stages of the process, like initial equilibration stage, intermediate locally equilibrated fluid dynamical stage, and final freeze-out stage. For the last stage, the best known is the Cooper-Frye description used to generate the phase space distribution of emitted, noninteracting particles from a fluid dynamical expansion or explosion, assuming a final ideal gas distribution, or (less frequently) an out-of-equilibrium distribution. In this work we do not want to replace the Cooper-Frye description, but rather clarify the ways of using it and how to choose the parameters of the distribution and, eventually, how to choose the form of the phase space distribution used in the Cooper-Frye formula. Moreover, the Cooper-Frye formula is used in connection with the freeze-out problem, while the discussion of transition between different stages of the collision is applicable to other transitions also. More recently, hadronization and molecular dynamics models have been matched to the end of a fluid dynamical stage to describe hadronization and freeze-out. The stages of the model description can be matched to each other on space-time hypersurfaces (just like through the frequently used freeze-out hypersurface). This work presents a generalized description of how to match the stages of the description of a reaction to each other, extending the methodology used at freeze-out, in simple covariant form which is easily applicable in its simplest version for most applications.

Effects of algal turbidity on foraging and antipredator behaviour of the three-spined stickleback (Gasterosteus aculeatus)

The aim of this thesis was to examine how aquatic organisms, such as fish, behave in an altered environmental condition. Many species of fish use vision as their primary tool to gain information about their surrounding environment. The visual conditions of aquatic habitats are often altered as a result of anthropogenic disturbance, such as eutrophication that initiates algal turbidity. In general, turbidity reduces the visibility and can be hypothesized to have an influence on the behaviour of fish. I used the three-spined stickleback (Gasterosteus aculeatus) as a model species and conducted four studies in the laboratory to test how algal turbidity affects its behaviour. In this thesis, two major behavioural aspects are discussed. The first is antipredator behaviour. In study I, the combined effects of turbidity and shoot density on habitat choice (shelter vs open) behaviour was tested on a group of sticklebacks (20 fish) in the presence and absence of piscivorous perch (Perca fluviatilis). In study II, I examined the behavioural responses of feeding sticklebacks when they were exposed to the sudden appearance of an avian predator (the silhouette of a common tern, Sterna hirundo). The study was done in turbid and clear water using three different groups sizes (1, 3 and 6 fish). The second aspect is foraging behaviour. Study III & IV focused on the effects of algal turbidity on the foraging performance of sticklebacks. In study III, I conducted two separate experiments to examine the effects of turbidity on prey consumption and prey choice of sticklebacks. In this experiment turbidity levels and the proportion of large and small prey (Daphnia spp.) were manipulated. In study IV, I studied whether a group of six sticklebacks can distribute themselves according to food input at two feeding stations in a way that provided each fish with the same amount of food in clear and turbid water. I also observed whether the fish can follow changes in resource distribution between the foraging patches. My results indicate an overall influence of algal turbidity on the antipredator and foraging behaviour of sticklebacks. In the presence of a potential predator, the use of the sheltered habitat was more pronounced at higher turbidity. Besides this, sticklebacks reduced their activity levels with predator presence at higher turbidity and shoot density levels, suggesting a possible antipredator adaptation to avoid a predator. When exposed to a sudden appearance of an avian predator, sticklebacks showed a weaker antipredator response in turbid water, which suggests that turbidity degrades the risk assessment capabilities of sticklebacks. I found an effect of group size but not turbidity in the proportion of sticklebacks that fled to the shelter area, which indicates that sticklebacks are able to communicate among group members at the experimental turbidity levels. I found an overall negative effect of turbidity on food intake. Both turbidity and changes in the proportion of prey sizes played a significant role in a stickleback’s prey selection. At lower turbidity levels (clear <1 and 5 NTU) sticklebacks showed preferences for large prey, whereas in more turbid conditions and when the proportion of large to small prey increased sticklebacks became increasingly random in their prey selection. Finally, my results showed that groups of sticklebacks disperse themselves between feeding stations according to the reward ratios following the predictions of the ideal free distribution theory. However, they took a significantly longer time to reach the equilibrium distribution in turbid water than in clear water. In addition, they showed a slower response to changes in resource distribution in a turbid environment. These findings suggest that turbidity interferes with the information transfer among group foragers. It is important to understand that aquatic animals are often exposed to a degraded environment. The findings of this thesis suggest that algal turbidity negatively affects their behavioural performance. The results also shed light on the underlying behavioural strategies of sticklebacks in turbid conditions that might help them adapt to an altered environmental situation and increase their survival. In conclusion, I hold that although algal turbidity has detrimental effects on the antipredator and foraging behaviour of sticklebacks, their behavioural adjustment might help them adapt to a changing environment.

Characterizations of some continuous distributions using partial moments

Inthis paper,we define partial moments for a univariate continuous random variable. A recurrence relationship for the Pearson curve using the partial moments is established. The interrelationship between the partial moments and other reliability measures such as failure rate, mean residual life function are proved. We also prove some characterization theorems using the partial moments in the context of length biased models and equilibrium distributions

The determinants of local population growth: a study of Oxfordshire in the nineteenth century

This paper presents a new econometric model for analysing population growth at the village and town level. It develops and applies a theory of the equilibrium distribution of population over space. The theory emphasises geographical fundamentals, such as rivers as transport corridors, and soil types that govern agricultural specialisation; also institutional factors such as town government, market charters and the concentration of land ownership. Nineteenth century Oxfordshire is used as a case study, but the method can also be applied at a multi-county and national level. The results show that the development of railways in nineteenth-century Oxfordshire accelerated a long-term shake-out in the market system, whereby rural markets disappeared and urban markets grew. This shake-out had significant implications for population growth at the local level.

Anomalous dependence on the diffusion coefficients of the ionic relaxation time in electrolytes

We show, by using a numerical analysis, that the dynamic toward equilibrium for an electrolytic cell subject to a step-like external electric field is a multirelaxation process when the diffusion coefficients of positive and negative ions are different. By assuming that the diffusion coefficient of positive ions is constant, we observe that the number of involved relaxation processes increases when the diffusion coefficient of the negative ions diminishes. Furthermore, two of the relaxation times depend nonmonotonically on the ratio of the diffusion coefficients. This result is unexpected, because the ionic drift velocity, by means of which the ions move to reach the equilibrium distribution, increases with increasing ionic mobility.

Microscopic origin of non-Gaussian distributions of financial returns

In this paper we study the possible microscopic origin of heavy-tailed probability density distributions for the price variation of financial instruments. We extend the standard log-normal process to include another random component in the so-called stochastic volatility models. We study these models under an assumption, akin to the Born-Oppenheimer approximation, in which the volatility has already relaxed to its equilibrium distribution and acts as a background to the evolution of the price process. In this approximation, we show that all models of stochastic volatility should exhibit a scaling relation in the time lag of zero-drift modified log-returns. We verify that the Dow-Jones Industrial Average index indeed follows this scaling. We then focus on two popular stochastic volatility models, the Heston and Hull-White models. In particular, we show that in the Hull-White model the resulting probability distribution of log-returns in this approximation corresponds to the Tsallis (t-Student) distribution. The Tsallis parameters are given in terms of the microscopic stochastic volatility model. Finally, we show that the log-returns for 30 years Dow Jones index data is well fitted by a Tsallis distribution, obtaining the relevant parameters. (c) 2007 Elsevier B.V. All rights reserved.

Maintenance of phosphatidylserine asymmetry in erythroid cells during differentiation, aging, and its significance for macrophage recognition

Phosphatidylserine (PS) is distributed almost entirely in the inner leaflet of the erythrocyte membrane bilayer, and appears to be maintained by a 32 kDa integral membrane protein (PS translocase). The expression of PS on the outer leaflet may serve as a recognition signal for macrophages, since insertion of PS into erythrocytes enhances their adherence to macrophages and clearance from the circulation. Therefore I have hypothesized that erythroid cells display PS on their outer leaflet early in differentiation and upon aging. Analysis of murine erythroleukemia cells (MELC, undifferentiated erythroid progenitor cells) showed high levels of PS on the outer leaflet that decreased during differentiation, correlating with the pattern of macrophage adherence. The activity of the PS translocase during differentiation appears to be unchanged although the equilibrium distribution of PS differs. This difference may be due to qualitative changes in the PS translocase. $\sp{125}$I-Bolton/Hunter-labeled-pyridyldithioethylamine ($\sp{125}$I-B/H-PDA), a radiolabeled probe for the PS translocase, labeled a 32 kDa protein in mature erythrocytes whereas in MELC a 45 kDa protein as well as a 32 kDa protein was identified. The abundance of the 45 kDa protein in relation to the 32 kDa protein declined during differentiation, possibly indicating this protein was a precursor of the 32 kDa protein. Analysis of the 45 kDa protein by N-glycosidase F and endoproteinase cleavage suggested this protein was not a glycosylated form of the 32 kDa protein but appeared to share some structural homology. Aged murine erythrocytes had elevated levels of PS on their outer leaflet, as well as decreased PS translocase activity. $\sp{125}$I-B/H-PDA labeled a 32 kDa protein in both normal and aged erythrocytes. However, the latter cells also contained a 28 kDa protein. Experimental evidence suggests that the appearance of the 28 kDa protein may be due to increased oxidation of aged erythrocytes. Examination of PS distribution showed that the levels of PS on the outer leaflet were elevated early in differentiation, decreased during the mature state, and returned to high levels as the erythrocyte aged. In conclusion,the levels of outer leaflet PS correlated with the differentiation status and macrophage recognition of erythroid cells. ^