Critical behavior of a contact process with aperiodic transition rates

We performed Monte Carlo simulations to investigate the steady-state critical behavior of a one-dimensional contact process with an aperiodic distribution of rates of transition. As in the presence of randomness, spatial fluctuations can lead to changes of critical behavior. For sufficiently weak fluctuations, we give numerical evidence to show that there is no departure from the universal critical behavior of the underlying uniform model. For strong spatial fluctuations, the analysis of the data indicates a change of critical universality class.

POSTMARITAL RESIDENCE PRACTICE IN SOUTHERN BRAZILIAN COASTAL GROUPS: CONTINUITY AND CHANGE

The coastal plains of the States of Parana and Santa Catarina, in Southern Brazil, were first settled around 6000 B.P. by shellmound builders, a successful fisher-hunter-gatherer population that inhabited the coastal lowlands practically unchanged for almost five thousand years. Shellmounds were typically occupied as residential sites as well as cemeteries, and are usually associated with rich alimentary zones. Around 1200 B.P., the first evidence of ceramics brought from the interior is found in coastal areas, and together with ceramics there is a progressive abandonment of shellmound construction in favor of flat cold shallow sites. Here we consider if these changes were reflected in the postmarital residence practice of coastal groups, i.e., if the arrival or intensification of contact with groups from the interior resulted in changes in this aspect of social structure among the coastal groups. To test the postmarital residence practice we analyzed within-group variability ratios between males and females, following previous studies on the topic. and between-group, correlations between Mahalanobis distances and geographic distances. The results suggest that in the pre-ceramic series a matrilocal, postmarital residential system predominated, while in the ceramic period there was a shift toward patrilocality. This favors the hypothesis that the changes experienced by coastal groups after 1200 B.P. affected not only their economy and material culture, but important aspects of their sociopolitical organization as well.

Density-Profile Processes Describing Biological Signaling Networks: Almost Sure Convergence to Deterministic Trajectories

We introduce jump processes in R(k), called density-profile processes, to model biological signaling networks. Our modeling setup describes the macroscopic evolution of a finite-size spin-flip model with k types of spins with arbitrary number of internal states interacting through a non-reversible stochastic dynamics. We are mostly interested on the multi-dimensional empirical-magnetization vector in the thermodynamic limit, and prove that, within arbitrary finite time-intervals, its path converges almost surely to a deterministic trajectory determined by a first-order (non-linear) differential equation with explicit bounds on the distance between the stochastic and deterministic trajectories. As parameters of the spin-flip dynamics change, the associated dynamical system may go through bifurcations, associated to phase transitions in the statistical mechanical setting. We present a simple example of spin-flip stochastic model, associated to a synthetic biology model known as repressilator, which leads to a dynamical system with Hopf and pitchfork bifurcations. Depending on the parameter values, the magnetization random path can either converge to a unique stable fixed point, converge to one of a pair of stable fixed points, or asymptotically evolve close to a deterministic orbit in Rk. We also discuss a simple signaling pathway related to cancer research, called p53 module.

Billiards in a General Domain with Random Reflections

We study stochastic billiards on general tables: a particle moves according to its constant velocity inside some domain D R(d) until it hits the boundary and bounces randomly inside, according to some reflection law. We assume that the boundary of the domain is locally Lipschitz and almost everywhere continuously differentiable. The angle of the outgoing velocity with the inner normal vector has a specified, absolutely continuous density. We construct the discrete time and the continuous time processes recording the sequence of hitting points on the boundary and the pair location/velocity. We mainly focus on the case of bounded domains. Then, we prove exponential ergodicity of these two Markov processes, we study their invariant distribution and their normal (Gaussian) fluctuations. Of particular interest is the case of the cosine reflection law: the stationary distributions for the two processes are uniform in this case, the discrete time chain is reversible though the continuous time process is quasi-reversible. Also in this case, we give a natural construction of a chord ""picked at random"" in D, and we study the angle of intersection of the process with a (d - 1) -dimensional manifold contained in D.

Minimal surfaces in S(3) with constant contact angle

We provide a characterization of the Clifford Torus in S(3) via moving frames and contact structure equations. More precisely, we prove that minimal surfaces in S(3) with constant contact angle must be the Clifford Torus. Some applications of this result are then given, and some examples are discussed.

On the composite of irreducible morphisms in almost sectional paths

We study here when the composite of it irreducible morphisms in almost sectional paths is non-zero and lies in Rn+1 (C) 2007 Elsevier B.V. All rights reserved.

The bar-radical of a class of almost alternative baric algebras

In this article we prove that, if (U, ) is a finite dimensional baric algebra of (gamma, delta) type over a field F of characteristic not equal 2,3,5 such that gamma(2) - delta(2) + delta = 1 and 0,1, then rad(U) = R(U)boolean AND(bar(U))(2), where R(U) is the nilradical (maximal nil ideal) of U.

On the manifold structure of the set of unparameterized embeddings with low regularity

Given manifolds M and N, with M compact, we study the geometrical structure of the space of embeddings of M into N, having less regularity than C(infinity) quotiented by the group of diffeomorphisms of M.

On the Multiplicity of Orthogonal Geodesics in Riemannian Manifold With Concave Boundary. Applications to Brake Orbits and Homoclinics

Let (M, g) be a complete Riemannian Manifold, Omega subset of M an open subset whose closure is diffeomorphic to an annulus. If partial derivative Omega is smooth and it satisfies a strong concavity assumption, then it is possible to prove that there are at least two geometrically distinct geodesics in (Omega) over bar = Omega boolean OR partial derivative Omega starting orthogonally to one connected component of partial derivative Omega and arriving orthogonally onto the other one. The results given in [6] allow to obtain a proof of the existence of two distinct homoclinic orbits for an autonomous Lagrangian system emanating from a nondegenerate maximum point of the potential energy, and a proof of the existence of two distinct brake orbits for a. class of Hamiltonian systems. Under a further symmetry assumption, it is possible to show the existence of at least dim(M) pairs of geometrically distinct geodesics as above, brake orbits and homoclinics.

Geodesics and Almost Geodesic Cycles in Random Regular Graphs

A geodesic in a graph G is a shortest path between two vertices of G. For a specific function e(n) of n, we define an almost geodesic cycle C in G to be a cycle in which for every two vertices u and v in C, the distance d(G)(u, v) is at least d(C)(u, v) - e(n). Let omega(n) be any function tending to infinity with n. We consider a random d-regular graph on n vertices. We show that almost all pairs of vertices belong to an almost geodesic cycle C with e(n)= log(d-1)log(d-1) n+omega(n) and vertical bar C vertical bar =2 log(d-1) n+O(omega(n)). Along the way, we obtain results on near-geodesic paths. We also give the limiting distribution of the number of geodesics between two random vertices in this random graph. (C) 2010 Wiley Periodicals, Inc. J Graph Theory 66: 115-136, 2011

Applicatiion of Almost ideal demand system for a pharmaceutical

This thesis is an application of the Almost Ideal Demand System approach of Deaton and Muellbauer,1980, for a particular pharmaceutical, Citalopram, in which GORMAN´s (1971) multi-stage budgeting approach is applied basically since it is one of the most useful approach in estimating demand for differentiated products. Citalopram is an antidepressant drug that is used in the treatment of major depression. As for most other pharmaceuticals whose the patent has expired, there exist branded and generic versions of Citalopram. This paper is aimed to define its demand system with two stage models for the branded version and five generic versions, and to show whether generic versions are able to compete with the branded version. I calculated the own price elasticities, and it made me possible to compare and make a conclusion about the consumers’ choices over the brand and generic drugs. Even though the models need for being developed with some additional variables, estimation results of models and uncompensated price elasticities indicated that the branded version has still power in the market, and generics are able to compete with lower prices. One important point that has to be taken into consideration is that the Swedish pharmaceutical market faced a reform on October 1, 2002, that aims to make consumer better informed about the price and decrease the overall expenditures for pharmaceuticals. Since there were not significantly enough generic sales to take into calculation before the reform, my paper covers sales after the reform.

Who gets the cats...you or me? Analyzing contact and residence issues regarding pets upon divorce or separation

Mills and Akers outline the statistical incidence of pet ownership and people's need for domestic pets, discuss ownership or property rights in domestic pets, outline the criteria used by the courts when ruling on implied contact and residence rights regarding domestic pets upon the irretrievable breakdown between the "owners" of the particular pets, and highlight both the shortcomings in the existing law and possible means of overcoming those shortcomings.

Identifying Heel Contact and Toe-Off Using Forceplate Thresholds With a Range of Digital-Filter Cutoff Frequencies

Analysis of human gait requires accurate measurement of foot-ground contact, often determined using either foot-ground reaction force thresholds or kinematic data. This study examined the differences in calculating event times across five vertical force thresholds and validated a vertical acceleration-based algorithm as a measure of heel contact and toe-off.

Direct current electric potential in an anisotropic half-space with vertical contact containing a conductive 3D body

Detailed studies of anomalous conductors in otherwise homogeneous media have been modelled. Vertical contacts form common geometries in galvanic studies when describing geological formations with different electrical conductivities on either side. However, previous studies of vertical discontinuities have been mainly concerned with isotropic environments. In this paper, we deal with the effect on the electric potentials, such as mise-`a-la-masse anomalies, due to a conductor near a vertical contact between two anisotropic regions. We also demonstrate the interactive effects when the conductive body is placed across the vertical contact. This problem is normally very difficult to solve by the traditional numerical methods. The integral equations for the electric potential in anisotropic half-spaces are established. Green’s function is obtained using the reflection and transmission image method in which five images are needed to fit the boundary conditions on the vertical interface and the air-earth surface. The effects of the anisotropy of the environments and the conductive body on the electric potential are illustrated with the aid of several numerical examples.