When telegrapher's equation furnishes a better approximation to transport equation than the difussion approximation

It has been suggested that a solution to the transport equation which includes anisotropic scattering can be approximated by the solution to a telegrapher's equation [A.J. Ishimaru, Appl. Opt. 28, 2210 (1989)]. We show that in one dimension the telegrapher's equation furnishes an exact solution to the transport equation. In two dimensions, we show that, since the solution can become negative, the telegrapher's equation will not furnish a usable approximation. A comparison between simulated data in three dimensions indicates that the solution to the telegrapher's equation is a good approximation to that of the full transport equation at the times at which the diffusion equation furnishes an equally good approximation.

Generalization of the persistent random walk to dimensions greater than 1

We propose a generalization of the persistent random walk for dimensions greater than 1. Based on a cubic lattice, the model is suitable for an arbitrary dimension d. We study the continuum limit and obtain the equation satisfied by the probability density function for the position of the random walker. An exact solution is obtained for the projected motion along an axis. This solution, which is written in terms of the free-space solution of the one-dimensional telegraphers equation, may open a new way to address the problem of light propagation through thin slabs.

Non independent continuous-time random walks

The usual development of the continuous-time random walk (CTRW) assumes that jumps and time intervals are a two-dimensional set of independent and identically distributed random variables. In this paper, we address the theoretical setting of nonindependent CTRWs where consecutive jumps and/or time intervals are correlated. An exact solution to the problem is obtained for the special but relevant case in which the correlation solely depends on the signs of consecutive jumps. Even in this simple case, some interesting features arise, such as transitions from unimodal to bimodal distributions due to correlation. We also develop the necessary analytical techniques and approximations to handle more general situations that can appear in practice.

On a class of exact solutions to the Fokker-Planck equations

In this paper we study under which circumstances there exists a general change of gross variables that transforms any FokkerPlanck equation into another of the OrnsteinUhlenbeck class that, therefore, has an exact solution. We find that any FokkerPlanck equation will be exactly solvable by means of a change of gross variables if and only if the curvature tensor and the torsion tensor associated with the diffusion is zero and the transformed drift is linear. We apply our criteria to the Kubo and Gompertz models.

Exact temporal evolution for some non-linear diffusion process

Exact solutions to FokkerPlanck equations with nonlinear drift are considered. Applications of these exact solutions for concrete models are studied. We arrive at the conclusion that for certain drifts we obtain divergent moments (and infinite relaxation time) if the diffusion process can be extended without any obstacle to the whole space. But if we introduce a potential barrier that limits the diffusion process, moments converge with a finite relaxation time.

Effective squark/chargino/neutralino couplings: MadGraph implementation

We have included the effective description of squark interactions with charginos/neutralinos in the MadGraph MSSM model. This effective description includes the effective Yukawa couplings, and another logarithmic term which encodes the supersymmetry-breaking. We have performed an extensive test of our implementation analyzing the results of the partial decay widths of squarks into charginos and neutralinos obtained by using FeynArts/FormCalc programs and the new model file in MadGraph. We present results for the cross-section of top-squark production decaying into charginos and neutralinos.

Schmidtea mediterranea phylogeography: an old species surviving on a few mediterranean islands?

Schmidtea mediterranea (Platyhelminthes, Tricladida, Continenticola) is found in scattered localities on a few islands and in coastal areas of the western Mediterranean. Although S. mediterranea is the object of many regeneration studies, little is known about its evolutionary history. Its present distribution has been proposed to stem from the fragmentation and migration of the Corsica-Sardinia microplate during the formation of the western Mediterranean basin, which implies an ancient origin for the species. To test this hypothesis, we obtained a large number of samples from across its distribution area. Using known and new molecular markers and, for the first time in planarians, a molecular clock, we analysed the genetic variability and demographic parameters within the species and between its sexual and asexual populations to estimate when they diverged. Results: A total of 2 kb from three markers (COI, CYB and a nuclear intron N13) was amplified from ~200 specimens. Molecular data clustered the studied populations into three groups that correspond to the west, central and southeastern geographical locations of the current distribution of S. mediterranea. Mitochondrial genes show low haplotype and nucleotide diversity within populations but demonstrate higher values when all individuals are considered. The nuclear marker shows higher values of genetic diversity than the mitochondrial genes at the population level, but asexual populations present lower variability than the sexual ones. Neutrality tests are significant for some populations. Phylogenetic and dating analyses show the three groups to be monophyletic, with the west group being the basal group. The time when the diversification of the species occurred is between ~20 and ~4 mya, although the asexual nature of the western populations could have affected the dating analyses. Conclusions: S. mediterranea is an old species that is sparsely distributed in a harsh habitat, which is probably the consequence of the migration of the Corsica-Sardinia block. This species probably adapted to temperate climates in the middle of a changing Mediterranean climate that eventually became dry and hot. These data also suggest that in the mainland localities of Europe and Africa, sexual individuals of S. mediterranea are being replaced by asexual individuals that are either conspecific or are from other species that are better adapted to the Mediterranean climate.

On the existence of doubling measures with certain regularity properties

Given a compact pseudo-metric space, we associate to it upper and lower dimensions, depending only on the pseudo-metric. Then we construct a doubling measure for which the measure of a dilated ball is closely related to these dimensions.

Periodic points of holomorphic maps via Lefschetz numbers

In this paper we study the set of periods of holomorphic maps on compact manifolds, using the periodic Lefschetz numbers introduced by Dold and Llibre, which can be computed from the homology class of the map. We show that these numbers contain information about the existence of periodic points of a given period; and, if we assume the map to be transversal, then they give us the exact number of such periodic orbits. We apply this result to the complex projective space of dimension n and to some special type of Hopf surfaces, partially characterizing their set of periods. In the first case we also show that any holomorphic map of CP(n) of degree greater than one has infinitely many distinct periodic orbits, hence generalizing a theorem of Fornaess and Sibony. We then characterize the set of periods of a holomorphic map on the Riemann sphere, hence giving an alternative proof of Baker's theorem.

HLA class II antigens (DR, DQ LOCI) and peripheral arthritis in ankylosing spondylitis.

Fifty one patients with ankylosing spondylitis (AS) were typed for HLA-A, B, C, DR, and DQ antigens. The antigen frequencies were compared with those of a normal population and with a B27 positive control group. All but one of the patients with AS were HLA-B27 positive. A positive linkage disequilibrium between Cw1, Cw2, DR1, and the B27 antigen was observed. Patients with AS showed a significant increase in DQw2 antigen compared with the B27 positive control group. No differences in antigenic frequencies were observed in patients having peripheral arthritis and patients with only axial involvement. Seven out of nine patients (78%) with an erosive peripheral arthritis were DR7 positive, suggesting that DR7 or genes closely linked could be related with a more aggressive peripheral joint involvement in patients with AS.

Early use of TIPS in patients with cirrhosis and variceal bleeding.

Background Patients with cirrhosis in ChildPugh class C or those in class B who have persistent bleeding at endoscopy are at high risk for treatment failure and a poor prognosis, even if they have undergone rescue treatment with a transjugular intrahepatic porto - systemic shunt (TIPS). This study evaluated the earlier use of TIPS in such patients. Methods We randomly assigned, within 24 hours after admission, a total of 63 patients with cirrhosis and acute variceal bleeding who had been treated with vasoactive drugs plus endoscopic therapy to treatment with a polytetrafluoroethylene-covered stent within 72 hours after randomization (early-TIPS group, 32 patients) or continuation of vasoactive-drug therapy, followed after 3 to 5 days by treatment with propranolol or nadolol and long-term endoscopic band ligation (EBL), with insertion of a TIPS if needed as rescue therapy (pharmacotherapyEBL group, 31 patients). Results During a median follow-up of 16 months, rebleeding or failure to control bleeding occurred in 14 patients in the pharmacotherapyEBL group as compared with 1 patient in the early-TIPS group (P=0.001). The 1-year actuarial probability of remaining free of this composite end point was 50% in the pharmacotherapyEBL group versus 97% in the early-TIPS group (P<0.001). Sixteen patients died (12 in the pharmacotherapyEBL group and 4 in the early-TIPS group, P=0.01). The 1-year actuarial survival was 61% in the pharmacotherapyEBL group versus 86% in the early-TIPS group (P<0.001). Seven patients in the pharmacotherapyEBL group received TIPS as rescue therapy, but four died. The number of days in the intensive care unit and the percentage of time in the hospital during follow-up were significantly higher in the pharmacotherapyEBL group than in the early-TIPS group. No significant diferences were observed between the two treatment groups with respect to serious adverse events. Conclusions In these patients with cirrhosis who were hospitalized for acute variceal bleeding and at high risk for treatment failure, the early use of TIPS was associated with signif icant reductions in treatment failure and in mortality. (Current Controlled Trials number, ISRCTN58150114.)