Analytical Results for the Statistical Distribution Related to Memoryless Deterministic Tourist Walk: Dimensionality Effect and Mean Field Models

Consider a medium characterized by N points whose coordinates are randomly generated by a uniform distribution along the edges of a unitary d-dimensional hypercube. A walker leaves from each point of this disordered medium and moves according to the deterministic rule to go to the nearest point which has not been visited in the preceding \mu steps (deterministic tourist walk). Each trajectory generated by this dynamics has an initial non-periodic part of t steps (transient) and a final periodic part of p steps (attractor). The neighborhood rank probabilities are parameterized by the normalized incomplete beta function I_d = I_{1/4}[1/2,(d+1)/2]. The joint distribution S_{\mu,d}^{(N)}(t,p) is relevant, and the marginal distributions previously studied are particular cases. We show that, for the memory-less deterministic tourist walk in the euclidean space, this distribution is: S_{1,d}^{(\infty)}(t,p) = [\Gamma(1+I_d^{-1}) (t+I_d^{-1})/\Gamma(t+p+I_d^{-1})] \delta_{p,2}, where t=0,1,2,...,\infty, \Gamma(z) is the gamma function and \delta_{i,j} is the Kronecker's delta. The mean field models are random link model, which corresponds to d \to \infty, and random map model which, even for \mu = 0, presents non-trivial cycle distribution [S_{0,rm}^{(N)}(p) \propto p^{-1}]: S_{0,rm}^{(N)}(t,p) = \Gamma(N)/\{\Gamma[N+1-(t+p)]N^{t+p}\}. The fundamental quantities are the number of explored points n_e=t+p and I_d. Although the obtained distributions are simple, they do not follow straightforwardly and they have been validated by numerical experiments.Comment: 9 pages and 4 figure

Exploratory Behavior, Trap Models and Glass Transitions

A random walk is performed on a disordered landscape composed of $N$ sites randomly and uniformly distributed inside a $d$-dimensional hypercube. The walker hops from one site to another with probability proportional to $\exp [- \beta E(D)]$, where $\beta = 1/T$ is the inverse of a formal temperature and $E(D)$ is an arbitrary cost function which depends on the hop distance $D$. Analytic results indicate that, if $E(D) = D^{d}$ and $N \to \infty$, there exists a glass transition at $\beta_d = \pi^{d/2}/\Gamma(d/2 + 1)$. Below $T_d$, the average trapping time diverges and the system falls into an out-of-equilibrium regime with aging phenomena. A L\'evy flight scenario and applications to exploratory behavior are considered.Comment: 4 pages, 1 figure, new versio

Prognostic value of epidermal growth factor receptors in gastric cancer: a survival analysis by Weibull model incorporating long-term survivors

BACKGROUND: There is no consensus about the prognostic role of HER2 expression and that of other members of the EGFR family in gastric cancer patients. The aim of this study was to evaluate the prognostic value of the EGFR family in gastric cancer. METHODS: This retrospective study included 201 patients with gastric and esophagogastric junction adenocarcinoma stages 0–IV (AJCC 6th edition) who underwent primary tumor resection. Tissues from primary tumors were analyzed by tissue microarray technology and immunohistochemistry. Correlations between receptor expression and clinicopathological characteristics were performed according to the chi-square test. Survival analysis was calculated according to the Weibull model with a mixture model incorporating long-term survivors. Multivariate analysis of prognostic factors was performed by a regression model incorporating long-term survivors with the Weibull distribution. RESULTS: Membrane expression of HER1, HER2, and HER4 were 9, 17, and 15 %, respectively. No membrane expression of HER3 was observed. Cytoplasmic expression of HER1, HER3, and HER4 were 45, 62, and 24 %, respectively. HER2 and HER3 expression were correlated (p < 0.001) and associated with intestinal-type histology (p = 0.001 and p < 0.001, respectively) and advanced age (p = 0.011 and p = 0.008, respectively). According to a regression model adjusted for age, surgical radicality, surgical modality, Laurén histology, adjuvant therapy, TNM stage, and receptor expressions, only TNM stage showed prognostic influence. CONCLUSIONS: According to analysis by a parametric model, the EGFR family did not have prognostic influence in the gastric cancer population studied. The data presented showed a correlation between HER2 and HER3 expression, which might suggest a potential role for HER2–HER3 heterodimerization inhibitors

Bacterial Killing Via A Type Iv Secretion System.

Type IV secretion systems (T4SSs) are multiprotein complexes that transport effector proteins and protein-DNA complexes through bacterial membranes to the extracellular milieu or directly into the cytoplasm of other cells. Many bacteria of the family Xanthomonadaceae, which occupy diverse environmental niches, carry a T4SS with unknown function but with several characteristics that distinguishes it from other T4SSs. Here we show that the Xanthomonas citri T4SS provides these cells the capacity to kill other Gram-negative bacterial species in a contact-dependent manner. The secretion of one type IV bacterial effector protein is shown to require a conserved C-terminal domain and its bacteriolytic activity is neutralized by a cognate immunity protein whose 3D structure is similar to peptidoglycan hydrolase inhibitors. This is the first demonstration of the involvement of a T4SS in bacterial killing and points to this special class of T4SS as a mediator of both antagonistic and cooperative interbacterial interactions.6645

Aquatic exercise associated or not with grape juice consumption-modulated oxidative parameters in Parkinson disease patients : a randomized intervention study

Parkinson's disease (PD) is a neurodegenerative disorder with significant motor disabilities and cognitive decline. Importantly, the imbalance of oxidative stress is related to PD physiopathology and progression. This study aimed to evaluate the impact of grape juice consumption associated with an aquatic exercise protocol on oxidative stress parameters and cognitive function in individuals with PD. The participants were randomized into two groups: grape juice group (GJG) and control group (CG) and were submitted to 4 weeks of an aquatic intervention (twice a week, approximately 60 minutes/session). The GJG also consumed 400 ml of grape juice per day (integral and conventional) during this period. Cognitive function was assessed by the Montreal Cognitive Assessment (MoCa) questionnaire. For the analysis of oxidative stress markers, specifically lipid oxidative damage (TBARS), proteins (Carbonil), acid uric and the activity of antioxidant enzymes (superoxide dismutase, glutathione peroxidase and catalase), blood collection were done before and after intervention. No changes were observed in cognitive function after intervention in both groups. Regarding biomarkers, a reduction of antioxidant enzymes, thiobarbituric acid reactive substances (TBARS) and uric acid was observed in both groups. However, only the GJG showed a significant reduction on protein oxidation levels after intervention. In conclusion, the consumption of grape juice associated with an aquatic exercise protocol might be consider an effective alternative to reduce the oxidative damage in PD, reinforcing the importance of this intervention in promoting beneficial impact in this population