Two repelling random walks on Z\mathbb Z

We consider two interacting random walks on $\mathbb{Z}$ such that the transition probability of one walk in one direction decreases exponentially with the number of transitions of the other walk in that direction. The joint process may thus be seen as two random walks reinforced to repel each other. The strength of the repulsion is further modulated in our model by a parameter $\beta \geq 0$. When $\beta = 0$ both processes are independent symmetric random walks on $\mathbb{Z}$, and hence recurrent. We show that both random walks are further recurrent if $\beta \in (0,1]$. We also show that these processes are transient and diverge in opposite directions if $\beta > 2$. The case $\beta \in (1,2]$ remains widely open. Our results are obtained by considering the dynamical system approach to stochastic approximations.Comment: 17 pages. Added references and corrected typos. Revised the argument for the convergence to equilibria of the vector field. Improved the proof for the recurrence when beta belongs to (0,1); leading to the removal of a previous conjectur

Lattice Gauge Theories and the Heisenberg Antiferromagnetic Chain

We study the strongly coupled 2-flavor lattice Schwinger model and the SU(2)-color QCD_2. The strong coupling limit, even with its inherent nonuniversality, makes accurate predictions of the spectrum of the continuum models and provides an intuitive picture of the gauge theory vacuum. The massive excitations of the gauge model are computable in terms of spin-spin correlators of the quantum Heisenberg antiferromagnetic spin-1/2 chain.Comment: Proceedings LATTICE99 (spin models), 3 page

The CONEstrip algorithm

Uncertainty models such as sets of desirable gambles and (conditional) lower previsions can be represented as convex cones. Checking the consistency of and drawing inferences from such models requires solving feasibility and optimization problems. We consider finitely generated such models. For closed cones, we can use linear programming; for conditional lower prevision-based cones, there is an efficient algorithm using an iteration of linear programs. We present an efficient algorithm for general cones that also uses an iteration of linear programs

Strongly coupled 't Hooft model on the lattice

A lattice strong coupling calculation of the spectrum and chiral condensate of the 't Hooft model is presented. The agreement with the results of the continuum theory is strikingly good even at the fourth order in the strong coupling expansion.Comment: LATTICE99(Spin Models), talk presented by F. Berruto, 3 pages, LaTex, espcrc2.st

Tumor microenvironment autophagic processes and cachexia: the missing link?

Cachexia is a syndrome that affects the entire organism and presents a variable plethora of symptoms in patients, always associated with continuous and involuntary degradation of skeletal muscle mass and function loss. In cancer, this syndrome occurs in 50% of all patients, while prevalence increases to 80% as the disease worsens, reducing quality of life, treatment tolerance, therapeutic response, and survival. Both chronic systemic inflammation and immunosuppression, paradoxically, correspond to important features in cachexia patients. Systemic inflammation in cachexia is fueled by the interaction between tumor and peripheral tissues with significant involvement of infiltrating immune cells, both in the peripheral tissues and in the tumor itself. Autophagy, as a process of regulating cellular metabolism and homeostasis, can interfere with the metabolic profile in the tumor microenvironment. Under a scenario of balanced autophagy in the tumor microenvironment, the infiltrating immune cells control cytokine production and secretion. On the other hand, when autophagy is unbalanced or dysfunctional within the tumor microenvironment, there is an impairment in the regulation of immune cell’s inflammatory phenotype. The inflammatory phenotype upregulates metabolic consumption and cytokine production, not only in the tumor microenvironment but also in other tissues and organs of the host. We propose that cachexia-related chronic inflammation can be, at least, partly associated with the failure of autophagic processes in tumor cells. Autophagy endangers tumor cell viability by producing immunogenic tumor antigens, thus eliciting the immune response necessary to counteract tumor progression, while preventing the establishment of inflammation, a hallmark of cachexia. Comprehensive understanding of this complex functional dichotomy may enhance cancer treatment response and prevent/mitigate cancer cachexia. This review summarizes the recent available literature regarding the role of autophagy within the tumor microenvironment and the consequences eliciting the development of cancer cachexia

Salophen and salen oxo vanadium complexes as catalysts of sulfides oxidation with H 2O 2: Mechanistic insights

The application of V(V) catalysts in oxidation of sulfides with peroxides offers an efficient procedure, that is compatible with different functional groups, and leads to good yields and selectivities. However, the understanding of the factors affecting the reactivity of different catalysts is still far to be complete. An experimental and theoretical study on a series of V(V) complexes containing variously substituted salen and salophen ligands is reported with the aim to correlate the activity of the catalysts with the electronic character of the vanadium center. The results obtained indicate that steric factors play a major role in determining the outcome of the reaction, often overcoming the electronic effects. Theoretical results suggest the intervention in the catalytic cycle of an hydroperoxo vanadium species

Investigation of VO-salophen complexes electronic structure

Vanadyl N,N'-bis(salicylidene)-o-phenylenediamine (salophen) complexes have been extensively investigated by cyclic voltammetry, UV-visible spectroscopy and theoretical calculations in MeCN, THF (tetrahydrofuran) and DMF (N,N-dimethylformamide), in order to elucidate the overall factors that influence the electronic density of the metal and therefore the properties of these complexes in various applications. Different substituents were introduced into the salophen skeleton to change the vanadium electron density. Results obtained and here presented showed that the substituents influence the metal electronic character in a way that cannot be easily predicted by considering only the electronic effect. Similarly, the solvent polarity or coordination ability affects the metal complex properties in an unpredictable way. Therefore, experimental and theoretical data here collected are a powerful tool to a priori design salophen ligands to obtain vanadyl complexes having the specific electronic properties suitable for desired applications