Fock-space approach to stochastic susceptible-infected-recovered models.

We investigate the stochastic susceptible-infected-recovered (SIR) model of infectious disease dynamics in the Fock-space approach. In contrast to conventional SIR models based on ordinary differential equations for the subpopulation sizes of S, I, and R individuals, the stochastic SIR model is driven by a master equation governing the transition probabilities among the system's states defined by SIR occupation numbers. In the Fock-space approach the master equation is recast in the form of a real-valued Schrödinger-type equation with a second quantization Hamiltonian-like operator describing the infection and recovery processes. We find exact analytic expressions for the Hamiltonian eigenvalues for any population size N. We present small- and large-N results for the average numbers of SIR individuals and basic reproduction number. For small N we also obtain the probability distributions of SIR states, epidemic sizes and durations, which cannot be found from deterministic SIR models. Our Fock-space approach to stochastic SIR models introduces a powerful set of tools to calculate central quantities of epidemic processes, especially for relatively small populations where statistical fluctuations not captured by conventional deterministic SIR models play a crucial role.

Ultrafast convergent power-balance model for Raman random fiber laser with half-open cavity.

The power-relevant features of Raman random fiber laser (RRFL), such as lasing threshold, slope efficiency, and power distribution, are among the most critical parameters to characterize its operation status. In this work, focusing on the power features of the half-open cavity RRFL, an ultrafast convergent power-balance model is proposed, which highlights the physical essence of the most common RRFL type and sharply reduces the computation workload. By transforming the time-consuming serial calculation to a parallel one, the calculation efficiency can be improved by more than 100 times. Particularly, for different point-mirror reflectivities and different fiber lengths, the input-output power curves and power distribution curves calculated by the present model match nicely with those of the conventional model, as well as with the experimental data. Moreover, through the present model the relationship between point-mirror reflectivity and laser threshold is analytically derived, and the way for improving RRFL's slope efficiency is also provided with a lucid theoretical explanation.

Lévy flights between absorbing boundaries: Revisiting the survival probability and the shift from the exponential to the Sparre-Andersen limit behavior.

We revisit the problem of calculating the survival probability of Lévy flights in a finite interval with absorbing boundaries. Our approach is based on the master equation for discrete Lévy fliers, previously considered to treat the semi-infinite domain. We argue that, although the semi-infinite case can be treated exactly due to Wiener-Hopf factorization, the approximation involved in the problem with the finite interval is actually fairly good. We evidence the shift in the universal behavior of the long-term survival probability from the exponential decay in the presence of two absorbing barriers to the Sparre-Andersen power-law dependence in the single-barrier limit. In some cases, we also calculate the short- and intermediate-term behavior and present the explicit dependence of the survival probability on the Lévy flier's starting position. Our analytical results are confirmed by numerical simulations.

Role of the endocannabinoid system in the neuroendocrine responses to inflammation.

A few years ago the endocannabinoid system has been recognized as a major neuromodulatory system whose main functions are to exert and maintain the body homeostasis. Several different endocannabinoids are synthesized in a broad class of cell types, including those in the brain and the immune system; they bind to cannabinoid G-protein-coupled receptors, having profound effects on a variety of behavioral, neuroendocrine and autonomic functions. The coordinated neural, immune, behavioral and endocrine responses to inflammation are orchestrated to provide an important defense against infections and help homeostasis restoration in the body. These responses are executed and controlled mainly by the hypothalamic-pituitary adrenal axis. Also, the hypothalamic-neurohypophyseal system is essential for survival and plays a role recovering the homeostasis under a variety of stress conditions, including inflammation and infection. Since the endocannabinoid system components are present at sites involved in the hypothalamic-pituitary axis regulation, several studies were performed in order to investigate the endocannabinoid-mediated neurotransmitters and hormones secretion under physiological and pathological conditions. In the present review we focused on the endocannabinoids actions on the neuroendocrine response to inflammation and infection. We provide a detailed overview of the current understanding of the role of the endocannabinoid system in the recovering of homeostasis as well as potential pharmacological therapies based on the manipulation of endocannabinoid system components that could provide novel treatments for a wide range of disorders.