Noise-induced escape in an excitable system

We consider the stochastic dynamics of escape in an excitable system, the FitzHugh-Nagumo (FHN) neuronal model, for different classes of excitability. We discuss, first, the threshold structure of the FHN model as an example of a system without a saddle state. We then develop a nonlinear (nonlocal) stability approach based on the theory of large fluctuations, including a finite-noise correction, to describe noise-induced escape in the excitable regime. We show that the threshold structure is revealed via patterns of most probable (optimal) fluctuational paths. The approach allows us to estimate the escape rate and the exit location distribution. We compare the responses of a monostable resonator and monostable integrator to stochastic input signals and to a mixture of periodic and stochastic stimuli. Unlike the commonly used local analysis of the stable state, our nonlocal approach based on optimal paths yields results that are in good agreement with direct numerical simulations of the Langevin equation

Colorectal reconstructions following Hartmann’s procedure: challenges and solutions

The availability of a stoma after Hartmann’s procedure significantly limits the patient’s ability to work and worsens the quality of his/her life, as it partially isolates him/her from society. Performing plastic colon surgeries is challenging due to the active formation of intestinal adhesions and low rectal stump. At present many different devices, equipment, operating methods, and techniques have been proposed for reconstructive surgery on the colon. However, the issues of access to the surgical area, providing constant visual control, both at the stage of isolation for the short stump of the rectum in the narrow pelvis and in formation process of low colorectal anastomosis, are not covered in the scientific publications

On the stability of stationary solutions in diffusion models of oncological processes

We prove a sufficient condition for the stability of a stationary solution to a system of nonlinear partial differential equations of the diffusion model describing the growth of malignant tumors. We also numerically simulate stable and unstable scenarios involving the interaction between tumor and immune cell

On the Huygens principle in the Puu model

We consider the macroeconomic model of T. Puu, describing the fluctuations of gross income in a given regio

Employing machine learning for theory validation and identification of experimental conditions in laser-plasma physics

The validation of a theory is commonly based on appealing to clearly distinguishable and describable features in properly reduced experimental data, while the use of ab-initio simulation for interpreting experimental data typically requires complete knowledge about initial conditions and parameters. We here apply the methodology of using machine learning for overcoming these natural limitations. We outline some basic universal ideas and show how we can use them to resolve long-standing theoretical and experimental difficulties in the problem of high-intensity laser-plasma interactions. In particular we show how an artificial neural network can “read” features imprinted in laser-plasma harmonic spectra that are currently analysed with spectral interferometry

Generalized compactness in linear spaces and its applications

The class of subsets of locally convex spaces called $\mu$-compact sets is considered. This class contains all compact sets as well as several noncompact sets widely used in applications. It is shown that many results well known for compact sets can be generalized to $\mu$-compact sets. Several examples are considered. The main result of the paper is a generalization to $\mu$-compact convex sets of the Vesterstrom-O'Brien theorem showing equivalence of the particular properties of a compact convex set (s.t. openness of the mixture map, openness of the barycenter map and of its restriction to maximal measures, continuity of a convex hull of any continuous function, continuity of a convex hull of any concave continuous function). It is shown that the Vesterstrom-O'Brien theorem does not hold for pointwise $\mu$-compact convex sets defined by the slight relaxing of the $\mu$-compactness condition. Applications of the obtained results to quantum information theory are considered.Comment: 27 pages, the minor corrections have been mad

Юбилей Владимира Михайловича Бенсмана (18 ноября 1927)

The article presents a brief biography of an outstanding surgeon and a scientist of the Kuban region in 20th and 21st centuries Dr. Vladimir Bensman (11/18/1927). It is dedicated to his 95th anniversary. 72 years of his professional life were dedicated to medical science and national health care!В статье представлена краткая биография выдающегося хирурга Кубани XX–XXI столетий Владимира Михайловича Бенсмана (18.11.1927). Статья приурочена к 95-летнему юбилею ученого, 72 года из которых проведены в служении медицинской науке и отечественному здравоохранению

Advances in and Issues With Minimally Invasive Surgery for Rectal Cancer in Elderly Patients

Colorectal cancer ranks third after breast cancer in terms of incidence and second after lung cancer in terms of mortality.Management of rectal cancer requires a multidisciplinary approach, with the surgical management playing the main role. There are currently three resective techniques that complement the traditional open surgery: laparoscopic surgery, robotic surgery, and transanal total mesorectal excision.Rectal cancer in elderly patients is particularly hard to diagnose and treat surgically due to multiple comorbidities and limited functional reserve. Treatment of such patients may be associated with poorer outcomes after both open and minimally invasive surgery.This article reviews the current state of advances in minimally invasive surgery for rectal cancer in general and in elderly patients in particular

On properties of the space of quantum states and their application to construction of entanglement monotones

We consider two properties of the set of quantum states as a convex topological space and some their implications concerning the notions of a convex hull and of a convex roof of a function defined on a subset of quantum states. By using these results we analyze two infinite-dimensional versions (discrete and continuous) of the convex roof construction of entanglement monotones, which is widely used in finite dimensions. It is shown that the discrete version may be 'false' in the sense that the resulting functions may not possess the main property of entanglement monotones while the continuous version can be considered as a 'true' generalized convex roof construction. We give several examples of entanglement monotones produced by this construction. In particular, we consider an infinite-dimensional generalization of the notion of Entanglement of Formation and study its properties.Comment: 34 pages, the minor corrections have been mad