Polyhedral approximations of strictly convex compacta

We consider polyhedral approximations of strictly convex compacta in finite dimensional Euclidean spaces (such compacta are also uniformly convex). We obtain the best possible estimates for errors of considered approximations in the Hausdorff metric. We also obtain new estimates of an approximate algorithm for finding the convex hulls

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

SPECIMEN EXAMINATION FOLLOWING SURGERY FOR RECTAL CANCER: OUR TECHNIQUE

Standard surgical treatment for rectal cancer is a total mesorectumectomy (TME) and it demands performing proper pathohistological examination of the removed specimen to select patients with high risk of local recurrence development and those indicated for adjuvant therapy. Pathologists should value quality of surgical intervention, examine both distal and circular resection margins (surgically mobilized mesorectal surface), define surgical clearance (distance from the circular resection margine to the tumor itself), perform pathological staging ((у)pTpN), determine histological type and stage of tumor differentiation. In this paper we describe a route of the specimen removed after the surgery for rectal cancer and its pathohistological examination technique which is based on the guidances of the British Royal Society of Pathologists specialized to the Regional Clinic Hospital requirements

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 properties of riemannian metrics associated with B-Elliptic operators

In this paper, we consider a Riemannian metric in which the Laplace-Beltrami operator coincides with a B-elliptic operator up to a facto

Meckel’s diverticulum: a cause of recurrent gastrointestinal bleeding

Background: Obscure gastrointestinal bleedings accounting for 5%-30% of all gastrointestinal bleedings continue to be a challenge and usually originate from the small bowel.Clinical case: We present a case of a female patient hospitalized with signs of gastrointestinal bleeding three times within 3 months. We could not identify the source of bleeding using standard methods, such as abdominal computed tomography and ultrasonography, esophagogastroduodenoscopy, and colonoscopy. We detected a Meckel’s diverticulum during a diagnostic laparoscopy and performed wedge resection of the small bowel. Histopathology results revealed an acute progressive ulcer in the wall of the small bowel diverticulum.Conclusions: Diagnostic laparoscopy is one of the available minimally invasive procedures, which in some cases can successfully identify the source of small bowel bleeding

On the stability of stationary states in diffusion models in biology and humanities

We consider an initial-boundary value problem for the system of partial differential equations describing processes of growth and spread of substance in biology, sociology, economics and linguistic

Weakly convex sets and modulus of nonconvexity

We consider a definition of a weakly convex set which is a generalization of the notion of a weakly convex set in the sense of Vial and a proximally smooth set in the sense of Clarke, from the case of the Hilbert space to a class of Banach spaces with the modulus of convexity of the second order. Using the new definition of the weakly convex set with the given modulus of nonconvexity we prove a new retraction theorem and we obtain new results about continuity of the intersection of two continuous set-valued mappings (one of which has nonconvex images) and new affirmative solutions of the splitting problem for selections. We also investigate relationship between the new definition and the definition of a proximally smooth set and a smooth set

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

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