A Cortical-Inspired Contour Completion Model Based on Contour Orientation and Thickness.

An extended four-dimensional version of the traditional Petitot-Citti-Sarti model on contour completion in the visual cortex is examined. The neural configuration space is considered as the group of similarity transformations, denoted as M=SIM(2). The left-invariant subbundle of the tangent bundle models possible directions for establishing neural communication.

Liouville Integrability in a Four-Dimensional Model of the Visual Cortex.

We consider a natural extension of the Petitot-Citti-Sarti model of the primary visual cortex. In the extended model, the curvature of contours is taken into account. The occluded contours are completed via sub-Riemannian geodesics in the four-dimensional space M of positions, orientations, and curvatures.

Entropic Balance Conditions and Optimization of Distillation Column System.

The paper considers the limitation problem of the distillation column systems separating multicomponent mixtures with serial and parallel structures. The solution takes into account the irreversibility of processes. Using entropic balance conditions, the dependence of load on heat consumption is obtained for a binary distillation column.

Sociological modeling of smart city with the implementation of UN sustainable development goals.

Unlabelled: The COVID-19 pandemic before mass vaccination can be restrained only by the limitation of contacts between people, which makes the digital economy a key condition for survival. More than half of the world's population lives in urban areas, and many cities have already transformed into "smart" digital/virtual hubs. Digital services ensure city life safe without an economy lockout and unemployment.

Averaged Optimization and Finite-Time Thermodynamics.

The paper considers typical extremum problems that contain mean values of control variables or some functions of these variables. Relationships between such problems and cyclic modes of dynamical systems are explained and optimality conditions for these modes are found. The paper shows how these problems are linked to the field of finite-time thermodynamics.

Finite-Time Thermodynamics in Economics.

In this paper, we consider optimal trading processes in economic systems. The analysis is based on accounting for irreversibility factors using the wealth function concept. The existence of the welfare function is proved, the concept of capital dissipation is introduced as a measure of the irreversibility of processes in the microeconomic system, and the economic balances are recorded, including capital dissipation.

Approaches to Medical Decision-Making Based on Big Clinical Data.

The paper discusses different approaches to building a medical decision support system based on big data. The authors sought to abstain from any data reduction and apply universal teaching and big data processing methods independent of disease classification standards. The paper assesses and compares the accuracy of recommendations among three options: case-based reasoning, simple single-layer neural network, and probabilistic neural network.

Finding limiting possibilities of thermodynamic systems by optimization.

We consider typical problems of the field called the finite time thermodynamics (also called the optimization thermodynamics). We also outline selected formal methods applied to solve these problems and discuss some results obtained. It is shown that by introducing constraints imposed on the intensity of fluxes and on the magnitude of coefficients in kinetic equations, it is possible not only to investigate limiting possibilities of thermodynamic systems within the considered class of irreversible processes, but also to state and solve problems whose formulation has no meaning in the class of reversible processes.

Tracking of Lines in Spherical Images via Sub-Riemannian Geodesics in .

In order to detect salient lines in spherical images, we consider the problem of minimizing the functional for a curve on a sphere with fixed boundary points and directions. The total length is free, denotes the spherical arclength, and denotes the geodesic curvature of  . Here the smooth external cost is obtained from spherical data.

Precedent Approach to Decision Making in Clinical Processes.

This poster describes the results of promising research in the field of clinical processes management and decision making support. The authors formulated common scientific problems connected with the modelling of treatment processes. The research is supported by grants from the Ministry of Education and Science of the Russian Federation (the project RFMEFI60714X0089).

Association Fields via Cuspless Sub-Riemannian Geodesics in SE(2).

To model association fields that underly perceptional organization (gestalt) in psychophysics we consider the problem of minimizing [Formula: see text] for a planar curve having fixed initial and final positions and directions. Here () is the curvature of the curve with free total length . This problem comes from a model of geometry of vision due to Petitot (in J.

Neural network models in a set selection problem.

WE INTRODUCE A CONTINUOUS FAMILY OF HIGH ORDER NEURAL NETWORK MODELS WHICH SOLVE THE SET SELECTION PROBLEM: given a finite list of finite sets, find a set that intersects each of them in exactly one element. The additive model proposed earlier by Clark Jeffries belongs to this family. We study deformations of the additive model within our family in a case when 50% of its attracting equilibria do not correspond to answer sets of the problem.

Maximal work problem in finite-time thermodynamics.

In this paper three problems are considered: (a) the maximal work that can be produced in a finite time in a thermodynamic system; (b) the minimal work which must be done in order to transform an equilibrium thermodynamic system into a number of subsystems that are out of equilibrium with each other in finite time; and (c) the maximal power that can be achieved in a finite time. The mathematical features of these problems are investigated. It is shown that in many cases the limiting work processes here are processes where intensive variables are piecewise-constant functions of time, and that these functions take not more than some predefined number of values.