A Geometric Complementarity-Based Tool for Protein–Protein Docking

The computationally hard protein–protein complex structure prediction problem is continuously fascinating to the scientific community due to its biological impact. The field has witnessed the application of geometric algorithms, randomized algorithms, and evolutionary algorithms to name a few. These techniques improve either the searching or scoring phase. An effective searching strategy does not generate a large conformation space that perhaps demands computational power. Another determining factor is the parameter chosen for score calculation. The proposed method is an attempt to curtail the conformations by limiting the search procedure to probable regions. In this method, partial derivatives are calculated on the coarse-grained representation of the surface residues to identify the optimal points on the protein surface. Contrary to the existing geometric-based algorithms that align the convex and concave regions of both proteins, this method aligns the concave regions of the receptor with convex regions of the ligand only and thus reduces the size of conformation space. The method’s performance is evaluated using the 55 newly added targets in Protein–Protein Docking Benchmark v 5 and is found to be successful for around 47% of the targets.

PROBLEM OF A DISCRETE DATA ARRAY APPROXIMATION BY A SET OF ELEMENTARY GEOMETRIC ALGORITHMS

Context. In this paper, a problem of a discrete data array approximation by a set of elementary geometric algorithms and a recognition model representation in a form of algorithmic classification tree has been solved. The object of the present study is a concept of a classification tree in a form of an algorithm trees. The subject of this study are the relevant models, methods, algorithms and schemes of different classification tree construction. Objective. The goal of this work is to create a simple and efficient method and algorithmic scheme of building the tree-like recognition and classification models on the basis of the algorithm trees for training selections of large-volume discrete information characterized by a modular structure of independent recognition algorithms assessed in accordance with the initial training selection data for a wide class of applied tasks. Method. A scheme of classification tree (algorithm tree) synthesis has been suggested being based on the data array approximation by a set of elementary geometric algorithms that constructs a tree-like structure (the ACT model) for a preset initial training selection of arbitrary size. The latter consists of a set of autonomous classification/recognition algorithms assessed at each step of the ACT construction according to the initial selection. A method of the algorithmic classification tree construction has been developed with the basic idea of step-by-step arbitrary-volume and structure initial selection approximation by a set of elementary geometric classification algorithms. When forming a current algorithm tree vertex, node and generalized attribute, this method provides alignment of the most effective and high-quality elementary classification algorithms from the initial set and complete construction of only those paths in the ACT structure, where the most of classification errors occur. The scheme of synthesizing the resulting classification tree and the ACT model developed allows one to reduce considerably the tree size and complexity. The ACT construction structural complexity is being assessed on the basis of a number of transitions, vertices and tiers of the ACT structure that allows the quality of its further analysis to be increased, the efficient decomposition mechanism to be provided and the ACT structure to be built in conditions of fixed limitation sets. The algorithm tree synthesis method allows one to construct different-type tree-like recognition models with various sets of elementary classifiers at the preset accuracy for a wide class of artificial intelligence theory problems. Results. The method of discrete training selection approximation by a set of elementary geometric algorithms developed and presented in this work has received program realization and was studied and compared with those of logical tree classification on the basis of elementary attribute selection for solving the real geological data recognition problem. Conclusions. Both general analysis and experiments carried out in this work confirmed capability of developed mechanism of constructing the algorithm tree structures and demonstrate possibility of its promising use for solving a wide spectrum of applied recognition and classification problems. The outlooks of the further studies and approbations might be related to creating the othertype algorithmic classification tree methods with other initial sets of elementary classifiers, optimizing its program realizations, as well experimental studying this method for a wider circle of applied problems.

An Advanced Photogrammetric Solution to Measure Apples

This work presents an advanced photogrammetric pipeline for inspecting apple trees in the field, automatically detecting fruits from videos and quantifying their size and number. The proposed approach is intended to facilitate and accelerate farmers’ and agronomists’ fieldwork, making apple measurements more objective and giving a more extended collection of apples measured in the field while also estimating harvesting/apple-picking dates. In order to do this rapidly and automatically, we propose a pipeline that uses smartphone-based videos and combines photogrammetry, deep learning and geometric algorithms. Synthetic, laboratory and on-field experiments demonstrate the accuracy of the results and the potential of the proposed method. Acquired data, labelled images, code and network weights, are available at 3DOM-FBK GitHub account.

MODELING OF THE 2ND ORDER CURVES AND SURFACES OF ENGINEERING STRUCTURES SHELLS BASED ON THEIR BASIS

The paper describes an example of modeling an arc of a 2nd order curve using an engineering discriminant and its analytical description based on a graphical algorithm for constructing a curve in point calculus. Examples of modeling the surfaces of engineering structures shells on an elliptical and rectangular plan are given. Research methods include geometric algorithms: modeling of 2nd order curves passing through 3 predetermined points in advance and having tangents at the start and end points, and shell surfaces based on them; analytical definition of curves arcs and sections of surfaces using the mathematical apparatus point calculation in a given parametrization and taking into account all predetermined geometric conditions. This approach can be widely used in the practice of modeling the shells of engineering structures for various technical purposes. It allows the designer to choose the best curvature of the shell surface, which will have the necessary strength characteristics, technical aesthetics and artistic expressiveness. The possibility of dividing the surface of the shell into finite elements of a given amount is also provided for studying the stress-strain state of the shell under the action of various loads in the systems of finite element analysis.

VARIATIVE GEOMETRIC ALGORITHMS FOR MODELING MULTIFACTOR PROCESSES

The work is investigated by the influence of variable geometric algorithms in modeling multifactor processes using multidimensional interpolation. Geometric models of multifactorial processes obtained using multidimensional interpolation inherent variability, which is a consequence of the multiplicity of the choice of reference lines during the development of geometric modeling schemes. At the same time, all possible variations of geometric interpolyns are fully satisfying the initial data. It has been established that the number of variations of geometric schemes directly depends on the number of current parameters and the dimension of the space in which the simulated geometrical object is located. Thus, a variable approach to geometrical modeling of multifactor processes generates a number of scientific tasks, the main one is the need to determine the effect of the variability of geometric algorithms on the final results of the computational experiment and, as a result, the choice of the best modeling results. To this end, the article presents the studies of variable geometric algorithms and computational experiments on the example of 2-parametric geometric interpolyns. A classification of 2-parametric geometric interpolytesses, which were conditionally divided into 3 types. Depending on the geometric scheme of constructing interpolynta, the square geometric scheme, a rectangular geometric scheme, a mixed geometric scheme. As a result of computational experiments, it was found that for a square geometric scheme, the variability does not affect the final results, in rectangular geometric schemes, the variability has a slight influence, and mixed geometric schemes may have significant differences and require additional research to select the highest quality geometric process model. Comparison of geometric models were performed by the methods of scientific visualization by overlaying the response surfaces on each other.

Interval arithmetic to support effective indoor positioning of software agents

The provision of advanced location-based services in indoor environments is based on the possibility of estimating the positions of mobile devices with sufficient accuracy and robustness. An algorithm to allow a software agent hosted on a mobile device to estimate the position of its device in a known indoor environment is proposed under the ordinary assumption that fixed beacons are installed in the environment at known locations. Rather than making use of geometric considerations to estimate the position of the device, the proposed algorithm first transforms the localization problem into a related optimization problem, which is then solved by means of interval arithmetic to provide the agent with accurate and robust position estimates. The adopted approach solves a major problem that severely limits the accuracy of the position estimates that ordinary geometric algorithms provide when the beacons are positioned to maximize line-of-sight coverage. Experimental results confirm that the proposed algorithm provides position estimates that are independent of the positions of the beacons, and they show that the algorithm outperforms a well-known geometric algorithm.

The Siegel–Klein Disk: Hilbert Geometry of the Siegel Disk Domain

We study the Hilbert geometry induced by the Siegel disk domain, an open-bounded convex set of complex square matrices of operator norm strictly less than one. This Hilbert geometry yields a generalization of the Klein disk model of hyperbolic geometry, henceforth called the Siegel–Klein disk model to differentiate it from the classical Siegel upper plane and disk domains. In the Siegel–Klein disk, geodesics are by construction always unique and Euclidean straight, allowing one to design efficient geometric algorithms and data structures from computational geometry. For example, we show how to approximate the smallest enclosing ball of a set of complex square matrices in the Siegel disk domains: We compare two generalizations of the iterative core-set algorithm of Badoiu and Clarkson (BC) in the Siegel–Poincaré disk and in the Siegel–Klein disk: We demonstrate that geometric computing in the Siegel–Klein disk allows one (i) to bypass the time-costly recentering operations to the disk origin required at each iteration of the BC algorithm in the Siegel–Poincaré disk model, and (ii) to approximate fast and numerically the Siegel–Klein distance with guaranteed lower and upper bounds derived from nested Hilbert geometries.