Query-Points Visibility Constraint Minimum Link Paths in Simple Polygons

We study the query version of constrained minimum link paths between two points inside a simple polygon P with n vertices such that there is at least one point on the path, visible from a query point. The method is based on partitioning P into a number of faces of equal link distance from a point, called a link-based shortest path map (SPM). Initially, we solve this problem for two given points s, t and a query point q. Then, the proposed solution is extended to a general case for three arbitrary query points s, t and q. In the former, we propose an algorithm with O(n) preprocessing time. Extending this approach for the latter case, we develop an algorithm with O(n3) preprocessing time. The link distance of a q-visible path between s, t as well as the path are provided in time O(log n) and O(m + log n), respectively, for the above two cases, where m is the number of links.

Omega Index of Line and Total Graphs

A derived graph is a graph obtained from a given graph according to some predetermined rules. Two of the most frequently used derived graphs are the line graph and the total graph. Calculating some properties of a derived graph helps to calculate the same properties of the original graph. For this reason, the relations between a graph and its derived graphs are always welcomed. A recently introduced graph index which also acts as a graph invariant called omega is used to obtain such relations for line and total graphs. As an illustrative exercise, omega values and the number of faces of the line and total graphs of some frequently used graph classes are calculated.

Robust Hybrid High-Order Method on Polytopal Meshes with Small Faces

We design a Hybrid High-Order (HHO) scheme for the Poisson problem that is fully robust on polytopal meshes in the presence of small edges/faces. We state general assumptions on the stabilisation terms involved in the scheme, under which optimal error estimates (in discrete and continuous energy norms, as well as L 2 L^{2} -norm) are established with multiplicative constants that do not depend on the maximum number of faces in each element, or the relative size between an element and its faces. We illustrate the error estimates through numerical simulations in 2D and 3D on meshes designed by agglomeration techniques (such meshes naturally have elements with a very large numbers of faces, and very small faces).

An improved Loop subdivision to coordinate the smoothness and the number of faces via multi-objective optimization

3D mesh subdivision is essential for geometry modeling of complex surfaces, which benefits many important applications in the fields of multimedia such as computer animation. However, in the ordinary adaptive subdivision, with the deepening of the subdivision level, the benefits gained from the improvement of smoothness cannot keep pace with the cost caused by the incremental number of faces. To mitigate the gap between the smoothness and the number of faces, this paper devises a novel improved mesh subdivision method to coordinate the smoothness and the number of faces in a harmonious way. First, this paper introduces a variable threshold, rather than a constant threshold used in existing adaptive subdivision methods, to reduce the number of redundant faces while keeping the smoothness in each subdivision iteration. Second, to achieve the above goal, a new crack-solving method is developed to remove the cracks by refining the adjacent faces of the subdivided area. Third, as a result, the problem of coordinating the smoothness and the number of faces can be formulated as a multi-objective optimization problem, in which the possible threshold sequences constitute the solution space. Finally, the Non-dominated sorting genetic algorithm II (NSGA-II) is improved to efficiently search the Pareto frontier. Extensive experiments demonstrate that the proposed method consistently outperforms existing mesh subdivision methods in different settings.

INFLUENCE OF THE MESH SHAPE OF THE FINE LITTER CLEANER FOR RAW COTTON ON THE CLEANING EFFECT

Increasing the efficiency of cleaning raw cotton from weeds will ultimately improve the quality of products in the textile industry. It has been established that when using cylindrical mesh on purifiers with peg drums, the exciting force acting on the strips from the side of the net has a stable frequency, determined mainly by the frequency of rotation of the peg drum. This mode of operation of the cleaner does not effectively remove trash impurities. To improve the efficiency of the cleaner, it is proposed to use a grid in the form of a multifaceted prism. It was found that, by design conditions, the minimum number of mesh faces is four. The dependence of the cleaning effect on the number of faces of the perforated mesh of the cleaner has been experimentally obtained. It was found that with an increase in the number of mesh edges, the cleaning effect and fiber damage decrease. With the number of faces equal to six, it is possible to achieve an increase in the cleaning effect by an average of 16 % with a slight increase in fibre damage.

MULTIPARAMETRIC OPTIMIZATION OF THE SHAPE AND THICKNESS OF INSULATED ENERGY EFFICIENT CONSTRUCTED BUILDING WITH A SPECIFIC NUMBER OF FACES

To calculate the optimal parameters of outbuildings, a mathematical model and method for optimizing the shape and resistance of heat transfer for opaque and transparent structures with a certain constant number of faces, building volume and amount of insulation to minimize the thermal balance of enclosing structures with the environment during the heating period In the course of calculations the geometrical parameters of translucent, opaque structures in the heat-insulating shell of buildings are determined taking into account heat losses, heat influx from solar radiation by the criterion of ensuring minimum heat losses through enclosing structures, rational parameters (buildings) The given technique and mathematical models should be used in the future in the design of energy efficient buildings in the reconstruction and thermal modernization of buildings. This will increase their energy efficiency and, accordingly, the energy efficiency class of buildings. For the research faceted attached building in the form of a triangular pyramid, the reduction in heat loss was 14.82 percent only due to the optimization of the shape and redistribution of the insulation. Similar results were obtained for other initial forms. For the first time, a computerized method was proposed, an algorithm and application package Optimparam for multiparameter shape optimization and insulation of translucent and opaque structures for outbuildings with a given number of arbitrarily arranged faces were developed.

Increased face detection responses on the mooney faces test in people at clinical high risk for psychosis

Identifying state-sensitive measures of perceptual and cognitive processes implicated in psychosis may allow for objective, earlier, and better monitoring of changes in mental status that are predictive of an impending psychotic episode, relative to traditional self-report-based clinical measures. To determine whether a measure of visual perception that has demonstrated sensitivity to the clinical state of schizophrenia in multiple prior studies is sensitive to features of the at-risk mental state, we examined differences between young people identified as being at clinical high risk for psychosis (CHR; n = 37) and non-psychiatric matched controls (n = 29) on the Mooney Faces Test (MFT). On each trial of the MFT, participants report whether they perceive a face in a degraded face image. The CHR group reported perceiving a greater number of faces in both upright and inverted MFT stimuli. Consistent with prior work, males reported more faces on the MFT than females in both conditions. However, the finding of greater reported face perception among CHR subjects was robustly observed in the female CHR group relative to the female control group. Among male CHR participants, greater reported face perception was related to increased perceptual abnormalities. These preliminary results are consistent with a small but growing literature suggesting that heightened perceptual sensitivity may characterize individuals at increased clinical risk for psychosis. Further studies are needed to determine the contributions of specific perceptual, cognitive, and motivational mechanisms to the findings.

Planarity and non-separating cycles in uniform high genus quadrangulations

We study large uniform random bipartite quadrangulations whose genus grows linearly with the number of faces. Their local convergence was recently established by Budzinski and the author [9, 10]. Here we study several properties of these objects which are not captured by the local topology. Namely we show that balls around the root are planar with high probability up to logarithmic radius, and we prove that there exist non-contractible cycles of constant length with positive probability.

SINGLE-SHOT FACE DETECTION AND RECOGNITION BASED ON CNN

The paper proposes an architecture and training method of a deep convolutional neural network for simultaneous face detection and recognition. The implemented approach combines the ideas of SSD (Single Shot Detector) and Faster R-CNN (Region proposal Convolutional Neural Networks) algorithms. Face detection is performed similarly to single-stage detection algorithms, and then a biometric template is built by employing RoI (Region of Interest) pooling layers and using the separate branch of the neural network. Training process includes three stages: pretraining of thebasic CNN for face recognition on face images, fine-tuning by using RoI pooling on in painted face images, adding SSD layers and fine-tuning on face detection. Wherein, at the latter stage, training is performed by using shared layers technology for two databases simultaneously. The main feature of the algorithm is high processing speed, which does not depend on the number of faces in the input image. For example, in case of using ResNet-34 as the core architecture for the algorithm, the required time for detecting faces and building biometric templates on an image with 100 faces is less than 13 ms. For training purposes we use CASIA-WebFace for face recognition task and Wider Face for face detection task. Testing is performed on FDDB (Face Detection Dataset and Benchmark), since this database is closer to practical applications than Wider. As long as the main practical task the developed method is intended for is face reidentification, we use Fei Face DataBase for face recognition quality testing. We obtain TPR (True Positive Rate) = 0.928@1000 on FDDB Face DataBase and FAR (Face Acceptance Rate) = 0.03309@FRR (Face Rejection Rate) = 10–4. Therefore, the proposed algorithm allows solving face detection and reidentification tasks in real time with any number of faces on an input image.