Maximum Circle Research Articles

CRAFT: a web-integrated cavity prediction tool based on flow transfer algorithm

Numerous computational methods, including evolutionary-based, energy-based, and geometrical-based methods, are utilized to identify cavities inside proteins. Cavity information aids protein function annotation, drug design, poly-pharmacology, and allosteric site investigation. This article introduces “flow transfer algorithm” for rapid and effective identification of diverse protein cavities through multidimensional cavity scan. Initially, it identifies delimiter and susceptible tetrahedra to establish boundary regions and provide seed tetrahedra. Seed tetrahedron faces are precisely scanned using the maximum circle radius to transfer seed flow to neighboring tetrahedra. Seed flow continues until terminated by boundaries or forbidden faces, where a face is forbidden if the estimated maximum circle radius is less or equal to the user-defined maximum circle radius. After a seed scanning, tetrahedra involved in the flow are clustered to locate the cavity. The CRAFT web interface integrates this algorithm for protein cavity identification with enhanced user control. It supports proteins with cofactors, hydrogens, and ligands and provides comprehensive features such as 3D visualization, cavity physicochemical properties, percentage contribution graphs, and highlighted residues for each cavity. CRAFT can be accessed through its web interface at http://pitools.niper.ac.in/CRAFT, complemented by the command version available at https://github.com/PGlab-NIPER/CRAFT/.Scientific contributionFlow transfer algorithm is a novel geometric approach for accurate and reliable prediction of diverse protein cavities. This algorithm employs a distinct concept involving maximum circle radius within the 3D Delaunay triangulation to address diverse van der Waals radii while existing methods overlook atom specific van der Waals radii or rely on complex weighted geometric techniques.

ON THE MAXIMUM CIRCULAR INVERSES OF MAXIMUM CIRCLES

In this study, the inverses of maximum circles under the maximum circular inversion are examined. The maximum circular inversion is observed to transform maximum circles to curves consisting of parabolic arcs, line segments, and sometimes rays. It is seen that the image curve occurs in different shapes depending on the relative positions of the inversion circle and the maximum circle. While the images of maximum circles not passing through the inversion center are closed curves, the images of those passing through the inversion center are not closed. Inverse curves have been studied by considering the radii of the maximum circles and the positions of the lines joining their centers and the center of maximum inversion. Classifications of the inverses of maximum circles are presented.

A Note on the Maximum Circle Inverses of Lines in the Maximum Plane

In this study, the images of lines under inversion in maximum circle are analytically examined. It is observed that the image of line not passing through the center of the inversion is not a maximum circle, but the closed curve containing at least one parabola arc. Some properties regarding the images of lines are introduced. Then, the images of line segments are examined according to the positions of their end points . In addition, it is seen that the inversion in maximum circle transforms the pencil of parallel lines (except line passing the center) to the set of the closed curves passing the center of inversion. Also, the images of the concurrent lines under inversion with respect to a maximum circle are considered and the results are presented.

Synthesis and Activity of Aurone and Indanone Derivatives.

Based on bioactive group splicing, classical bioisosterism, and the rule of alkene insertion, forty-eight aurone, and indanone derivatives were designed and synthesized. They were evaluated for inhibitory activity against C. albicans, E. coli, and S. aureus. Among them, thirty compounds exhibited moderate to excellent antibacterial activity. The maximum circle of inhibition was 18 mm (compounds B15, B16, and E7), and the minimum values of MIC and MBC were respectively 15.625 μM (compounds A5 and D2) and 62.5 μM (compounds A6, A8, and E7). The SAR showed that aurone and indanone derivatives could strongly inhibit the growth of Gram-positive bacteria. The introduction of electron-withdrawing groups or hydroxyl is beneficial to the activity. It was exciting that the 3-phenylallylbenzofuranone and 3-allylindanone skeletons with antimicrobial activity were first reported in this study. Compounds A5 and E7 were selected for molecular docking studies with targets MetRS (PBD: 7WPI) and PBP (PDB: 6C3K) to determine the binding interactions at the active site. On this basis, the physicochemical and pharmacological properties of the compounds were predicted and analyzed. The influence of these properties on antimicrobial activity and their implications for subsequent work were discussed. The ADMET (Absorption, Distribution, Metabolism, Excretion, Toxicity) predictions showed that most of the compounds had good pharmacokinetic profiles and high safety profiles.

Quantitative Characteristics of Micro Bedding Fractures in the Wufeng–Longmaxi Formation Based on High-Resolution Map Imaging Technology

The study of microfractures in shale is mainly based on qualitative description. Conversely, quantitative description of the parameters of shale microfractures can provide a quantitative basis for shale fracture characterization and shale physical properties. Nine shale reservoir samples of the Wufeng–Longmaxi Formation in the Jiaoshiba area were studied, using the backscattered two-dimensional multiscale resolution imaging technology, combined with high-resolution map imaging technology (MAPS), and thousands of images were obtained using scanning electron microscopy. Gray image analysis was used to extract microfracture information from images (2 × 2 cm multiresolution). The “maximum circle method” was used to calculate the length and aperture characteristics of the fractures. Parameters such as the area of the bedding fractures, the surface rate of the fractures, and the linear density of the fractures were obtained by the integration of apertures. The fracture length was between 2~7 mm, the aperture was between 1~6 μm, the linear density was between 1~6/m and the surface rate was 1%. The bedding fractures do not contribute much to the porosity of the shale reservoir; however, shale reservoirs with high porosity have a high development of bedding fractures and good permeability. The development of a bedding fracture is controlled by the lithology within shale reservoirs. Different types of lithology contain different bedding fractures, but they have a certain regularity. Moreover, the content of organic matter and TOC (total organic content) in the shale reservoir control the development of a bedding fracture, where a high organic and TOC content are accompanied by a high number of fractures.

On the Maximum Apollonian Sets

In this study, the Apollonian sets are analytically examined in the plane equipped with the maximum distance function. It is determined that the maximum Apollonian set is not a maximum circle, but the closed simple rectilinear figure. Also, the classifications of the maximum Apollonian sets are given. In the case that the pair of points is on the gradual line or the steep line, the maximum Apollonian set is classified with respect to the condition.

FEATURES OF INTERACTION IN THE COMPANIES IN СONDITIONS OF DIGITALIZATION DEVELOPMENT

Digitalization in the modern world has an impact on all spheres of life. Interactions within the company are also changing. For the company to remain flexible, a special approach to workflows and communications is required. Digital tools allow build interaction in the company at a such level, when the maximum circle of people is involved in decision-making in direct contact with customers. The latter are full partners of the company. Hierarchical organizations are being replaced by self-governing systems and new concepts of organizational behavior.

The Landscape of the Spiked Tensor Model

We consider the problem of estimating a large rank‐one tensor u⊗k ∈ (ℝn)⊗k, k ≥ 3, in Gaussian noise. Earlier work characterized a critical signal‐to‐noise ratio λ Bayes = O(1) above which an ideal estimator achieves strictly positive correlation with the unknown vector of interest. Remarkably, no polynomial‐time algorithm is known that achieved this goal unless λ ≥ Cn(k − 2)/4, and even powerful semidefinite programming relaxations appear to fail for 1 ≪ λ ≪ n(k − 2)/4.In order to elucidate this behavior, we consider the maximum likelihood estimator, which requires maximizing a degree‐k homogeneous polynomial over the unit sphere in n dimensions. We compute the expected number of critical points and local maxima of this objective function and show that it is exponential in the dimensions n, and give exact formulas for the exponential growth rate. We show that (for λ larger than a constant) critical points are either very close to the unknown vector u or are confined in a band of width Θ(λ−1/(k − 1)) around the maximum circle that is orthogonal to u. For local maxima, this band shrinks to be of size Θ(λ−1/(k − 2)). These “uninformative” local maxima are likely to cause the failure of optimization algorithms. © 2019 Wiley Periodicals, Inc.

Analysis of Satellite Constellations for the Continuous Coverage of Ground Regions

This paper studies the problem of analyzing multisatellite constellations with respect to their coverage capacity of areas on Earth’s surface. The geometric configuration of constellation projection points on Earth’s surface is investigated. A geometric subdivision approach is described, and the coverage target area belonging to each satellite and its maximum circle radius are defined and calculated. Accordingly, the target area can be decomposed into subregions, and thus the multisatellite coverage problem is decomposed into a one-satellite coverage problem. An accurate and effective solution method is proposed that solves both continuous and discontinuous coverage problems for any type of ground area. In addition, a procedure for calculating satellite orbital parameters is also proposed. The performance of our approach is analyzed using the Globalstar system as an example, and it is shown that it compares favorably with the classical grid-point technique and the longitude method.

An efficiency enhanced cluster expanding block algorithm for copy-move forgery detection

The proposed scheme detects the copy-move forgery detection regions through the invariant features extracted from each block. First, an image is divided into overlapping blocks, and seven invariant moments of the maximum circle area in each block are calculated as moment features. Two clustering features, denoted by mean and variance of these seven moment features, are acquired for block comparison to reduce computation time. Therefore, the proposed scheme takes limited computation time because the seven moment features in each block are only compared to other blocks under the intersection of closed mean and variance features. The copy-move forgery regions can be found by matching the detected blocks with relative distance calculation. Experimental results show that the adopted moment features are efficient for detecting rotational or flipped duplicated regions.

A Randomized Controlled Study to Establish the Effect of Articulating Instruments on Performance in Single-Incision Laparoscopic Surgery

In single-incision laparoscopic surgery (SILS), operating through 1 incision presents ergonomic challenges. No consensus exists on whether articulating instruments (ARTs) may help. This study evaluated their effect on simulated SILS, hypothesizing that they would affect performance and workload. Surgeons were randomized to 2 straight instruments (STRs), 1 ART and 1 STR, or 2 ARTs. After baseline testing, 25 repetitions of the Fundamentals of Laparoscopic Surgery (FLS) peg-transfer (PEG) task and 5 repetitions of the short-hand for the FLS pattern-cutting task (CIRCLE) were performed. Primary outcomes were maximum FLS PEG scores, CIRCLE times and errors, and Imperial College Surgical Assessment Device hand motion analysis. National Aeronautics and Space Administration (NASA) Raw Task Load Index (RTLX) questionnaires evaluated a secondary outcome--workload. The trial took place in a simulated operating theater within the Academic Surgical Unit at St Mary's Hospital, London, UK. Eligible surgeons had completed at least 5 laparoscopic cases as a primary operator. Surgeons were stratified by laparoscopic experience into intermediate (less than 25 previous procedures as primary operator) or advanced (25 procedures or more). A total of 21 surgeons were recruited and randomized; 7 of them to each instrument combination group. All surgeons completed PEG, and 5 from each group completed CIRCLE. Groups' baseline PEG scores were similar (p = 0.625). STR-ART achieved higher maximum PEG scores than STR or ART did (median = 236 vs 198 vs 193, respectively, p = 0.002). Fastest CIRCLE times were similar (median = 190s vs 130s vs 186s, p = 0.129) as were minimum errors (median = 1 vs 2 vs 3, p = 0.101). For PEG, Imperial College Surgical Assessment Device demonstrated similar total path lengths (median = 12.3m vs 12.3m vs 16.0m, p = 0.545) and total numbers of movements (median = 89.6 vs 86.4 vs 171, p = 0.080). Groups' NASA Raw Task Load Index scores were similar (p = 0.708). Combining 1 STR and 1 ART improved SILS performance in the PEG task. Therefore, this may be the optimum instrument configuration for use within some clinical SILS applications.

How to Determine the Maximum Circle That Can Be Enclosed in a Convex Quadrilateral

How to Determine the Maximum Circle That Can Be Enclosed in a Convex Quadrilateral

Staying safe and visible via message sharing in online social networks

As an imperative channel for fast information propagation, online social networks (OSNs) also have their defects. One of them is the information leakage, i.e., information could be spread via OSNs to the users whom we are not willing to share with. Thus the problem of constructing a circle of trust to share information with as many friends as possible without further spreading it to unwanted targets has become a challenging research topic but still remained open. Our work is the first attempt to study the Maximum Circle of Trust problem seeking to share the information with the maximum expected number of poster's friends such that the information spread to the unwanted targets is brought to its knees. First, we consider a special and more practical case with the two-hop information propagation and a single unwanted target. In this case, we show that this problem is NP-hard, which denies the existence of an exact polynomial-time algorithm. We thus propose a Fully Polynomial-Time Approximation Scheme (FPTAS), which can not only adjust any allowable performance error bound but also run in polynomial time with both the input size and allowed error. FPTAS is the best approximation solution one can ever wish for an NP-hard problem. We next consider the number of unwanted targets is bounded and prove that there does not exist an FPTAS in this case. Instead, we design a Polynomial-Time Approximation Scheme (PTAS) in which the allowable error can also be controlled. When the number of unwanted targets are not bounded, we provide a randomized algorithm, along with the analytical theoretical bound and inapproximaibility result. Finally, we consider a general case with many hops information propagation and further show its #P-hardness and propose an effective Iterative Circle of Trust Detection (ICTD) algorithm based on a novel greedy function. An extensive experiment on various real-world OSNs has validated the effectiveness of our proposed approximation and ICTD algorithms. Such an extensive experiment also highlights several important observations on information leakage which help to sharpen the security of OSNs in the future.

Dotting the Dot Map, Revisited

Dot maps show the geographic distribution of a phenomenon in an area by placing dots representing a certain quantity of the phenomenon where it is most likely to occur. The fundamental steps in dot mapping are selecting the dot size, determining the dot unit value, and placing the correct number of dots in a manner that correctly reflects the geographic distribution of features. Selecting the dot size is a subjective decision, but the dot unit value has long been determined with the aid of the Mackay nomograph. Close examination of the nomograph finds it is not appropriate for determining the dot unit value when dot placement is based on computer-generated random numbers that result in overlapping dots. A new graphical aid for the determination of dot unit value was created by modeling aggregate area of dots and amount of dot overlap using a truncated form of the unification equation from probability theory. Aggregate dot areas predicted by this equation were tested against actual random dots created for several common dot sizes, and high agreement was found between measured and predicted aggregate areas. Pseudo-random dot placement with a maximum overlap constraint for dot pairs appears to mimic more closely how cartographers have traditionally placed dots. Pseudo-random dot placement can be thought of as similar to rigid random placement of circles in a square with maximum circle overlap limits from mutually exclusive to completely random dots. Thinking of dot placement in this manner allowed a general equation for aggregate dot area to be devised as a weighted combination of the mutually exclusive and completely random dot endpoint equations. Aggregate areas predicted by this general equation were found to match actual assemblages of pseudo-random dots with differing maximum dot pair overlaps closely.

Material flow patterns and cavity model in friction-stir welding of aluminum alloys

Friction-stir welding (FSW) of 3-mm-thick plates of 6061 Al and LF6 Al was conducted and the materials’ flow patterns in the weld nugget along three perpendicular planes were analyzed. The onion structure viewed on any cross section normal to the travel direction is independent of weld position. The weld morphology was examined along its length by considering planes of different depths parallel to the surface. These showed semicircle streaks whose shapes depended on the depth of the observation plane. It is determined that the weld nugget is composed of a series of identical half ellipsoid regions. A tentative simplified cavity model is presented to explain the mass flow pattern and formation of defects in the weld nugget. This model is based on the assumption that only the metal between the pin surface and the last maximum circle created by the pin rotation is in a plasticized state. From this model, it is shown that the location and size of the cavity formed during the rotation of the pin changes cyclically and it is related to the position of the pin’s center. The holes or slots left in the weld nugget center or near the advancing side are directly related to the size of the cavity. The welding parameters or weld pitch affects the volume of the cavity, and consequently influence the weld defects. A large weld pitch will cause holes to be formed in the weld nugget because of the large cavity. The flow patterns, which show that the plasticized material flows from both advancing and retreating sides to the weld center behind the pin, can be easily explained with this cavity model.

Stroke segmentation by bernstein-bezier curve fitting

Stroke segmentation is essential to the recognition of handwritten Chinese characters. Here some new and reliable techniques are proposed. First, the thinning process is applied to each character to obtain the skeleton, then a maximum circle technique is used to remove the spurious branches and merge the split 4- fork points. All possible pairs of stroke segments connected at the same fork point are considered, and the Bernstein-Bezier curve is used to fit each pair to smooth the data and find its trend. Then from the result of this curve fitting we can decide which pair belongs to the same stroke. Finally the inflection points with very small radius of curvature are found, and the stroke segmentation is carried out based on these inflection points. Experiments on some Chinese characters show that the proposed new techniques are reliable and time saving compared with the direction method.

Influence of the input state of polarization on interferometric and polarimetric measurements of birefringence

Using a general model to schematize polarimetric and interferometric measurements, we derive the dependence of the output signal on the input state of polarization. We show that in any birefringent medium, in addition to the eigenvectors that maximize the interferometric phase signal, there exist dual vectors that maximize the amplitude of the polarimetric signal. The dual vectors lie on the maximum circle normal to the eigenvector axis.