Square Of Distance Research Articles

An Algorithm for Simplifying 3D Building Models with Consideration for Detailed Features and Topological Structure

To tackle problems such as the destruction of topological structures and the loss of detailed features in the simplification of 3D building models, we propose a 3D building model simplification algorithm that considers detailed features and topological structures. Based on the edge collapse algorithm, the method defines the region formed by the first-order neighboring triangles of the endpoints of the edge to be collapsed as the simplification unit. It incorporates the centroid displacement of the simplification unit, significance level, and approximate curvature of the edge as influencing factors for the collapse cost to control the edge collapse sequence and preserve model details. Additionally, considering the unique properties of 3D building models, boundary edge detection and face overlay are added as constraints to maintain the model’s topological structure. The experimental results show that the algorithm is superior to the classic QEM algorithm in terms of preserving the topological structure and detailed features of the model. Compared to the QEM algorithm and the other two comparison algorithms selected in this paper, the simplified model resulting from this algorithm exhibit a reduction in Hausdorff distance, mean error, and mean square error to varying degrees. Moreover, the advantages of this algorithm become more pronounced as the simplification rate increases. The research findings can be applied to the simplification of 3D building models.

Residential proximity to conventional and unconventional wells and exposure to indoor air volatile organic compounds in the Exposures in the Peace River Valley (EXPERIVA) study

BackgroundIn a previous study located in Northeastern British Columbia (Canada), we observed associations between density and proximity of oil and gas wells and indoor air concentrations of certain volatile organic compounds (VOCs). Whether conventional or unconventional well types and phases of unconventional development contribute to these associations remains unknown. ObjectiveTo investigate the associations between proximity-based metrics for conventional and unconventional wells and measured indoor air VOC concentrations in the Exposures in the Peace River Valley (EXPERIVA) study samples. MethodsEighty-four pregnant individuals participated in EXPERIVA. Passive indoor air samplers were analyzed for 47 VOCs. Oil and gas well legacy data were sourced from the British Columbia Energy Regulator. For each participant's home, 5 km, 10 km and no buffer distances were delineated, then density and Inverse Distance Square Weighted (ID2W) metrics were calculated to estimate exposure to conventional and unconventional wells during pregnancy and the VOC measurement period. Multiple linear regression models were used to test for associations between the well exposure metrics and indoor air VOCs. For exposure metrics with >30% participants having a value of 0, we dichotomized exposure (0 vs. >0) and performed ANOVAs to assess differences in mean VOCs concentrations. ResultsAnalyses indicated that: 1) conventional well density and ID2W metrics were positively associated with indoor air acetone and decanal; 2) unconventional well density and ID2W metrics were positively associated with indoor air chloroform and decamethylcyclopentasiloxane, and negatively associated with decanal; 3) drilling specific ID2W metrics for unconventional wells were positively associated with indoor air chloroform. ConclusionOur analysis revealed that the association between the exposure metrics and indoor air acetone could be attributed to conventional wells and the association between exposure metrics and indoor air chloroform and decamethylcyclopentasiloxane could be attributed to unconventional wells.

Large-space and large-time asymptotic properties of vector rogon-soliton and soliton-like solutions for n-component NLS equations.

In this paper, we analyze the large-space and large-time asymptotic properties of the vector rogon-soliton and soliton-like solutions of the n-component nonlinear Schrödinger equation with mixed nonzero and zero boundary conditions. In particular, we find that these solutions have different decay velocities along different directions of the x axis, that is, the solutions exponentially and algebraically decay along the positive and negative directions of the x axis, respectively. Moreover, we study the change of the acceleration of soliton moving with the increase in time or distance along the characteristic line (i.e., soliton moving trajectory). As a result, we find that the product of the acceleration and distance square tends to some constant value as time increases. These results will be useful to better understand the related multi-wave phenomena and to design physical experiments.

Deep learning‐based location prediction in VANET

AbstractIn recent years, Vehicular Ad‐hoc Network (VANET) has become an essential component of intelligent transportation systems that, along with the previous systems such as traffic condition, accident alert, automatic parking, and cruise control, use the communication of vehicle to vehicle and vehicle to the roadside unit to facilitate road transportation. Several challenges hinder efforts to improve traffic conditions and reduce traffic fatalities through VANET. A critical challenge is achieving highly accurate and reliable vehicle localization within the VANET. Additionally, the frequent unavailability of Global Positioning System (GPS), particularly in tunnels and parking lots, presents another significant obstacle. Traditional methods like Dead Reckoning offer low accuracy and reliability due to accumulating errors. Similarly, GPS positioning, map matching with mobile phone location services, and other existing solutions struggle with accuracy and economic feasibility. In this article, two Kalman filter approaches are used based on signal statistical information and the other learning‐based networks, including traditional neural network, deep neural network and LSTM (long short‐term memory) to locate the car. The prediction error of car position with root mean square measures. The squared error and distance prediction error are evaluated. It is shown that in terms of prediction time and processing time of vehicle localization, all the vehicle localization methods are efficient in terms of response time for localization, and Kalman filter methods, traditional neural network and deep neural network are faster than LSTM method. Also, in terms of localization error, Kalman filter works better than learning‐based methods, and in learning‐based methods, both deep neural network and LSTM methods perform better than traditional neural network in terms of localization error.

Physicochemical Characteristics of Porous Starch Obtained by Combined Physical and Enzymatic Methods-Part 2: Potential Application as a Carrier of Gallic Acid.

Wettability measurements were performed for aqueous dispersions of native and modified corn, potato, and pea starch granules deposited on glass plates by the thin layer method using test liquids of a different chemical nature (polar water and formamide or non-polar diiodomethane). High values of the determination coefficient R2 confirm that the linear regression model describes the relationship between the wetting time and the square of the penetration distance very well, indicating the linear nature of the Washburn relationship. A change in free energy (enthalpy) during the movement of the liquid in the porous layer was determined for all starches before and after modification in contact with test liquids. Wetting times for polar liquids increased significantly (from 3 to 4 fold), especially for corn starch. The lower the value of the adhesive tension, the easier the wetting process takes place, and consequently, the adsorption process is facilitated. Adhesive tension for polar substances applies to the adsorption of hydrophilic substances, while in the case of apolar substances, adhesive tension applies to the adsorption of hydrophobic substances. For the adsorption of gallic acid on starch, the relationships obtained for polar substances are crucial. The adsorption of gallic acid by forming hydrogen bonds or, more generally, donor-acceptor (acid-base) bonds is definitely higher for corn starch than other starches. Therefore, this starch has the most significant potential for use as a carrier of gallic acid or, more broadly, compounds from the polyphenol group.

Bridge Sampling for Connections via Multiple Scattering Events

AbstractExplicit sampling of and connecting to light sources is often essential for reducing variance in Monte Carlo rendering. In dense, forward‐scattering participating media, its benefit declines, as significant transport happens over longer multiple‐scattering paths around the straight connection to the light. Sampling these paths is challenging, as their contribution is shaped by the product of reciprocal squared distance terms and the phase functions. Previous work demonstrates that sampling several of these terms jointly is crucial. However, these methods are tied to low‐order scattering or struggle with highly‐peaked phase functions.We present a method for sampling a bridge: a subpath of arbitrary vertex count connecting two vertices. Its probability density is proportional to all phase functions at inner vertices and reciprocal squared distance terms. To achieve this, we importance sample the phase functions first, and subsequently all distances at once. For the latter, we sample an independent, preliminary distance for each edge of the bridge, and afterwards scale the bridge such that it matches the connection distance. The scale factor can be marginalized out analytically to obtain the probability density of the bridge. This approach leads to a simple algorithm and can construct bridges of any vertex count. For the case of one or two inserted vertices, we also show an alternative without scaling or marginalization.For practical path sampling, we present a method to sample the number of bridge vertices whose distribution depends on the connection distance, the phase function, and the collision coefficient. While our importance sampling treats media as homogeneous we demonstrate its effectiveness on heterogeneous media.

Effectiveness of laser pulsed irradiation for antimicrobial photodynamic therapy

The aim of this study was to compare two types of light irradiation devices for antimicrobial photodynamic therapy (aPDT). A 660-nm light-emitting diode (LED) and a 665-nm laser diode (LD) were used for light irradiation, and 0.1 mg/L TONS 504, a cationic chlorin derivative, was used as the photosensitizer. We evaluated the light attenuation along the vertical and horizontal directions, temperature rise following light irradiation, and aPDT efficacy against Staphylococcus aureus under different conditions: TONS 504 only, light irradiation only, and TONS 504 with either LED (30 J/cm2) or LD light irradiation (continuous: 30 J/cm2; pulsed: 20 J/cm2 at 2/3 duty cycle, 10 J/cm2 at 1/3 duty cycle). Both LED and LD light intensities were inversely proportional to the square of the vertical distance from the irradiated area. Along the horizontal distance from the nadir of the light source, the LED light intensity attenuated according to the cosine quadrature law, while the LD light intensity did not attenuate within the measurable range. Following light irradiation, the temperature rise increased as the TONS 504 concentration increased in the order of pulsed LD < continuous LD < LED irradiation. aPDT with light irradiation only or TONS 504 only had no antimicrobial effect, while aPDT with TONS 504 under continuous or pulsed LD light irradiation provided approximately 3 log reduction at 30 J/cm2 and 20 J/cm2 and approximately 2 log reduction at 10 J/cm2. TONS 504-aPDT under pulsed LD light irradiation provided anti-microbial effect without significant temperature rise.

Cardiac MRI segmentation using shifted-window multilayer perceptron mixer networks

Objectives. In this work, we proposed a deep-learning segmentation algorithm for cardiac magnetic resonance imaging to aid in contouring of the left ventricle, right ventricle, and Myocardium (Myo). Approach. We proposed a shifted window multilayer perceptron (Swin-MLP) mixer network which is built upon a 3D U-shaped symmetric encoder-decoder structure. We evaluated our proposed network using public data from 100 individuals. The network performance was quantitatively evaluated using 3D volume similarity between the ground truth contours and the predictions using Dice score coefficient, sensitivity, and precision as well as 2D surface similarity using Hausdorff distance (HD), mean surface distance (MSD) and residual mean square distance (RMSD). We benchmarked the performance against two other current leading edge networks known as Dynamic UNet and Swin-UNetr on the same public dataset. Results. The proposed network achieved the following volume similarity metrics when averaged over three cardiac segments: Dice = 0.952 ± 0.017, precision = 0.948 ± 0.016, sensitivity = 0.956 ± 0.022. The average surface similarities were HD = 1.521 ± 0.121 mm, MSD = 0.266 ± 0.075 mm, and RMSD = 0.668 ± 0.288 mm. The network shows statistically significant improvement in comparison to the Dynamic UNet and Swin-UNetr algorithms for most volumetric and surface metrics with p-value less than 0.05. Overall, the proposed Swin-MLP mixer network demonstrates better or comparable performance than competing methods. Significance. The proposed Swin-MLP mixer network demonstrates more accurate segmentation performance compared to current leading edge methods. This robust method demonstrates the potential to streamline clinical workflows for multiple applications.

Design of Quantum Gates Using Quantum Scattering Theory

Given two Hamiltonians \(H_0,H_1=H_0+V\) corresponding respectively to a free particle Hamiltonian and the free particle Hamiltonian plus its interaction energy with a scattering centre, we can compute the S-matrix, i.e., the matrix that determines the quantum mechanical amplitude of the process involving a particle coming from a free particle state at an infinite distance from the scattering centre at time \(t=-\infty\), entering into an initial scattered state, interacting with the scattering centre, entering into a final scattered state, and then escaping away to infinity at time \(t\rightarrow\infty\) to a final free particle state. Such amplitudes were first studied by Lippmann and Schwinger (Steven Weinberg, The Quantum Theory of Fields, Vol. 1, W.O. Amrein, Hilbert Space Methods in Quantum Mechanics) and then analyzed in a mathematically precise way by [T. Kato], [W. Amrein], and [K.B. Sinha]. In this paper, we first derive the Lippmann-Schwinger equation for the input and output scattered states in terms of the input and output free particle states using intuitive arguments originally due to Lippmann and Schwinger, and then, using rigorous operator theoretic arguments revolving around the spectral theorem for unbounded self-adjoint operators in a Hilbert space, we obtain an elegant formula for the scattering matrix elements in terms of the interaction potential and the free particle Hamiltonian between two free particle states corresponding to the same measure. We then discuss a computationally more efficient method based on the Dyson series expansion (Steven Weinberg, The Quantum Theory of Fields, Vol. 1), which works even in the case when the interaction Hamiltonian is time varying, in contrast to the Lippmann-Schwinger method, for calculating the S-matrix. We assume that the scattering potential, which can be time varying, can be controlled by incorporating control parameters and explain how the resulting unitary S-matrix can be made to approximate a given unitary gate in infinite-dimensional Hilbert space by optimizing the Hilbert-Schmidt/Frobenius norm distance between the given gate and the S-matrix gate, in which the latter is approximated by a truncated Dyson series. Of course, the S-matrix given by the Dyson series is a Taylor series functional expansion in the interaction potential and hence is a highly nonlinear function of the control parameters, and hence we propose numerical methods for such optimization. We then observe that if the control parameters are taken as random variables with joint moments, then the TPCP map involving statistical averaging of the adjoint action of the S-matrix acting on an initial mixed state w.r.t. the probability distribution of the control parameters will result in a final mixed state that is linear in the statistical moments of the control parameters, and hence optimization w.r.t. these moments can be easily carried out. Our method of TPCP map design is to optimize the sum of Frobenius distance squares between a sequence of desired output mixed states and the S-matrix based formula for the TPCP map acting on the corresponding input mixed states w.r.t. the statistical moments of the control parameters. We then generalize this method to include the case of TPCP maps obtained from the Hudson-Parthasarathy quantum noisy Schrödinger equation. In summary, we simulate the S-matrix gate for independent realizations of the control parameters having a probability distribution defined by their joint moments obtained by the above optimization procedure and apply the adjoint action of these independent S-matrices on a given input state, and take their ensemble average to obtain a good approximation to the action of the desired TPCP map on any given input state. This suggests that TPCP maps of arbitrarily large size can be realized using scattering experiments in the laboratory.

Gradient Weakly Sensitive Multi-Source Sensor Image Registration Method

Aiming at the nonlinear radiometric differences between multi-source sensor images and coherent spot noise and other factors that lead to alignment difficulties, the registration method of gradient weakly sensitive multi-source sensor images is proposed, which does not need to extract the image gradient in the whole process and has rotational invariance. In the feature point detection stage, the maximum moment map is obtained by using the phase consistency transform to replace the gradient edge map for chunked Harris feature point detection, thus increasing the number of repeated feature points in the heterogeneous image. To have rotational invariance of the subsequent descriptors, a method to determine the main phase angle is proposed. The phase angle of the region near the feature point is counted, and the parabolic interpolation method is used to estimate the more accurate main phase angle under the determined interval. In the feature description stage, the Log-Gabor convolution sequence is used to construct the index map with the maximum phase amplitude, the heterogeneous image is converted to an isomorphic image, and the isomorphic image of the region around the feature point is rotated by using the main phase angle, which is in turn used to construct the feature vector with the feature point as the center by the quadratic interpolation method. In the feature matching stage, feature matching is performed by using the sum of squares of Euclidean distances as a similarity metric. Finally, after qualitative and quantitative experiments of six groups of five pairs of different multi-source sensor image alignment correct matching rates, root mean square errors, and the number of correctly matched points statistics, this algorithm is verified to have the advantage of robust accuracy compared with the current algorithms.

Improved ellipsoid fitting aided geomagnetic sensor calibration algorithm

Aiming at the problems that the traditional single ellipsoid fitting fails to eliminate the errors of the geomagnetic sensor and does not consider the geomagnetic anomaly information, etc., this paper proposes a robust least squares combined with the Levenberg–Marquardt (LM-RLS) algorithm to fit an accurate ellipsoid to achieve accurate data calibration. According to the geomagnetic sensor error model, the total amount of geomagnetism is used as the constraint, the fitted ellipsoid coefficients of RLS are used as the initial values, and the LM algorithm is used to calculate the magnetic field dispersion points to the nearest point of the fitted ellipsoid surface. Then, the initial calibration value is solved by the criterion of the minimum weighted sum of squares of the closest point distance. Finally, the accurate ellipsoid is obtained to realize data calibration. The results of the dynamic experiment show that after the ellipsoid is precisely fitted by the LM-RLS algorithm, the sum of the absolute values of the distance from the magnetic field discrete data to the ellipsoid surface is reduced by 48.33% (RLS) and 43.10% (RWTLS). The relative errors of the magnetic field in the X, Y, and Z axes are reduced from 0.48%, 0.78%, 1.48% (RLS) and 0.30%, 0.58%, 1.14% (RWTLS) to 0.10%, 0.04% 0.16 %, respectively. The accuracy of geomagnetic calibration is improved by 68.06% (RLS) and 61.02% (RWTLS) in the dynamic experiment. The algorithm improves the accuracy of geomagnetic measurement, which provides a new idea for the calibration of three-axis geomagnetic sensors.

Acoustic testing of the inverse-square law using the infrared signal of a remote control

In this work, the inverse-square law has been tested for the electromagnetic radiation in the infrared range. As a point-source, a TV remote control has been used. The intensities registered by a solar cell plugged to a speaker have been measured acoustically by recording the sound produced by the infrared pulses. The recorded audio is edited to find the intensities for different distances between the remote control and the solar cell. The results were fitted with a parametric function of the intensity inversely proportional to the distance square. A very good agreement was achieved.

Mean Distance on Metric Graphs

We introduce a natural notion of mean (or average) distance in the context of compact metric graphs, and study its relation to geometric properties of the graph. We show that it exhibits a striking number of parallels to the reciprocal of the spectral gap of the graph Laplacian with standard vertex conditions: it is maximised among all graphs of fixed length by the path graph (interval), or by the loop in the restricted class of doubly connected graphs, and it is minimised among all graphs of fixed length and number of edges by the equilateral flower graph. We also establish bounds for the correctly scaled product of the spectral gap and the square of the mean distance which depend only on combinatorial, and not metric, features of the graph. This raises the open question whether this product admits absolute upper and lower bounds valid on all compact metric graphs.

Nonunion scaphoid bone shape prediction using iterative kernel principal polynomial shape analysis.

The scaphoid is an important mechanical stabilizer for both the proximal and distal carpal columns. The precise estimation of the complete scaphoid bone based on partial bone geometric information is a crucial factor in the effective management of scaphoid nonunion. Statistical shape model (SSM) could be utilized to predict the complete scaphoid shape based on the defective scaphoid. However, traditional principal component analysis (PCA) based SSM is limited by its linearity and the inability to adjust the number of modes used for prediction. This study proposes an iterative kernel principal polynomial shape analysis (iKPPSA)-based SSM to predict the pre-morbid shape of the scaphoid, aiming at enhancing the accuracy as well as the robustness of the model. Sixty-five sets of scaphoid images were used to train SSM and nine sets of scaphoid images were used for validation. For each validation image set, three defect types (tubercle, proximal pole, and avascular necrosis) were virtually created. The predicted shapes of the scaphoid by PCA, PPSA, KPCA, and iKPPSA-based SSM were evaluated against the original shape in terms of mean error, Hausdorff distance error, and Dice coefficient. The proposed iKPPSA-based scaphoid SSM demonstrates significant robustness, with a generality of 0.264mm and a specificity of 0.260mm. It accounts for 99% of variability with the first seven principal modes of variation. Compared to the traditional PCA-based model, the iKPPSA-based scaphoid model prediction demonstrated superior performance for the proximal pole type fracture, with significant reductions of 25.2%, 24.7%, and 24.6% in mean error, Hausdorff distance, and root mean square error (RMSE), respectively, and a 0.35% improvement in Dice coefficient. This study showed that the iKPPSA-based SSM exploits the nonlinearity of data features and delivers high reconstruction accuracy. It can be effectively integrated into preoperative planning for scaphoid fracture management or morphology-based biomechanical modeling of the scaphoid.

Theoretically Motivated Dark Electromagnetism as the Origin of Relativistic Modified Newtonian Dynamics

The present paper is a modest attempt to initiate the research program outlined in this abstract. We propose that general relativity and relativistic MOND (RelMOND) are analogues of broken electroweak symmetry. That is, SU(2)R×U(1)YDEM→U(1)DEM (DEM stands for dark electromagnetism), and GR is assumed to arise from the broken SU(2)R symmetry and is analogous to the weak force. RelMOND is identified with dark electromagnetism U(1)DEM, which is the remaining unbroken symmetry after the spontaneous symmetry breaking of the dark electro-grav sector SU(2)R×U(1)YDEM. This sector, as well as the electroweak sector, arises from the breaking of an E8×E8 symmetry in a recently proposed model of unification of the standard model with pre-gravitation, with the latter based on an SU(2)R gauge theory. The source charge for the dark electromagnetic force is the square root of mass, motivated by the experimental fact that the ratio of the square roots of the masses of the electron, up-quark, and down-quark is 1:2:3, which is the opposite of the ratio of their electric charges at 3:2:1. The introduction of the dark electromagnetic force helps us understand the peculiar mass ratios of the second and third generations of charged fermions. We also note that in the deep MOND regime, acceleration is proportional to the square root of mass, which motivates us to propose the relativistic U(1)DEM gauge symmetry as the origin of MOND. We explain why the dark electromagnetic force falls inversely with distance, as in MOND, rather than following the inverse square of distance. We conclude that dark electromagnetism effectively mimics cold dark matter, and the two are essentially indistinguishable in cosmological situations where CDM successfully explains observations, such as CMB anisotropies and gravitational lensing.

Structural insights into non-hotspot KRAS mutations and their potential as targets for effective cancer therapies

Kirsten rat sarcoma virus protein (KRAS) is a protein that plays a central role in signal transduction using extracellular signal regulated kinase (ERK) and mitogen activated protein kinase (MAPK) cellular signaling pathway. KRAS is a frequently mutated oncogene and plays a pivotal role in tumor initiation and progression. Hotspot mutations on codon 12, 13 and 61 in KRAS are well-known for their role in drug resistance and non-hotspot mutations also play a significant part in contributing to resistance mechanisms. The understanding of how these non-hotspot mutations might affect the signal transduction of KRAS and their contribution towards drug resistance is understudied. Here we provide structural insights into the interaction of non-hotspot KRAS mutants with GTP (the native ligand) using a molecular docking and molecular dynamics simulation approach. Extensive molecular docking and simulation studies suggest that non-hotspot mutations (E31D and E63K) show stable interaction with native ligand using all five trajectories, as evidenced by root mean square of distance (RMSD), root mean square of fluctuation (RMSF), radius of gyration (RoG), coulomb short-range energy and MMGBSA analysis. These results suggest that non-hotspot mutations do not undermine the oncogenic nature of KRAS. This observation is consistent with previous findings where overexpressing E31D and E63K mutations share phenotypic features with G12D and G13D transfected cells, including increased proliferative capacity, actin cytoskeleton organization, and migration rates. We further test whether FDA-approved KRAS inhibitors sotorasib and adagrasib successfully inhibit the E31D and E63K mutants. Results suggest that these two non-hotspot mutants can be inhibited by both drugs with following trend of structural stability (E31D > E63K > wild-KRAS > Q61H > G12C). Based on sharp coherence in trajectories between wild KRAS and non-hotspot mutants, it is suggested that these novel mutants do not contribute to drug resistance mechanism. Overall, we provide a comprehensive understanding of the impact of non-hotspot mutations on KRAS and their potential as targets for effective cancer therapies. Communicated by Ramaswamy H. Sarma

Root Mean Squares of Distance and Geodesic between Two Constituent Particles within Fractal Aggregates Prepared by BCCA, DLA, and GSAW Procedures

Root Mean Squares of Distance and Geodesic between Two Constituent Particles within Fractal Aggregates Prepared by BCCA, DLA, and GSAW Procedures

Advancing single-cell RNA-seq data analysis through the fusion of multi-layer perceptron and graph neural network.

The advancement of single-cell sequencing technology has smoothed the ability to do biological studies at the cellular level. Nevertheless, single-cell RNA sequencing (scRNA-seq) data presents several obstacles due to the considerable heterogeneity, sparsity and complexity. Although many machine-learning models have been devised to tackle these difficulties, there is still a need to enhance their efficiency and accuracy. Current deep learning methods often fail to fully exploit the intrinsic interconnections within cells, resulting in unsatisfactory results. Given these obstacles, we propose a unique approach for analyzing scRNA-seq data called scMPN. This methodology integrates multi-layer perceptron and graph neural network, including attention network, to execute gene imputation and cell clustering tasks. In order to evaluate the gene imputation performance of scMPN, several metrics like cosine similarity, median L1 distance and root mean square error are used. These metrics are utilized to compare the efficacy of scMPN with other existing approaches. This research utilizes criteria such as adjusted mutual information, normalized mutual information and integrity score to assess the efficacy of cell clustering across different approaches. The superiority of scMPN over current single-cell data processing techniques in cell clustering and gene imputation investigations is shown by the experimental findings obtained from four datasets with gold-standard cell labels. This observation demonstrates the efficacy of our suggested methodology in using deep learning methodologies to enhance the interpretation of scRNA-seq data.

О задаче рассеяния на потенциале, убывающем пропорционально обратному квадрату расстояния

Получено решение задачи рассеяния для уравнения Шредингера с потенциалом индуцированного дипольного взаимодействия, который убывает пропорционально обратному квадрату расстояния. Такой потенциал возникает при столкновении налетающей заряженной частицы с комплексом заряженных частиц (например, при столкновении электронов с атомами). Для волновой функции построено интегральное уравнение для произвольного значения орбитального момента относительного движения. С помощью этого решения получено точное интегральное представление для $K$-матрицы задачи в терминах волновой функции. На базе этого представления проанализировано поведение $K$-матрицы при низких энергиях и получена исчерпывающая информация о ее пороговом поведении для различных значений дипольного момента. Полученное решение используется для исследования поведения сечений рассеяния в системе электрон-позитрон-антипротон.

On the scattering problem for a potential decreasing as the inverse square of distance

On the scattering problem for a potential decreasing as the inverse square of distance