Reciprocal Distance Research Articles

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.

LiDAR Point Cloud Super-Resolution Reconstruction Based on Point Cloud Weighted Fusion Algorithm of Improved RANSAC and Reciprocal Distance

LiDAR Point Cloud Super-Resolution Reconstruction Based on Point Cloud Weighted Fusion Algorithm of Improved RANSAC and Reciprocal Distance

Adaptive track approach for multiple sources scenarios during radar survey for space surveillance applications

The increasing population of resident space objects is currently fostering many space surveillance initiatives, which rely on the use of on-ground sensors. In particular, survey radars allow to first characterise the target orbit from a single transit, through measurements which are Doppler shift, slant range and angular profile. In this framework, the Music Approach for Track Estimate and Refinement (MATER) algorithm was developed to compute the angular track through the MUltiple SIgnal Classification (MUSIC), by solving possible ambiguities which may arise because of the receiver array geometry.This work presents the MATER extension to the case in which multiple sources are simultaneously detected by the sensor. For each detected source, the signal Direction of Arrival (DOA) is computed through MUSIC, and, if no prediction is exploited, possible ambiguous solutions arise. The computation is repeated for the entire observation, and all the estimations related to a specific target are grouped based on the angular sequence shape and the detection epochs. Finally, the possible ambiguity problem is solved, and the angular profile is obtained through a quadratic regression in time.The algorithm is numerically tested on a survey observation simulation. The detection length depends on the impinging signal intensity, and the angular accuracy is in the order of 1e-03 deg. A sensitivity analysis highlights that a transmitted power decrease shortens the detection length, with no remarkable angular accuracy deterioration. An additional simulation shows that in proximity operation monitoring MATER performance depends on the mutual geometry between target and chaser, as it may bring down the reciprocal angular distance under the resolution level. Nevertheless, it is always possible to identify the presence of both sources through the eigenvalues analysis of the signal correlation matrix. Finally, the simulation of a fragments cloud observation highlights that MATER performance depends both on the size of the observed fragment, as this is strictly linked to the signal detected by the receiver, and on the simultaneous detection of other fragments with a more effective signal.

Altruism, reciprocity, and probability: Examining relations through a discounting framework

Probability and reciprocation have been implicated as key variables for understanding altruism and cooperation. Social discounting, which describes the decline in reward value as the recipient increases in social distance, has provided a framework through which to examine altruistic and cooperative choice. A previous study introduced reciprocal discounting as a way of studying perceived altruism from others (termed reciprocal altruism). But probability discounting has not yet been examined in relation to reciprocal discounting. In order to extend research on reciprocal discounting, the present study evaluated correlations between social, reciprocal, and probability discounting as well as relations between standard social distance (used in social discounting) and reciprocal social distance (the participant’s perceived social distance placement on someone else’s list) among 129 participants. Upon evaluation, the fit of median reciprocal discount rates to the hyperbolic form was replicated. A strong correlation between social and reciprocal discount rates and a moderate correlation between social and probability discount rates were found as well. Additionally, reciprocal and probability discount rates yielded moderate correlations while reciprocal and standard social distance analyses revealed more correspondence between reward values when persons were socially close (i.e., Person 1) or socially distant (i.e., Person 100). This study provides further evidence that reciprocation and probability likely impact altruistic choice while laying groundwork for further investigations into social distance.

Sufficient conditions for [formula omitted]-leaf-connected graphs in terms of the first Zagreb index, the reciprocal degree distance and the forgotten topological index

For integer k≥2, a graph G is called k-leaf-connected if |V(G)|≥k+1 and given any subset S⊆V(G) with |S|=k, G always has a spanning tree T such that S is precisely the set of leaves of T. Thus a graph is 2-leaf-connected if and only if it is Hamiltonian-connected. The first Zagreb index M1(G) is equal to the sum of squares of the degrees of the vertices of the underlying molecular graph G. The reciprocal degree distance (RDD), defined as vertex-degree-weighted sum of the reciprocal distances, that is, RDD(G)=∑vi≠vjdegG(vi)+degG(vj)dG(vi,vj), where degG(vi) is the degree of the vertex vi in G and dG(vi,vj) denotes the distance between two vertices vi and vj in G. The forgotten topological index of G is the sum of cubes of all its vertex degrees, which plays a significant role in measuring the branching of the carbon atom skeleton. Finding sufficient conditions for graphs possessing certain properties is an important and meaningful problem. In this paper, we give sufficient conditions in terms of the first Zagreb index, the reciprocal degree distance or the forgotten topological index for a graph to be k-leaf-connected, which generalizes two results of An (2022). All of these results are best possible.

Reciprocal distance Laplacian spectral properties double stars and their complements

Several matrices are associated with graphs in order to study their properties. In such a study, researchers are interested in the spectra of the matrix under consideration, therefore, the properties are called spectral properties, with reference to the matrix. One of the interesting and hard problems in the spectral study of graphs is to order the graphs based on some spectral graph invariant, like the spectral radius, the second smallest eigenvalue, the energy, etc. Due to hardness of this problem it has been considered in the literature for small classes of graphs. Here we continue this study and add some more classes of graphs which can be ordered on the basis of spectral graph invariants. In this article, we study spectral properties of trees of diameter three, called double stars, and their complements through their reciprocal distance Laplacian eigenvalues. We give ordering of these graphs based on their reciprocal distance Laplacian spectral radius, on their second smallest reciprocal distance Laplacian eigenvalue, and on their reciprocal distance Laplacian energy.

Modulation of Ferrocene–Ferrocene Interactions by Varying Their Reciprocal Positions in L-Dap/Aib Helical Peptides

In this work, we developed two new polyfunctional hybrid systems in which the presence of Fc redox “antennas” on peptide scaffolds allows for a modulation of their electronic properties. Specifically, we synthesized two helical hexapeptides containing four Aib (α-amionoisobutyric acid) and two L-Dap (2,3-diamino propionic acid) residues. L-Dap side chains were then functionalized with Fc moieties. The structures of the two 310 helical peptides, namely Z-Aib-L-Dap(Fc)-Aib-Aib-L-Dap(Fc)-Aib-NH-iPr and Z-Aib-L-Dap(Fc)-Aib-L-Dap(Fc)-Aib-Aib-NH-iPr, were investigated by X-ray diffraction, 2D-NMR, CD and IR spectroscopies. Due to the helical conformation, in Z-Aib-L-Dap(Fc)-Aib-Aib-L-Dap(Fc)-Aib-NH-iPr, the Fc groups are located on the same face of the helix, but in Z-Aib-L-Dap(Fc)-Aib-L-Dap(Fc)-Aib-Aib-NH-iPr, they are located on opposite faces. Surprisingly, two bands were found through DPV for Z-Aib-L-Dap(Fc)-Aib-L-Dap(Fc)-Aib-Aib-NH-iPr, indicating an electrostatic interaction between the Fc groups despite their longer reciprocal distance with respect to that in Z-Aib-L-Dap(Fc)-Aib-Aib-L-Dap(Fc)-Aib-NH-iPr. CD experiments at different concentrations evidenced aggregation for Z-Aib-L-Dap(Fc)-Aib-L-Dap(Fc)-Aib-Aib-NH-iPr, even at high dilutions, thus suggesting that the Fc-Fc electrostatic interaction could be of an intermolecular nature.

Development of some novel resistance distance based topological indices for certain special types of graph networks

A graph network consisting of nodes and edges, forms an electrical network if its edges are replaced by a unit resistor. The resistance distance between any two nodes of a connected network is defined as the net effective resistance between them. This work derives mathematical closed form expressions for the resistance distance based topological indices of four families of graph networks such as and Firstly, we compute the multiplicative eccentricity resistance-distance sum index, multiplicative degree-Kirchhoff index and the reciprocal degree resistance-distance index for the four families of graphs. Secondly, we introduce some new versions of resistance distance based topological indices viz. the additive reciprocal degree-Kirchhoff index, the additive reciprocal eccentric resistance-distance index, the reciprocal eccentric resistance distance index, modified eccentric resistance distance index and the modified degree resistance distance index for the above four families of graph networks. These resistance distance based topological indices are introduced for the first time in the literature, which can surely be useful to investigate the electrical networks.

Reciprocal degree distance and Hamiltonian properties of graphs

For a connected graph G, the reciprocal degree distance (RDD) of the graph G is defined as; RDD(G)=∑u≠vdegG⁡(u)+degG⁡(v)dG(u,v), where degG⁡(u) is the degree of u in G and dG(u,v) is the distance between u and v in G. In this article, we give sufficient condition for a graph to be traceable, Hamiltonian, Hamiltonian-connected in terms of RDD(G).

Steiner Distance Related Parameters of Wheel graphs

For a connected graph of order at least and the Steiner distance among the vertices of is the minimum size among all the connected subgraphs whose vertex sets contain In this paper, we calculate the Steiner distance parameters such as Steiner degree distance, Steiner Gutman index, Steiner Harary index and Steiner reciprocal degree distance of a wheel graphs.

On reciprocal degree distance of graphs

Given a connected graph H, its reciprocal degree distance is defined asRDD(H)=∑x≠ydH(vx)+dH(vy)dH(vx,vy), where dH(vx) denotes the degree of the vertex vx in the graph H and dH(vx,vy) is the shortest distance between vx and vy in H. The goal of this paper is to establish some sufficient conditions to judge that a graph to be ħ-hamiltonian, ħ-path-coverable or ħ-edge-hamiltonian by employing the reciprocal degree distance.

Phonological similarity between words is represented in declarative memory as spatial distance.

Space can be used as a metaphor to describe semantic and perceptual similarity. Research has shown that similarity and spatial information can influence each other. On the one hand, similarity entails spatial closeness; on the other hand, proximity leads to similarity judgment. This spatial information can be stored in declarative memory and measured later on. However, it is unknown if phonological similarity/dissimilarity between words is represented as spatial closeness/distance in declarative memory. In this study, 61 young adults were tested on a remember-know (RK) spatial distance task. Participants learned noun pairs on the PC screen that were manipulated concerning their phonological similarity (similar vs. dissimilar) and reciprocal spatial distance (near vs. far). In the recognition phase, old-new, RK, and spatial distance judgments were asked. We found that for hit responses in both R and K judgments, phonologically similar word pairs were remembered closer compared to phonologically dissimilar pairs. This was also true for false alarms after K judgments. Lastly, the actual spatial distance at encoding was only retained for hit R responses. Results suggest that phonological similarity/dissimilarity is represented respectively with spatial closeness/distance and that this information is stored in the neurocognitive system of declarative memory.

Reciprocal distance signless Laplacian spread of connected graphs

Reciprocal distance signless Laplacian spread of connected graphs

On graphs with a few distinct reciprocal distance Laplacian eigenvalues

<abstract><p>For a $ \nu $-vertex connected graph $ \Gamma $, we consider the reciprocal distance Laplacian matrix defined as $ RD^L(\Gamma) = RT(\Gamma)-RD(\Gamma) $, i.e., $ RD^L(\Gamma) $ is the difference between the diagonal matrix of the reciprocal distance degrees $ RT(\Gamma) $ and the Harary matrix $ RD(\Gamma) $. In this article, we determine the graphs with exactly two distinct reciprocal distance Laplacian eigenvalues.We completely characterize the graph classes with a $ RD^L $ eigenvalue of multiplicity $ \nu-2 $. Moreover, we characterize families of graphs with reciprocal distance Laplacian eigenvalue whose multiplicity is $ \nu-3 $.</p></abstract>

Satellite Swarm-Based Antenna Arrays for 6G Direct-to-Cell Connectivity

Direct connectivity in L/S frequency bands between satellites and common mobile terrestrial user equipment (UE), such as smartphones, is an essential feature for future 6G non-terrestrial networks. The technical trend in closing the link between the communication endpoints is to develop large phased antenna arrays to be launched in LEO orbit. Satellite swarms represent an innovative and promising approach. Swarms are composed of several small and lightweight satellites organized in a free-flying formation (i.e., wireless connected) or a tethered formation (i.e., wired connected) creating a distributed phased antenna array. It has the potential to provide an enhanced gain, narrower beam width and lower launch/build costs compared to conventional single satellite systems with large phased antenna arrays. The first objective of this work is the design of swarm-based antenna arrays, in which the impact of key parameters such as the number of satellites in the swarm, their reciprocal distance and the array geometry, is thoroughly analyzed. It is shown that the undesired phenomenon of grating lobes can be mitigated via optimized array geometries and a new geometry named the enhanced logarithmic spiral array (ELSA) is presented. The second objective of this work is the identification of the most important research directions and system design aspects for the swarm system. In particular, it is shown that tethered swarms with ELSA geometries, innovative deployable structures and very small satellites can foster the deployment of swarms in future satellite systems.

On the distribution of eigenvalues of the reciprocal distance Laplacian matrix of graphs

The reciprocal distance Laplacian matrix of a connected graph G is defined as RDL(G) = RT(G) ? RD(G), where RT(G) is the diagonal matrix of reciprocal distance degrees and RD(G) is the Harary matrix. Since RDL(G) is a real symmetric matrix, we denote its eigenvalues as ?1(RDL(G)) ? ?2(RDL(G)) ?...? ?n(RDL(G)). The largest eigenvalue ?1(RDL(G)) of RDL(G) is called the reciprocal distance Laplacian spectral radius. In this article, we prove that the multiplicity of n as a reciprocal distance Laplacian eigenvalue of RDL(G) is exactly one less than the number of components in the complement graph G of G. We show that the class of the complete bipartite graphs maximize the reciprocal distance Laplacian spectral radius among all the bipartite graphs with n vertices. Also, we show that the star graph Sn is the unique graph having the maximum reciprocal distance Laplacian spectral radius in the class of trees with n vertices. We determine the reciprocal distance Laplacian spectrum of several well known graphs. We prove that the complete graph Kn, Kn ? e, the star Sn, the complete balanced bipartite graph Kn/2 ,n/2 and the complete split graph CS(n, ?) are all determined from the RDL-spectrum.

A Discriminative Feature Learning Approach With Distinguishable Distance Metrics for Remote Sensing Image Classification and Retrieval

The fast data acquisition rate due to the shorter revisit periods and wider observation coverage of satellites results in large amounts of remote sensing images every day. This brings the challenge of how to accurately search the images with similar visual content as the query image. Content-based image retrieval (CBIR) is a solution to this challenge, its performance heavily depends on the effectiveness of the image representation features and similarity evaluation metrics. Ideal image feature representations have dispersed interclass, compact intraclass distribution. However, the neural networks employed by many CBIR methods are trained with cross entropy loss, which does not directly optimize the metrics that evaluates interclass variance over intraclass variance, hence, their feature representations are suboptimal. Meanwhile, the traditional distance metrics used by many CBIR methods cannot index the similarity of feature representations well in high-dimensional space. For better CBIR performance, we propose a discriminative feature learning approach with distinguishable distance metrics for remote sensing image classification and retrieval. By balancing the diagonal elements and nondiagonal elements of the within-class scatter matrix of deep linear discriminant analysis, our proposed loss function, balanced deep linear discriminant analysis, can better optimize the Rayleigh–Ritz quotient, which measures interclass variance over intraclass variance. In addition, the proposed distance metrics, reciprocal exponential distance (RED), is more capable of maintaining distance contrast in high dimensionality, therefore, it can better index similarity for feature representations in high dimensionality. Both visual interpretations and quantitative metrics of extensive experiments demonstrated the effectiveness of our approach.

Reciprocal distance energy of complete multipartite graphs

In this paper, first we compute the energy of a special partitioned matrix under some cases. As a consequence, we obtain the reciprocal distance energy of the complete multipartite graph and also we give various other energies of complete multipartite graphs. Next, we show that among all complete [Formula: see text]-partite graphs on [Formula: see text] vertices, the complete split graph [Formula: see text] has minimum reciprocal distance energy and the reciprocal distance energy is maximum for the Turan graph [Formula: see text]. At last, it is shown that the reciprocal distance energy of the complete bipartite graph [Formula: see text] decreases under deletion of an edge if [Formula: see text], and increases if [Formula: see text]. Also, we show that the reciprocal distance energy of the complete tripartite graph does not increase under edge deletion.

Решение задачи Молоденского по чистым аномалиям силы тяжести с относительной ошибкой порядка квадрата сжатия

The solution of the geodetic boundary value problem for determining the anomalous potential from gravity measurements in the spherical approximation, taking into account the relief and compression, was developed in sufficient detail in 1960 and is also based on the results of G. G. Stokes. Flattening of the reference surface was taken into account by D. V. Zagrebin in several works dated 1940–1970; in 1956 M. S. Molodensky proposed a simpler method for an oblate ellipsoid, based on the already known one for a sphere. It turned out that at the very beginning of developing the mentioned solution, an error was made when obtaining the derivative of the reciprocal distance between two points on the ellipsoid in the direction of the outward normal; later it was repeated in issue 131 of the Proceedings of the TsNIIGAiK. That inaccuracy did not influence the conclusions of V. V. Brovar in 1996 and 1999, where the relief was added to the consideration of compression. This solution of Molodensky’s problem, taking the compression into account, was seldom used, and that is probably why the mistake went unnoticed. V. V. Popadyev saw it and found the correct expression for the mentioned derivative, I. I. Mezhenova adapted subsequent conclusions for the gravity disturbances.

Extracellular local field potentials in men and women based on a theoretical model of voltage decrease as a function of distance

Extracellular microelectrodes determine the field potential difference adjacent to the neuron and depend on the composition of the tissue, including ohmic resistance and distance from the source. Based on theoretical aspects, a reciprocal voltage versus distance model is postulated, which was assessed by means of clinical neurographical data in men and women. Data of women showed higher voltages and could be slightly better fitted to the model. Voltage amplitude and to a lesser extent rise time (RT) were the only action potential characteristics which could predict the gender in a discriminant analysis model. In conclusion, neurographical studies may be a suitable option to assess ohmic resistance of tissue and composition of tissue in addition to bioimpedance (BIA) methods.