Reciprocal Property Research Articles

A New Group Decision Making Method With Distributed Indeterminacy Form Under Neutrosophic Environment: An Introduction to Neutrosophic Social Choice Theory

We present a novel social choice theory based multi-criteria decision making method under neutrosophic environment and a new form of truth representation of neutrosophic theory called Distributed Indeterminacy Form (DIF). Our hybrid method consists of classical methods and an aggregation operator used in social choice theory. In addition to this, we also use DIF function to provide a more sensitive indeterminacy approach towards accuracy functions. We also consider reciprocal property for all individuals. This provides, as in intuitionistic fuzzy decision making theory, a consistent decision making for each individual. The solution approach presented in this paper in group decision making is treated under neutrosophic individual preference relations. These new approaches seem to be more consistent with natural human behaviour, hence should be more plausible and feasible. Moreover, the use of a similar approach to develop some deeper soft degrees of consensus is outlined. Finally, we give a Python implementation of our work in the Appendix section.

Geometric error analysis of an over-constrained parallel tracking mechanism using the screw theory

This paper deals with geometric error modeling and sensitivity analysis of an over-constrained parallel tracking mechanism. The main contribution is the consideration of over-constrained features that are usually ignored in previous research. The reciprocal property between a motion and a force is applied to tackle this problem in the framework of the screw theory. First of all, a nominal kinematic model of the parallel tracking mechanism is formulated. On this basis, the actual twist of the moving platform is computed through the superposition of the joint twist and geometric errors. The actuation and constrained wrenches of each limb are applied to exclude the joint displacement. After eliminating repeated errors brought by the multiplication of wrenches, a geometric error model of the parallel tracking mechanism is built. Furthermore, two sensitivity indices are defined to select essential geometric errors for future kinematic calibration. Finally, the geometric error model with minimum geometric errors is verified by simulation with SolidWorks software. Two typical poses of the parallel tracking mechanism are selected, and the differences between simulation and calculation results are very small. The results confirm the correctness and accuracy of the geometric error modeling method for over-constrained parallel mechanisms.

Automated Trait Extraction using ClearEarth, a Natural Language Processing System for Text Mining in Natural Sciences

The cTAKES package (using the ClearTK Natural Language Processing toolkit Bethard et al. 2014,http://cleartk.github.io/cleartk/) has been successfully used to automatically read clinical notes in the medical field (Albright et al. 2013, Styler et al. 2014). It is used on a daily basis to automatically process clinical notes and extract relevant information by dozens of medical institutions. ClearEarth is a collaborative project that brings together computational linguistics and domain scientists to port Natural Language Processing (NLP) modules trained on the same types of linguistic annotation to the fields of geology, cryology, and ecology. The goal for ClearEarth in the ecology domain is the extraction of ecologically-relevant terms, including eco-phenotypic traits from text and the assignment of those traits to taxa. Four annotators used Anafora (an annotation software; https://github.com/weitechen/anafora) to mark seven entity types (biotic, aggregate, abiotic, locality, quality, unit, value) and six reciprocal property types (synonym of/has synonym, part of/has part, subtype/supertype) in 133 documents from primarily Encyclopedia of Life (EOL) and Wikipedia according to project guidelines (https://github.com/ClearEarthProject/AnnotationGuidelines). Inter-annotator agreement ranged from 43% to 90%. Performance of ClearEarth on identifying named entities in biology text overall was good (precision: 85.56%; recall: 71.57%). The named entities with the best performance were organisms and their parts/products (biotic entities - precision: 72.09%; recall: 54.17%) and systems and environments (aggregate entities - precision: 79.23%; recall: 75.34%). Terms and their relationships extracted by ClearEarth can be embedded in the new ecocore ontology after vetting (http://www.obofoundry.org/ontology/ecocore.html). This project enables use of advanced industry and research software within natural sciences for downstream operations such as data discovery, assessment, and analysis. In addition, ClearEarth uses the NLP results to generate domain-specific ontologies and other semantic resources.

Decentralized Event-triggered Stability Analysis of Neutral-type BAM Neural Networks with Markovian Jump Parameters and Mixed Time Varying Delays

This paper investigates decentralized event-triggered stability analysis of neutral-type BAM neural networks with Markovian jump parameters and mixed time varying delays. We apply the decentralized event triggered approach to the bidirectional associative memory (BAM) neural networks to reduce the network traffic and the resource of computation. A bidirectional associative memory neural networks is constructed with the mixed time varying delays and Markov process parameters. The criteria for the asymptotically stability are proposed by using with the Lyapunov-Krasovskii functional method, reciprocal convex property and Jensen’s inequality. Stability condition of neutral-type BAM neural networks with Markovian jump parameters and mixed delays is established in terms of linear matrix inequalities. Finally three numerical examples are given to demonstrate the effectiveness of the proposed results

Geometric Error Modeling of Parallel Manipulators Based on Conformal Geometric Algebra

An approach for geometric error modeling of parallel manipulators (PMs) based on the visual representation and direct calculation of conformal geometric algebra is introduced in this paper. In this method, the finite motion of an open-loop chain is firstly formulated. Through linearization of the finite motion, error propagation of the open-loop chain is analyzed. Then the error sources are separated in terms of joint perturbations and geometric errors. Next, motions and constraints of PMs are analyzed visually by their reciprocal property. Finally geometric error model of PMs are formulated considering the actuations and constraints. The merits of this new approach are twofold: (1) complete and continuous geometric error modeling can be achieved since finite motions are considered, (2) visual and analytical computation of motions and constraints are applied for transferring geometric errors from the open-loop chain to the PM. A 2-DoF rotational PM is applied to demonstrate the geometric error modeling process. Comparisons between simulation and analytical models show that this approach is highly effective.

On a new approach to estimate the shape parameter of the inverse Gaussian distribution

In this paper, we propose a new simple method for estimating the shape parameter of the inverse Gaussian distribution. This new method makes use of the reciprocal property of the distribution. Also, bias-reduced versions of this proposed estimator are introduced. Furthermore, a new test for the coefficient of variation in an inverse Gaussian distribution is derived. The performance of the estimators are evaluated via Monte Carlo simulations. In general, compared with the maximum likelihood estimator, the proposed method has smaller bias. Two real data sets are used to illustrate the proposed methodology.

Experimental demonstration of robust entanglement distribution over reciprocal noisy channels assisted by a counter-propagating classical reference light

Embedding a quantum state in a decoherence-free subspace (DFS) formed by multiple photons is one of the promising methods for robust entanglement distribution of photonic states over collective noisy channels. In practice, however, such a scheme suffers from a low efficiency proportional to transmittance of the channel to the power of the number of photons forming the DFS. The use of a counter-propagating coherent pulse can improve the efficiency to scale linearly in the channel transmission, but it achieves only protection against phase noises. Recently, it was theoretically proposed [Phys. Rev. A 87, 052325(2013)] that the protection against bit-flip noises can also be achieved if the channel has a reciprocal property. Here we experimentally demonstrate the proposed scheme to distribute polarization-entangled photon pairs against a general collective noise including the bit flip noise and the phase noise. We observed an efficient sharing rate scaling while keeping a high quality of the distributed entangled state. Furthermore, we show that the method is applicable not only to the entanglement distribution but also to the transmission of arbitrary polarization states of a single photon.

Self-inverse unicyclic graphs and strong reciprocal eigenvalue property

We consider only simple graphs. A graph G is said to be nonsingular if its adjacency matrix A(G) is nonsingular. The inverse of a nonsingular graph G is the unique weighted graph whose adjacency matrix is similar to the inverse of the adjacency matrix A(G) via a diagonal matrix of ±1s. An invertible graph G is said to be a self-inverse graph if G is isomorphic to its inverse. Let H be the class of connected bipartite graphs with unique perfect matchings. We consider the problem of characterizing the graphs in H which are self-inverse graphs. In this article, we answer this problem for the class of unicyclic graphs.The study of the strong reciprocal eigenvalue property is closely related to the study of graphs which are isomorphic to their inverse graphs. A nonsingular graph G is said to satisfy the property (SR) if the reciprocal of each eigenvalue of the adjacency matrix A(G) is also an eigenvalue of A(G) and they both have the same multiplicities. In this article, we show that if a unicyclic graph G in H has property (SR), then G is invertible and the inverse graph of G is unicyclic. As an application, we show that a noncorona unicyclic graph in H with property (SR) can have one of the five specified structures. Finally, our discussions lead to the following problem. Does there exist a unicyclic graph G∈H which has property (SR) but G is not self-inverse?

On some graphs which satisfy reciprocal eigenvalue properties

We consider only simple graphs. Consider connected bipartite graphs with unique perfect matchings such that the graph obtained by contracting all matching edges is also bipartite. On the class Hg of such graphs G the equivalence of the following statements are known.i)The reciprocal of the spectral radius of the adjacency matrix A(G) is the least positive eigenvalue of the adjacency matrix.ii)The graph is isomorphic to its inverse, where the inverse of a graph G is the unique weighted graph whose adjacency matrix is similar to the inverse of the adjacency matrix A(G) via a diagonal matrix of ±1s.iii)The graph has the reciprocal eigenvalue property, that is, the reciprocal of each eigenvalue of the adjacency matrix A(G) is also an eigenvalue of A(G).iv)The graph has the strong reciprocal eigenvalue property, that is, the reciprocal of each eigenvalue of the adjacency matrix A(G) is also an eigenvalue of A(G) and they both have the same multiplicities.v)The graph is a corona graph, that is, it is obtained by taking a bipartite graph and then by inserting a new adjacent vertex of degree one at each vertex. It is known that the statements iii) and iv) are not equivalent, if we allow nonbipartite graphs. However, the equivalence of these two is not yet known for the class of bipartite graphs with unique perfect matchings, where we relax the condition of bipartiteness of the contracted graph.In this article, we establish the equivalence of the first four statements for a class larger than Hg. We then supply a constructive structural description of those graphs.

Accelerating Hessian-free Gauss-Newton full-waveform inversion via l-BFGS preconditioned conjugate-gradient algorithm

Full-waveform inversion (FWI) has emerged as a powerful strategy for estimating subsurface model parameters by iteratively minimizing the difference between synthetic data and observed data. The Hessian-free (HF) optimization method represents an attractive alternative to Newton-type and gradient-based optimization methods. At each iteration, the HF approach obtains the search direction by approximately solving the Newton linear system using a matrix-free conjugate-gradient (CG) algorithm. The main drawback with HF optimization is that the CG algorithm requires many iterations. In our research, we develop and compare different preconditioning schemes for the CG algorithm to accelerate the HF Gauss-Newton (GN) method. Traditionally, preconditioners are designed as diagonal Hessian approximations. We additionally use a new pseudo diagonal GN Hessian as a preconditioner, making use of the reciprocal property of Green’s function. Furthermore, we have developed an [Formula: see text]-BFGS inverse Hessian preconditioning strategy with the diagonal Hessian approximations as an initial guess. Several numerical examples are carried out. We determine that the quasi-Newton [Formula: see text]-BFGS preconditioning scheme with the pseudo diagonal GN Hessian as the initial guess is most effective in speeding up the HF GN FWI. We examine the sensitivity of this preconditioning strategy to random noise with numerical examples. Finally, in the case of multiparameter acoustic FWI, we find that the [Formula: see text]-BFGS preconditioned HF GN method can reconstruct velocity and density models better and more efficiently compared with the nonpreconditioned method.

An axiomatic approach to approximation-consistency of triangular fuzzy reciprocal preference relations

Under the assumption of rational economics, the consistency of judgments is one of the important issues in multiple criteria decision making (MCDM) methods. We propose three axiomatic properties of the consistent judgments in relative measurements being considered from the perspective of strict logic and rationality: (A1) the reciprocal property of pairwise comparisons, (A2) the invariance of consistency with respect to permutations of alternatives, and (A3) the robustness of the ranking of alternatives. These properties are further applied to analyze the consistency of the judgments expressed by positive real numbers and triangular fuzzy numbers, respectively. The inconsistency of comparison matrices encountered in the Analytic Hierarchy Process (AHP) can be considered to be the case of weakening the axiomatic property (A3). Fuzzifying the judgments is due to the weakening of axiomatic property (A1). A method of weakening the axiomatic properties for triangular fuzzy reciprocal matrices is proposed and a new concept of approximation-consistency is put forward to distinguish from the typical consistency. By considering the permutations of alternatives, an illustrative example is presented to show the use of the proposed procedures for solving the decision making problems with triangular fuzzy reciprocal preference relations.

Strong reciprocal eigenvalue property of a class of weighted graphs

Let H be the class of connected bipartite graphs G with a unique perfect matching M. For G∈H, let WG be the set of weight functions w on the edge set E(G) such that w(e)=1 for each matching edge and w(e)>0 for each nonmatching edge. Let Gw denote the weighted graph with G∈H and w∈WG. The graph Gw is said to satisfy the reciprocal eigenvalue property, property (R), if 1/λ is an eigenvalue of the adjacency matrix A(Gw) whenever λ is an eigenvalue of A(Gw). Moreover, if the multiplicities of the reciprocal eigenvalues are the same, we say Gw has the strong reciprocal eigenvalue property, property (SR). Let Hg={G∈H|G/M is bipartite}, where G/M is the graph obtained from G by contracting each edge in M to a vertex.Recently in [12], it was shown that if G∈Hg, then Gw has property (SR) for some w∈WG if and only if Gw has property (SR) for each w∈WG if and only if G is a corona graph (obtained from another graph H by adding a new pendant vertex to each vertex of H).Now we have the following questions. Is there a graph G∈H∖Hg such that Gw has property (SR) for each w∈WG? Are there graphs G∈H∖Hg such that Gw never has property (SR), not even for one w∈WG? Are there graphs G∈H such that Gw has property (SR) for some w∈WG but not for all w∈WG? In this article, we supply answers to these three questions. We also supply a graph class larger than Hg where for any graph G, if Gw has property (SR) for one w∈WG, then G is a corona graph.

Theoretical investigation on a general class of 2D quasicrystals with the rectangular projection method

Abstract We take a theoretical investigation on the reciprocal property of a class of 2D nonlinear photonic quasicrystal proposed by Lifshitz et al. in PRL 95, 133901 (2005). Using the rectangular projection method, the analytical expression for the Fourier spectrum of the quasicrystal structure is obtained explicitly. It is interesting to find that the result has a similar form to the corresponding expression of the well-known 1D Fibonacci lattice. In addition, we predict a further extension of the result to higher dimensions. This work is of practical importance for the photonic device design in nonlinear optical conversion progresses.

Neurons the decision makers, Part I: The firing function of a single neuron

This paper is concerned with understanding synthesis of electric signals in the neural system based on making pairwise comparisons. Fundamentally, every person and every animal are born with the talent to compare stimuli from things that share properties in space or over time. Comparisons always need experience to distinguish among things. Pairwise comparisons are numerically reciprocal. If a value is assigned to the larger of two elements that have a given property when compared with the smaller one, then the smaller has the reciprocal of that value when compared with the larger. Because making comparisons requires the reciprocal property, we need mathematics that can cope with division. There are four division algebras that would allow us to use our reciprocals arising from comparisons: The real numbers, the complex numbers, the non-commutative quaternions and the non-associative octonions. Rather than inferring function as from electric flow in a network, in this paper we infer the flow from function. Neurons fire in response to stimuli and their firings vary relative to the intensities of the stimuli. We believe neurons use some kind of pairwise comparison mechanism to determine when to fire based on the stimuli they receive. The ideas we develop here about flows are used to deduce how a system based on this kind of firing determination works and can be described. Furthermore the firing of neurons requires continuous comparisons. To develop a formula describing the output of these pairwise comparisons requires solving Fredholm’s equation of the second kind which is satisfied if and only if a simple functional equation has solutions. The Fourier transform of the real solution of this equation leads to inverse square laws like those that are common in physics. The Fourier transform applied to a complex valued solution leads to Dirac type of firings. Such firings are dense in the very general fields of functions known as Sobolev spaces and thus can be used to represent the very diverse phenomena in and around us. The non-commutative solution in quaternions can be interpreted as rotations in space. The also non-commutative and non-associative solution in octonions has yet to be adequately interpreted outside physics.

Graphs with reciprocal eigenvalue properties

In this paper, only simple graphs are considered. A graph G is nonsingular if its adjacency matrix A(G) is nonsingular. A nonsingular graph G satisfies reciprocal eigenvalue property (property R) if the reciprocal of each eigenvalue of the adjacency matrix A(G) is also an eigenvalue of A(G) and G satisfies strong reciprocal eigenvalue property (property SR) if the reciprocal of each eigenvalue of the adjacency matrix A(G) is also an eigenvalue of A(G) and they both have the same multiplicities. From the definitions property SR implies property R. Furthermore, for some classes of graphs (for example, trees), it is known that these properties are equivalent. However, the equivalence of these two properties is not yet known for any nonsingular graph. In this article, it is shown that these properties are not equivalent in general.

Property $ \bf{(wL)}$ and the reciprocal Dunford-Pettis property in projective tensor products

A Banach space $X$ has the reciprocal Dunford-Pettis property ($RDPP$) if every completely continuous operator $T$ from $X$ to any Banach space $Y$ is weakly compact. A Banach space $X$ has the $RDPP$ (resp. property $(wL)$) if every $L$-subset of $X^*$ is relatively weakly compact (resp. weakly precompact). We prove that the projective tensor product $X \otimes{_\pi} Y$ has property $(wL)$ when $X$ has the $RDPP$, $Y$ has property $(wL)$, and $L(X,Y^*)=K(X,Y^*)$.

A reciprocal eigenvalue property for unicyclic weighted directed graphs with weights from [formula omitted

A weighted directed graph is a directed graph G whose underlying undirected graph is simple and whose edges have nonzero (directional) complex weights, that is, the presence of an edge (u,v) of weight w is as good as the presence of the edge (v,u) with weight w¯, the complex conjugate of w. Let G be a weighted directed graph on vertices 1,2,…,n. Denote by wuv the weight of an edge (u,v)∈E(G). The adjacency matrix A(G) of G is an n×n matrix with entries aij=wij or w¯ji or 0, depending on whether (i,j)∈E(G) or (j,i)∈E(G) or otherwise, respectively. We supply a characterization of those unicyclic weighted directed graphs G whose edges have weights from the set {±1,±i} and whose adjacency matrix A(G) satisfies the following property: ‘λ is an eigenvalue of A(G) with multiplicity k if and only if 1/λ is an eigenvalue of A(G) with the same multiplicity’.

Piecewise-linear and birational toggling

We define piecewise-linear and birational analogues of toggle-involutions, rowmotion, and promotion on order ideals of a poset $P$ as studied by Striker and Williams. Piecewise-linear rowmotion relates to Stanley's transfer map for order polytopes; piecewise-linear promotion relates to Schützenberger promotion for semistandard Young tableaux. When $P = [a] \times [b]$, a reciprocal symmetry property recently proved by Grinberg and Roby implies that birational rowmotion (and consequently piecewise-linear rowmotion) is of order $a+b$. We prove some homomesy results, showing that for certain functions $f$, the average of $f$ over each rowmotion/promotion orbit is independent of the orbit chosen. Nous définissons et étudions certains analogues linéaires-par-morceaux et birationnels d’involutions toggles, rowmotion et promotion sur les idéaux d’un poset $P$, comme étudié par Striker et Williams. La rowmotion linéaire-par-morceaux est liée à la fonction transfert de Stanley pour les polytopes d’ordre; la promotion linéaire-par-morceaux se rapporte à la promotion de Schützenberger pour les tableaux semi-standards de Young. Lorsque $P = [a] \times [b]$, une propriété de symétrie réciproque récemment prouvée par Grinberg et Roby implique que la rowmotion birationnelle (et par conséquent la rowmotion linéaire-par-morceaux) est de l’ordre $a+b$. Nous démontrons quelques résultats d’homomésie, montrant que pour certaines fonctions $f$, la moyenne de $f$ sur chaque orbite de rowmotion/promotion est indépendante de l’orbite choisie.

Duality problem for the class of limited completely continuous operators

We establish necessary and sufficient conditions under which the class Lcc(E,F) of limited completely continuous operators between two Banach lattices verifies the direct and reciprocal duality property. Mathematics subject classification (2010): 46B42, 47B60, 47B65.

Rciprocal Property of Different Types of Lorentz Transformations

Lorentz transformation is the basic tool for the study of Relativistic mechanics. There are different types of Lorentz transformations such as Special, Most general, Mixed number, Geometric product, and Quaternion Lorentz transformations. In this paper we have studied the reciprocal property of the above Lorentz transformations where the velocity of a particle is very close to the speed of light.