Symmetric Set Research Articles

Visualizing symmetric and asymmetric settings in MMQR for natural resources extraction and economic performance: A COVID-19 perspective

Since the contradictory debate is undergoing in the scientific work regarding the resource blessings/curse hypothesis. To solve the issue, this research analyzes the asymmetric impact of natural resources on the economic performance of four natural resources dependent economies (India, China, USA, and Japan) during the last three decades. Also, this research explored the important role of globalization, foreign direct investment, and renewable energy consumption in economic performance. The long-run equilibrium association among the parameters exists using the panel cointegration technique. Owing to the data's non-normal spread, the study opted for a non-parametric approach and found that both positive and negative resource rents adversely affect economic performance. Besides, the consumption of renewable energy significantly harms the region's economic performance. On the contrary, the impact of globalization and foreign direct investment is positive and significant during the researched period. This study evaluates the results' robustness and consistency with the literature. Based on findings, sustainable extraction of natural resources and further boosts foreign direct investment and globalization are suggested by this research.

The Modal Components of Judgements in a Quantum Model of Psychoanalytic Theory.

In the present paper, we develop a theory of thinking based on an attempt to formalize the construction of mental representations as described in psychoanalytic theory. In previous work, we described Freud's and Matte Blanco's structural Unconscious in a formal model in which the properties of unconscious representations are captured by particular sets-infinite singletons-that can be derived in first-order logic language. Here, we afford the issue of the finitization of unconscious representations by assuming that the mind can form an all-purpose modality, originating from abstraction from infinite singletons; in this way, a symmetric prelogical setting for mental representations is formally created, and this is interpreted in a quantum spin model by a modal (necessity) projector. Then, by introducing time, one can describe the links that mental representations can establish with reality, and hence finitize the representations. The modality is so split into finite components, here termed positive, negative and irreal; the splitting of the modality is traced back to the decomposition of the spin observables by means of the Pauli matrices, which can offer a quantum semantics to the method applied. Here, we suggest that the development of the modal approach and its quantum logic implementation can be considered as a proper formalization of some aspect of the psychoanalytic theory of thinking proposed by Bion; namely, we will show that the process of abstraction leading from raw data to preconceptions, and therefore to the definition of the content-container relationship, is adequately captured by our model, and further correspondences can be detected with Bion's theory about links and transformations, implying different ways in which the mind can get in touch with both internal and external reality.

Oxygen Incorporated MoS2 for Rectification‐Mediated Resistive Switching and Artificial Neural Network

AbstractMolybdenum disulfide (MoS2) based memristor presents intriguing chance for the implementation bio‐inspired artificial synapse and neural interactions. However, the electrical properties of intrinsic MoS2 single‐crystal film suffer from inevitable lattice defects or structure vacancies as well as restraining reliable resistive switching mechanism. Here, a fundamental study on tunable p‐type doping in MoS2 film by controllable oxygen passivation is reported. In situ KPFM measurements reveal a near‐linear increase in Fermi‐level energy. The TiN/O‐MoS2 memristor exhibits surprising bipolar switching feature, revealing an interesting transition between rectification‐mediated and conduction‐mediated characteristics by means of controllable surficial oxygen kinetics. The resistive window demonstrates nearly symmetric SET and RESET domain and capability to analog programming conductance. Moreover, based on the MoS2 memristor, the accuracy up to 94% for MINST recognition ensures the implementation of neural network and LTP/LTD behaviors. This as‐prepared memristor is capable of mimicking synaptic feature through regulated resistive mechanics and electrode contact interaction, which can be an up‐and‐coming strategy for bio‐realistic electronics.

Correction to Lagrangian for bouncing cosmologies in f(Q) gravity

Symmetric teleparallel gravity offers to reformulate the gravitational formalism without the presence of curvature and torsion with the help of non-metricity tensors. Interestingly, Symmetric teleparallel gravity can be formulated equivalently to teleparallel gravity or general relativity for an appropriate setup. In this study, our aim lies in exploring the bouncing cosmologies as an alternative to the initial singularity of the Universe in the background of modified symmetric teleparallel gravity. To explore this, we adopt the reconstruction technique to present the possible reconstructed Lagrangian for various cosmological bouncing solutions in a flat Friedmann–Lemaître–Robertson–Walker spacetime with a perfect fluid matter distribution. We study the reconstructed gravitational Lagrangians, which are capable of reproducing analytical or semianalytical solutions for symmetric bounce, super-bounce, oscillatory bounce, matter bounce, and exponential bouncing model settings. Further, we examine the dark energy profiles of the models using reconstructed Lagrangians. In addition, we found that an additional term arises in each reconstructed Lagrangian compared to general relativity (GR). That extra term corrected the background GR to present bouncing cosmology in modified gravity. These newly motivated cosmological models may have an effect on gravitational phenomena at other cosmological scales.

RELEVANT CONSEQUENCE RELATIONS: AN INVITATION

AbstractWe generalize the notion ofconsequence relationstandard in abstract treatments of logic to accommodate intuitions ofrelevance. The guiding idea follows theuse criterion, according to which in order for some premises to have some conclusion(s) as consequence(s), the premises must each beusedin some way to obtain the conclusion(s). This relevance intuition turns out to require not just a failure of monotonicity, but also a move to considering consequence relations as obtaining betweenmultisets. We motivate and state basic definitions of relevant consequence relations, both in single conclusion (asymmetric) and multiple conclusion (symmetric) settings, as well as derivations and theories, guided by the use intuitions, and prove a number of results indicating that the definitions capture the desired results (at least in many cases).

A Novel Odd Beta Prime-Logistic Distribution: Desirable Mathematical Properties and Applications to Engineering and Environmental Data

In parametric statistical modeling, it is important to construct new extensions of existing probability distributions (PDs) that can make modeling data more flexible and help stakeholders make better decisions. In the present study, a new family of probability distributions (FPDs) called the odd beta prime generalized (OBP-G) FPDs is proposed to improve the traditional PDs. A new PD called the odd beta prime-logistic (OBP-logistic) distribution has been developed based on the developed OBP-G FPDs. Some desirable mathematical properties of the proposed OBP-logistic distribution, including the moments, moment-generating function, information-generating function, quantile function, stress–strength, order statistics, and entropies, are studied and derived. The proposed OBP-logistic distribution’s parameters are determined by adopting the maximum likelihood estimation (MLE) method. The applicability of the new PD was demonstrated by employing three data sets and these were compared by the known extended logistic distributions, such as the gamma generalized logistic distribution, new modified exponential logistic distribution, gamma-logistic distribution, exponential modified Weibull logistic distribution, exponentiated Weibull logistic distribution, and transmuted Weibull logistic distribution. The findings reveal that the studied distribution provides better results than the competing PDs. The empirical results showed that the new OBP-logistic distribution performs better than the other PDs based on several statistical metrics. We hoped that the newly constructed OBP-logistic distribution would be an alternative to other well-known extended logistic distributions for the statistical modeling of symmetric and skewed data sets.

Adapting the centred simplex gradient to compensate for misaligned sample points

Abstract The centred simplex gradient (CSG) is a popular gradient approximation technique in derivative-free optimization. Its computation requires a perfectly symmetric set of sample points and is known to provide an accuracy of $\mathcal {O}(\varDelta ^2)$, where $\varDelta $ is the radius of the sampling set. In this paper, we consider the situation where the set of sample points is not perfectly symmetric. By adapting the formula for the CSG to compensate for the misaligned points, we define a new Adapted-CSG. We study the error bounds and the numerical stability of the Adapted-CSG. We also present numerical examples to demonstrate its properties relative to each new parameter and make a comparison to an alternative method.

Reactive Power Control Characteristics and Parameter Identification of PV Inverter

For getting the reactive power control model parameters of PV inverters, a method was proposed to test and identify parameters of the fault model of PV inverters based on symmetric and asymmetric fault sets. Firstly, the reactive power control structure of a grid-connected PV inverter is analyzed, and the parameters to be identified are defined. subsequently, according to various types and amplitudes of voltage that may occur in course of the operation of the test system, the overall data set is obtained, and the model given by the manufacturer is comprehensively tested. Finally, according to the test results, the manufacturer’s reactive power control model was obtained, and the parameters of the corresponding PSD-BPA model are identified by the Least Square method. The correctness of test results is verified by simulation.

INVESTIGATION OF FACE MILLED SURFACE TOPOGRAPHY ON C45 WORKPIECE ASSUMING MOVEMENT AT 30° AND 60° TO FEED DIRECTION

When surfaces with anisotropic texture are moved in different directions related to their assembled counterpart during operation, the friction conditions change, as they are determined by the lay of the topographies. In the article, contributing to the exploration of this characteristic, we analyze the inhomogeneity of the topography on a face milled plane surface with a symmetrical setting in sections at an angle of 30° or 60° to the feed direction. Roughness profiles are recorded at 13 points located equidistantly from each other in each measurement plane, and the degree and distribution of the roughness deviations are determined on the surface.

A sum-bracket theorem for simple Lie algebras

Let g be an algebra over K with a bilinear operation [⋅,⋅]:g×g→g not necessarily associative. For A⊆g, let Ak be the set of elements of g written combining k elements of A via + and [⋅,⋅].We show a “sum-bracket theorem” for simple Lie algebras over K of the form g=sln,son,sp2n,e6,e7,e8,f4,g2: if char(K) is not too small, we have growth of the form |Ak|≥|A|1+ε for all generating symmetric sets A away from subfields of K. Over Fp in particular, we have a diameter bound matching the best analogous bounds for groups of Lie type [2].As an independent intermediate result, we prove also an estimate of the form |A∩V|≤|Ak|dim⁡(V)/dim⁡(g) for linear affine subspaces V of g. This estimate is valid for all simple algebras, and k is especially small for a large class of them including associative, Lie, and Mal'cev algebras, and Lie superalgebras.

A Variable Structure Multiple-Model Estimation Algorithm Aided by Center Scaling

The accuracy for target tracking using a conventional interacting multiple-model algorithm (IMM) is limited. In this paper, a new variable structure of interacting multiple-model (VSIMM) algorithm aided by center scaling (VSIMM-CS) is proposed to solve this problem. The novel VSIMM-CS has two main steps. Firstly, we estimate the approximate location of the true model. This is aided by the expected-mode augmentation algorithm (EMA), and a new method—namely, the expected model optimization method—is proposed to further enhance the accuracy of EMA. Secondly, we change the original model set to ensure the current true model as the symmetry center of the current model set, and the model set is scaled down by a certain percentage. Considering the symmetry and linearity of the system, the errors produced by symmetrical models can be well offset. Furthermore, narrowing the distance between the true model and the default model is another effective method to reduce the error. The second step is based on two theories: symmetric model set optimization method and proportional reduction optimization method. All proposed theories aim to minimize errors as much as possible, and simulation results highlight the correctness and effectiveness of the proposed methods.

A Complete Breakdown of Politics Coverage Using the Concept of Domination and Double Domination in Picture Fuzzy Graph

The notion of fuzzy graph (FG) is widely used in many problems arising from partial or incomplete descriptions of the real world and in particular from fields such as engineering, economics, computer science, social disciplines, or medical diagnostics, and has been used in many fields of pure mathematics as well as in several areas of applied sciences such as decision making, statistics and networking. In this paper we will deal with the graph of the picture fuzzy(symmetric) set using the notion of domination in picture fuzzy graph (PFG) as a generalization of both the concept of fuzzy graph domination and intuitionistic fuzzy graph (IFG) domination. The concepts of domination theory (DT) and double domination theory (DDT) of a PFG are introduced, studied and concretely applied to the real case of an election competition to determine the minimum number of citizens a politician should meet in person in order to win the election. The choice of fuzzification (symmetric) and defuzzification (anti-symmetric) methods depends on the specific application and the type of fuzzy sets being used, whether they are symmetric or anti-symmetric. There are various methods for each process, such as centroid, max-min, and weighted average methods for defuzzification. Finally, in the last section, drawing from the application example, the features and benefits of PFGs with respect to fuzzy graphs and intuitionistic fuzzy graphs are compared and discussed.

Improved log-concavity for rotationally invariant measures of symmetric convex sets

Improved log-concavity for rotationally invariant measures of symmetric convex sets

Matrix concentration inequalities and efficiency of random universal sets of quantum gates

For a random set S⊂U(d) of quantum gates we provide bounds on the probability that S forms a δ-approximate t-design. In particular we have found that for S drawn from an exact t-design the probability that it forms a δ-approximate t-design satisfies the inequality P(δ≥x)≤2Dte−|S|xarctanh(x)(1−x2)|S|/2=O(2Dt(e−x21−x2)|S|), where Dt is a sum over dimensions of unique irreducible representations appearing in the decomposition of U↦U⊗t⊗U¯⊗t. We use our results to show that to obtain a δ-approximate t-design with probability P one needs O(δ−2(tlog⁡(d)−log⁡(1−P))) many random gates. We also analyze how δ concentrates around its expected value Eδ for random S. Our results are valid for both symmetric and non-symmetric sets of gates.

Topology of real multi-affine hypersurfaces and a homological stability property

Let R be a real closed field. We prove that the number of semi-algebraically connected components of a real hypersurface in Rn defined by a multi-affine polynomial of degree d is bounded by 2d−1. This bound is sharp and is independent of n (as opposed to the classical bound of d(2d−1)n−1 on the Betti numbers of hypersurfaces defined by arbitrary polynomials of degree d in Rn due to Petrovskiĭ and Oleĭnik, Thom and Milnor). Moreover, we show there exists c>1, such that given a sequence (Bn)n>0 where Bn is a closed ball in Rn of positive radius, there exist hypersurfaces (Vn⊂Rn)n>0 defined by symmetric multi-affine polynomials of degree 4, such that ∑i⩽5bi(Vn∩Bn)>cn, where bi(⋅) denotes the i-th Betti number with rational coefficients. Finally, as an application of the main result of the paper we verify a representational stability conjecture due to Basu and Riener on the cohomology modules of symmetric real algebraic sets for a new and much larger class of symmetric real algebraic sets than known before.

Structured encryption for triangle counting on graph data

Triangle counting is an important metric on graph analysis for graph data such as social networks. To protect the privacy of graph data, researchers have proposed differential privacy-based triangle counting methods, but the counting results are flawed by estimation errors. A recent study proposes approximate triangle counting on encrypted graph data to achieve triangle counting of the entire graph, but cannot calculate the number of triangles formed between each individual node and its neighbors. In addition, triangle counting on graph is not fully investigated based on other privacy-preserving techniques, such as structured encryption for triangle counting on graph data. To improve the accuracy of triangle counting on graph data, we proposed two types of structured encryption for triangle counting on graph data (STE-TC) with various efficiency-security tradeoffs and combined it with homomorphic encryption to achieve triangle counting between each individual node and its neighbors that can evaluate the importance of this node. We proposed two triangle counting methods in both asymmetric key and symmetric key settings to satisfy different sharing requirements in the cloud. The security analysis and experimental results show that the proposed methods are feasible and practical.

Finite image homomorphisms of the braid group and its generalizations

AbstractUsing totally symmetric sets, Chudnovsky–Kordek–Li–Partin gave a superexponential lower bound on the cardinality of non-abelian finite quotients of the braid group. In this paper, we develop new techniques using multiple totally symmetric sets to count elements in non-abelian finite quotients of the braid group. Using these techniques, we improve the lower bound found by Chudnovsky et al. We exhibit totally symmetric sets in the virtual and welded braid groups and use our new techniques to find superexponential bounds for the finite quotients of the virtual and welded braid groups.

A Generalization of Burr Type XII Distribution with Properties, Copula and Modeling Symmetric and Skewed Real Data Sets

A new generalization of Burr type XII model is introduced and studied. The genesis of the new model is based on the family of Cordeiro et al. (2016). The new model generalizes at least eight important sub-models. The new density can be unimodal, symmetric and left skewed. Some useful properties related to the new model are derived. The Clayton Copula-based construction is used to generate many bivariate and multivariate type distributions. Graphically, we performed the simulation experiments to assess of the finite sample behavior of the estimations.

Symmetrical Z-Complementary code sets for optimal training in generalized spatial modulation

This paper considers the optimal training design for broadband generalized spatial modulation systems over frequency-selective channels using a novel class of code sets introduced, called “symmetrical Z-complementary code sets”, whose aperiodic auto- and cross- correlation sums exhibit zero-correlation zones at both the front-end and tail-end of the entire correlation window. Two constructions of (optimal) symmetrical Z-complementary code sets based on generalized Boolean functions are presented. Numerical evaluations indicate that the proposed training sequences for generalized spatial modulation can achieve optimal channel estimation performance and outperform other classes of sequences.

Correlated dynamics of collective droplet excitations in a one-dimensional harmonic trap

We address the existence and dynamics of one-dimensional harmonically confined quantum droplets, appearing in two-component mixtures by deploying a nonperturbative approach. We find that, in symmetric homonuclear settings, beyond Lee-Huang-Yang correlations result in flat-top droplet configurations for either decreasing intercomponent attraction or larger atom number. Asymmetric mixtures feature spatial mixing among the involved components with the more strongly interacting or heavier one exhibiting flat-top structures. Applying quenches on the harmonic trap we trigger the lowest-lying collective droplet excitations. The interaction-dependent breathing frequency, being slightly reduced in the presence of correlations, shows a decreasing trend for stronger attractions. Semi-analytical predictions are also obtained within the Lee-Huang-Yang framework. For relatively large quench amplitudes the droplet progressively delocalizes and higher-lying motional excitations develop in its core. Simultaneously, enhanced intercomponent entanglement and long-range two-body intracomponent correlations arise. In sharp contrast, the dipole motion remains robust irrespectively of the system parameters. Species selective quenches lead to a correlation-induced dephasing of the droplet or to irregular dipole patterns due to intercomponent collisions.