Symmetry — Open Access Journal

We confront a non-relativistic Bose–Einstein Condensate (BEC) model of light bosons interacting gravitationally either through a Newtonian or a Yukawa potential with the observed rotational curves of 12 dwarf galaxies. The baryonic component is modeled as an axisymmetric exponential disk and its characteristics are derived from the surface luminosity profile of the galaxies. The purely baryonic fit is unsatisfactory, hence a dark matter component is clearly needed. The rotational curves of five galaxies could be explained with high confidence level by the BEC model. For these galaxies, we derive: (i) upper limits for the allowed graviton mass; and (ii) constraints on a velocity-type and a density-type quantity characterizing the BEC, both being expressed in terms of the BEC particle mass, scattering length and chemical potential. The upper limit for the graviton mass is of the order of ${10}^{-26}$ eV/c², three orders of magnitude stronger than the limit derived from recent gravitational wave detections. Full article

Lung cancer is one of the highest causes of cancer-related death in both men and women. Therefore, various diagnostic methods for lung nodules classification have been proposed to implement the early detection. Due to the limited amount and diversity of samples, these methods encounter some bottlenecks. In this paper, we intend to develop a method to enlarge the dataset and enhance the performance of pulmonary nodules classification. We propose a data augmentation method based on generative adversarial network (GAN), called Forward and Backward GAN (F&BGAN), which can generate high-quality synthetic medical images. F&BGAN has two stages, Forward GAN (FGAN) generates diverse images, and Backward GAN (BGAN) is used to improve the quality of images. Besides, a hierarchical learning framework, multi-scale VGG16 (M-VGG16) network, is proposed to extract discriminative features from alternating stacked layers. The methodology was evaluated on the Lung Image Database Consortium and Image Database Resource Initiative (LIDC-IDRI) dataset, with the best accuracy of 95.24%, sensitivity of 98.67%, specificity of 92.47% and area under ROC curve (AUROC) of 0.980. Experimental results demonstrate the feasibility of F&BGAN in generating medical images and the effectiveness of M-VGG16 in classifying malignant and benign nodules. Full article

Many open quantum systems encountered in both natural and synthetic situations are embedded in classical-like baths. Often, the bath degrees of freedom may be represented in terms of canonically conjugate coordinates, but in some cases they may require a non-canonical or non-Hamiltonian representation. Herein, we review an approach to the dynamics and statistical mechanics of quantum subsystems embedded in either non-canonical or non-Hamiltonian classical-like baths which is based on operator-valued quasi-probability functions. These functions typically evolve through the action of quasi-Lie brackets and their associated Quantum-Classical Liouville Equations, or through quasi-Lie brackets augmented by dissipative terms. Quasi-Lie brackets possess the unique feature that, while conserving the energy (which the Noether theorem links to time-translation symmetry), they violate the time-translation symmetry of their algebra. This fact can be heuristically understood in terms of the dynamics of the open quantum subsystem. We then describe an example in which a quantum subsystem is embedded in a bath of classical spins, which are described by non-canonical coordinates. In this case, it has been shown that an off-diagonal open-bath geometric phase enters into the propagation of the quantum-classical dynamics. Next, we discuss how non-Hamiltonian dynamics may be employed to generate the constant-temperature evolution of phase space degrees of freedom coupled to the quantum subsystem. Constant-temperature dynamics may be generated by either a classical Langevin stochastic process or a Nosé–Hoover deterministic thermostat. These two approaches are not equivalent but have different advantages and drawbacks. In all cases, the calculation of the operator-valued quasi-probability function allows one to compute time-dependent statistical averages of observables. This may be accomplished in practice using a hybrid Molecular Dynamics/Monte Carlo algorithms, which we outline herein. Full article

In banks, governments, and Internet companies, inconsistent data problems may often arise when various information systems are collecting, processing, and updating data due to human or equipment reasons. The emergence of inconsistent data makes it impossible to obtain correct information from the data and reduces its availability. Such problems may be fatal in data-intensive enterprises, which causes huge economic losses. Moreover, it is very difficult to clean inconsistent data in databases, especially for data containing conditional functional dependencies with built-in predicates (CFDPs), because it tends to contain more candidate repair values. For the inconsistent data containing CFD^Ps to detect incomplete and repair difficult problems in databases, we propose a dependency lifting algorithm (DLA) based on the maximum dependency set (MDS) and a reparation algorithm (C-Repair) based on integrating the minimum cost and attribute correlation, respectively. In detection, we find recessive dependencies from the original dependency set to obtain the MDS and improve the original algorithm by dynamic domain adjustment, which extends the applicability to continuous attributes and improves the detection accuracy. In reparation, we first set up a priority queue (PQ) for elements to be repaired based on the minimum cost idea to select a candidate element; then, we treat the corresponding conflict-free instance ($I_{nv}$) as the training set to learn the correlation among attributes and compute the weighted distance (WDis) between the tuple of the candidate element and other tuples in $I_{nv}$ according to the correlation; and, lastly, we perform reparation based on the WDis and re-compute the PQ after each reparation round to improve the efficiency, and use a label, flag, to mark the repaired elements to ensure the convergence at the same time. By setting up a contrast experiment, we compare the DLA with the CFD^Ps based algorithm, and the C-Repair with a cost-based, interpolation-based algorithm on a simulated instance and a real instance. From the experimental results, the DLA and C-Repair algorithms have better detection and repair ability at a higher time cost. Full article

In this paper, the concept of fuzzy normed ring is introduced and some basic properties related to it are established. Our definition of normed rings on fuzzy sets leads to a new structure, which we call a fuzzy normed ring. We define fuzzy normed ring homomorphism, fuzzy normed subring, fuzzy normed ideal, fuzzy normed prime ideal, and fuzzy normed maximal ideal of a normed ring, respectively. We show some algebraic properties of normed ring theory on fuzzy sets, prove theorems, and give relevant examples. Full article

A finite-type immersion or smooth map is a nice tool to classify submanifolds of Euclidean space, which comes from the eigenvalue problem of immersion. The notion of generalized 1-type is a natural generalization of 1-type in the usual sense and pointwise 1-type. We classify ruled surfaces with a generalized 1-type Gauss map as part of a plane, a circular cylinder, a cylinder over a base curve of an infinite type, a helicoid, a right cone and a conical surface of G-type. Full article

A quaternionic commutator bracket for position and momentum shows that the quaternionic wave function, viz.$\tilde{\psi }=(\frac{i}{c}{\psi }_0,\overrightarrow{\psi })$, represents a state of a particle with orbital angular momentum, $L=3\hslash$, resulting from the internal structure of the particle. This angular momentum can be attributed to spin of the particle. The vector $\overrightarrow{\psi }$, points in an opposite direction of $\overrightarrow{L}$. When a charged particle is placed in an electromagnetic field, the interaction energy reveals that the magnetic moments interact with the electric and magnetic fields giving rise to terms similar to Aharonov–Bohm and Aharonov–Casher effects. Full article

It is very well known that real-life applications of fixed point theory are restricted with the transformation of the problem in the form of $f\left(x\right)=x$. (1) The Knaster–Tarski fixed point theorem underlies various approaches of checking the correctness of programs. (2) The Brouwer fixed point theorem is used to prove the existence of Nash equilibria in games. (3) Dlala et al. proposed a solution for magnetic field problems via the fixed point approach. Full article

We consider Pisot family substitution tilings in ${\mathbb{R}}^d$ whose dynamical spectrum is pure point. There are two cut-and-project schemes (CPSs) which arise naturally: one from the Pisot family property and the other from the pure point spectrum. The first CPS has an internal space ${\mathbb{R}}^m$ for some integer $m\in \mathbb{N}$ defined from the Pisot family property, and the second CPS has an internal space H that is an abstract space defined from the condition of the pure point spectrum. However, it is not known how these two CPSs are related. Here we provide a sufficient condition to make a connection between the two CPSs. For Pisot unimodular substitution tiling in $\mathbb{R}$, the two CPSs turn out to be same due to the remark by Barge-Kwapisz. Full article

In this paper, we design and develop a new class of linear algebraic codes defined as soft linear algebraic codes using soft sets. The advantage of using these codes is that they have the ability to transmit m-distinct messages to m-set of receivers simultaneously. The methods of generating and decoding these new classes of soft linear algebraic codes have been developed. The notion of soft canonical generator matrix, soft canonical parity check matrix, and soft syndrome are defined to aid in construction and decoding of these codes. Error detection and correction of these codes are developed and illustrated by an example. Full article

In this paper, we find all Fibonacci and Lucas numbers written in the form $2^a+3^b+5^c+7^d$, in non-negative integers $a,b,c,d$, with $0\le \max \{a,b,c\}\le d$. Full article

In this paper, we investigate the existence of an absolute continuous solution to a class of first-order nonlinear differential equation with integral boundary conditions (BCs) or with infinite-point BCs. The Liouville-Caputo fractional derivative is involved in the nonlinear function. We first consider the existence of a solution for the first-order nonlinear differential equation with m-point nonlocal BCs. The existence of solutions of our problems is investigated by applying the properties of the Riemann sum for continuous functions. Several examples are given in order to illustrate our results. Full article

Aiming at the problem of computational complexity of channel estimation, this paper proposes a low-complexity block matching pursuit (BMP) algorithm based on antenna grouping and block sparsity for frequency division duplex (FDD) massive Multiple-input Multiple-output orthogonal frequency division multiplexing (OFDM) systems. The system coherence time may be exceeded as a result of time consumption when adopting an orthogonal pilot symbol in the time domain. To solve this problem, an antenna grouping transmission scheme is proposed to reduce the total channel estimation time by sacrificing the observed data length. The simulation results show that the proposed BMP algorithm has good anti-noise performance, and it can accurately determine the non-zero position of the sparse vector and adaptively determine the sparsity of the channel, which effectively translates to improved channel estimation performance and better overall system performance than the existing algorithms. Full article

In this work, we prove a Nekhoroshev-type stability theorem for the Toda lattice with Dirichlet boundary conditions, i.e., with fixed ends. The Toda lattice is a member of the family of Fermi-Pasta-Ulam (FPU) chains, and in view of the unexpected recurrence phenomena numerically observed in these chains, it has been a long-standing research aim to apply the theory of perturbed integrable systems to these chains, in particular to the Toda lattice which has been shown to be a completely integrable system. The Dirichlet Toda lattice can be treated mathematically by using symmetries of the periodic Toda lattice. Precisely, by treating the phase space of the former system as an invariant subset of the latter one, namely as the fixed point set of an important symmetry of the periodic lattice, the results already obtained for the periodic lattice can be used to obtain analogous results for the Dirichlet lattice. In this way, we transfer our stability results for the periodic lattice to the Dirichlet lattice. The Nekhoroshev theorem is a perturbation theory result which does not have the probabilistic character of related theorems, and the lattice with fixed ends is more important for applications than the periodic one. Full article

In this paper, we extend the Hamy mean (HM) operator and dual Hamy mean (DHM) operator with Pythagorean fuzzy numbers (PFNs) to propose Pythagorean fuzzy Hamy mean (PFHM) operator, weighted Pythagorean fuzzy Hamy mean (WPFHM) operator, Pythagorean fuzzy dual Hamy mean (PFDHM) operator, weighted Pythagorean fuzzy dual Hamy mean (WPFDHM) operator. Then the multiple attribute group decision making (MAGDM) methods are proposed with these operators. In the end, we utilize an applicable example for supplier selection to prove the proposed methods. Full article

Symmetric graphs have non-trivial automorphism groups. This article starts with the proof that all partition comparison measures we have found in the literature fail on symmetric graphs, because they are not invariant with regard to the graph automorphisms. By the construction of a pseudometric space of equivalence classes of permutations and with Hausdorff’s and von Neumann’s methods of constructing invariant measures on the space of equivalence classes, we design three different families of invariant measures, and we present two types of invariance proofs. Last, but not least, we provide algorithms for computing invariant partition comparison measures as pseudometrics on the partition space. When combining an invariant partition comparison measure with its classical counterpart, the decomposition of the measure into a structural difference and a difference contributed by the group automorphism is derived. Full article

In this paper, solutions for systems of linear fractional differential equations are considered. For the commensurate order case, solutions in terms of matrix Mittag–Leffler functions were derived by the Picard iterative process. For the incommensurate order case, the system was converted to a commensurate order case by newly introducing unknown functions. Computation of matrix Mittag–Leffler functions was considered using the methods of the Jordan canonical matrix and minimal polynomial or eigenpolynomial, respectively. Finally, numerical examples were solved using the proposed methods. Full article

When we perform particle-based water simulation, water particles are often increased dramatically because of particle splitting around breaking holes to maintain the thin fluid sheets. Because most of the existing approaches do not consider the volume of the water particles, the water particles must have a very low mass to satisfy the law of the conservation of mass. This phenomenon smears the motion of the water, which would otherwise result in splashing, thereby resulting in artifacts such as numerical dissipation. Thus, we propose a new fluid-implicit, particle-based framework for maintaining and representing the thin sheets and turbulent flows of water. After splitting the water particles, the proposed method uses the ghost density and ghost mass to redistribute the difference in mass based on the volume of the water particles. Next, small-scale turbulent flows are formed in local regions and transferred in a smooth manner to the global flow field. Our results show us the turbulence details as well as the thin sheets of water, thereby obtaining an aesthetically pleasing improvement compared with existing methods. Full article