Fault Detection Based on Multi-Dimensional KDE and Jensen–Shannon Divergence

Weak fault signals, high coupling data, and unknown faults commonly exist in fault diagnosis systems, causing low detection and identification performance of fault diagnosis methods based on T2 statistics or cross entropy. This paper proposes a new fault diagnosis method based on optimal bandwidth kernel density estimation (KDE) and Jensen–Shannon (JS) divergence distribution for improved fault detection performance. KDE addresses weak signal and coupling fault detection, and JS divergence addresses unknown fault detection. Firstly, the formula and algorithm of the optimal bandwidth of multidimensional KDE are presented, and the convergence of the algorithm is proved. Secondly, the difference in JS divergence between the data is obtained based on the optimal KDE and used for fault detection. Finally, the fault diagnosis experiment based on the bearing data from Case Western Reserve University Bearing Data Center is conducted. The results show that for known faults, the proposed method has 10% and 2% higher detection rate than T2 statistics and the cross entropy method, respectively. For unknown faults, T2 statistics cannot effectively detect faults, and the proposed method has approximately 15% higher detection rate than the cross entropy method. Thus, the proposed method can effectively improve the fault detection rate.     

Fictitious Domain approach with hp-finite element approximation for incompressible fluid flow

We consider the application of Fictitious Domain approach combined with least squares spectral elements for the numerical solution of fluid dynamic incompressible equations. Fictitious Domain methods allow problems formulated on a complicated shaped domain Ω$\Omega$ to be solved on a simpler domain Π$\Pi$ containing Ω$\Omega$. Least Squares Spectral Element Method has been used to develop the discrete model, as this scheme combines the generality of finite element methods with the accuracy of spectral methods. Moreover the least squares methods have theoretical and computational advantages in the algorithmic design and implementation. This paper presents the formulation and validation of the Fictitious Domain Least Squares Spectral Element approach for the steady incompressible Navier–Stokes equations. The convergence of the approximated solution is verified solving two-dimensional benchmark problems, demonstrating the predictive capability of the proposed formulation.     

Thermal Management and Modeling of Forced Convection and Entropy Generation in a Vented Cavity by Simultaneous Use of a Curved Porous Layer and Magnetic Field

The effects of using a partly curved porous layer on the thermal management and entropy generation features are studied in a ventilated cavity filled with hybrid nanofluid under the effects of inclined magnetic field by using finite volume method. This study is performed for the range of pertinent parameters of Reynolds number (100≤Re≤1000), magnetic field strength (0≤Ha≤80), permeability of porous region (10−4≤Da≤5×10−2), porous layer height (0.15H≤tp≤0.45H), porous layer position (0.25H≤yp≤0.45H), and curvature size (0≤b≤0.3H). The magnetic field reduces the vortex size, while the average Nusselt number of hot walls increases for Ha number above 20 and highest enhancement is 47% for left vertical wall. The variation in the average Nu with permeability of the layer is about 12.5% and 21% for left and right vertical walls, respectively, while these amounts are 12.5% and 32.5% when the location of the porous layer changes. The entropy generation increases with Hartmann number above 20, while there is 22% increase in the entropy generation for the case at the highest magnetic field. The porous layer height reduced the entropy generation for domain above it and it give the highest contribution to the overall entropy generation. When location of the curved porous layer is varied, the highest variation of entropy generation is attained for the domain below it while the lowest value is obtained at yp=0.3H. When the size of elliptic curvature is varied, the overall entropy generation decreases from b = 0 to b=0.2H by about 10% and then increases by 5% from b=0.2H to b=0.3H.     

基于对偶约束最小二乘支持向量机的混沌海杂波背景中的微弱信号检测

基于复杂非线性系统的相空间重构理论,提出一种改进的提取混沌背景中微弱信号的最小二乘支持向量机(LS-SVM)的方法.通过将信号以db3小波逐层分解,进行LS-SVM预测,再进行重构,同时通过增加对偶约束项、改进核函数的方法,建立改进的混沌序列的一步预测模型,从预测误差中检测湮没在混沌背景中的微弱目标信号(包括周期和瞬态信号).最后以Lorenz系统和真实海杂波数据作为混沌背景噪声进行了仿真实验,实验表明此方法能够有效地检测出混沌背景噪声中的微弱信号、抑制噪声对混沌背景信号的影响,与传统RBF神经网络和LS-SVM预测方法相比,预测精度和检测门限方面的性能有显著的提高.     

Solvable Model of a Generic Driven Mixture of Trapped Bose–Einstein Condensates and Properties of a Many-Boson Floquet State at the Limit of an Infinite Number of Particles

A solvable model of a periodically driven trapped mixture of Bose–Einstein condensates, consisting of N1 interacting bosons of mass m1 driven by a force of amplitude fL,1 and N2 interacting bosons of mass m2 driven by a force of amplitude fL,2, is presented. The model generalizes the harmonic-interaction model for mixtures to the time-dependent domain. The resulting many-particle ground Floquet wavefunction and quasienergy, as well as the time-dependent densities and reduced density matrices, are prescribed explicitly and analyzed at the many-body and mean-field levels of theory for finite systems and at the limit of an infinite number of particles. We prove that the time-dependent densities per particle are given at the limit of an infinite number of particles by their respective mean-field quantities, and that the time-dependent reduced one-particle and two-particle density matrices per particle of the driven mixture are 100% condensed. Interestingly, the quasienergy per particle does not coincide with the mean-field value at this limit, unless the relative center-of-mass coordinate of the two Bose–Einstein condensates is not activated by the driving forces fL,1 and fL,2. As an application, we investigate the imprinting of angular momentum and its fluctuations when steering a Bose–Einstein condensate by an interacting bosonic impurity and the resulting modes of rotations. Whereas the expectation values per particle of the angular-momentum operator for the many-body and mean-field solutions coincide at the limit of an infinite number of particles, the respective fluctuations can differ substantially. The results are analyzed in terms of the transformation properties of the angular-momentum operator under translations and boosts, and as a function of the interactions between the particles. Implications are briefly discussed.     

Measure Theoretic Entropy of Discrete Geodesic Flow on Nagao Lattice Quotient

The discrete geodesic flow on Nagao lattice quotient of the space of bi-infinite geodesics in regular trees can be viewed as the right diagonal action on the double quotient of PGL2Fq((t−1)) by PGL2Fq[t] and PGL2(Fq[[t−1]]). We investigate the measure-theoretic entropy of the discrete geodesic flow with respect to invariant probability measures.     

Confined Quantum Hard Spheres

We present computer simulation and theoretical results for a system of N Quantum Hard Spheres (QHS) particles of diameter σ and mass m at temperature T, confined between parallel hard walls separated by a distance Hσ, within the range 1≤H≤∞. Semiclassical Monte Carlo computer simulations were performed adapted to a confined space, considering effects in terms of the density of particles ρ*=N/V, where V is the accessible volume, the inverse length H−1 and the de Broglie’s thermal wavelength λB=h/2πmkT, where k and h are the Boltzmann’s and Planck’s constants, respectively. For the case of extreme and maximum confinement, 0.5<H−1<1 and H−1=1, respectively, analytical results can be given based on an extension for quantum systems of the Helmholtz free energies for the corresponding classical systems.     

Degrees-Of-Freedom in Multi-Cloud Based Sectored Cellular Networks

This paper investigates the achievable per-user degrees-of-freedom (DoF) in multi-cloud based sectored hexagonal cellular networks (M-CRAN) at uplink. The network consists of N base stations (BS) and K≤N base band unit pools (BBUP), which function as independent cloud centers. The communication between BSs and BBUPs occurs by means of finite-capacity fronthaul links of capacities CF=μF·12log(1+P) with P denoting transmit power. In the system model, BBUPs have limited processing capacity CBBU=μBBU·12log(1+P). We propose two different achievability schemes based on dividing the network into non-interfering parallelogram and hexagonal clusters, respectively. The minimum number of users in a cluster is determined by the ratio of BBUPs to BSs, r=K/N. Both of the parallelogram and hexagonal schemes are based on practically implementable beamforming and adapt the way of forming clusters to the sectorization of the cells. Proposed coding schemes improve the sum-rate over naive approaches that ignore cell sectorization, both at finite signal-to-noise ratio (SNR) and in the high-SNR limit. We derive a lower bound on per-user DoF which is a function of μBBU, μF, and r. We show that cut-set bound are attained for several cases, the achievability gap between lower and cut-set bounds decreases with the inverse of BBUP-BS ratio 1r for μF≤2M irrespective of μBBU, and that per-user DoF achieved through hexagonal clustering can not exceed the per-user DoF of parallelogram clustering for any value of μBBU and r as long as μF≤2M. Since the achievability gap decreases with inverse of the BBUP-BS ratio for small and moderate fronthaul capacities, the cut-set bound is almost achieved even for small cluster sizes for this range of fronthaul capacities. For higher fronthaul capacities, the achievability gap is not always tight but decreases with processing capacity. However, the cut-set bound, e.g., at 5M6, can be achieved with a moderate clustering size.     

Coupling between Blood Pressure and Subarachnoid Space Width Oscillations during Slow Breathing

The precise mechanisms connecting the cardiovascular system and the cerebrospinal fluid (CSF) are not well understood in detail. This paper investigates the couplings between the cardiac and respiratory components, as extracted from blood pressure (BP) signals and oscillations of the subarachnoid space width (SAS), collected during slow ventilation and ventilation against inspiration resistance. The experiment was performed on a group of 20 healthy volunteers (12 females and 8 males; BMI =22.1±3.2 kg/m2; age 25.3±7.9 years). We analysed the recorded signals with a wavelet transform. For the first time, a method based on dynamical Bayesian inference was used to detect the effective phase connectivity and the underlying coupling functions between the SAS and BP signals. There are several new findings. Slow breathing with or without resistance increases the strength of the coupling between the respiratory and cardiac components of both measured signals. We also observed increases in the strength of the coupling between the respiratory component of the BP and the cardiac component of the SAS and vice versa. Slow breathing synchronises the SAS oscillations, between the brain hemispheres. It also diminishes the similarity of the coupling between all analysed pairs of oscillators, while inspiratory resistance partially reverses this phenomenon. BP–SAS and SAS–BP interactions may reflect changes in the overall biomechanical characteristics of the brain.     

Matroidal Entropy Functions: A Quartet of Theories of Information,Matroid, Design,and Coding

In this paper, we study the entropy functions on extreme rays of the polymatroidal region which contain a matroid, i.e., matroidal entropy functions. We introduce variable strength orthogonal arrays indexed by a connected matroid M and positive integer v which can be regarded as expanding the classic combinatorial structure orthogonal arrays. It is interesting that they are equivalent to the partition-representations of the matroid M with degree v and the (M,v) almost affine codes. Thus, a synergy among four fields, i.e., information theory, matroid theory, combinatorial design, and coding theory is developed, which may lead to potential applications in information problems such as network coding and secret-sharing. Leveraging the construction of variable strength orthogonal arrays, we characterize all matroidal entropy functions of order n≤5 with the exception of log10·U2,5 and logv·U3,5 for some v.     

Measurement of the Ratio between g‐Factors of the Ground States of 87Rb and 85Rb

The ratio between the Landé g‐factors of the ${}^{87}$Rb $F=2$ and ${}^{85}$Rb $F=3$ ground‐state hyperfine levels is experimentally measured to be $g_F(87)/g_F(85)=1.4988586(1)$, consistent with previous measurements. The g‐factor ratio is determined by comparing the Larmor frequencies of overlapping ensembles of ${}^{87}$Rb and ${}^{85}$Rb atoms contained within an evacuated, antirelaxation‐coated vapor cell. The atomic spins are polarized via synchronous optical pumping and the Larmor frequencies are measured by off‐resonant probing using optical rotation of linearly polarized light. The accuracy of this measurement of $g_F(87)/g_F(85)$ exceeds that of previous measurements by a factor of ≈50 and is sensitive to effects related to quantum electrodynamics.     

Dark Energy with Phantom Crossing and the H0 Tension

We investigate the possibility of phantom crossing in the dark energy sector and the solution for the Hubble tension between early and late universe observations. We use robust combinations of different cosmological observations, namely the Cosmic Microwave Background (CMB), local measurement of Hubble constant (H0), Baryon Acoustic Oscillation (BAO) and SnIa for this purpose. For a combination of CMB+BAO data that is related to early universe physics, phantom crossing in the dark energy sector was confirmed at a 95% confidence level and we obtained the constraint H0=71.0−3.8+2.9 km/s/Mpc at a 68% confidence level, which is in perfect agreement with the local measurement by Riess et al. We show that constraints from different combinations of data are consistent with each other and all of them are consistent with phantom crossing in the dark energy sector. For the combination of all data considered, we obtained the constraint H0=70.25±0.78 km/s/Mpc at a 68% confidence level and the phantom crossing happening at the scale factor am=0.851−0.031+0.048 at a 68% confidence level.     

Exploring the Neighborhood of q-Exponentials

The q-exponential form eqx≡[1+(1−q)x]1/(1−q)(e1x=ex) is obtained by optimizing the nonadditive entropy Sq≡k1−∑ipiqq−1 (with S1=SBG≡−k∑ipilnpi, where BG stands for Boltzmann–Gibbs) under simple constraints, and emerges in wide classes of natural, artificial and social complex systems. However, in experiments, observations and numerical calculations, it rarely appears in its pure mathematical form. It appears instead exhibiting crossovers to, or mixed with, other similar forms. We first discuss departures from q-exponentials within crossover statistics, or by linearly combining them, or by linearly combining the corresponding q-entropies. Then, we discuss departures originated by double-index nonadditive entropies containing Sq as particular case.     

Higher Dimensional Rotating Black Hole Solutions in Quadratic f(R) Gravitational Theory and the Conserved Quantities

We explore the quadratic form of the f(R)=R+bR2 gravitational theory to derive rotating N-dimensions black hole solutions with ai,i≥1 rotation parameters. Here, R is the Ricci scalar and b is the dimensional parameter. We assumed that the N-dimensional spacetime is static and it has flat horizons with a zero curvature boundary. We investigated the physics of black holes by calculating the relations of physical quantities such as the horizon radius and mass. We also demonstrate that, in the four-dimensional case, the higher-order curvature does not contribute to the black hole, i.e., black hole does not depend on the dimensional parameter b, whereas, in the case of N>4, it depends on parameter b, owing to the contribution of the correction R2 term. We analyze the conserved quantities, energy, and angular-momentum, of black hole solutions by applying the relocalization method. Additionally, we calculate the thermodynamic quantities, such as temperature and entropy, and examine the stability of black hole solutions locally and show that they have thermodynamic stability. Moreover, the calculations of entropy put a constraint on the parameter b to be b<116Λ to obtain a positive entropy.     

A Note on Causation versus Correlation in an Extreme Situation

Recently, it has been shown that the information flow and causality between two time series can be inferred in a rigorous and quantitative sense, and, besides, the resulting causality can be normalized. A corollary that follows is, in the linear limit, causation implies correlation, while correlation does not imply causation. Now suppose there is an event A taking a harmonic form (sine/cosine), and it generates through some process another event B so that B always lags A by a phase of π/2. Here the causality is obviously seen, while by computation the correlation is, however, zero. This apparent contradiction is rooted in the fact that a harmonic system always leaves a single point on the Poincaré section; it does not add information. That is to say, though the absolute information flow from A to B is zero, i.e., TA→B=0, the total information increase of B is also zero, so the normalized TA→B, denoted as τA→B, takes the form of 00. By slightly perturbing the system with some noise, solving a stochastic differential equation, and letting the perturbation go to zero, it can be shown that τA→B approaches 100%, just as one would have expected.     

Efficient Inverted Index Compression Algorithm Characterized by Faster Decompression Compared with the Golomb-Rice Algorithm

This article deals with compression of binary sequences with a given number of ones, which can also be considered as a list of indexes of a given length. The first part of the article shows that the entropy H of random n-element binary sequences with exactly k elements equal one satisfies the inequalities klog2(0.48·n/k)<H<klog2(2.72·n/k). Based on this result, we propose a simple coding using fixed length words. Its main application is the compression of random binary sequences with a large disproportion between the number of zeros and the number of ones. Importantly, the proposed solution allows for a much faster decompression compared with the Golomb-Rice coding with a relatively small decrease in the efficiency of compression. The proposed algorithm can be particularly useful for database applications for which the speed of decompression is much more important than the degree of index list compression.     

A Two-Steps-Ahead Estimator for Bubble Entropy

Aims: Bubble entropy (bEn) is an entropy metric with a limited dependence on parameters. bEn does not directly quantify the conditional entropy of the series, but it assesses the change in entropy of the ordering of portions of its samples of length m, when adding an extra element. The analytical formulation of bEn for autoregressive (AR) processes shows that, for this class of processes, the relation between the first autocorrelation coefficient and bEn changes for odd and even values of m. While this is not an issue, per se, it triggered ideas for further investigation. Methods: Using theoretical considerations on the expected values for AR processes, we examined a two-steps-ahead estimator of bEn, which considered the cost of ordering two additional samples. We first compared it with the original bEn estimator on a simulated series. Then, we tested it on real heart rate variability (HRV) data. Results: The experiments showed that both examined alternatives showed comparable discriminating power. However, for values of 10<m<20, where the statistical significance of the method was increased and improved as m increased, the two-steps-ahead estimator presented slightly higher statistical significance and more regular behavior, even if the dependence on parameter m was still minimal. We also investigated a new normalization factor for bEn, which ensures that bEn=1 when white Gaussian noise (WGN) is given as the input. Conclusions: The research improved our understanding of bubble entropy, in particular in the context of HRV analysis, and we investigated interesting details regarding the definition of the estimator.     

Real Space Triplets in Quantum Condensed Matter: Numerical Experiments Using Path Integrals,Closures, and Hard Spheres

Path integral Monte Carlo and closure computations are utilized to study real space triplet correlations in the quantum hard-sphere system. The conditions cover from the normal fluid phase to the solid phases face-centered cubic (FCC) and cI16 (de Broglie wavelengths 0.2≤λB*<2, densities 0.1≤ρN*≤0.925). The focus is on the equilateral and isosceles features of the path-integral centroid and instantaneous structures. Complementary calculations of the associated pair structures are also carried out to strengthen structural identifications and facilitate closure evaluations. The three closures employed are Kirkwood superposition, Jackson–Feenberg convolution, and their average (AV3). A large quantity of new data are reported, and conclusions are drawn regarding (i) the remarkable performance of AV3 for the centroid and instantaneous correlations, (ii) the correspondences between the fluid and FCC salient features on the coexistence line, and (iii) the most conspicuous differences between FCC and cI16 at the pair and the triplet levels at moderately high densities (ρN*=0.9, 0.925). This research is expected to provide low-temperature insights useful for the future related studies of properties of real systems (e.g., helium, alkali metals, and general colloidal systems).