Real-valued Parameters Research Articles

Fusion regression methods with repeated functional data

Linear regression and classification methods with repeated functional data are considered. For each statistical unit in the sample, a real-valued parameter is observed over time under different conditions related by some neighborhood structure (spatial, group, etc.). Two regression methods based on fusion penalties are proposed to consider the dependence induced by this structure. These methods aim to obtain parsimonious coefficient regression functions, by determining if close conditions are associated with common regression coefficient functions. The first method is a generalization to functional data of the variable fusion methodology based on the 1-nearest neighbor. The second one relies on the group fusion lasso penalty which assumes some grouping structure of conditions and allows for homogeneity among the regression coefficient functions within groups. Numerical simulations and an application of electroencephalography data are presented.

Impact of charge and non-minimal fluid-geometry coupling on anisotropic interiors

This paper explores the interior configuration of various charged anisotropic compact models within the framework of f(R,T,RληTλη) gravity. The chosen model in this theory is represented by R+γRληTλη , where γ is a real-valued parameter. We adopt a static spherical metric to describe the interior of compact strange stars and derive the corresponding field equations. The solution to these equations is then obtained using the Finch-Skea metric and a linear equation of state. Taking the radius and mass of the compact star model 4U 1820-30 as a case study, we investigate the impact of charge and modified corrections on its internal distribution. The stability of the resulting model is also determined within a specific range of γ. Additionally, we determine the values of the model parameter through the vanishing radial pressure constraint, aligning with the experimental data of eight different stars. Our findings indicate that the resulting model adheres to the conditions necessary for physically relevant interiors, particularly in the case of lower charge.

A Partial Information Decomposition for Multivariate Gaussian Systems Based on Information Geometry.

There is much interest in the topic of partial information decomposition, both in developing new algorithms and in developing applications. An algorithm, based on standard results from information geometry, was recently proposed by Niu and Quinn (2019). They considered the case of three scalar random variables from an exponential family, including both discrete distributions and a trivariate Gaussian distribution. The purpose of this article is to extend their work to the general case of multivariate Gaussian systems having vector inputs and a vector output. By making use of standard results from information geometry, explicit expressions are derived for the components of the partial information decomposition for this system. These expressions depend on a real-valued parameter which is determined by performing a simple constrained convex optimisation. Furthermore, it is proved that the theoretical properties of non-negativity, self-redundancy, symmetry and monotonicity, which were proposed by Williams and Beer (2010), are valid for the decomposition Iig derived herein. Application of these results to real and simulated data show that the Iig algorithm does produce the results expected when clear expectations are available, although in some scenarios, it can overestimate the level of the synergy and shared information components of the decomposition, and correspondingly underestimate the levels of unique information. Comparisons of the Iig and Idep (Kay and Ince, 2018) methods show that they can both produce very similar results, but interesting differences are provided. The same may be said about comparisons between the Iig and Immi (Barrett, 2015) methods.

Distributions for Compositionally Differentiating Parametric Discontinuities

Computations in physical simulation, computer graphics, and probabilistic inference often require the differentiation of discontinuous processes due to contact, occlusion, and changes at a point in time. Popular differentiable programming languages, such as PyTorch and JAX, ignore discontinuities during differentiation. This is incorrect for parametric discontinuities —conditionals containing at least one real-valued parameter and at least one variable of integration. We introduce Potto, the first differentiable first-order programming language to soundly differentiate parametric discontinuities. We present a denotational semantics for programs and program derivatives and show the two accord. We describe the implementation of Potto, which enables separate compilation of programs. Our prototype implementation overcomes previous compile-time bottlenecks achieving an 88.1x and 441.2x speed up in compile time and a 2.5x and 7.9x speed up in runtime, respectively, on two increasingly large image stylization benchmarks. We showcase Potto by implementing a prototype differentiable renderer with separately compiled shaders.

Discrete Federated Multi-behavior Recommendation for Privacy-Preserving Heterogeneous One-Class Collaborative Filtering

Recently, federated recommendation has become a research hotspot mainly because of users’ awareness of privacy in data. As a recent and important recommendation problem, in heterogeneous one-class collaborative filtering (HOCCF), each user may involve of two different types of implicit feedback, that is, examinations and purchases. So far, privacy-preserving HOCCF has received relatively little attention. Existing federated recommendation works often overlook the fact that some privacy sensitive behaviors such as purchases should be collected to ensure the basic business imperatives in e-commerce for example. Hence, the user privacy constraints can and should be relaxed while deploying a recommendation system in real scenarios. In this article, we study the federated multi-behavior recommendation problem under the assumption that purchase behaviors can be collected. Moreover, there are two additional challenges that need to be addressed when deploying federated recommendation. One is the low storage capacity for users’ devices to store all the item vectors, and the other is the low computational power for users to participate in federated learning. To release the potential of privacy-preserving HOCCF, we propose a novel framework, named discrete federated multi-behavior recommendation (DFMR), which allows the collection of the business necessary behaviors (i.e., purchases) by the server. As to reduce the storage overhead, we use discrete hashing techniques, which can compress the parameters down to 1.56% of the real-valued parameters. To further improve the computation-efficiency, we design a memorization strategy in the cache updating module to accelerate the training process. Extensive experiments on four public datasets show the superiority of our DFMR in terms of both accuracy and efficiency.

Expressive power of ReLU and step networks under floating-point operations

The study of the expressive power of neural networks has investigated the fundamental limits of neural networks. Most existing results assume real-valued inputs and parameters as well as exact operations during the evaluation of neural networks. However, neural networks are typically executed on computers that can only represent a tiny subset of the reals and apply inexact operations, i.e., most existing results do not apply to neural networks used in practice. In this work, we analyze the expressive power of neural networks under a more realistic setup: when we use floating-point numbers and operations as in practice. Our first set of results assumes floating-point operations where the significand of a float is represented by finite bits but its exponent can take any integer value. Under this setup, we show that neural networks using a binary threshold unit or ReLU can memorize any finite input/output pairs and can approximate any continuous function within an arbitrary error. In particular, the number of parameters in our constructions for universal approximation and memorization coincides with that in classical results assuming exact mathematical operations. We also show similar results on memorization and universal approximation when floating-point operations use finite bits for both significand and exponent; these results are applicable to many popular floating-point formats such as those defined in the IEEE 754 standard (e.g., 32-bit single-precision format) and bfloat16.

Positivity of the hypergeometric Veneziano amplitude

Recently, an infinite family of one-parameter generalizations of the Veneziano amplitude were bootstrapped using as input assumptions an integer mass spectrum, crossing symmetry, high-energy boundedness, and exchange of finite spins. This new result was dubbed the hypergeometric Veneziano amplitude, with a real-valued deformation parameter r. For concreteness we work in a setup where the lowest-mass state is a tachyon of mass m02=−1 and using the partial-wave decomposition and the positivity of said decomposition’s coefficients we are able to bound the deformation parameter to r≥0 and, also, to obtain an upper bound on the number of spacetime dimensions D≤26, which is the critical dimension of bosonic string theory. Published by the American Physical Society 2024

Operational transfer path analysis based on neural network

Noise, vibration, and harshness (NVH) issues induced by vibrating source to receivers are sensitive concerns in the automotive industry, significantly determining the product quality. Transfer path analysis (TPA) serves as a crucial tool in addressing these concerns. However, classical and component-based TPA methods necessitate the measurement of all transfer functions associated with the NVH phenomenon, causing high experimental costs; moreover, operational TPA (OTPA) involves matrix inversion processes that may result in the loss of important information. In this study, a neural network-based OTPA (NOTPA) method is proposed that eliminates the need for a matrix inversion process and utilizes only operational measurement. To derive the physical meaning of transmissibility obtained from the trained neural network model, the learning algorithm for NOTPA was developed, and appropriate learning rules were applied to the model. In the general neural network model, training was performed using real-valued parameters. However, the phase of the signal is crucial information in the theoretical formulation of TPA; thus, a complex-valued propagation algorithm was established. Furthermore, an appropriate activation function was chosen to derive the actual transfer mechanism from the trained complex-valued parameters. To experimentally verify the NOTPA method, a testbed resembling automotive vehicle structure was constructed. Estimation of sound pressure and noise contribution analysis were conducted using the NOTPA method and compared with conventional TPA methods. The proposed method demonstrated higher accuracy compared to the conventional OTPA method and successfully identified the main transfer path compared to the classical TPA. Furthermore, by comparing the estimated sound pressure according to the architecture of the model, the consistency of the proposed model was verified.

Connectivity Matrix Seriation via Relaxation.

Volume electron microscopy together with computer-based image analysis are yielding neural circuit diagrams of ever larger regions of the brain. These datasets are usually represented in a cell-to-cell connectivity matrix and contain important information about prevalent circuit motifs allowing to directly test various theories on the computation in that brain structure. Of particular interest are the detection of cell assemblies and the quantification of feedback, which can profoundly change circuit properties. While the ordering of cells along the rows and columns doesn't change the connectivity, it can make special connectivity patterns recognizable. For example, ordering the cells along the flow of information, feedback and feedforward connections are segregated above and below the main matrix diagonal, respectively. Different algorithms are used to renumber matrices such as to minimize a given cost function, but either their performance becomes unsatisfying at a given size of the circuit or the CPU time needed to compute them scales in an unfavorable way with increasing number of neurons. Based on previous ideas, I describe an algorithm which is effective in matrix reordering with respect to both its performance as well as to its scaling in computing time. Rather than trying to reorder the matrix in discrete steps, the algorithm transiently relaxes the integer program by assigning a real-valued parameter to each cell describing its location on a continuous axis ('smooth-index') and finds the parameter set that minimizes the cost. I find that the smooth-index algorithm outperforms all algorithms I compared it to, including those based on topological sorting.

Teleportation Revealed

Quantum teleportation is the name of a problem: How can the real-valued parameters encoding the state at Alice’s location make their way to Bob’s location via shared entanglement and only two bits of classical communication? Without an explanation, teleportation appears to be a conjuring trick. Investigating the phenomenon with Schrödinger states and reduced density matrices shall always leave loose ends because they are not local and complete descriptions of quantum systems. Upon demonstrating that the Heisenberg picture admits a local and complete description, Deutsch and Hayden rendered its explanatory power manifest by revealing the trick behind teleportation, namely, by providing an entirely local account. Their analysis is re-exposed and further developed.

Half-plane point retrieval queries with independent and dependent geometric uncertainties

This paper addresses a family of geometric half-plane retrieval queries of points in the plane in the presence of geometric uncertainty. The problems include exact and uncertain point sets and half-plane queries defined by an exact or uncertain line whose location uncertainties are independent or dependent and are defined by k real-valued parameters. Point coordinate uncertainties are modeled with the Linear Parametric Geometric Uncertainty Model (LPGUM), an expressive and computationally efficient worst-case, first order linear approximation of geometric uncertainty that supports parametric dependencies between point locations. We present an efficient O(k2) time and space algorithm for computing the envelope of the LPGUM line that defines the half-plane query. For an exact line and an LPGUM n points set, we present an O(log⁡nk+mk) time query and O(nk) space algorithm, where m is the number of LPGUM points on or above the half-plane line. For a LPGUM line and an exact points set, we present a O(k2+(klog⁡nlog⁡log⁡n)ε+m) time and O(n2log⁡n+kε) space approximation algorithm, where 0<ε≤1 is the desired approximation error. For a LPGUM line and an LPGUM points set, we present two O(k2+(klog⁡nklog⁡log⁡nk)ε+mk) and O(mk2+(klog⁡nklog⁡log⁡nk)ε) time query and O((nk)2log⁡nk+kε) space approximation algorithms for the independent and dependent case, respectively.

Equality of critical parameters for percolation of Gaussian free field level sets

We consider upper level sets of the Gaussian free field (GFF) on Zd, for d≥3, above a given real-valued height parameter h. As h varies, this defines a canonical percolation model with strong, algebraically decaying correlations. We prove that three natural critical parameters associated with this model, respectively describing a well-ordered subcritical phase, the emergence of an infinite cluster, and the onset of a local uniqueness regime in the supercritical phase, actually coincide. At the core of our proof lies a new interpolation scheme aimed at integrating out the long-range dependence of the GFF. Due to the strength of correlations, its successful implementation requires that we work in an effectively critical regime. Our analysis relies extensively on certain novel renormalization techniques that bring into play all relevant scales simultaneously. The approach in this article paves the way to a complete understanding of the off-critical phases for strongly correlated disordered systems.

Three-Decision Methods: A Sensible Formulation of Significance Tests—and Much Else

For real-valued parameters, significance tests can be motivated as three-decision methods, in which we either assert the sign of the parameter above or below a specified null value, or say nothing either way. Tukey viewed this as a “sensible formulation” of tests, unlike the widely taught null hypothesis significance testing (NHST) system that is today's default. We review the three-decision framework, collecting the substantial literature on how other statistical tools can be usefully motivated in this way. These tools include close Bayesian analogs of frequentist power calculations, p-values, confidence intervals, and multiple testing corrections. We also show how three-decision arguments can straightforwardly resolve some well-known difficulties in the interpretation and criticism of testing results. Explicit results are shown for simple conjugate analyses, but the methods discussed apply generally to real-valued parameters.

General Five-Component Scattering Power Decomposition with Unitary Transformation (G5U) of Coherency Matrix

The polarimetric synthetic aperture radar (PolSAR) provides us with a two-by-two scattering matrix data set. The ensemble averaged coherency matrix in an imaging window derived using a scattering matrix has all non-zero elements in its three-by-three matrix. It is a full 3 × 3 matrix that bears nine real-valued and independent polarimetric parameters inside. In the proposed decomposition method, G5U, we preprocess observed coherency matrix [T] by using two consecutive unitary transformations to become an ideal form for five-component decomposition. The transformation reduces nine parameters to seven, which is the best fit for five-component scattering model expansion. We can retrieve five powers corresponding to surface scattering, double bounce scattering, volume scattering, oriented dipole scattering, and compound dipole scattering, directly. These powers can be calculated easily and used to display superb polarimetric RBG images as never before, and are further applicable for polarimetric calibration, classification, validation, etc.

Target Parameter Estimation Algorithm Based on Real-Valued HOSVD for Bistatic FDA-MIMO Radar

Since there is a frequency offset between each adjacent antenna of FDA radar, there exists angle-range two-dimensional dependence in the transmitter. For bistatic FDA-multiple input multiple output (MIMO) radar, range-direction of departure (DOD)-direction of arrival (DOA) information is coupled in transmitting the steering vector. How to decouple the three information has become the focus of research. Aiming at the issue of target parameter estimation of bistatic FDA-MIMO radar, a real-valued parameter estimation algorithm based on high-order-singular value decomposition (HOSVD) is developed. Firstly, for decoupling DOD and range in transmitter, it is necessary to divide the transmitter into subarrays. Then, the forward–backward averaging and unitary transformation techniques are utilized to convert complex-valued data into real-valued data. The signal subspace is obtained by HOSVD, and the two-dimensional spatial spectral function is constructed. Secondly, the dimension of spatial spectrum is reduced by the Lagrange algorithm, so that it is only related to DOA, and the DOA estimation is obtained. Then the frequency increment between subarrays is used to decouple the DOD and range information, and eliminate the phase ambiguity at the same time. Finally, the DOD and range estimation automatically matched with DOA estimation are obtained. The proposed algorithm uses the multidimensional structure of high-dimensional data to promote performance. Meanwhile, the proposed real-valued tensor-based method can effectively cut down the computing time. Simulation results verify the high efficiency of the developed method.

Charged anisotropic spherical collapse in f(R,T,Q) gravity

This paper discusses the gravitational collapse of dynamical self-gravitating fluid distribution in f ( R , T , Q ) gravity, where Q = R φ ϑ T φ ϑ . In this regard, we assume a charged anisotropic spherical geometry involving dissipation flux and adopt standard model of the form R + Φ T + Ψ Q , where Φ and Ψ symbolize real-valued coupling parameters. The Misner–Sharp as well as Müler–Israel Stewart mechanisms are employed to formulate the corresponding dynamical and transport equations. We then interlink these evolution equations which help to study the impact of state variables, heat dissipation, modified corrections and charge on the collapse rate. The Weyl scalar is further expressed in terms of the modified field equations. The necessary and sufficient condition of conformal flatness of the considered configuration and homogeneous energy density is obtained by applying some constraints on the model along with disappearing charge and anisotropy. Finally, we discuss different cases to investigate how the spherical matter source is affected by the charge and modified corrections. • We discuss the gravitational collapse of dynamical self-gravitating fluid distribution. • We assume a charged anisotropic spherical geometry involving dissipation flux. • The necessary and sufficient condition of conformal flatness and homogeneous energy density is obtained. • We discuss different cases how the spherical matter source is affected by the charge and modified corrections.

ARSENY: A program for computing inelastic transitions via hidden crossings in one-electron atomic ion–ion collisions with classical description of nuclear motion

The ARSENY program is intended to compute cross-sections of inelastic transitions via hidden crossings upon slow one-electron atomic ion–ion collisions using the approximation of classical description of nuclear motion in the collision energy region E<20 KeV/nucleon. Particular attention is paid to the calculation of the analytical properties of adiabatic potential energy curves of the two-center Coulomb problem for complex values of the internuclear distance. Complex branch points and hidden crossings are calculated and their significance for the dynamics of one-electron collisional systems is revealed. Benchmark calculations of cross sections for charge exchange, excitation, and ionization in slow He2++H(1s) collisions are presented and compared with experimental data. Program summaryProgram Title: ARSENYCPC Library link to program files:https://doi.org/10.17632/n43srxwdnm.1Licensing provisions: CC By 4.0Programming language: FORTRAN 90/95. Compilers: Intel(R) Visual Fortran Compiler 19.0.4.245 [IA-32]Nature of problem: The processes of charge exchange, excitation, and ionization in one-electron atomic ion–ion collisions in a low-temperature plasma are actively studied in astrophysics and tokamak Charge-eXchange Recombination Spectroscopy (CXRS) Edge diagnostics in ITER [1–7]. Numerical calculations of cross sections for charge exchange, excitation, and ionization for slow one-electron atomic ion–ion collisions within the approximation of classical description of nuclear motion have been conventionally implemented, in particular, by the electron-nuclear dynamics approach [8] and the close-coupled channel method using basis functions of the two-center Coulomb problem (see, e.g., [9–13]). However, with real-valued internuclear distance these approaches did not allow for the dynamical structure of discrete-discrete and discrete-continuous transitions in the two-center Coulomb problem. This disadvantage manifests itself in the disagreement between the theoretical and experimental cross-sections at small velocity of ions [13–15]. In a number of papers [1,14,16–20] the dynamical structure of the transitions is considered in terms of hidden crossing of potential curves, when using the analytic continuation to a complex plane of the internuclear distance. This approach is implemented in the ARSENY program aimed at computing cross sections of inelastic discrete-discrete and discrete-continuous transitions via hidden crossings for slow one-electron atomic ion–ion collisions within the approximation of classical description of nuclear motion announced in [1]. Benchmark calculations of cross sections for charge exchange, excitation, and ionization in slow He2++H(1s) collisions are presented and compared with experimental data.Solution method: The potential energy curves E=E(R) and the separation constant λ=λ(R) depending on the real-valued and complex-valued parameter R of the two-center Coulomb problem are calculated from the minimization condition for a quadratic functional corresponding to a pair of nonlinear equations with respect to a pair of unknowns E(R) and λ(R) by iterating three-term recurrent relations [21,22] using a mean least square method [23]. These equations are obtained from the known recurrent relations for the expansion coefficients of quasiradial and quasiangular spheroidal Coulomb functions. The series of branching points Rc sought for in the complex plane of internuclear distance R and the hidden crossings of complex potential energy curves E(R) are calculated by an iterative method using the known analytical behavior in the form of a square root of difference E(R)−E(Rc) in the vicinity of the unknown branch points Rc. Calculations of cross-sections of inelastic transitions via hidden crossings for the slow one-electron atomic ion–ion collisions within the approximation of classical description of nuclear motion are carried out by integration over the impact parameter of the nonadiabatic transition probability expressed in terms of the Stückelberg parameter determined integral of difference of imaginary parts of each pair of complex potential energy curves E(R) by a contour around the branching point Rc [18,19].Additional comments including restrictions and unusual features: In calculations of cross sections and required branch points, about 220 adiabatic states of the lower part of the discrete spectrum of the two-center problem are used.

Proximity Queries on Terrain Surface

Due to the advance of the geo-spatial positioning and the computer graphics technology, digital terrain data has become increasingly popular nowadays. Query processing on terrain data has attracted considerable attention from both the academic and the industry communities. Proximity queries such as the shortest path/distance query, k nearest/farthest neighbor query, and top- k closest/farthest pairs query are fundamental and important queries in the context of the terrain surfaces, and they have a lot of applications in Geographical Information System, 3D object feature vector construction, and 3D object data mining. In this article, we first study the most fundamental type of query, namely, shortest distance and path query, which is to find the shortest distance and path between two points of interest on the surface of the terrain. As observed by existing studies, computing the exact shortest distance/path is very expensive. Some existing studies proposed ϵ -approximate distance and path oracles, where ϵ is a non-negative real-valued error parameter. However, the best-known algorithm has a large oracle construction time, a large oracle size, and a large query time. Motivated by this, we propose a novel ϵ -approximate distance and path oracle called the S pace E fficient distance and path oracle (SE), which has a small oracle construction time, a small oracle size, and a small distance and path query time, thanks to its compactness of storing concise information about pairwise distances between any two points-of-interest. Then, we propose several algorithms for the k nearest/farthest neighbor and top- k closest/farthest pairs queries with the assistance of our distance and path oracle SE . Our experimental results show that the oracle construction time, the oracle size, and the distance and path query time of SE are up to two, three, and five orders of magnitude faster than the best-known algorithm, respectively. Besides, our algorithms for other proximity queries including k nearest/farthest neighbor queries and top- k closest/farthest pairs queries significantly outperform the state-of-the-art algorithms by up to two orders of magnitude.

Poincaré Beams at the Tight Focus: Inseparability, Radial Spin Hall Effect, and Reverse Energy Flow

The family of Poincaré beams has three parameters, including two real-valued angular parameters, which specify a definite polarization state on the Poincaré sphere, and a third integer parameter n specifying the beam singularity order. We show theoretically and through a numerical simulation that, while being inseparable and not allowing for the separation of polarization and orbital degrees of freedom in the general case, the Poincaré beams display remarkable properties when tightly focused. We find that at n = 2, a reverse energy flow occurs near the optical axis, which is mathematically expressed as the negative projection of the Poynting vector. We also reveal that given certain parameters of the Poincaré beams, the energy flow rotates around the optical axis due to spin–orbital conversion. We also reveal a radial optical Hall effect that occurs at the tight focus of Poincaré beams, when the on-axis components of the spin angular momentum vector have different signs on certain different-radius circles centered at the focal spot center.

Polarization spectrograms: Unraveling the polarization of ocean acoustic normal modes using the Stokes framework

Coastal oceanic environments act as dispersive waveguides for acoustic propagation, which is conveniently described using normal mode theory. Here we propose a framework to describe and estimate the polarization of normal modes, as measured using a single vector sensor in the water column. We introduce the Stokes parameters, four real-valued parameters widely used to describe polarization properties in wave physics, notably optics, but largely ignored in ocean acoustics. Analytic expressions for modal Stokes parameters are derived, and a signal processing framework to estimate them is introduced. The concept of polarization spectrograms, which enables visualization of the Stokes parameters in the time-frequency domain, is notably introduced. The whole framework is illustrated for dispersed impulsive signals using both simulations and experimental marine data collected during the Seabed Characterization Experiment. [Work supported by the Direction Générale de l’Armement and by the Office of Naval Research.]