Arbitrary Dependence Research Articles

Lie group classification of the nonlinear transmission line model and exact traveling wave solutions

A nonlinear transmission line (NLTL) model is very essential tools in understanding of propagation of electrical solitons which can propagate in the form of voltage waves in nonlinear dispersive media. These models are often formulated using nonlinear partial differential equations. One of the basic tools available to study these equations are numerical methods such as finite difference method, finite element method, etc, have been developed for nonlinear partial differential equations. These methods require a great amount of time and memory due to the discretization and usually the effect of round-off error causes loss of accuracy in the results. So in this paper, we use one of the most famous analytical methods the Lie group analysis due to Sophus Lie. One of the advantages of this approach is that requires only algebraic calculations. The main aim of this study is to explore the nonlinear transmission line model with arbitrary capacitor's voltage dependence, through the use of Lie group classification, we show that the specifying form of arbitrary capacitor's voltage are power law nonlinearity, exponential law nonlinearity and constant capacitance. The exact solutions and similarity reductions generated from the symmetries are also provided. Furthermore, translational symmetries were utilized to find a family of traveling wave solutions via the \(\tanh\)-method of the governing nonlinear problem.

WIMPs without weakness: Generalized mass window with entropy injection

We study general freeze-out scenarios where an arbitrary number of initial and final dark matter particles participate in the number-changing freeze-out interaction. We consider a simple sector with two particle species undergoing such a thermal freeze-out; one of the relics is stable and gives rise to the dark matter today, while the other one decays to the Standard Model, injecting significant entropy into the thermal bath that dilutes the dark matter abundance. We show that this setup can lead to a stable relic population that reproduces the observed dark matter abundance without requiring weak scale masses or couplings. The final dark matter abundance is estimated analytically. We carry out this calculation for arbitrary temperature dependence in the freeze-out process and identify the viable dark matter mass and cross section ranges that explain the observed dark matter abundance. This setup can be used to open parameter space for both heavy (above the unitarity bound) or light (sub-GeV) dark matter candidates. We point out that the best strategy for probing most parts of our parameter space is to look for signatures of an early matter-dominant epoch.

НЕКОТО РЫЕ ВОПРОСЫ СТАТ ИКИ ГЕОМЕТРИЧЕСКИ И ФИЗИЧЕСКИ НЕЛИНЕЙНОЙ СПЛОШНОЙ СРЕДЫ

We consider the generalized plane deformation of physically and geometrically nonlinear continuous medium. The mathematical model of medium is described by physically nonlinear relations in the form of arbitrary cross dependences between the first invariants of tensors and the second invariants of stress and strain deviators, taking into account geometrical nonlinearity (according to V.V. Novozhilov). The system of resolving partial differential equations of equilibrium, done in displacements, is quasilinear. This type is being investigated. Despite the fact that the type of the system of quasilinear partial differential equations in a certain part of space can be determined only for a specific solution, it is stated that in the general case the system of differential equations of equilibrium of generalized plane deformation is a system of mixed type. The type of the system of partial differential equations in a given area of space is completely determined by the values of its coefficients, and therefore depends both on the value of physical constants of continuous medium material and also on the value of derivatives of displacements in spatial coordinates.

Quantum transport for electron quasiparticles interacting with a disordered binary alloy: A Wigner approach

Quantum transport is developed in the Wigner function representation for a Bloch electron quasiparticle interacting with a disordered binary alloy in the presence of a homogeneous electric field of arbitrary time dependence and amplitude. The electron quasiparticle is described by a single-band effective Hamiltonian, and the homogeneous electric field is treated in the vector potential gauge. The methodology for the quantum transport analysis proceeds by first transforming the Liouville equation to one in which the interaction Hamiltonian (the binary alloy Hamiltonian) appears quadratically. The basis states employed in evaluating the requisite matrix elements are the instantaneous eigenstates of the electron quasiparticle Hamiltonian in the presence of the electric field. The Wigner quantum transport equations are derived, and the binary alloy collision term is suitably ensemble averaged over the disordered binary alloy matrix elements. In addition, the general drift and diffusion terms are exactly obtained, resulting in the complete Wigner-Boltzmann equation for the binary alloy system. In approximating the collision term for the two separate cases of parabolic energy dispersion and the long-wavelength limit, it is found that the reduced Wigner-Boltzmann equation includes the manifestation of the intracollisional field effect and other quantum generalities. As a contrast to the actual random alloy treatment, attention is given to the canonical problem of quantum transport for a virtual crystal (VC). As an alternative to the random binary alloy scattering problem, the VC Hamiltonian adopted for this treatment is derived by ensemble averaging the random binary alloy Hamiltonian. The resulting Wigner transport equation for the VC case is descriptive of Bloch dynamics in a graded semiconductor alloy.

Random sources with rectangular coherence.

A convenient method for modeling partially coherent sources with rectangular coherence is introduced by structuring the degree of coherence as two separable arbitrary functions with arbitrary dependence of variables. The included examples have demonstrated new opportunities of modeling random sources for beam shaping applications by coherence modulation. The first example discusses a class of rectangular sinc-correlated models generating radiating fields with self-focusing features. As a second example, we introduce a new type of partially coherent vortex beams, which has a unique feature of self-rotation around the optical axis upon propagation.

Nonparametric methods for clustered data in pre-post intervention design

In pre-post factorial designs involving clustered units, parametric methods such as generalized linear mixed effects models are used to handle within subject correlations. However, the distributional and parametric model assumptions in these methods are not always satisfied, especially so with modern data sets, and are often difficult to verify in practice. Often times, the assumptions may not even be realistic when data are measured in a non-metric scale as commonly happens, for example, in Quality-of-Life outcomes. In this article, nonparametric effect-size measures for clustered data in factorial designs with pre-post measurements will be introduced. In our setup, the pre and post occasions may also be viewed as two treatment conditions. Arbitrary dependence among observations within a cluster and across treatment groups is allowed. The effect-size estimators along with their asymptotic properties for computing confidence intervals and performing hypotheses tests are investigated. The proposed methods handle within-cluster as well as between-cluster treatment assignments seamlessly. The methods are shown to be effective in finite samples using simulation studies and they have high powers, especially in situations with multiple forms of clustering. Applications are illustrated with data from a three-arm Randomized Trial of Indoor Wood Smoke reduction.

Kernel machine learning methods to handle missing responses with complex predictors. Application in modelling five-year glucose changes using distributional representations

Background and objectivesMissing data is a ubiquitous problem in longitudinal studies due to the number of patients lost to follow-up. Kernel methods have enriched the machine learning field by successfully managing non-vectorial predictors, such as graphs, strings, and probability distributions, and have emerged as a promising tool for the analysis of complex data stemming from modern healthcare. This paper proposes a new set of kernel methods to handle missing data in the response variables. These methods will be applied to predict long-term changes in glycated haemoglobin (A1c), the primary biomarker used to diagnose and monitor the progression of diabetes mellitus, making emphasis on exploring the predictive potential of continuous glucose monitoring (CGM). MethodsWe propose a new framework of non-linear kernel methods for testing statistical independence, selecting relevant predictors, and quantifying the uncertainty of the resultant predictive models. As a novelty in the clinical analysis, we used a distributional representation of CGM as a predictor and compared its performance with that of traditional diabetes biomarkers. ResultsThe results show that, after the incorporation of CGM information, predictive ability increases from R2=0.61 to R2=0.71. In addition, uncertainty analysis is useful for characterising some subpopulations where predictivity is worsened, and a more personalised clinical follow-up is advisable according to expected patient uncertainty in glucose values. ConclusionsThe proposed methods have proven to deal effectively with missing data. They also have the potential to improve the results of predictive tasks by including new complex objects as explanatory variables and modelling arbitrary dependence relations. The application of these methods to a longitudinal study of diabetes showed that the inclusion of a distributional representation of CGM data provides greater sensitivity in predicting five-year A1c changes than classical diabetes biomarkers and traditional CGM metrics.

Capacity of Backscatter Communication Under Arbitrary Fading Dependence

We analyze the impact of arbitrary dependence between the forward and backward links in backscatter communication systems. Specifically, we quantify the effect of positive and negative dependence between these fading links on channel capacity by using Copula theory. The benefits of this approach are highlighted over the classical framework of linear dependence based on Pearson’s correlation coefficient, which is also analyzed. Results show that for a fixed transmit power budget, capacity grows with positive dependence as well as with fading severity in the low signal-to-noise ratio (SNR) regime. Conversely, fading dependence becomes immaterial in the high SNR regime.

Combining p-values for Multivariate Predictive Ability Testing

In this paper, we propose an intersection-union test for multivariate forecast accuracy based on the combination of a sequence of univariate tests. The testing framework evaluates a global null hypothesis of equal predictive ability using any number of univariate forecast accuracy tests under arbitrary dependence structures, without specifying the underlying multivariate distribution. An extensive Monte-Carlo simulation exercise shows that our proposed test has very good size and power properties under several relevant scenarios, and performs well in both low- and high-dimensional settings. We illustrate the empirical validity of our testing procedure using a large dataset of 84 daily exchange rates running from 1 January 2011 to 1 April 2021. We show that our proposed test addresses inconclusive results that often arise in practice.

Admissible ways of merging p-values under arbitrary dependence

Methods of merging several p-values into a single p-value are important in their own right and widely used in multiple hypothesis testing. This paper is the first to systematically study the admissibility (in Wald’s sense) of p-merging functions and their domination structure, without any information on the dependence structure of the input p-values. As a technical tool, we use the notion of e-values, which are alternatives to p-values recently promoted by several authors. We obtain several results on the representation of admissible p-merging functions via e-values and on (in)admissibility of existing p-merging functions. By introducing new admissible p-merging functions, we show that some classic merging methods can be strictly improved to enhance power without compromising validity under arbitrary dependence.

Precise large deviations in a bidimensional risk model with arbitrary dependence between claim-size vectors and waiting times

Consider a bidimensional risk model in which an insurer simultaneously confronts two types of claims sharing a common non-stationary arrival process, and the claim-sizes {X→k;k≥1} form a sequence of i.i.d. random vectors with nonnegative components being dependent on each other. Supposing that the univariate marginal distributions of the claim-size vectors have dominatedly varying tails, precise large deviations for the aggregate amount of claims are obtained, by allowing that the claim-size vectors and claim inter-arrival (waiting) times are arbitrarily dependent.

Moderate deviations for a Hawkes-type risk model with arbitrary dependence between claim sizes and waiting times

Consider a risk model with consistently-varying-tailed claim sizes following a Hawkes-type arrival process. By allowing that the extended negatively dependent claim sizes and the claim inter-arrival (waiting) times are arbitrarily dependent, moderate deviation results for the aggregate amount of claims are obtained.

Precise large deviations of aggregate claims in a nonstandard risk model with arbitrary dependence between claim sizes and waiting times

<abstract><p>Recently, Chen et al.<sup>[<xref ref-type="bibr" rid="b3">3</xref>]</sup> investigated the precise large deviations of aggregate claims in a renewal risk model with arbitrary dependence between claim sizes and their waiting times. In this paper, we extend their results to a nonstandard risk model in which various dependence structures are imposed on the modeling components, and obtain the asymptotic lower and upper bounds of precise large deviations for aggregate claims, which hold uniformly for all $ x $ in a $ t $-interval.</p></abstract>

Precise Large Deviations of Aggregate Claims in a Compound Risk Model with Arbitrary Dependence between Claim Sizes and Waiting Times

Precise Large Deviations of Aggregate Claims in a Compound Risk Model with Arbitrary Dependence between Claim Sizes and Waiting Times

Estimations for aggregate amount of claims in a risk model with arbitrary dependence between claim sizes and inter-arrival times

<abstract><p>This paper considers a compound risk model, in which the individual claim sizes and their inter-arrival times can be arbitrarily dependent. We mainly investigate the claim sizes are extended negatively dependent. When the claim sizes have consistently-varying-tailed distributions, we obtain precise large deviations of the aggregate amount of claims in the above dependent compound risk model.</p></abstract>

Investigation of Attenuation Properties of Liquid Materials by Gamma Absorption-Scattering Method

In this work, a system for the characterization of materials using transmission and scattering of gamma rays is described and used to assess the attenuation properties of some liquid materials. The apparatus consists of a 45 mCi point source of 124Am and thin NaI (Tl) detector. Measurements are presented for sucrose solutions with densities ranging from 1 to 1.86 g/cm3. For the absorbance, the solution Z (0.66 g/cm3) with the lowest density has higher absorption with chances to attenuate more than some higher density absorber solution like the sucrose (1.37 g/cm3) while sucrose (1.86 g/cm3) solution with the highest density possessing highest absorption and attenuation capabilities. This however did not fully accord to the conformity with the theory in low-density absorber which will give rise to less attenuation than a high-density absorber since the chances of an interaction between the radiation and the atoms of the absorber are relatively lower. Consequently, the variation of the ratio of scattered and transmitted intensity against the density of the solutions display some arbitrary dependence with energy of the photons interacting with the density of the absorber solution with some little deviation to the exact ideal scattering and transmission case. With gamma rays, most likely the scattering is in the forward direction and that the probability of scattering backwards or in larger angles is relatively constant as the angle approaches 90.

Time domain analysis of impulse electromagnetic field at the interface of two media

Background. Ultrashort pulses of electromagnetic field are widely used in construction, archeology and demining, etc., by constructing effective georadars of the underlying surface, but theoretical study of physical processes of irradiation of medium is had a limit range of simplified model problems, usually in frequency domain. Therefore, the solutions of the problems of penetration of a pulsed wave with arbitrary time dependence into material medium are of special importance for understanding the possibilities and limitations of georadar’s study. Objectives. To obtain the analytical solution in time domain of the problems of reflection and propagation of a impulse electromagnetic wave through the interface of two media, which is the first model approximation to the description of physical processes that occur during operation of pulsed ultrawideband radar. Materials and methods. The problem of irradiation by nonstationary electric field of a lossless medium with a given permittivity is solved analytically by application of evolutionary approach. It consists in solving of Cauchy’s problem for the second-order partial differential equation Klein–Gordon type with respect to evolutionary coefficients. The components of the electromagnetic field in free space are found by integration by spectral parameters and summation by angular modes with appropriate combinations of basis functions. Results. Cauchy’s problems for differential equations that describe the behavior of reflected and refracted waves are solved. The electrical transverse components of the reflected and refracted waves as a function of time on the longitudinal axis were found for the case of irradiation with the step-like time dependence. Graphs of dependence of electric components on time and coordinates are plotted and analyzed. Conclusion. The phenomenon of an electromagnetic missiles in the medium that was irradiated by a pulsed electromagnetic wave of ultrashort duration was demonstrated for the first time. The obtained results can be generalized for the case of an arbitrary impulse by the Duhamel’s integral method. In addition, the electric field for observation point that do not lie on the longitudinal axis can be considered. An even more interesting continuation of the researches in terms of energy analysis is the study of the behavior of longitudinal electric and transverse magnetic components.

Bloch-electron dynamics in homogeneous electric fields: Application to multiphoton absorption in semiconductors and insulators

The theory of Bloch-electron dynamics for carriers in a homogeneous electric field of arbitrary time dependence is developed in consideration of the properties of multiphoton absorption (MPA) in semiconductors and insulators. The general approach is to utilize the accelerated Bloch-state representation (ABR) as a basis thereby treating the electric field exactly; also, the electric field is described in the vector potential gauge. In developing the ABR, the instantaneous eigenstates for the central Hamiltonian are obtained as the accelerated Bloch states and utilized to find the time-dependent solution to the Schr\"odinger equation. In introducing the Wigner-Weisskopf approximation (WWA), the transition probability amplitude between the states of the system is obtained and used in the application to MPA in semiconductors and insulators. The probability amplitude for MPA is derived for a plane-polarized radiation field. The periodicity of the time-dependent electric field serves as a principle time constant in developing the probability amplitude per period. Utilizing the WWA, the general MPA transition probability is derived for transitions between an arbitrary set of valence and conduction bands for a time-varying electric field in the $x$ direction. Within the WWA, the MPA transition probability, equivalent to the well-known Keldysh transition amplitude, is derived and expressed in terms of infinite-variable generalized Bessel functions and modified Bessel functions. The exact MPA result is analyzed in the small ($\ensuremath{\lesssim}{10}^{6}$ V/cm) and large ($\ensuremath{\gtrsim}{10}^{8}$ V/cm) electric field amplitude limits.

Inverse Nonlinear Eigenvalue Problem Framework for the Synthesis of Coupled-Resonator Filters With Nonresonant Nodes and Arbitrary Frequency-Variant Reactive Couplings

A novel, general circuit-level description of coupled-resonator microwave filters is introduced in this article. Unlike well-established coupling-matrix models based on frequency-invariant couplings or linear frequency-variant couplings (LFVCs), a model with arbitrary reactive frequency-variant coupling (AFVC) networks is proposed. The engineered formulation is more general than prior-art ones—with the only restriction that the coupling network is a reactive-type two-port circuit—and can be treated as an extension of previous synthesis models since constant or linear couplings are special cases of arbitrary frequency dependence. The suggested model is fully general, which allows for AFVCs with highly nonlinear (even singular) characteristics, loaded or unloaded nonresonating nodes (NRNs), frequency-dependent source–load coupling, multiple frequency-variant cross couplings, and/or multiple dispersive couplings for connecting the source and load to the filter network. The model is accompanied by a powerful synthesis technique that is based on the zeros and poles of the admittance or scattering parameters and the eigenvalues of properly defined eigenproblems. In the most general case, the zeros and poles of the admittance or scattering parameters are related to solutions of nonlinear eigenvalue problems. The synthesis is defined as an inverse nonlinear eigenvalue problem (INEVP) where the matrix is constructed from three sets of eigenvalues. This is accomplished by optimization using an iterative nonlinear least-squares solver with excellent convergence property. Finally, the third- and fifth-order examples of bandpass filter topologies involving AFVCs are shown, and the experimental validation of the proposed theory is presented through the manufacturing and characterization of a microstrip filter prototype with transmission zeros (TZs).

Probing small-scale baryon and dark matter isocurvature perturbations with cosmic microwave background anisotropies

The Universe's initial conditions, in particular baryon and cold dark matter (CDM) isocurvature perturbations, are poorly constrained on sub-Mpc scales. In this paper, we develop a new formalism to compute the effect of small-scale baryon perturbations on the mean free-electron abundance, thus on cosmic microwave background (CMB) anisotropies. Our framework can accommodate perturbations with arbitrary time and scale dependence. We apply this formalism to four different combinations of baryon and CDM isocurvature modes, and use Planck CMB-anisotropy data to probe their initial amplitude. We find that Planck data is consistent with no small-scale isocurvature perturbations, and that this additional ingredient does not help alleviate the Hubble tension. We set upper bounds to the dimensionless initial power spectrum $\Delta_{\mathcal{I}}^2(k)$ of these isocurvature modes at comoving wavenumbers $1~\textrm{Mpc}^{-1} \le k \le 10^3$ Mpc$^{-1}$, for several parameterizations. For a scale-invariant power spectrum, our 95% confidence-level limits on $\Delta_{\mathcal{I}}^2$ are 0.023 for pure baryon isocurvature, 0.099 for pure CDM isocurvature, 0.026 for compensated baryon-CDM perturbations, and 0.009 for joint baryon-CDM isocurvature perturbations. Using a Fisher analysis generalized to non-analytic parameter dependence, we forecast that a CMB Stage-4 experiment would be able to probe small-scale isocurvature perturbations with initial power 3 to 10 times smaller than Planck limits. The formalism introduced in this work is very general and can be used more widely to probe any physical processes or initial conditions sourcing small-scale baryon perturbations.