Degeneracy Problem Research Articles

Octant of 𝜃23, MH, 0νββ decay and vacuum alignment of A4 flavor symmetry in an inverse seesaw model

Measurements of disappearance channel of long baseline accelerator-based experiments (like NO[Formula: see text]A) are inflicted with the problem of octant degeneracy. In these experiments, the mass hierarchy (MH) sensitivity depends upon the value of CP-violating phase [Formula: see text]. Moreover, MH of light neutrino masses is still not fixed. Also, the flavor structure of fermions is yet not fully understood. We discuss all these issues in a highly predictive, low-scale inverse seesaw (ISS) model within the framework of [Formula: see text] flavor symmetry. Recent global analysis has shown a preference for normal hierarchy and higher octant of [Formula: see text], and hence we discuss our results with reference to these, and find that the vacuum alignment of [Formula: see text] triplet flavon [Formula: see text] favors these results. Finally, we check if our very precise prediction on [Formula: see text] and the lightest neutrino mass falls within the range of sensitivities of the neutrinoless double beta decay [Formula: see text] experiments. We note that when octant of [Formula: see text] and MH is fixed by more precise measurements of future experiments, then through our results, it would be possible to precisely identify the favorable vacuum alignment corresponding to the [Formula: see text] triplet field as predicted in our model.

Study of weak solutions to a nonlinear fourth‐order parabolic equation with boundary degeneracy

A double degenerate fourth‐order parabolic equation with a nonlinear second‐order diffusion from thin film theory is introduced, and the existence of weak solutions for the boundary degeneracy problem is studied. For this purpose, a non‐degenerate fourth‐order elliptic problem is constructed, and the corresponding existence and uniqueness are given by the variational method. From it, two kinds of approximate solutions are defined and then the existence and uniqueness of weak solutions for the related non‐degenerate parabolic problem are shown by the iterative estimate, energy method, and compactness argument. Finally, the parabolic problem with boundary degeneracy is solved by applying energy estimate and several limit procedures.

Basic formulation and first-principles implementation of nonlinear magneto-optical effects

First-principles calculation of nonlinear magneto-optical effects has become an indispensable tool to reveal the geometric and topological nature of electronic states and to understand light-matter interactions. While intriguingly rich physics could emerge in magnetic materials, further methodological developments are required to deal with time-reversal symmetry breaking, due to the degeneracy and gauge problems caused by symmetry and the low-frequency divergence problem in the existing calculation formalism. Here we present a gauge-covariant and low-frequency convergent formalism for the first-principles computation. Remarkably, this formalism generally works for both non-magnetic and magnetic materials with or without band degeneracy. Reliability and capability of our method are demonstrated by studying example materials (i.e., bilayers of MnBi$_2$Te$_4$ and CrI$_3$) and comparing with published results. Moreover, an importance correction term that ensures gauge covariance of degenerate states is derived, whose influence on physical responses is systematically checked. Our method enables computation of nonlinear magneto-optical effects in magnetic materials and paves the way for exploring rich physics created by the interplay of light and magnetism.

Compact star in general F(R) gravity: Inevitable degeneracy problem and non-integer power correction

We investigate a compact star in the general F(R) gravity. Developing a novel formulation in the spherically symmetric and static space-time with the matter, we confirm that an arbitrary relation between the mass M and the radius Rs of the compact star can be realized by adjusting the functional form of F(R). Such a degeneracy with a choice of the equation of state (EOS) suggests that only mass-radius relation is insufficient to constrain the F(R) gravity. Furthermore, by solving the differential equation for dF(R)dR|R=R(r) near and inside the surface of the compact star with the polytropic EOS, the boundary condition demands a weak curvature correction to the Einstein gravity could be non-integer power of the scalar curvature, which gives a stringent constraint on the functional form of F(R). This consequence follows that the equation of motion in F(R) gravity includes the second-order derivative of Ricci scalar R, and thus, it is applicable to general F(R) models.

How will our knowledge of short gamma-ray bursts affect the distance measurement of binary neutron stars?

Gravitational waves from binary neutron stars associated with short gamma-ray bursts have drawn considerable attention due to their prospect in cosmology. For such events, the sky locations of sources can be pinpointed with techniques such as identifying the host galaxies. However, the cosmological applications of these events still suffer from the problem of degeneracy between luminosity distance and inclination angle. To address this issue, a technique was proposed in previous study, i.e., using the collimation property of short gamma-ray bursts. Based on the observations, we assume that the cosine of inclination follows a Gaussian distribution, which may act as a prior in the Bayes analysis to break the degeneracy. This paper investigates the effects of different Gaussian priors and detector configurations on distance measurement and cosmological research. We first derive a simplified Fisher information matrix for demonstration, and then conduct quantitative analyses via simulation. By varying the number of third-generation detectors and the scale of prior, we generate four catalogs of 1000 events. It is shown that, in the same detecting period, a network of detectors can recognize more and farther events than a single detector. Besides, adopting tighter prior and employing multiple detectors both decrease the error of luminosity distance. Also considered is the performance of a widely adopted formula in the error budget, which turns out to be a conservative choice in each case. As for cosmological applications, for the ΛCDM model, 500, 200, 600, and 300 events are required for the four configurations to achieve 1% H0 accuracy. With all 1000 events in each catalog, H0 and Ωm can be constrained to (0.66%, 0.37%, 0.76%, 0.49%), and (0.010, 0.006, 0.013, 0.010), respectively. The results of the Gaussian process also show that the gravitational wave standard siren can serve as a probe of cosmology at high redshifts.

Understanding degeneracy of two-point correlation functions via Debye random media.

It is well known that the degeneracy of two-phase microstructures with the same volume fraction and two-point correlation function S_{2}(r) is generally infinite. To elucidate the degeneracy problem explicitly, we examine Debye random media, which are entirely defined by a purely exponentially decaying two-point correlation function S_{2}(r). In this work, we consider three different classes of Debye random media. First, we generate the "most probable" class using the Yeong-Torquato construction algorithm [Yeong and Torquato, Phys. Rev. E 57, 495 (1998)1063-651X10.1103/PhysRevE.57.495]. A second class of Debye random media is obtained by demonstrating that the corresponding two-point correlation functions are effectively realized in the first three space dimensions by certain models of overlapping, polydisperse spheres. A third class is obtained by using the Yeong-Torquato algorithm to construct Debye random media that are constrained to have an unusual prescribed pore-size probability density function. We structurally discriminate these three classes of Debye random media from one another by ascertaining their other statistical descriptors, including the pore-size, surface correlation, chord-length probability density, and lineal-path functions. We also compare and contrast the percolation thresholds as well as the diffusion and fluid transport properties of these degenerate Debye random media. We find that these three classes of Debye random media are generally distinguished by the aforementioned descriptors, and their microstructures are also visually distinct from one another. Our work further confirms the well-known fact that scattering information is insufficient to determine the effective physical properties of two-phase media. Additionally, our findings demonstrate the importance of the other two-point descriptors considered here in the design of materials with a spectrum of physical properties.

Deriving physical parameters of unresolved star clusters

Context. This study is the sixth of a series that investigates degeneracy and stochasticity problems present in the determination of the age, mass, extinction, and metallicity of partially resolved or unresolved star clusters in external galaxies when using Hubble Space Telescope broadband photometry. In the fifth publication, it was noticed that inconsistencies in cluster colour indices, which arise due to projected foreground and background stars on the apertures, enhance age-metallicity-extinction degeneracies. Aims. In this work we aim to present new aperture photometry results for a sample of star clusters from the M 31 Panchromatic Hubble Andromeda Treasury (PHAT) survey. Methods. We employed two methods of aperture photometry. The first method is ordinary aperture photometry to measure total cluster fluxes. The second method was introduced to avoid the brightest foreground and background stars that project onto large apertures. This method employs smaller apertures, adapted to cover a central part of clusters, and applies an aperture correction, derived for the F475W passband, to other passbands. We note that this procedure is valid only for clusters without prominent systematic gradients of colour indices beyond half-light radii. Results. We present two catalogues of star cluster aperture photometry (produced by applying ordinary aperture photometry and adaptive aperture photometry methods) with estimated uncertainties for a sample of 1181 star clusters from the M 31 PHAT survey. Compared to the M 31 PHAT fundamental star cluster aperture photometry catalogue published by Johnson et al., there are changes made in the following: cluster centre coordinates, aperture sizes, and sky background estimates.

Neural networks for parameter estimation in microstructural MRI: Application to a diffusion-relaxation model of white matter

Specific features of white matter microstructure can be investigated by using biophysical models to interpret relaxation-diffusion MRI brain data. Although more intricate models have the potential to reveal more details of the tissue, they also incur time-consuming parameter estimation that may converge to inaccurate solutions due to a prevalence of local minima in a degenerate fitting landscape. Machine-learning fitting algorithms have been proposed to accelerate the parameter estimation and increase the robustness of the attained estimates. So far, learning-based fitting approaches have been restricted to microstructural models with a reduced number of independent model parameters where dense sets of training data are easy to generate. Moreover, the degree to which machine learning can alleviate the degeneracy problem is poorly understood. For conventional least-squares solvers, it has been shown that degeneracy can be avoided by acquisition with optimized relaxation-diffusion-correlation protocols that include tensor-valued diffusion encoding. Whether machine-learning techniques can offset these acquisition requirements remains to be tested. In this work, we employ artificial neural networks to vastly accelerate the parameter estimation for a recently introduced relaxation-diffusion model of white matter microstructure. We also develop strategies for assessing the accuracy and sensitivity of function fitting networks and use those strategies to explore the impact of the acquisition protocol. The developed learning-based fitting pipelines were tested on relaxation-diffusion data acquired with optimal and sub-optimal acquisition protocols. Networks trained with an optimized protocol were observed to provide accurate parameter estimates within short computational times. Comparing neural networks and least-squares solvers, we found the performance of the former to be less affected by sub-optimal protocols; however, model fitting networks were still susceptible to degeneracy issues and their use could not fully replace a careful design of the acquisition protocol.

Constraining the cosmic ray propagation halo thickness using Fermi-LAT observations of high-latitude clouds * *Supported by the National Key R&D Program of China (2018YFA0404202) and the National Natural Science Foundation of China (11635011, 11875264, 11722328, 11851305, U1738205, U2031110)

The diffusive halo is a basic characteristic of cosmic ray (CR) propagation and can advance our understanding of many CR-related phenomena and indirect dark matter. The method used to derive the halo size often has degeneracy problems and is thus affected by large uncertainties. The diffuse rays from high-latitude clouds might shed light on the halo size independently. Because predictions using the spatially dependent propagation (SDP) model have better agreement with the observed CRs than those of the conventional propagation model, in this work, we investigated halo thickness based on the SDP model using Fermi-LAT -ray observations of high- and intermediate-velocity clouds. We found that to avoid exceeding the relative -ray emissivity in high-latitude clouds, the halo thickness should be in the range of 3.3-9 kpc. Moreover, the spatial morphology of -rays estimated based on the SDP model for different values of the halo thickness are distinctive, which provides us with a tool to determine the halo size. This newly developed model can be tested and tuned using multi-wavelength observations in future studies.

A New Algorithm for Computing Disjoint Orthogonal Components in the Parallel Factor Analysis Model with Simulations and Applications to Real-World Data

In this paper, we extend the use of disjoint orthogonal components to three-way table analysis with the parallel factor analysis model. Traditional methods, such as scaling, orthogonality constraints, non-negativity constraints, and sparse techniques, do not guarantee that interpretable loading matrices are obtained in this model. We propose a novel heuristic algorithm that allows simple structure loading matrices to be obtained by calculating disjoint orthogonal components. This algorithm is also an alternative approach for solving the well-known degeneracy problem. We carry out computational experiments by utilizing simulated and real-world data to illustrate the benefits of the proposed algorithm.

Assimilation of probabilistic flood maps from SAR data into a coupled hydrologic–hydraulic forecasting model: a proof of concept

Abstract. Coupled hydrologic and hydraulic models represent powerful tools for simulating streamflow and water levels along the riverbed and in the floodplain. However, input data, model parameters, initial conditions, and model structure represent sources of uncertainty that affect the reliability and accuracy of flood forecasts. Assimilation of satellite-based synthetic aperture radar (SAR) observations into a flood forecasting model is generally used to reduce such uncertainties. In this context, we have evaluated how sequential assimilation of flood extent derived from SAR data can help improve flood forecasts. In particular, we carried out twin experiments based on a synthetically generated dataset with controlled uncertainty. To this end, two assimilation methods are explored and compared: the sequential importance sampling method (standard method) and its enhanced method where a tempering coefficient is used to inflate the posterior probability (adapted method) and reduce degeneracy. The experimental results show that the assimilation of SAR probabilistic flood maps significantly improves the predictions of streamflow and water elevation, thereby confirming the effectiveness of the data assimilation framework. In addition, the assimilation method significantly reduces the spatially averaged root mean square error of water levels with respect to the case without assimilation. The critical success index of predicted flood extent maps is significantly increased by the assimilation. While the standard method proves to be more accurate in estimating the water levels and streamflow at the assimilation time step, the adapted method enables a more persistent improvement of the forecasts. However, although the use of a tempering coefficient reduces the degeneracy problem, the accuracy of model simulation is lower than that of the standard method at the assimilation time step.

Degeneracy and finiteness problems for holomorphic curves from a disc into $\mathbf{P}^n(C)$ with finite growth index

Let $f^1,f^2,f^3$ are three holomorphic curves from a complex disc $\Delta (R)$ into $\mathbf{P}^n(\mathbf{C})\ (n\ge 2)$ with finite growth indexes $c_{f^1},c_{f^2},c_{f^3}$ and sharing $q (q \ge 2n+2)$ hyperplanes in general position regardless of multiplicity. In this paper, we will show the above bounds for the sum $c_{f^1}+c_{f^2}+c_{f^3}$ to ensure that $f^1\wedge f^2\wedge f^3=0$ or there are two curves among $\{f^1,f^2,f^3\}$ coincide to each other. Our results are generalizations of the previous degeneracy and finiteness results for linearly non-degenerate meromorphic mappings from $\mathbf{C}^m$ into $\mathbf{P}^n(\mathbf{C})$ sharing $(2n+2)$ hyperplanes regardless of multiplicities.

Residues of Destructed Resonance Torus

In this paper, we propose a method to handle the problem of complete degeneracy in the study of lower dimensional invariant tori surviving from destructed resonant torus. As its application, we obtain a different proof of the existence of co-dimension one invariant tori. No other condition is assumed on the perturbation except for the smallness.

A particle flow filter for high-dimensional system applications.

A novel particle filter proposed recently, the particle flow filter (PFF), avoids the long‐existing weight degeneracy problem in particle filters and, therefore, has great potential to be applied in high‐dimensional systems. The PFF adopts the idea of a particle flow, which sequentially pushes the particles from the prior to the posterior distribution, without changing the weight of each particle. The essence of the PFF is that it assumes the particle flow is embedded in a reproducing kernel Hilbert space, so that a practical solution for the particle flow is obtained. The particle flow is independent of the choice of kernel in the limit of an infinite number of particles. Given a finite number of particles, we have found that a scalar kernel fails in high‐dimensional and sparsely observed settings. A new matrix‐valued kernel is proposed that prevents the collapse of the marginal distribution of observed variables in a high‐dimensional system. The performance of the PFF is tested and compared with a well‐tuned local ensemble transform Kalman filter (LETKF) using the 1,000‐dimensional Lorenz 96 model. It is shown that the PFF is comparable to the LETKF for linear observations, except that explicit covariance inflation is not necessary for the PFF. For nonlinear observations, the PFF outperforms LETKF and is able to capture the multimodal likelihood behavior, demonstrating that the PFF is a viable path to fully nonlinear geophysical data assimilation.

Performance evaluation of dielectric modulation and metalloid T-shaped source/drain on gate-all-around junctionless transistor for improved analog/RF application

In this work, the impact of SiO2 dielectric channel modulation along with metalloid T-shaped source-drain on the analog-RF characteristics of gate-all-around Junctionless Nanowire Transistor (JNT) has been analysed. Metalloid T-shaped source-drain contacts create the charge plasma therefore it is also referred as Charge Plasma Transistor (CPT). Impact of different source/drain materials on band gap energy, drain current, transconductance etc. is studied. Ambipolarity, Non-linear behavior and impact of high temperature on novel CPT-JNT device have also been analysed. A dielectric modulated CPT-JNT is proposed. Results demonstrate that charge plasma technique resolve the degeneracy problem of semiconductor in junctionless transistor. Use of dielectric pocket completely reduces the ambipolar nature of CPT-JNT. Use of Charge plasma technique along with gate-all-around junctionless transistor tremendously increases transconductance, device gain (current and power). The device is well suitable for analog/RF applications.

Weighted approximate Bayesian computation via Sanov\u2019s theorem

We consider the problem of sample degeneracy in Approximate Bayesian Computation. It arises when proposed values of the parameters, once given as input to the generative model, rarely lead to simulations resembling the observed data and are hence discarded. Such “poor” parameter proposals do not contribute at all to the representation of the parameter’s posterior distribution. This leads to a very large number of required simulations and/or a waste of computational resources, as well as to distortions in the computed posterior distribution. To mitigate this problem, we propose an algorithm, referred to as the Large Deviations Weighted Approximate Bayesian Computation algorithm, where, via Sanov’s Theorem, strictly positive weights are computed for all proposed parameters, thus avoiding the rejection step altogether. In order to derive a computable asymptotic approximation from Sanov’s result, we adopt the information theoretic “method of types” formulation of the method of Large Deviations, thus restricting our attention to models for i.i.d. discrete random variables. Finally, we experimentally evaluate our method through a proof-of-concept implementation.

A. P. CHEKHOV AND THE CONCEPT OF “DEGENERATION”: TO THE PROBLEM OF CRYPTOPOETICS OF RUSSIAN LITERATURE

The concept of “degeneration” is associated with the fin-de-siècle period and came to Russian soil from Western Europe. First and foremost, it was represented there by Cesare Lombroso and his popularizer, the author of the book Degeneration, Max Nordau. The concept of degeneracy was studied by the scientist using the work of outstanding representatives of European art, including Leo Tolstoy. The book was a scandalous success in Russia and a subject of numerous magazine reviews. Chekhov implicitly participated in this polemic. The writer’s cryptic review of the fashionable problem of degeneracy can be seen in the image of Dr. Dorn, which allows to examine the elements of Chekhov’s cryptopoetics. The surname of this character in The Seagull is considered as a transformation of the surname Nordau. An analysis of Dorn’s behavior and speech suggests that the author of the play uses it to express his position regarding the “nervous age” and the fatigue and degeneration associated with it. The intertextually expressed polemic between Chekhov and Nordau allows to define the role of Dorn as a hidden trickster. This is an additional argument that proves the validity of the author’s definition of The Seagull as a comedy.

Coordinated Optimal Power Flow for Integrated Active Distribution Network and Virtual Power Plants Using Decentralized Algorithm

With the wide application of distributed energy technology in active distribution networks (ADNs), virtual power plants (VPPs) are introduced as a promising integration and management technology. To coordinate their operation schedule and ensure confidentiality, we establish a coordinated optimal power flow (OPF) model and propose an efficient decentralized algorithm based on multi-parametric quadratic programming and Benders decomposition. In feasible sub-problems, the quadratic exchanging functions are built, which greatly accelerates the convergence process. In infeasible sub-problems, feasible cut sets can be calculated based on benders decomposition. Besides, an effective relaxation method is developed to address the degeneracy problem. To eliminate redundant feasible cut sets, a predetermined feasible region is constructed according to the characteristics of each VPP. The effectiveness of the proposed method is demonstrated via numerical tests using two cases of different scales. The results show that the proposed method converges much faster than some prevailing methods. Furthermore, the coordinated OPF has a better fuel economy than the conventional OPF scheme.

A Genetic Optimization Resampling Based Particle Filtering Algorithm for Indoor Target Tracking

In indoor target tracking based on wireless sensor networks, the particle filtering algorithm has been widely used because of its outstanding performance in coping with highly non-linear problems. Resampling is generally required to address the inherent particle degeneracy problem in the particle filter. However, traditional resampling methods cause the problem of particle impoverishment. This problem degrades positioning accuracy and robustness and sometimes may even result in filtering divergence and tracking failure. In order to mitigate the particle impoverishment and improve positioning accuracy, this paper proposes an improved genetic optimization based resampling method. This resampling method optimizes the distribution of resampled particles by the five operators, i.e., selection, roughening, classification, crossover, and mutation. The proposed resampling method is then integrated into the particle filtering framework to form a genetic optimization resampling based particle filtering (GORPF) algorithm. The performance of the GORPF algorithm is tested by a one-dimensional tracking simulation and a three-dimensional indoor tracking experiment. Both test results show that with the aid of the proposed resampling method, the GORPF has better robustness against particle impoverishment and achieves better positioning accuracy than several existing target tracking algorithms. Moreover, the GORPF algorithm owns an affordable computation load for real-time applications.

An Adaptive Particle Filter for Target Tracking Based on Double Space-Resampling

Particle filter has been widely applied in nonlinear target tracking due to the ability to carry multiple hypothesis and relaxation of linearity/Gaussian assumption. In this paper, an adaptive double space-resampling particle filter is proposed to increase the efficiency and robustness of filtering by adjusting the sample size. The first resampling operation, adopted before the prediction of samples, generates a larger number of equal-weighted samples and some auxiliary samples to enhance the robustness of filtering. The second resampling, adopted between the prediction and updating step, decreases the sample size for weight updating which is the most time consumption part of particle filter. The particle space sampling technique is used in both space-resampling, which adjusts the sample size according to not only the weights of samples but also their spatial distribution. The efficiency of filtering is improved and the robustness of algorithm is enhanced, simultaneously. The degeneracy and sample impoverishment problems can be counteracted. Simulation and experiment contrast results demonstrate that the proposed method is robust and efficient.