Degenerate Models Research Articles

Expected constraints on Phobos interior from the MMX gravity and rotation observations

The origin of the Martian moons is still uncertain, and knowledge about their interior could provide support to some of its leading theories. In preparation for the JAXA Martian Moons eXploration (MMX) mission, we review our current knowledge on the interior of Phobos, and provide synthetic tests showing how the gravity and rotation determination could allow the detection of specific interior-structure properties. The inversion of the geodetic observables for the retrieval of the internal mass distribution of a set of synthetic interior models is performed via non-linear least-squares, where the interior parameterization is based on the level-set method. We additionally provide simple expressions allowing to relate some of these interior models to the geodetic observables of Phobos. The results, based on realistic measurement resolution and noise scenarios, show good retrievals for most of the models at the data resolutions expected from MMX. Specifically, we find the gravity information is realistically sufficient for the detection of mass anomalies below the Stickney crater, as well as large scale heterogeneous regions within plausible rubble-pile structures. Libration helps retrieve the more degenerate models for gravity, such as those with concentric layers or with density varying linearly with depth. The incremental improvement from further adding an hypothetical mean obliquity measurement is marginal. Finally, we apply the level-set inversion and the analytical formulas to estimate possible interior characteristics of the ‘real’ Phobos from the currently-available scarce geodetic observables. The level-set solutions for the real-data inversion generally converge to a higher mass concentration towards the surface in the equatorial region. Markov chain Monte Carlo estimations of parameters relative to a simple 2-layer model or a radial density distribution similarly hint at a lighter region inside of Phobos.

Well-posedness of the Optimal Control Problem Related to Degenerate Chemo-attraction Models

This paper delves into the mathematical analysis of optimal control for a nonlinear degenerate chemotaxis model with volume-filling effects. The control is applied in a bilinear form specifically within the chemical equation. We establish the well-posedness (existence and uniqueness) of the weak solution for the direct problem using the Faedo Galerkin method (for existence), and the duality method (for uniqueness). Additionally, we demonstrate the existence of minimizers and establish first-order necessary conditions for the adjoint problem. The main novelty of this work concerns the degeneracy of the diffusive term and the presence of control over the concentration in our nonlinear degenerate chemotaxis model. Furthermore, the state, consisting of cell density and chemical concentration, remains in a weak setting, which is uncommon in the literature for solving optimal control problems involving chemotaxis models.

A Stone–von Neumann equivalence of categories for smooth representations of the Heisenberg group

The classical Stone–von Neumann theorem relates the irreducible unitary representations of the Heisenberg group Hn to non-trivial unitary characters of its center Z, and plays a crucial role in the construction of the oscillator representation for the metaplectic group. In this paper we extend these ideas to non-unitary and non-irreducible representations, thereby obtaining an equivalence of categories between certain representations of Z and those of Hn. Our main result is a smooth equivalence, which involves the fundamental ideas of du Cloux on differentiable representations and smooth imprimitivity systems for Nash groups. We show how to extend the oscillator representation to the smooth setting and give an application to degenerate Whittaker models for representations of reductive groups. We also include an algebraic equivalence, which can be regarded as a generalization of Kashiwara’s lemma from the theory of D-modules.

A stabilised Benders decomposition with adaptive oracles for large-scale stochastic programming with short-term and long-term uncertainty

Benders decomposition with adaptive oracles was proposed to solve large-scale optimisation problems with a column-bounded block-diagonal structure, where subproblems differ only in the right-hand side and cost coefficients. Adaptive Benders reduces computational effort significantly by iteratively building inexact cutting planes and valid upper and lower bounds. However, Adaptive Benders and standard Benders may suffer severe oscillation when solving degenerate models. Therefore, we propose stabilising Adaptive Benders with the level method and adaptively selecting which subproblems to solve each iteration for more accurate information. In addition, we propose a dynamic level method to improve the robustness of stabilised Adaptive Benders by adjusting the level set each iteration. We compare stabilised Adaptive Benders with the unstabilised versions of Adaptive Benders with one subproblem solved per iteration and standard Benders on a multi-region long-term power system investment planning problem with short-term and long-term uncertainty. The problem is formulated as multi-horizon stochastic programming. Four algorithms were implemented to solve linear programming with up to 1 billion variables and 4.5 billion constraints. The computational results show that: (a) for a 1.00% convergence tolerance, the proposed stabilised method is up to 113.7 times faster than standard Benders and 2.1 times faster than unstabilised Adaptive Benders; (b) for a 0.10% convergence tolerance, the proposed stabilised method is up to 45.5 times faster than standard Benders and unstabilised Adaptive Benders cannot solve the largest instance to convergence tolerance due to severe oscillation and (c) dynamic level method makes stabilisation more robust.

OGLE-2014-BLG-0221Lb: A Jupiter Mass Ratio Companion Orbiting Either a Late-type Star or a Stellar Remnant

We present the analysis of the microlensing event OGLE-2014-BLG-0221, a planetary candidate event discovered in 2014. The photometric light curve is best described by a binary-lens single-source model. Our light-curve modeling finds two degenerate models, with event timescales of t E ∼ 70 days and ∼110 days. These timescales are relatively long, indicating that the discovered system would possess a substantial mass. The two models are similar in their planetary parameters with a Jupiter mass ratio of q ∼ 10−3 and a separation of s ∼ 1.1. Bayesian inference is used to estimate the physical parameters of the lens, revealing that the shorter timescale model predicts 65% and 25% probabilities of a late-type star and white dwarf host, respectively, while the longer timescale model favors a black hole host with a probability ranging from 60% to 95%, under the assumption that stars and stellar remnants have equal probabilities of hosting companions with planetary mass ratios. If the lens is a remnant, this would be the second planet found by microlensing around a stellar remnant. The current separation between the source and lens stars is 41–139 mas depending on the models. This indicates the event is now ready for high-angular-resolution follow-up observations to rule out either of the models. If precise astrometric measurements are conducted in multiple bands, the centroid shift due to the color difference between the source and lens would be detected in the luminous lens scenario.

Measuring spatial visual loss in rats by retinotopic mapping of the superior colliculus using a novel multi-electrode array technique

BackgroundThe retinotopic map property of the superior colliculus (SC) is a reliable indicator of visual functional changes in rodents. Electrophysiological mapping of the SC using a single electrode has been employed for measuring visual function in rat and mouse disease models. Single electrode mapping is highly laborious requiring long-term exposure to the SC surface and prolonged anesthetic conditions that can adversely affect the mapping data. New methodTo avoid the above-mentioned issues, we fabricated a fifty-six (56) electrode multi-electrode array (MEA) for rapid and reliable visual functional mapping of the SC. Since SC is a dome-shaped structure, the array was made of electrodes with dissimilar tip lengths to enable simultaneous and uniform penetration of the SC. ResultsSC mapping using the new MEA was conducted in retinal degenerate (RD) Royal College of Surgeons (RCS) rats and rats with focal retinal damage induced by green diode laser. For SC mapping, the MEA was advanced into the SC surface and the visual activities were recorded during full-filed light stimulation of the eye. Based on the morphological examination, the MEA electrodes covered most of the exposed SC area and penetrated the SC surface at a relatively uniform depth. MEA mapping in RCS rats (n=9) demonstrated progressive development of a scotoma in the SC that corresponded to the degree of photoreceptor loss. MEA mapping in the laser damaged rats demonstrated the presence of a scotoma in the SC area that corresponded to the location of retinal laser injury. Comparison with existing methods and conclusionsThe use of MEA for SC mapping is advantageous over single electrode recording by enabling faster recordings and reducing anesthesia time. This study establishes the feasibility of the MEA technique for rapid and efficient SC mapping, particularly advantageous for evaluating therapeutic effects in retinal degenerate rat disease models.

On degenerate reaction-diffusion epidemic models with mass action or standard incidence mechanism

Abstract In this paper, we consider reaction-diffusion epidemic models with mass action or standard incidence mechanism and study the impact of limiting population movement on disease transmissions. We set either the dispersal rate of the susceptible or infected people to zero and study the corresponding degenerate reaction-diffusion model. Our main approach to study the global dynamics of these models is to construct delicate Lyapunov functions. Our results show that the consequences of limiting the movement of susceptible or infected people depend on transmission mechanisms, model parameters and population size.

Degenerate orthorhombic models

SUMMARY We define the degenerate orthorhombic anisotropy models which have two symmetric singularity lines with constant phase velocity for S1 and S2 waves. Depending on the singularity line trajectory, we consider two types of degenerate models (VTI- and HTI-type). In addition to this singularity line, seriethere is always one isolated singularity point in one of non-essential symmetry planes. The degenerate orthorhombic model has seven independent parameters and can be parametrized by different combinations of the stiffness coefficients. Exploiting the fact that the second-order derivatives matrix computed from the Christoffel polynomial is degenerate, we also compute the group velocity image of this singularity line.

Big Bang Nucleosynthesis Constraints and Indications for Beyond Standard Model Neutrino Physics

We use Big Bang Nucleosynthesis (BBN) to probe Beyond Standard Model physics in the neutrino sector. Recently, the abundances of primordially produced light elements D and He-4 were determined from observations with better accuracy. The good agreement between the theoretically predicted abundances of primordially produced light elements and those derived from observations allows us to update the BBN constraints on Beyond Standard Model (BSM) physics. We provide numerical analysis of several BSM models of BBN and obtain precise cosmological constraints and indications for new neutrino physics. Namely, we derive more stringent BBN constraints on electron neutrino–sterile neutrino oscillations corresponding to 1% uncertainty of the observational determination of the primordial He-4. The cosmological constraints are obtained both for the zero and non-zero cases of the initial population of the sterile neutrino state. Then, in a degenerate BBN model with neutrino νe↔νs oscillations, we analyze the change in the cosmological constraints in case lepton asymmetry L is big enough to suppress oscillations. We obtain constraints on the lepton asymmetry L. We discuss a possible solution to the dark radiation problem in degenerate BBN models with νe↔νs oscillations in case L is large enough to suppress neutrino oscillations during the BBN epoch. Interestingly, the required value of L for solving the DR problem is close to the value of L indicated by the EMPRESS experiment, and also it is close to the value of lepton asymmetry that is necessary to relax Hubble tension.

Large-time asymptotics for degenerate cross-diffusion population models with volume filling

The large-time asymptotics of the solutions to a class of degenerate parabolic cross-diffusion systems is analyzed. The equations model the interaction of an arbitrary number of population species in a bounded domain with no-flux boundary conditions. Compared to previous works, we allow for different diffusivities and degenerate nonlinearities. The proof is based on the relative entropy method, but in contrast to usual arguments, the relative entropy and entropy production are not directly related by a logarithmic Sobolev inequality. The key idea is to apply convex Sobolev inequalities to modified entropy densities including “iterated” degenerated functions.

Artificial Neural Networks and Time Series of Counts: A Class of Nonlinear INGARCH Models

Abstract Time series of counts are frequently analyzed using generalized integer-valued autoregressive models with conditional heteroskedasticity (INGARCH). These models employ response functions to map a vector of past observations and past conditional expectations to the conditional expectation of the present observation. In this paper, it is shown how INGARCH models can be combined with artificial neural network (ANN) response functions to obtain a class of nonlinear INGARCH models. The ANN framework allows for the interpretation of many existing INGARCH models as a degenerate version of a corresponding neural model. Details on maximum likelihood estimation, marginal effects and confidence intervals are given. The empirical analysis of time series of bounded and unbounded counts reveals that the neural INGARCH models are able to outperform reasonable degenerate competitor models in terms of the information loss.

Properties of singular points in a special case of orthorhombic media

The position of singular lines for orthorhombic (ORT) media with fixed diagonal elements of the elasticity matrix cij, i=1…6 is studied under the condition that c11, c22, c33>c66>c44>c55. In this case, the off-diagonal coefficients of the elasticity matrix c12, c13, c23 are chosen so that some of the values of d12=c12+c66, d13=c13+c55, d23=c23+c44 are zero. For orthorhombic medium, where the only one of d12, d13, d23 is zero, contains only singular points in the planes of symmetry. If two or all three dij are zero, then the ORT medium contains singular lines and discrete singular points. We call such media pathological. A degenerate ORT medium with positive d12, d13, d23 has at most two singular lines, which are the intersection of a quadratic cone with a sphere. The pathological media may have up to 6 singular lines on the surface of the slowness. Singular lines for pathological media are described by more complex equations than conventional degenerate ORT models. The article proposes to using squares x, y, z of the components of the slowness vector in the equations. In a new coordinate system, equations defining singular lines for pathological media become linear or quadratic. Intersecting with the plane x+y+z =1, they define the straight lines, ellipses, or hyperbolas. If non-zero values d12, d13, d23 increase, the singular lines pass through four fixed points on the plane x+y+z =1, which makes it possible to describe the evolution of their change. Conditions are derived under which the singular curves of pathological ORT models are limiting the singular curves for degenerate ORT models with positive values of d12, d13, d23. Formulas are derived for transforming surfaces of slowness and singular lines of pathological media into the region of group velocities. The results are demonstrated with examples of pathological models obtained from the standard model of the ORT medium by changing the elasticity coefficients c12, c13, c23 so that some of the values d12, d13, d23 are zero

Cross-platform privacy-preserving CT image COVID-19 diagnosis based on source-free domain adaptation

In the wake of the Coronavirus disease (COVID-19) pandemic, chest computed tomography (CT) has become an invaluable component in the rapid and accurate detection of COVID-19. CT scans traditionally require manual inspections from medical professionals, which is expensive and tedious. With advancements in machine learning, deep neural networks have been applied to classify CT scans for efficient diagnosis. However, three challenges hinder this application of deep learning: (1) Domain shift across CT platforms and human subjects impedes the performance of neural networks in different hospitals. (2) Unsupervised Domain Adaptation (UDA), the traditional method to overcome domain shift, typically requires access to both source and target data. This is not realistic in COVID-19 diagnosis due to the sensitivity of medical data. The privacy of patients must be protected. (3) Data imbalance may exist between easy/hard samples and between data classes which can overwhelm the training of deep networks, causing degenerate models. To overcome these challenges, we propose a Cross-Platform Privacy-Preserving COVID-19 diagnosis network (CP3Net) that integrates domain adaptation, self-supervised learning, imbalanced label learning, and rotation classifier training into one synergistic framework. We also create a new CT benchmark by combining real-world datasets from multiple medical platforms to facilitate the cross-domain evaluation of our method. Through extensive experiments, we demonstrate that CP3Net outperforms many popular UDA methods and achieves state-of-the-art results in diagnosing COVID-19 using CT scans.

Correlations between X-ray spectral parameters of Mkn 421 using long-term Swift–XRT data

ABSTRACT We have performed a detailed analysis of the X-ray spectra of the blazar Mkn 421 using Swift–XRT observations taken between 2005 and 2020, to quantify the correlations between spectral parameters for different models. In an earlier work, it has been shown that such spectral parameter correlations obtained from a single short flare of duration ∼5 d of Mkn 421, can be used to distinguish spectrally degenerate models and provide estimates of physical quantities. In this work, we show that the results from the long-term spectral parameter correlations are consistent with those obtained from the single flare. In particular, that the observed spectral curvature is due to maximum cut-off energy in the particle distribution is ruled out. Instead, models where the curvature is due to the energy dependence of escape or acceleration time-scale of the particles are favoured. The estimated values of the physical parameters for these models are similar to the ones obtained from the single flare analysis and are somewhat incompatible with the physical assumption of the models, suggesting that more complex physical models are required. The consistency of the results obtained from the long- and short-term evolution of the source, underlines the reliability of the technique to use spectral parameter correlations to distinguish physical models.

On the stability of the compacton waves for the degenerate KdV and NLS models

In this paper, we consider the degenerate semi-linear Schrödinger and Korteweg-de Vries equations in one spatial dimension. We construct special solutions of the two models, namely standing wave solutions of NLS and traveling waves, which turn out to have compact support, compactons. We show that the compactons are unique bell-shaped solutions of the corresponding PDEs and for appropriate variational problems as well. We provide a complete spectral characterization of such waves, for all values of p p . Namely, we show that all waves are spectrally stable for 2 > p ≤ 8 2>p\leq 8 , while a single mode instability occurs for p > 8 p>8 . This extends previous work of Germain, Harrop-Griffiths and Marzuola [Quart. Appl. Math. 78 (2020), pp. 1–32] who have previously established orbital stability for some specific waves, in the range p > 8 p>8 .

OGLE-2014-BLG-0319: A Sub-Jupiter-mass Planetary Event Encountered Degeneracy with Different Mass Ratios and Lens-source Relative Proper Motions

Abstract We report the discovery of a sub-Jovian-mass planet, OGLE-2014-BLG-0319Lb. The characteristics of this planet will be added into a future extended statistical analysis of the Microlensing Observations in Astrophysics (MOA) collaboration. The planetary anomaly of the light curve is characterized by MOA and OGLE survey observations and results in three degenerate models with different planetary-mass ratios of q = (10.3, 6.6, 4.5) × 10−4. We find that the last two models require unreasonably small lens-source relative proper motions of μ rel ∼ 1 mas yr−1. Considering Galactic prior probabilities, we rule out these two models from the final result. We conduct a Bayesian analysis to estimate physical properties of the lens system using a Galactic model and find that the lens system is composed of a 0.49 − 0.27 + 0.35 M Jup sub-Jovian planet orbiting a 0.47 − 0.25 + 0.33 M ⊙ M dwarf near the Galactic Bulge. This analysis demonstrates that Galactic priors are useful to resolve this type of model degeneracy. This is important for estimating the mass-ratio function statistically. However, this method would be unlikely successful in shorter timescale events, which are mostly due to low-mass objects, like brown dwarfs or free-floating planets. Therefore, careful treatment is needed for estimating the mass-ratio function of the companions around such low-mass hosts, which only the microlensing can probe.

Численные эксперименты двойственным методом нулевого поля в задаче Дирихле для уравнения Лапласа в эллиптических областях с эллиптическими отверстиями

Dual techniques have been used in many engineering papers to deal with singularity and ill-conditioning of the boundary element method (BEM). In the first part of the two-part article, our efforts were focused on studying the theoretical aspects of this problem, including the analysis of errors and the study of stability. We provided the theoretical analysis for Laplace equation in elliptic domains with elliptic holes. To bypass the degenerate scales of Dirichlet problems, the second and the first kinds of the null field methods (NFM) are used for the exterior and the interior boundaries, simultaneously. This approach is called the dual null field method (DNFM). This paper is the second part of the study. Numerical results for degenerate models of an elliptic domain with one elliptic hole at 𝑎 + 𝑏 = 2 are carried out to verify the theoretical analysis obtained. The collocation Trefftz method (CTM) is also designed for comparisons. Both the DNFM and the CTM can provide excellent numerical performances. The convergence rates are the same but the stability of CTM is excellent and can achieve the constant condition numbers, Cond = 𝑂(1).

Redshift drift in radially inhomogeneous Lemaître-Tolman-Bondi spacetimes

We provide a formula for estimating the redshift and its secular change (redshift drift) in Lema\^{\i}tre-Tolman-Bondi (LTB) spherically symmetric universes. We compute the scaling of the redshift drift for LTB models that predict Hubble diagrams indistinguishable from those of the standard cosmological model, the flat lambda cold dark matter ($\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$) model. We show that the redshift drift for these degenerate LTB models is typically different from that predicted in the $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ scenario. We also highlight and discuss some unconventional redshift-drift signals that arise in LTB universes and give them distinctive features compared to the standard model. We argue that the redshift drift is a metric observable that allows us to reduce the degrees of freedom of spherically symmetric models and to make them more predictive and thus falsifiable.

Understanding the X-ray spectral curvature of Mkn 421 using broad-band AstroSat observations

ABSTRACT We present a time-resolved X-ray spectral study of the high energy peaked blazar Mkn 421 using simultaneous broad-band observations from the LAXPC and SXT instruments on-board AstroSat. The ∼400 ksec long observation taken during 2017 January 3–8 was divided into segments of 10 ksecs. Each segment was fitted using synchrotron emission from particles whose energy distribution was represented by a log-parabola model. We also considered particle energy distribution models where (i) the radiative cooling leads to a maximum energy (ξmax model), (ii) the system has energy-dependent diffusion (EDD) and (iii) has energy-dependent acceleration (EDA). We found that all these models describe the spectra, although the EDD and EDA models were marginally better. Time-resolved spectral analysis allowed for studying the correlation between the spectral parameters for different models. In the simplest and direct approach, the observed correlations are not compatible with the predictions of the ξmax model. While the EDD and EDA models do predict the correlations, the values of the inferred physical parameters are not compatible with the model assumptions. Thus, we show that spectrally degenerate models, can be distinguished based on spectral parameter correlations (especially those between the model normalization and spectral shape ones) making time-resolved spectroscopy a powerful tool to probe the nature of these systems.

Cosmic voids in modified gravity models with massive neutrinos

ABSTRACT Cosmic voids are progressively emerging as a new viable cosmological probe. Their abundance and density profiles are sensitive to modifications of gravity, as well as to dark energy and neutrinos. The main goal of this work is to investigate the possibility of exploiting cosmic void statistics to disentangle the degeneracies resulting from a proper combination of f(R) modified gravity and neutrino mass. We use N-body simulations to analyse the density profiles and size function of voids traced by both dark matter particles and haloes. We find clear evidence of the enhancement of gravity in f(R) cosmologies in the void density profiles at z = 1. However, these effects can be almost completely overridden by the presence of massive neutrinos because of their thermal free streaming. Despite the limited volume of the analysed simulations does not allow us to achieve a statistically relevant abundance of voids larger than 40 Mpc h−1, we find that the void size function at high redshifts and for large voids is potentially an effective probe to disentangle these degenerate cosmological models, which is key in the prospective of the upcoming wide-field redshift surveys.