Degenerate Conditions Research Articles

On the Unbounded Picture of KK-Theory

In the founding paper on unbounded $KK$-theory it was established by Baaj and Julg that the bounded transform, which associates a class in $KK$-theory to any unbounded Kasparov module, is a surjective homomorphism (under a separability assumption). In this paper, we provide an equivalence relation on unbounded Kasparov modules and we thereby describe the kernel of the bounded transform. This allows us to introduce a notion of topological unbounded $KK$-theory, which becomes isomorphic to $KK$-theory via the bounded transform. The equivalence relation is formulated entirely at the level of unbounded Kasparov modules and consists of homotopies together with an extra degeneracy condition. Our degenerate unbounded Kasparov modules are called spectrally decomposable since they admit a decomposition into a part with positive spectrum and a part with negative spectrum.

Analysis of a class of Kolmogorov systems

A two-dimensional Kolmogorov system depending on two independent parameters and having a degenerate condition is studied in this work. We obtain local analytical properties of the system when the parameters vary in a sufficiently small neighborhood of the origin. The behavior of the system is described by bifurcation diagrams. Applications of Kolmogorov systems can be found particularly in modeling population dynamics in biology and ecology.

Ghost from constraints: a generalization of Ostrogradsky theorem

Ostrogradsky theorem states that Hamiltonian is unbounded when Euler-Lagrange equations are higher than second-order differential equations under the nondegeneracy assumption. Since higher-order nondegenerate Lagrangian can be always recast into an equivalent system with at most first-order derivatives by introducing auxiliary variables and constraints, it is conceivable that the link between ghost and higher derivatives may be reinterpreted as a link between ghost and constraints and/or auxiliary variables. We find that the latter point of view actually provides more general perspective than the former, by exploring the un/boundedness of the Hamiltonian for general theories containing auxiliary variables, for which Euler-Lagrange equations can be essentially second order or lower than that. For Lagrangians including auxiliary variables nonlinearly, we derive the degeneracy condition to evade the Ostrogradsky ghost that can apply even if auxiliary variables can be solved only locally. For theories with constraints with Lagrange multipliers, we establish criteria for inclusion of nonholonomic (velocity-dependent) constraints leading to the absence of local minimum of Hamiltonian. Our criteria include the Ostrogradsky theorem as a special case, and can detect not only ghost associated with higher-order derivatives, but also ghost coming from lower-order derivatives in system with constraints. We discuss how to evade such a ghost. We also provide various specific examples to highlight application and limitation of our general arguments.

Neuroimaging in Pediatric Patients with Mild Traumatic Brain Injury: Relating the Current 2018 Centers for Disease Control Guideline and the Potential of Advanced Neuroimaging Modalities for Research and Clinical Biomarker Development.

The Center for Disease Control and Prevention (CDC)'s 2018 Guideline for current practices in pediatric mild traumatic brain injury (mTBI; also referred to as concussion herein) systematically identified the best up-to-date practices based on current evidence and, specifically, identified recommended practices regarding computed tomography (CT), magnetic resonance imaging (MRI), and skull radiograph imaging. In this article, we discuss types of neuroimaging not discussed in the guideline in terms of their safety for pediatric populations, their potential application, and the research investigating the future use of certain modalities to aid in the diagnosis and treatment of mTBI in children. The role of neuroimaging in pediatric mTBI cases should be considered for the potential contribution to children's neural and social development, in addition to the immediate clinical value (as in the case of acute structural findings). Selective use of specific neuroimaging modalities in research has already been shown to detect aspects of diffuse brain injury, disrupted cerebral blood flow, and correlate physiological factors with persistent symptoms, such as fatigue, cognitive decline, headache, and mood changes, following mTBI. However, these advanced neuroimaging modalities are currently limited to the research arena, and any future clinical application of advanced imaging modalities in pediatric mTBI will require robust evidence for each modality's ability to provide measurement of the subtle conditions of brain development, disease, damage, or degeneration, while accounting for variables at both non-injury and time-post-injury epochs. Continued collaboration and communication between researchers and healthcare providers is essential to investigate, develop, and validate the potential of advanced imaging modalities in pediatric mTBI diagnostics and management.

MicroRNA-223 Regulates Retinal Function and Inflammation in the Healthy and Degenerating Retina.

IntroductionMicroRNAs (miRNAs) are small, non-coding RNA molecules that have powerful regulatory properties, with the ability to regulate multiple messenger RNAs (mRNAs) and biological pathways. MicroRNA-223-3p (miR-223) is known to be a critical regulator of the innate immune response, and its dysregulation is thought to play a role in inflammatory disease progression. Despite miR-223 upregulation in numerous neurodegenerative conditions, largely in cells of the myeloid lineage, the role of miR-223 in the retina is relatively unexplored. Here, we investigated miR-223 in the healthy retina and in response to retinal degeneration.MethodsmiR-223-null mice were investigated in control and photo-oxidative damage-induced degeneration conditions. Encapsulated miR-223 mimics were intravitreally and intravenously injected into C57BL/6J wild-type mice. Retinal functional responses were measured using electroretinography (ERG), while extracted retinas were investigated by retinal histology (TUNEL and immunohistochemistry) and molecular analysis (qPCR and FACS).ResultsRetinal function in miR-223–/– mice was adversely affected, indicating that miR-223 may be critical in regulating the retinal response. In degeneration, miR-223 was elevated in the retina, circulating serum, and retinal extracellular vesicles. Conversely, retinal microglia and macrophages displayed a downregulation of miR-223. Further, isolated CD11b+ inflammatory cells from the retinas and circulation of miR-223-null mice showed an upregulation of pro-inflammatory genes that are critically linked to retinal inflammation and progressive photoreceptor loss. Finally, both local and systemic delivery of miR-223 mimics improved retinal function in mice undergoing retinal degeneration.ConclusionmiR-223 is required for maintaining normal retinal function, as well as regulating inflammation in microglia and macrophages. Further investigations are required to determine the targets of miR-223 and their key biological pathways and interactions that are relevant to retinal diseases. Future studies should investigate whether sustained delivery of miR-223 into the retina is sufficient to target these pathways and protect the retina from progressive degeneration.

Regular black holes via the Kerr-Schild construction in DHOST theories

We extend the standard Kerr-Schild solution generating method to higher order scalar tensor theories that are shift-invariant for the scalar field. Certain degeneracy conditions, crucial for the absence of Ostrogradski ghosts, are found to be required for the validity of the Kerr-Schild ansatz while on the other hand, theories with no parity symmetry are excluded from the solution generating method. The extended Kerr-Schild symmetry turns out to be a very useful tool to easily construct black hole solutions from simple seed configurations. In particular, the generating method developed is adapted to construct generic black holes but also regular black hole solutions within Degenerate Higher Order Scalar Tensor (DHOST) theories. As a particular example we show how to construct explicitly the Hayward metric as a solution to a specific DHOST theory.

Epidemiology of non-traumatic spinal cord injury in Ireland – a prospective population-based study

Objective: To carry out a study of non-traumatic spinal cord injury (NTSCI) epidemiology in Ireland Design: Prospective study of all new incident cases of NTSCI during 2017 Setting: Republic of Ireland Participants: All persons with a newly acquired NTSCI Interventions: None Outcome measures: Crude and age/sex specific incidences; ISCoS core dataset and non-traumatic dataset; population denominator was 2016 national census figures, adjusted to 2017. Results: Overall crude incidence of NTSCI in the Republic of Ireland in 2017 was 26.9 per million per year. Mean age at onset was 56.6 (SD 17.7) years. Females accounted for 51.2% of cases. Most frequent grade of ASIA impairment scale (AIS) was AIS D. Most common etiology was degenerate conditions (48.8%) followed by neoplastic (26.4%). The most common pattern of onset (51.2%) was lengthy (greater than one month). Conclusions: Incidence of NTSCI is more than double that for traumatic SCI in the Republic of Ireland. This suggests that the delivery of rehabilitation services to patients with spinal cord injuries requires prompt review and expansion.

Outer retinal tubulations in central serous chorioretinopathy associated with choroidal neovascularisation.

To report the prevalence and characteristics of outer retinal tubulations in eyes with choroidal neovascularisation associated with chronic central serous chorioretinopathy. Retrospective case series which included evaluation of optical coherence tomography B-scans and enface optical coherence tomography scans of eyes with choroidal neovascularisation associated with chronic central serous chorioretinopathy. The characteristics of outer retinal tubulations such as number, shape and distribution were noted. The location of the outer retinal tubulations was correlated with autofluorescence. Outer retinal tubulations were detected in 9.1% of the eyes (9 out of 87 eyes). The average number of outer retinal tubulations in each eye was 4.7 ± 4.6. Spheroidal outer retinal tubulations were more common than the branching tubules. Although presence of outer retinal tubulations was mostly associated with inactive disease, two eyes had coexistent subretinal fluid. Outer retinal tubulations associated with choroidal neovascularisation in chronic central serous chorioretinopathy, though less frequent, when present are more numerous, mostly extrafoveal and more spheroidal in shape compared to outer retinal tubulations associated with age-related macular degeneration and other degenerative conditions.

Generalized Dirac oscillator with κ-Poincaré algebra

In this paper, the generalized Dirac oscillator with [Formula: see text]-Poincaré algebra is structured by replacing the momentum operator p with [Formula: see text] in [Formula: see text]-deformation Dirac equation. The deformed radial equation is derived for this model. Particularly, by solving the deformed radial equation, the wave functions and energy spectra which depend on deformation parameter [Formula: see text] have been obtained for these quantum systems with [Formula: see text] being a Yukawa-type potential, inverse-square-type singular potential and central fraction power singular potential in two-dimensional space, respectively. The results show that the deformation parameter [Formula: see text] can lead to decreasing of energy levels for the above quantum systems. At the same time, the degeneracy of energy spectra has been discussed and the corresponding conditions of degeneracy have been given for each case.

Effective field theory of degenerate higher-order inflation

We extend the effective field theory of inflation to a general Lagrangian constructed from Arnowitt-Deser-Misner variables that encompasses the most general interactions with up to second derivatives of the scalar field whose background breaks temporal diffeomorphism invariance. Degeneracy conditions, corresponding to 8 distinct types -- only one of which corresponds to known degenerate higher-order scalar-tensor models -- provide necessary conditions for eliminating the Ostrogradsky ghost in a covariant theory at the level of the quadratic action in unitary gauge. Novel implications of the degenerate higher-order system for the Cauchy problem are illustrated with the phase space portrait of an explicit inflationary example: not all field configurations lead to physical solutions for the metric even for positive potentials; solutions are unique for a given configuration only up to a branch choice; solutions on one branch can apparently end at nonsingular points of the metric and their continuation on alternate branches lead to nonsingular bouncing solutions; unitary gauge perturbations can go unstable even when degenerate terms in the Lagrangian are infinitesimal. The attractor solution leads to an inflationary scenario where slow-roll parameters vary and running of the tilt can be large even with no explicit features in the potential far from the end of inflation, requiring the optimized slow-roll approach for predicting observables.

CSF levels of synaptosomal-associated protein 25 and synaptotagmin-1 in first-episode psychosis subjects

Post-mortem studies consistently show evidence of reduced synaptic protein levels in patients with schizophrenia. Clinically high-risk subjects show a steeper decrease in grey matter thickness and in vitro modeling using patient-derived cells implicate excessive synaptic pruning during neurodevelopment as a part of the schizophrenia pathophysiology. However, it is unclear to what extent synapse elimination is present during various stages of the disease, which is of clinical importance as in a real-world setting most subjects received their first-episode psychosis (FEP) diagnosis not until their mid-twenties. In the present study, we measured cerebrospinal fluid (CSF) concentrations of the two pre-synaptic proteins synaptosomal-associated protein 25 (SNAP-25) and synaptotagmin-1 (SYT-1), both of which are increased in conditions of ongoing synaptic degeneration, in 44 FEP subjects (mean age 29.9 years) and 21 healthy controls (25.9 years) using immunoprecipitation mass spectrometry. Neither protein was found to differ between healthy controls and patients, and they showed no correlation with symptom ratings, cognitive performance or antipsychotic medication. Additional studies in high-risk subjects in the early prodromal phase will be needed to address if excessive synapse destruction occurs before the development of overt psychotic symptoms.

Generation of resonant geometric modes from off-axis pumped degenerate cavity Nd:YVO4 lasers with external mode converters.

We propose a theoretical model to generate the resonant geometric modes localized on ray periodic trajectories with orbital angular momentum. Based on the numerical analysis, we realize resonant geometric modes in the off-axis pumped degenerate cavity ${\rm Nd}{:}{{\rm YVO}_4}$Nd:YVO4 lasers with an external mode converter. The experimental results reveal that laser output modes display the planar geometric modes when the off-axis displacement is sufficiently large, and the cavity length is set to satisfy the degenerate conditions. To generate the vortex beams, the planar geometric modes are transformed into circular geometric modes. Finally, the resonant geometric modes with large orbital angular momentum (OAM) can be generated from converting the circular geometric modes with an axicon lens. The experimental results are performed to approve the theoretical analyses.

Application of Forward-Scan Sonar Stereo for 3-D Scene Reconstruction

New generation of underwater 2-D forward-look sonar video cameras operating at near and over 1-MHz frequency offer images with enhanced target details. Within their limited range of only tens of meters, they are the most suitable imaging systems for conducting visually guided missions in turbid waters. These include, but are not limited to inspecting underwater structures for routine maintenance, search, and surveillance, the detection, localization, and identification of small sought after objects, as well as target-based positioning and navigation. To this end, the automatic 3-D reconstruction of 3-D target shape and establishing the 3-D spatial location of interest points are highly desired capabilities in many such operations. As achieved with 2-D optical images, multiple images from nearby positions may be utilized. This paper investigates the estimation of 3-D point locations from two overlapping images collected with two forward-scan (FS) sonar systems in stereo configuration, or with one FS sonar at known relative poses, established from visual motion cues. The first contribution includes the analysis of a sonar stereo epipolar geometry. Beyond reducing the correspondence problem to a 1-D search along epipolar curves, this reveals unique properties associated with sonar measurements of range and azimuth angle. Next, certain linear closed-form reconstruction solutions are presented, their degeneracies are established, and adjustments under degenerate conditions are proposed. Two preferred method for the degenerate and nondegenerate stereo configurations are identified: a regularization-based method and one employing a range constraint approximation, respectively. These primarily provide the initial estimate for an iterative nonlinear optimization scheme based on gradient descent. Finally, the results of experiments with synthetic data are presented to assess various estimation methods, and with real data sets to demonstrate performance under two subsea operational scenarios.

Protected Area Biodiversity Conservation: Population Dynamics

One of the methods for protecting the environment and conserving species biodiversity is the creation of protected areas, the task of which is to conserve rare species of animals and plants. The dynamics of populations can be studied quite effectively with the mathematical models. Modeling allows to study all possible scenarios of interaction and development of populations, to evaluate the influence of the environment on the spatial-temporal dynamics of biological communities. The paper considers a non-linear model of a protected population, the feature of which is the presence of a bilocal range and the exchange of species between its parts. It is a system of nonlinear parabolic partial differential equations that describes the dependence of migration flows on the uneven distribution of species in an area with a generalized resource. A complex of programs was coded in Python programming language for numerical study of diffusion models and visualization of the results obtained. Numerical simulation results of cross-diffusion effects and influence of generalized resource are analyzed in detail. The obtained results of research can be used for studying the processes in the protected population, for assessing the size of the protected areas being created, determining the conditions of population degeneration and recommendations for their stable existence.

Two-Dimensional Flow and Mass Transport through Variably Saturated Porous Media from a Surface Waste Storage

Numerical calculations in DHI FEFLOW software environment were used to assess the effect of variably saturated zone parameters on capillary barrier formation. The sensitivity of the model to these parameters was analyzed, and the conditions of barrier degeneracy were given.

Heat kernel approach for confined quantum gas

In this paper, based on the heat kernel technique, we calculate equations of state and thermodynamic quantities for ideal quantum gases in confined space with external potential. Concretely, we provide expressions for equations of state and thermodynamic quantities by means of heat kernel coefficients for ideal quantum gases. Especially, using an analytic continuation treatment, we discuss the application of the heat kernel technique to Fermi gases in which the expansion diverges when the fugacity [Formula: see text]. In order to calculate the modification of heat kernel coefficients caused by external potentials, we suggest an approach for calculating the expansion of the global heat kernel of the operator [Formula: see text] based on an approximate method of the calculation of spectrum in quantum mechanics. We discuss the properties of quantum gases under the condition of weak and complete degeneration, respectively. Moreover, we give an expansion of the one-loop effective action in D-dimensional space.

Dark degeneracy I: Dynamical or interacting dark energy?

We revisit the dark degeneracy that arises from the Einstein equations relating geometry to the total cosmic substratum but not resolving its individual components separately. We establish the explicit conditions for the dark degeneracy in the fluid description of the dark sector. At the background level, this degeneracy can be formally understood in terms of a unified dark sector Equation of State (EoS) that depends both on the dynamical nature of the dark energy (DE) as well as on its interaction with the pressureless dark matter. For linear perturbations, the degeneracy arises for specified DE pressure perturbations (or sound speed, equivalently) and DE anisotropic stress. Specializing to the degeneracy between non-interacting dynamical DE and interacting vacuum DE models, we perform a parameter estimation analysis for a range of dynamical DE parametrizations, where for illustration we explicitly break the degeneracy at the linear level by adopting a luminal sound speed for both scenarios. We conduct this analysis using cosmological background data alone and in combination with Planck measurements of the cosmic microwave background radiation. We find that although the overall phenomenology between the dynamical DE and interacting approaches is similar, there are some intriguing differences. In particular, there is an ambiguity in the strength of constraints on $\Omega_{m0}$ and $\sigma_8$, which are considerably weakened for interacting vacuum DE, indicating that the dark degeneracy can change the significance of tensions in cosmological parameters inferred from different data sets.

Micromorphological assessment of bone tissue remodeling in various hip degeneration conditions.

The reorganization of bone tissue is closely associated with its metabolism and changes in its internal structure. Metabolism of the bone, which results from the simultaneous processes of resorption and formation of new bone tissue, may depend on the presence and type of arthritis. The objective of the study was to assess, based on the morphological features and mineral composition of bone tissue, changes in the femoral head in various types of hip joint degeneration. The study group consisted of 21 patients surgically treated for hip joint degeneration. They included 17 women, aged 30-70 years (mean age 52.5 years), and 4 men, aged 38-51 (mean age 48.5 years). The assessment of the morphological condition of the bone and the mineral composition of bone tissue took into account quantitative and qualitative relationships among the mineral components and bone matrix. The structure of spongious bone tissue was analyzed in histological studies, with special attention paid to osteogenesis and osteoclastic processes and the advancement of degeneration. Three main types of degenerative changes in bone tissue of the examined femoral head were recognized: osteoporosis with a prevalence of coarse-fiber bone tissue and decreased osteogenic activity; osteolysis with few osteogenesis centers; and intensified reorganization of bone tissue. In more than half of the examined samples, coarse-fiber bone tissue was replaced by newly formed bone tissue. We observed bone resorption and osteogenesis, which indicate normal homeostasis of the bone tissue. Uneven saturation of spongious bone with mineral components was found. The content of organic and inorganic bone components measured with Ca : P and C : Ca + P ratios had similar values in all types of changes. Only the bone with intense osteolysis contained a smaller quantity of carbon (4.96-8.13%). Our observations indicate an intense adaptive reorganization of bone tissue depending on external and internal factors, including biomechanical condition.

Asymptotic behavior for nonlinear degenerate parabolic equations with irregular data

ABSTRACT This paper focuses on the following degenerate parabolic equation where Ω is a smooth bounded domain in , is positive almost everywhere and satisfies proper degenerate conditions. The existence and uniqueness result is proved in the framework of entropy solutions. For the long-time behavior, we prove the existence of a global attractor in by using some delicate estimates on the solution, which are derived by taking advantage of both the leading operator and the zero-order nonlinear term. The aforementioned results improve some previous results in the literature in several aspects.

Structure-preserving integrators for dissipative systems based on reversible- irreversible splitting.

We study the optimal design of numerical integrators for dissipative systems, for which there exists an underlying thermodynamic structure known as GENERIC (general equation for the nonequilibrium reversible–irreversible coupling). We present a frame-work to construct structure-preserving integrators by splitting the system into reversible and irreversible dynamics. The reversible part, which is often degenerate and reduces to a Hamiltonian form on its symplectic leaves, is solved by using a symplectic method (e.g. Verlet) with degenerate variables being left unchanged, for which an associated modified Hamiltonian (and subsequently a modified energy) in the form of a series expansion can be obtained by using backward error analysis. The modified energy is then used to construct a modified friction matrix associated with the irreversible part in such a way that a modified degeneracy condition is satisfied. The modified irreversible dynamics can be further solved by an explicit midpoint method if not exactly solvable. Our findings are verified by various numerical experiments, demonstrating the superiority of structure-preserving integrators over alternative schemes in terms of not only the accuracy control of both energy conservation and entropy production but also the preservation of the conformal symplectic structure in the case of linearly damped systems.