Degenerate System Research Articles

Noradrenergic cardiac denervation is associated with gait velocity in Parkinson disease: a dual ligand PET study.

Preliminary data suggest that gait abnormalities in Parkinson disease (PD) may be associated with sympathetic cardiac denervation. No kinematic gait studies were performed to confirm this observation. We aimed to correlate spatiotemporal kinematic gait parameters with cardiac sympathetic denervation as determined by cardiac [11C]HED PET in PD. Retrospective database analysis of 27 PD patients with cardiac sympathetic denervation. All patients underwent spatiotemporal kinematic gait assessment (medication 'off' state), cardiac [11C]HED and dopaminergic brain [11C]DTBZ PET scans. We employed a hierarchical regression approach to examine associations between the extent of cardiac denervation, dopaminergic nigrostriatal neurodegeneration, and three gait parameters - velocity, step length and cadence. More extensive cardiac denervation was associated with slower velocity (estimate: -1.034, 95% CI [-1.65, -0.42], p = 0.002), shorter step length (estimate: -0.818, 95% CI [-1.43, -0.21], p = 0.011) and lower cadence (estimate: -0.752, 95% CI [-1.28, -0.23], p = 0.007) explaining alone 30% (Adjusted-R²: 0.297), 20% (Adjusted-R²: 0.202) and 23% (Adjusted-R²: 0.227) of the variability, respecivetly. These associations remained independent of striatal dopaminergic impairment and confounding factors such as age, Hoehn and Yahr (HY) stages, peripheral neuropathy, cognition, and autonomic symptoms. In contrast, striatal dopaminergic denervation was significantly associated with step length (estimate: 0.883, 95% CI [0.29, 1.48], p = 0.005), explaining about 24% of the variability but was dependent of HY stage. More severe cardiac noradrenergic denervation was associated with lower gait velocity, independent of striatal dopaminergic denervation and HY stage, impacting both step length and cadence. These results suggest independent contributions of the peripheral autonomic system degeneration on gait dynsfunction in PD.

Regularization of the Solution to Degenerate Systems of Algebraic Equations Exemplified by Identification of the Virial Equation of State of a Real Gas

Regularization of the Solution to Degenerate Systems of Algebraic Equations Exemplified by Identification of the Virial Equation of State of a Real Gas

Searching Heterocyclic Scaffolds Used to Treat Alzheimer’s Disease: A Review

Abstract:: It is a known fact that Alzheimer's disease causes degeneration of the central nervous system, which progresses and causes memory loss as well as loss of cognition. For many years, extensive research has been undertaken to find out newer possibilities to fight this disease at a molecular level along with many long-standing and expensive clinical trials. Many scientific research programs have either been discarded or unsuccessful. However, the research has not stopped and in the process, many heterocyclic scaffolds have been tried to build up novel drug molecules to combat this disease. A literature survey reveals that many heterocycles have been explored and were found to be very useful in treating many neurodegenerative disorders, including Alzheimer’s disease, Parkinsonism and a few more. This review explains the journey and highlights the various strategies to develop new anti-Alzheimer drug candidates. It is a concise and rigorous literature excerpt involving research findings on heterocyclic scaffolds for treating this disease.

Global existence of solutions to some degenerate chemotaxis systems with superlinear growth in cross-diffusion rates and logistic sources

The objective is to investigate the global existence of solutions for degenerate chemotaxis systems with logistic sources in a two-dimensional domain. It is demonstrated that the inclusion of logistic sources can exclude the occurrence of blow-up solutions, even in the presence of superlinear growth in the cross-diffusion rate. Our proof relies on the application of elliptic and parabolic regularity in Orlicz spaces and variational approach.

A Candidate Period of 4.605 Days for FRB 20121102A and One Possible Implication of Its Origin

A firm establishment of the presence or the lack of periodicity in repeating fast radio bursts is crucial for determining their origins. Here, we compile 1145 radio bursts of FRB 20121102A with fluence larger than 0.15 Jy ms from observations using the Five-hundred-meter Aperture Spherical radio Telescope, the Arecibo Observatory, the Green Bank Telescope, the Effelsberg Telescope, the MeerKAT Telescope, the Lovell Telescope, the Deep Space Network 70 m radio telescopes, the Very Large Array, and the Westerbork Synthesis Radio Telescope, spanning the time interval of MJD 57175−58776. A quasi-period of 157.1−4.8+5.2 days and a candidate quasi-period of 4.605−0.010+0.003 days are found through the phase-folding probability binomial analysis. The former is consistent with previous findings and the latter is new. The 4.605 day periodicity is more obvious in high-energy bursts with fluence larger than 1 × 1038 erg. The presence of these (candidate) quasi-periods, together with the corresponding width of burst accumulation in the phase space, are consistent with the bursts originating from a binary degenerate star system with a close-by planet around the primary neutron star.

Double Hanle resonance dependence on light polarization angle and transverse magnetic field direction

We present experimental and theoretical investigations of the dependence of double Hanle resonance spectrum on the light polarization angle and the direction of the applied transverse magnetic field (TMF). The experiments are done for Fg=2→Fe=1 transition of 87Rb D1 line using a rubidium vapor cell containing buffer gas. We show that a small light polarization component along the direction of TMF introduces asymmetry in the double Hanle resonance signal. Both the magnitude and sign of asymmetry in the signal are sensitive to the TMF orientation, suggesting a possible method for in-situ measurement of the direction of the magnetic fields generated by the coils. The physical origin of this asymmetry is explained by considering the redistribution of population among the ground-state Zeeman sublevels in the presence of TMF. In addition, we systematically vary both the polarization angle and TMF direction to study their effect on the line profile of Hanle resonances. We demonstrate that a double Hanle resonance changes to a dark Hanle resonance by rotating the light polarization vector irrespective of the TMF direction. We have developed a simple theoretical model based on a degenerate two-level system to explain our experimental observations.

Higher order contribution to ion-acoustic Korteweg–de Vries (KdV) soliton in unmagnetized quantum plasmas with arbitrary degeneracy of electrons

The propagation of nonlinear ion-acoustic Korteweg–de Vries (KdV) solitons and dressed solitons (with higher order contribution term) in unmagnetized quantum plasmas with arbitrary degeneracy of electrons is investigated using quantum hydrodynamic model. The reductive perturbation method is used to derive the first order nonlinear ion-acoustic KdV equation and also higher order contribution of inhomogeneous differential equation is obtained for the dressed ion-acoustic wave soliton in arbitrary degenerate electron plasmas. Moreover, the higher order inhomogeneous differential equation is solved (nonsecular solution is obtained) using the renormalization method. The conditions for the validity of the higher order correction are also discussed in detail for ion-acoustic solitons in unmagnetized arbitrary degenerate electrons plasma case. The effects of chosen values of electron temperature, equilibrium fugacity and corresponding electron density of a physical quantum plasma system and quantum diffraction parameter H (for two conditions i.e., H < 2 or H > 2) on the amplitude and width of the KdV and dressed ion-acoustic wave solitons for both electrostatic potential hump (compressive) or dip (rarefactive) structures are investigated. The numerical plots are also presented for illustration with numerical values of a physical partially degenerate electrons plasma system exist in the astrophysical or laboratory conditions.

Neuropathologic Validation and Diagnostic Accuracy of Presynaptic Dopaminergic Imaging in the Diagnosis of Parkinsonism.

Degeneration of the presynaptic nigrostriatal dopaminergic system is one of the main biological features of Parkinson disease (PD), multiple system atrophy (MSA), progressive supranuclear palsy (PSP), and corticobasal degeneration (CBD), which can be measured using single-photon emission CT imaging for diagnostic purposes. Despite its widespread use in clinical practice and research, the diagnostic properties of presynaptic nigrostriatal dopaminergic (DAT) imaging in parkinsonism have never been evaluated against the diagnostic gold standard of neuropathology. The aim of this study was to evaluate the diagnostic parameters of DAT imaging compared with pathologic diagnosis in patients with parkinsonism. Retrospective cohort study of patients with DAT imaging for the investigation of a clinically uncertain parkinsonism with brain donation between 2010 and 2021 to the Queen Square Brain Bank (London). Patients with DAT imaging for investigation of pure ataxia or dementia syndromes without parkinsonism were excluded. Those with a pathologic diagnosis of PD, MSA, PSP, or CBD were considered presynaptic dopaminergic parkinsonism, and other pathologies were considered postsynaptic for the analysis. DAT imaging was performed in routine clinical practice and visually classified by hospital nuclear medicine specialists as normal or abnormal. The results were correlated with neuropathologic diagnosis to calculate diagnostic accuracy parameters for the diagnosis of presynaptic dopaminergic parkinsonism. All of 47 patients with PD, 41 of 42 with MSA, 68 of 73 with PSP, and 6 of 10 with CBD (sensitivity 100%, 97.6%, 93.2%, and 60%, respectively) had abnormal presynaptic dopaminergic imaging. Eight of 17 patients with presumed postsynaptic parkinsonism had abnormal scans (specificity 52.9%). DAT imaging has very high sensitivity and negative predictive value for the diagnosis of presynaptic dopaminergic parkinsonism, particularly for PD. However, patients with CBD, and to a lesser extent PSP (of various phenotypes) and MSA (with predominant ataxia), can show normal DAT imaging. A range of other neurodegenerative disorders may have abnormal DAT scans with low specificity in the differential diagnosis of parkinsonism. DAT imaging is a useful diagnostic tool in the differential diagnosis of parkinsonism, although clinicians should be aware of its diagnostic properties and limitations. This study provides Class II evidence that DAT imaging does not accurately distinguish between presynaptic dopaminergic parkinsonism and non-presynaptic dopaminergic parkinsonism.

Switching between slow light and fast light by static magnetic field in a degenerate four-level atomic system at room temperature

The optical response of a magnetic-degenerated four-level atom system to the two left and right circular polarization components of the probe field is represented at room temperature. The absorption spectrum and group index for the two polarization components of the probe field are controlled according to the static magnetic field and the coupling field under electromagnetically induced transparency condition. By varying the strength of the static magnetic field, the optical response of the atomic medium can be changed from transparency to absorption or vice versa and hence the amplitude of group index also changes from positive extreme to negative extreme or vice versa. The same phenomenon also occurs when changing the coupling field intensity. In addition, temperature also significantly influence on the optical response of the atomic medium, which changes not only the amplitude but also the sign of the group index as the temperature increases. Our analytical results can be useful for experimental observation and related applications of light group index/velocity at room temperature.

Dynamical bifurcation of a stochastic Holling-II predator–prey model with infinite distributed delays

This paper serves as a continuation and expansion of the previous achievement by B. Han and D. Jiang in their article (Han and Jiang, 2024). Our initial step involves transforming the more complex stochastic Holling-II model featuring a stronger kernel into a simplified yet degenerate stochastic system composed of five interconnected equations. For the deterministic component of this model, we delve into an extensive examination of the local asymptotic stability of its positive equilibrium state. Subsequently, for the stochastic model, we derive critical conditions that determine the thresholds for exponential extinction and persistence of both predator and prey populations. Importantly, our findings not only encompass scenarios where there are no stochastic disturbances but also shed light on how environmental noise impacts the population dynamics within the predator–prey system. Through the exploration of the homologous Fokker–Planck equations, we present approximate representations characterizing the probability density function of the stochastic predator–prey model. To substantiate these theoretical advancements, several illustrative examples are provided, offering numerical elucidations of our proposed results and emphasizing the profound effects of stochastic noises and some important parameters on the behaviors of the stochastic model.

Non-adaptive estimation for degenerate diffusion processes

We consider a degenerate system of stochastic differential equations. The first component of the system has a parameter θ 1 \theta _1 in a non-degenerate diffusion coefficient and a parameter θ 2 \theta _2 in the drift term. The second component has a drift term with a parameter θ 3 \theta _3 and no diffusion term. Parametric estimation of the degenerate diffusion system is discussed under a sampling scheme. We investigate the asymptotic behavior of the joint quasi-maximum likelihood estimator for ( θ 1 , θ 2 , θ 3 ) (\theta _1,\theta _2,\theta _3) . The estimation scheme is non-adaptive. The estimator incorporates information of the increments of both components, and under this construction, we show that the asymptotic variance of the estimator for θ 1 \theta _1 is smaller than the one for standard estimator based on the first component only, and that the convergence of the estimator for θ 3 \theta _3 is much faster than for the other parameters. By simulation studies, we compare the performance of the joint quasi-maximum likelihood estimator with the adaptive and one-step estimators investigated in Gloter and Yoshida [Electron. J. Statist 15 (2021), no. 1, 1424–1472].

Loss of Cholinergic and Monoaminergic Afferents in APPswe/PS1ΔE9 Transgenic Mouse Model of Cerebral Amyloidosis Preferentially Occurs Near Amyloid Plaques.

Alzheimer's disease (AD) is characterized by a loss of neurons in the cortex and subcortical regions. Previously, we showed that the progressive degeneration of subcortical monoaminergic (MAergic) neurons seen in human AD is recapitulated in the APPswe/PS1ΔE9 (APP/PS) transgenic mouse model. Because degeneration of cholinergic (Ach) neurons is also a prominent feature of AD, we examined the integrity of the Ach system in the APP/PS model. The overall density of Ach fibers is reduced in APP/PS1 mice at 12 and 18 months of age but not at 4 months of age. Analysis of basal forebrain Ach neurons shows no loss of Ach neurons in the APP/PS model. Thus, since MAergic systems show overt cell loss at 18 months of age, the Ach system is less vulnerable to neurodegeneration in the APP/PS1 model. We also examined whether the proximity to Aβ deposition affected the degeneration of Ach and 5-HT afferents. We found that the areas closer to the edges of compact Aβ deposits exhibit a more severe loss of afferents than the areas that are more distal to Aβ deposits. Collectively, the results indicate that the APP/PS model recapitulates the degeneration of multiple subcortical neurotransmitter systems, including the Ach system. In addition, the results indicate that Aβ deposits cause global as well as local toxicity to subcortical afferents.

L∞ bounds in a two-dimensional doubly degenerate nutrient taxis system with general cross-diffusive flux

The doubly degenerate nutrient taxis model{ut=∇⋅(uv∇u)−∇⋅(S(u)v∇v)+ℓuv,x∈Ω,t>0,vt=Δv−uv,x∈Ω,t>0, is considered under no-flux boundary conditions in a bounded convex planar domain Ω with smooth boundary.It is firstly shown that within a general framework involving a conveniently large class of nonlinearities S, under an a priori assumption on regularity of solutions to certain approximate problems one can construct a global weak solution whose first component is uniformly bounded.Applications of this to particular settings thereafter reveal global existence of such bounded weak solutions when either S∈C1([0,∞)) satisfieslimsupξ→∞S(ξ)ξα<∞with some α<2 and the initial data (u0,v0) are reasonably regular but arbitrary large, or S(ξ)=ξ2 for ξ≥0 and the initial data are such that v0 satisfies an appropriate smallness condition.

GMP production of [18F]FE-PE2I on a TRACERLab FX2 N synthesis module, a radiotracer for in vivo PET imaging of the dopamine transport

BackgroundParkinson's disease is a neurodegenerative disorder that is characterized by a degeneration of the dopaminergic system. Dopamine transporter (DAT) positron emission tomography (PET) imaging has emerged as a powerful and non-invasive method to quantify dopaminergic function in the living brain. The PET radioligand, [18F]FE-PE2I, a cocaine chemical derivative, has shown promising properties for in vivo PET imaging of DAT, including high affinity and selectivity for DAT, excellent brain permeability, and favorable metabolism. The aim of the current study was to scale up the production of [18F]FE-PE2I to fulfil the increasing clinical demand for this tracer.ResultsThus, a fully automated and GMP-compliant production procedure has been developed using a commercially available radiosynthesis module GE TRACERLab FX2 N. [18F]FE-PE2I was produced with a radiochemical yield of 39 ± 8% (n = 4, relative [18F]F− delivered to the module). The synthesis time was 70 min, and the molar activity was 925.3 ± 763 GBq/µmol (250 ± 20 Ci/µmol). The produced [18F]FE-PE2I was stable over 6 h at room temperature.ConclusionThe protocol reliably provides a sterile and pyrogen–free GMP-compliant product.

A c.726C>G (p.Tyr242Ter) nonsense mutation-associated with splicing alteration (NASA) of WDR45 gene underlies β-propeller protein-associated neurodegeneration (BPAN)

Neurodegeneration with brain iron accumulation (NBIA) is a clinically and genetically heterogeneous disease characterized by increased iron deposition in the basal ganglia and progressive degeneration of the nervous system in adulthood. However, in early childhood, there were no characteristic features to perform early diagnosis. In our study, a female child exhibited global developmental delay, intellectual disability, and febrile seizure without other distinct clinical phenotypes. Through whole exome sequencing (WES), a de novo nonsense mutation (c.726C > G, p. Tyr242Ter) of WDR45 gene was identified in this child. She was finally diagnosed as β‐propeller protein-associated neurodegeneration (BPAN), one of the recently identified subtypes of NBIA. This mutation could act as a premature stop codon (PSC) which rendered the mutated transcripts to be degraded by nonsense-mediated mRNA decay (NMD), leading to decreased levels of PSC-containing mRNAs. Additionally, through mini-gene splicing assays, this mutation could result in an unprecedented novel transcript with the exon 9 of WDR45 excluded by nonsense-associated splicing alteration (NASA). Transcriptome sequencing (RNA-seq) on total RNAs from PBMCs of the trio revealed three types of alternative splicing events in the patient. Further research implied that downregulation of iron transport genes (TFRC, TFR2, SCARA5) might be the underlying mechanism for the iron accumulation in patients with deficient WDR45. This is the first report about NASA happening in WDR45. It implies that nonsense mutations approximal to splicing sites could affect the disease pathogenesis through more than one molecular mechanism and should be taken into consideration when conducting genetic counseling.

The two autophagy-related proteins 8a and 8b play distinct physiological roles in Drosophila

Atg8 family proteins play crucial roles in autophagy to maintain cellular homeostasis. However, the physiological roles of Atg8 family proteins have not been systematically determined. In this study, we generated Atg8a and Atg8b (homologs of Atg8 in Drosophila melanogaster) knockout flies. We found that the loss of Atg8a affected autophagy and resulted in partial lethality, abnormal wings, decreased lifespan, and decreased climbing ability in flies. Furthermore, the loss of Atg8a resulted in reduced muscle integrity and the progressive degeneration of the neuron system. We also found that the phosphorylation at Ser88 of Atg8a is important for autophagy and neuronal integrity. The loss of Atg8b did not affect autophagy but induced male sterility in flies. Here, we take full advantage of the fly system to elucidate the physiological function of Atg8a and Atg8b in Drosophila.

Optical gain in a degenerate two-level system in the presence of a transverse magnetic field

Here we report a theoretical model that allows magnetically assisted narrowband probe beam amplification in a closed two-level system with triple Zeeman degeneracy. The gain mechanism can be understood in terms of coherent population transfer between the levels of the Zeeman ground state induced by the external magnetic field. The theoretical model we develop here using a simpler atomic transition Fg=1→Fe=0, in agreement with the experimental results already observed in recent literature. Additionally, we validate our theoretical predictions with the results obtained via density matrix numeric calculation and we believe our theoretical results could useful in communication protocols involving distant nodes.

Convergence of a TPFA finite volume scheme for nonisothermal immiscible compressible two-phase flow in porous media

This paper presents and analyzes a finite volume scheme for a fully degenerate parabolic system modeling the compressible two-phase flow, such as water-gas, problem in porous media considering the effects of temperature. The problem is written in terms of the phase formulation, i.e. the saturation of one phase, the pressure of the second phase and the temperature are primary unknowns. We use a first-order time implicit Euler scheme. The spatial discretization uses a fully coupled fully implicit cell-centered two-point flux approximation scheme where upwinding of the flux across an interface between two control volumes is performed for each fluid phase. Under physically relevant assumptions on the data, we prove the maximum principle for both saturation and temperature. We obtain a priori estimates and we show that the discrete problem is well posed. Also, we exploit various a priori estimates as well as compactness arguments to establish the convergence of the numerical scheme toward the weak solution. The open-source platform DuMuX was employed for the implementation of the developed algorithm based on the above scheme. Numerical result are presented to demonstrate the efficiency of this scheme. The test addresses the evolution in 2D of CO2 injection into a layered aquifer. The algorithm's convergence with first order is validated by our numerical results, which support the theoretical results. To our best knowledge, this is the first convergence result of a finite volume scheme in the case of nonisothermal immiscible compressible two-phase flow in porous media.

Computation of the Spatial Distribution of Charge-Carrier Density in Disordered Media.

The space- and temperature-dependent electron distribution n(r,T) determines optoelectronic properties of disordered semiconductors. It is a challenging task to get access to n(r,T) in random potentials, while avoiding the time-consuming numerical solution of the Schrödinger equation. We present several numerical techniques targeted to fulfill this task. For a degenerate system with Fermi statistics, a numerical approach based on a matrix inversion and one based on a system of linear equations are developed. For a non-degenerate system with Boltzmann statistics, a numerical technique based on a universal low-pass filter and one based on random wave functions are introduced. The high accuracy of the approximate calculations are checked by comparison with the exact quantum-mechanical solutions.

Connecting Poincaré Inequality with Sobolev Inequalities on Riemannian Manifolds

We connect the Poincaré inequality with the Sobolev inequality on Riemannian manifold in a family of integral inequalities $(1.5)$. For these continuum of inequalities, we obtain topological structure theorems of manifolds generalizing previous unification theorems in both intrinsic and extrinsic settings ([33]). Manifolds which admit any of these integral inequalities are nonparabolic, affect topology, geometry, analysis, and admit nonconstant bounded harmonic functions of finite energy. As a consequence, we have proven a Conjecture of Schoen-Yau ([27, p.74]) to be true in dimension two with hypotheses weaker than that used in [1] and [33]$($ which were weaker than the hypotheses set in the conjecture, $($ cf. Remark 1.5$)$. In the same philosophy and spirit as in ([31]), we prove that if $M$ is a complete $n$-manifold, satisfying $\operatorname{(i)}$ the volume growth condition $(1.1)$, $\operatorname{(ii)}$ Liouville Theorem for harmonic functions, and either $\operatorname{(v)}$ a generalized Poincaré- Sobolev inequality $(1.5)$, or $\operatorname{(vi)}$ a general integral inequality $(1.6)$, and Liouville Theorem for harmonic map $u : M \to K$ with $\operatorname{Sec}^K \le 0$, then $(1)$ $M$ has only one end and $(2)$ there is no nontrivial homomorphism from fundamental group $\pi_1(\partial D)$ into $\pi_1 (K)$ as stated in Theorem $1.5$. Some applications in geometry $(\S 3)$, geometric analysis $(\S 4)$, nonlinear partial differential systems $(\S 5)$, integral inequalities on complete noncompact manifolds $(\S 6)$ are made $($cf. e.g., Theorems $3.1$, $4.1$, $5.1$, and $6.1)$. Whereas we made the first study in ([29, 32]) on how the existence of an essential positive supersolution of a second order partial differential systems $Q(u)=0$ on a Riemannian manifold $M$, (by which we mean a $C^2$ function $v \ge 0$ on $M$ that is positive almost everywhere on $M$, and that satisfies $Q(v)=\operatorname{div}(A(x,v,\nabla v)\nabla v)+b(x,v,\nabla v)v\leq 0\quad (5.1)\, $) affects topology, geometry, analysis and variational problems on the manifold $M$. Whereas we generate the work in [35], under $p$-parabolic stable condition without assuming the $p$-th volume growth condition $\lim _{r \to \infty} r^{-p}\operatorname{Vol}(B_r) =0$. The techniques, concepts, and results employed in this paper can be combined with those of essential positive supersolutions of degenerate nonlinear partial differential systems $($cf. for example, Theorems 5.1 - 5.5, 6.1, etc.$)\, $ generalizing previous work in [32, 4.11], which in term recaptures the work of Schoen-Simon-Yau ([25, Theorem 2]). The combined techniques, concepts and method of [32] and [35] can also be used in other new manifolds we found by an extrinsic average variational method ([34]).