Dynamics of a metastable state nonlinearly coupled to a heat bath driven by an external noise

Based on a system-reservoir model, where the system is nonlinearly coupled to a heat bath and the heat bath is modulated by an external stationary Gaussian noise, we derive the generalized Langevin equation with space dependent friction and multiplicative noise and construct the corresponding Fokker-Planck equation, valid for short correlation time, with space dependent diffusion coefficient to study the escape rate from a metastable state in the moderate to large damping regime. By considering the dynamics in a model cubic potential we analyze the result numerically which are in good agreement with the theoretical prediction. It has been shown numerically that the enhancement of rate is possible by properly tuning the correlation time of the external noise.Comment: 13 pages, 5 figures, Revtex4. To appear in Physical Review

A proposal for a comprehensive grading of Parkinson's disease severity combining motor and non-motor assessments: meeting an unmet need.

Non-motor symptoms are present in Parkinson's disease (PD) and a key determinant of quality of life. The Non-motor Symptoms Scale (NMSS) is a validated scale that allows quantifying frequency and severity (burden) of NMS. We report a proposal for using NMSS scores to determine levels of NMS burden (NMSB) and to complete PD patient classification

Generalization of escape rate from a metastable state driven by external cross-correlated noise processes

We propose generalization of escape rate from a metastable state for externally driven correlated noise processes in one dimension. In addition to the internal non-Markovian thermal fluctuations, the external correlated noise processes we consider are Gaussian, stationary in nature and are of Ornstein-Uhlenbeck type. Based on a Fokker-Planck description of the effective noise processes with finite memory we derive the generalized escape rate from a metastable state in the moderate to large damping limit and investigate the effect of degree of correlation on the resulting rate. Comparison of the theoretical expression with numerical simulation gives a satisfactory agreement and shows that by increasing the degree of external noise correlation one can enhance the escape rate through the dressed effective noise strength.Comment: 9 pages, 1 figur

Multiplicative cross-correlated noise induced escape rate from a metastable state

We present an analytical framework to study the escape rate from a metastable state under the influence of two external multiplicative cross-correlated noise processes. Starting from a phenomenological stationary Langevin description with multiplicative noise processes, we have investigated the Kramers' theory for activated rate processes in a nonequilibrium open system (one-dimensional in nature) driven by two external cross-correlated noise processes which are Gaussian, stationary and delta correlated. Based on the Fokker-Planck description in phase space, we then derive the escape rate from a metastable state in the moderate to large friction limit to study the effect of degree of correlation on the same. By employing numerical simulation in the presence of external cross-correlated additive and multiplicative noises we check the validity of our analytical formalism for constant dissipation, which shows a satisfactory agreement between both the approaches for the specific choice of noise processes. It is evident both from analytical development and the corresponding numerical simulation that the enhancement of rate is possible by increasing the degree of correlation of the external fluctuations.Comment: 9 pages, 1 figures, RevTex

Time dependent current in a nonstationary environment: A microscopic approach

Based on a microscopic system reservoir model,where the associated bath is not in thermal equilibrium, we simulate the nonstationary Langevin dynamics and obtained the generalized nonstationary fluctuation dissipation relation (FDR) which asymptotically reduces to the traditional form. Our Langevin dynamics incorporates non-Markovian process also, the origin of which lies on the decaying term of the nonstationary FDR. We then follow the stochastic dynamics of the Langevin particle based on the Fokker-Planck-Smoluchowski description, in ratchet potential to obtain the steady and time dependent current in an analytic form. We also examine the influence of initial excitation and subsequent relaxation of bath modes on the transport of the Langevin particle to show that the nonequilibrium nature of the bath leads to both strong non-exponential dynamics as well as nonstationary current.Comment: 10 pages, RevTex4, references updated, final version to appear in Journal of Mathematical Physic

Impulse control disorders in Parkinson's disease: decreased striatal dopamine transporter levels

Objective Impulse control disorders are commonly associated with dopaminergic therapy in Parkinson's disease (PD). PD patients with impulse control disorders demonstrate enhanced dopamine release to conditioned cues and a gambling task on [11C]raclopride positron emission tomography (PET) imaging and enhanced ventral striatal activity to reward on functional MRI. We compared PD patients with impulse control disorders and age-matched and gender-matched controls without impulse control disorders using [123I]FP-CIT (2β-carbomethoxy-3β-(4-iodophenyl)tropane) single photon emission computed tomography (SPECT), to assess striatal dopamine transporter (DAT) density. Methods The [123I]FP-CIT binding data in the striatum were compared between 15 PD patients with and 15 without impulse control disorders using independent t tests. Results Those with impulse control disorders showed significantly lower DAT binding in the right striatum with a trend in the left (right: F(1,24)=5.93, p=0.02; left: F(1,24)=3.75, p=0.07) compared to controls. Conclusions Our findings suggest that greater dopaminergic striatal activity in PD patients with impulse control disorders may be partly related to decreased uptake and clearance of dopamine from the synaptic cleft. Whether these findings are related to state or trait effects is not known. These findings dovetail with reports of lower DAT levels secondary to the effects of methamphetamine and alcohol. Although any regulation of DAT by antiparkinsonian medication appears to be modest, PD patients with impulse control disorders may be differentially sensitive to regulatory mechanisms of DAT expression by dopaminergic medications

The noise properties of stochastic processes and entropy production

Based on a Fokker-Planck description of external Ornstein-Uhlenbeck noise and cross-correlated noise processes driving a dynamical system we examine the interplay of the properties of noise processes and the dissipative characteristic of the dynamical system in the steady state entropy production and flux. Our analysis is illustrated with appropriate examples.Comment: RevTex, 1 figure, To appear in Phys. Rev.

Clinical Non-Motor Phenotyping of Black and Asian Minority Ethnic Compared to White Individuals with Parkinson's Disease Living in the United Kingdom

BACKGROUND: Ethnic phenotypic differences in Parkinson's disease (PD) are important to understand the heterogeneity of PD and develop biomarkers and clinical trials. OBJECTIVE: To investigate (i) whether there are non-motor symptoms (NMS)-and comorbidity-based phenotypic differences between Black, Asian and Minority Ethnic (BAME) and White PD patients and (ii) whether clinically available biomarkers may help differentiate and explain the diversity. METHODS: This is a multicentre (four sites, London), real-life, cross-sectional study including PD patients of BAME or White ethnicity. The primary outcome was a detailed NMS assessment, additional measurements included disease and motor stage, comorbidity, sociodemographic parameters and brain MRI imaging. RESULTS: 271 PD patients (54 Asian, 71 Black, and 146 White) were included balanced for age, gender, and disease severity (HY). Black patients had a shorter disease duration compared to White and Asian populations. The SCOPA-Motor activities of daily living scores as well as the NMSS scores were significantly higher in both Black (total score and domain "miscellaneous") and Asian (total score and domains "sleep/fatigue", mood/apathy" and perception/hallucinations) than White individuals. Both BAME populations had higher prevalence of arterial hypertension, and the Black population had a higher prevalence of diabetes mellitus. Brain MRI revealed a greater severity of white matter changes in Black compared to the White and Asian cohorts. CONCLUSION: These findings suggest differences in phenotype of PD in BAME populations with greater burden of NMS and motor disability and a higher rate of cardiovascular comorbidities

Theory of Adiabatic fluctuations : third-order noise

We consider the response of a dynamical system driven by external adiabatic fluctuations. Based on the `adiabatic following approximation' we have made a systematic separation of time-scales to carry out an expansion in $\alpha |\mu|^{-1}$, where $\alpha$ is the strength of fluctuations and $|\mu|$ is the damping rate. We show that probability distribution functions obey the differential equations of motion which contain third order terms (beyond the usual Fokker-Planck terms) leading to non-Gaussian noise. The problem of adiabatic fluctuations in velocity space which is the counterpart of Brownian motion for fast fluctuations, has been solved exactly. The characteristic function and the associated probability distribution function are shown to be of stable form. The linear dissipation leads to a steady state which is stable and the variances and higher moments are shown to be finite.Comment: Plain Latex, no figures, 28 pages; to appear in J. Phys.

Dreaming Characteristics in Non-Rapid Eye Movement Parasomnia and Idiopathic Rapid Eye Movement Sleep Behaviour Disorder: Similarities and Differences

Background: Speech graph analysis (SGA) of dreams has recently shown promise as an objective and language-invariant diagnostic tool that can aid neuropsychiatric diagnosis. Whilst the notion that dreaming mentations reflect distinct physiologic processes is not new, such studies in patients with sleep disorders remain exceptionally scarce. Here, using SGA and other dream content analyses, we set to investigate structural and thematic differences in morning dream recalls of patients diagnosed with Non-Rapid Eye Movement Parasomnia (NREMP) and Idiopathic REM Sleep Behavior Disorder (iRBD). Methods: A retrospective cross-sectional study of morning dream recalls of iRBD and NREMP patients was undertaken. Traditional dream content analyses, such as Orlinsky and Hall and Van de Castle analyses, were initially conducted. Subsequently, SGA was performed in order to objectively quantify structural speech differences between the dream recalls of the two patient groups. Results: Comparable rate of morning recall of dreams in the sleep laboratory was recorded; 25% of iRBD and 18.35% of NREMP patients. Aggression in dreams was recorded by 28.57% iRBD versus 20.00% in NREMP group. iRBD patients were more likely to recall dreams (iRBD vs NREMP; P = 0.007), but they also had more white dreams, ie having a feeling of having dreamt, but with no memory of it. Visual and quantitative graph speech analyses of iRBD dreams suggested stable sequential structure, reflecting the linearity of the chronological narrative. Conversely, NREMP dream reports displayed more recursive, less stable systems, with significantly higher scores of graph connectivity measures. Conclusion: The findings of our exploratory study suggest that iRBD and NREMP patients may not only differ on what is recalled in their dreams but also, perhaps more strikingly, on how dreams are recalled. It is hoped that future SGA-led dream investigations of larger groups of patients will help discern distinct mechanistic underpinnings and any associated clinical implications