The universality of synchrony: critical behavior in a discrete model of stochastic phase coupled oscillators

We present the simplest discrete model to date that leads to synchronization of stochastic phase-coupled oscillators. In the mean field limit, the model exhibits a Hopf bifurcation and global oscillatory behavior as coupling crosses a critical value. When coupling between units is strictly local, the model undergoes a continuous phase transition which we characterize numerically using finite-size scaling analysis. In particular, the onset of global synchrony is marked by signatures of the XY universality class, including the appropriate classical exponents $\beta$ and $\nu$, a lower critical dimension $d_{lc} = 2$, and an upper critical dimension $d_{uc}=4$.Comment: 4 pages, 4 figure

Critical behavior and synchronization of discrete stochastic phase coupled oscillators

Synchronization of stochastic phase-coupled oscillators is known to occur but difficult to characterize because sufficiently complete analytic work is not yet within our reach, and thorough numerical description usually defies all resources. We present a discrete model that is sufficiently simple to be characterized in meaningful detail. In the mean field limit, the model exhibits a supercritical Hopf bifurcation and global oscillatory behavior as coupling crosses a critical value. When coupling between units is strictly local, the model undergoes a continuous phase transition which we characterize numerically using finite-size scaling analysis. In particular, we explicitly rule out multistability and show that that the onset of global synchrony is marked by signatures of the XY universality class. Our numerical results cover dimensions d=2, 3, 4, and 5 and lead to the appropriate XY classical exponents \beta and \nu, a lower critical dimension d_{lc} = 2, and an upper critical dimension d_{uc}=4

Bone health in patients with multiple sclerosis relapses

OBJECTIVES: To evaluate the bone health and vitamin D levels of a cohort of patients with relapses of multiple sclerosis (MS) and to propose an algorithm for the management of bone health in this patient group. METHODS: We prospectively studied 56 consecutive patients from our acute relapse clinic. 3 patients were excluded from analysis as they were not deemed to have experienced an acute MS relapse. Bone health was assessed with vitamin D levels and Dual Energy X-ray Absorptiometry (DEXA) scanning (10 patients failed to attend for DEXA). Statistical analyses were used to compare groups and identify predictive variables. A review of the literature led to a proposed management protocol. RESULTS: Pre-relapse the baseline EDSS was ≤6.5 in all subjects, and <4.0 in the majority (66%). Most received corticosteroids. 51% had low bone mineral density (BMD) as defined by a T-score less than −1.0 on DEXA scanning. Three were osteoporotic (T-score less than −2.5). Thirty one of fifty (62%) subjects were Vitamin D deficient (25(OH)D less than 50 nmol/L). A range of variables, including previous corticosteroid usage, were not significantly predictive of reduced BMD. CONCLUSIONS: There was a high frequency of both low BMD and Vitamin D deficiency in this cohort of relatively young and largely ambulatory patients experiencing MS relapses. Current tools, such as the WHO FRAX algorithm, are inadequate in assessing bone status and fracture risk in this patient group, predominantly as they are focused on older age groups. We propose a simple clinical management algorithm

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

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

The Relationship between Brachycephalic Head Features in Modern Persian Cats and Dysmorphologies of the Skull and Internal Hydrocephalus

Background: Cat breeders observed a frequent occurrence of internal hydrocephalus in Persian cats with extreme brachycephalic head morphology. Objective: To investigate a possible relationship among the grade of brachycephaly, ventricular dilatation, and skull dysmorphologies in Persian cats. Animals: 92 Persian-, 10 Domestic shorthair cats. Methods: The grade of brachycephaly was determined on skull models based on CT datasets. Cranial measurements were examined with regard to a possible correlation with relative ventricular volume, and cranial capacity. Persians with high (peke-face Persians) and lower grades of brachycephaly (doll-face Persians) were investigated for the presence of skull dysmorphologies. Results: The mean cranial index of the peke-face Persians (0.97 ± 0.14) was significantly higher than the mean cranial index of doll-face Persians (0.66 ± 0.04; P < 0.001). Peke-face Persians had a lower relative nasal bone length (0.15 ± 0.04) compared to doll-face (0.29 ± 0.08; P < 0.001). The endocranial volume was significantly lower in doll-face than peke-face Persians (89.6 ± 1.27% versus 91.76 ± 2.07%; P < 0.001). The cranial index was significantly correlated with this variable (Spearman´s r: 0.7; P < 0.0001). Mean ventricle: Brain ratio of the peke-face group (0.159 ± 0.14) was significantly higher compared to doll-face Persians (0.015 ± 0.01; P < 0.001). Conclusion and Clinical Relevance: High grades of brachycephaly are also associated with malformations of the calvarial and facial bones as well as dental malformations. As these dysmorphologies can affect animal welfare, the selection for extreme forms of brachycephaly in Persian cats should be reconsidered

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.

Phase-Induced (In)-Stability in Coupled Parametric Oscillators

We report results on a model of two coupled oscillators that undergo periodic parametric modulations with a phase difference $\theta$. Being to a large extent analytically solvable, the model reveals a rich $\theta$ dependence of the regions of parametric resonance. In particular, the intuitive notion that anti-phase modulations are less prone to parametric resonance is confirmed for sufficiently large coupling and damping. We also compare our results to a recently reported mean field model of collective parametric instability, showing that the two-oscillator model can capture much of the qualitative behavior of the infinite system.Comment: 19 pages, 8 figures; a version with better quality figures can be found in http://hypatia.ucsd.edu/~mauro/English/publications.htm

Non-commutative Geometry and Kinetic Theory of Open Systems

The basic mathematical assumptions for autonomous linear kinetic equations for a classical system are formulated, leading to the conclusion that if they are differential equations on its phase space $M$, they are at most of the 2nd order. For open systems interacting with a bath at canonical equilibrium they have a particular form of an equation of a generalized Fokker-Planck type. We show that it is possible to obtain them as Liouville equations of Hamiltonian dynamics on $M$ with a particular non-commutative differential structure, provided certain geometric in character, conditions are fulfilled. To this end, symplectic geometry on $M$ is developped in this context, and an outline of the required tensor analysis and differential geometry is given. Certain questions for the possible mathematical interpretation of this structure are also discussed.Comment: 22 pages, LaTe

Stationary and Oscillatory Spatial Patterns Induced by Global Periodic Switching

We propose a new mechanism for pattern formation based on the global alternation of two dynamics neither of which exhibits patterns. When driven by either one of the separate dynamics, the system goes to a spatially homogeneous state associated with that dynamics. However, when the two dynamics are globally alternated sufficiently rapidly, the system exhibits stationary spatial patterns. Somewhat slower switching leads to oscillatory patterns. We support our findings by numerical simulations and discuss the results in terms of the symmetries of the system and the ratio of two relevant characteristic times, the switching period and the relaxation time to a homogeneous state in each separate dynamics.Comment: REVTEX preprint: 12 pages including 1 (B&W) + 3 (COLOR) figures (to appear in Physical Review Letters