Fluid limit theorems for stochastic hybrid systems with application to neuron models

This paper establishes limit theorems for a class of stochastic hybrid systems (continuous deterministic dynamic coupled with jump Markov processes) in the fluid limit (small jumps at high frequency), thus extending known results for jump Markov processes. We prove a functional law of large numbers with exponential convergence speed, derive a diffusion approximation and establish a functional central limit theorem. We apply these results to neuron models with stochastic ion channels, as the number of channels goes to infinity, estimating the convergence to the deterministic model. In terms of neural coding, we apply our central limit theorems to estimate numerically impact of channel noise both on frequency and spike timing coding.Comment: 42 pages, 4 figure

Common perceptions of periodontal health and illness among adults : A qualitative study

Peer reviewe

MAMIQA: No-Reference Image Quality Assessment Based on Multiscale Attention Mechanism With Natural Scene Statistics

Peer reviewe

Safety and Efficacy of MLC601 in Iranian Patients after Stroke: A Double-Blind, Placebo-Controlled Clinical Trial

Objective. To investigate the safety and efficacy of MLC601 (NeuroAid) as a traditional Chinese medicine on motor recovery after ischemic stroke. Methods. This study was a double-blind, placebo-controlled clinical trial on 150 patients with a recent (less than 3 month) ischemic stroke. All patients were given either MLC601 (100 patients) or placebo (50 patients), 4 capsules 3 times a day, as an add-on to standard stroke treatment for 3 months. Results. Sex, age, elapsed time from stroke onset, and risk factors in the treatment group were not significantly different from placebo group at baseline (P > .05). Repeated measures analysis showed that Fugl-Meyer assessment was significantly higher in the treatment group during 12 weeks after stroke (P < .001). Good tolerability to treatment was shown, and adverse events were mild and transient. Conclusion. MLC601 showed better motor recovery than placebo and was safe on top of standard ischemic stroke medications especially in the severe and moderate cases

Dynamical aspects of mean field plane rotators and the Kuramoto model

The Kuramoto model has been introduced in order to describe synchronization phenomena observed in groups of cells, individuals, circuits, etc... We look at the Kuramoto model with white noise forces: in mathematical terms it is a set of N oscillators, each driven by an independent Brownian motion with a constant drift, that is each oscillator has its own frequency, which, in general, changes from one oscillator to another (these frequencies are usually taken to be random and they may be viewed as a quenched disorder). The interactions between oscillators are of long range type (mean field). We review some results on the Kuramoto model from a statistical mechanics standpoint: we give in particular necessary and sufficient conditions for reversibility and we point out a formal analogy, in the N to infinity limit, with local mean field models with conservative dynamics (an analogy that is exploited to identify in particular a Lyapunov functional in the reversible set-up). We then focus on the reversible Kuramoto model with sinusoidal interactions in the N to infinity limit and analyze the stability of the non-trivial stationary profiles arising when the interaction parameter K is larger than its critical value K_c. We provide an analysis of the linear operator describing the time evolution in a neighborhood of the synchronized profile: we exhibit a Hilbert space in which this operator has a self-adjoint extension and we establish, as our main result, a spectral gap inequality for every K>K_c.Comment: 18 pages, 1 figur

Genetic Dominant Variants in STUB1, Segregating in Families with SCA48, Display In Vitro Functional Impairments Indistinctive from Recessive Variants Associated with SCAR16.

Variants in STUB1 cause both autosomal recessive (SCAR16) and dominant (SCA48) spinocerebellar ataxia. Reports from 18 STUB1 variants causing SCA48 show that the clinical picture includes later-onset ataxia with a cerebellar cognitive affective syndrome and varying clinical overlap with SCAR16. However, little is known about the molecular properties of dominant STUB1 variants. Here, we describe three SCA48 families with novel, dominantly inherited STUB1 variants (p.Arg51_Ile53delinsProAla, p.Lys143_Trp147del, and p.Gly249Val). All the patients developed symptoms from 30 years of age or later, all had cerebellar atrophy, and 4 had cognitive/psychiatric phenotypes. Investigation of the structural and functional consequences of the recombinant C-terminus of HSC70-interacting protein (CHIP) variants was performed in vitro using ubiquitin ligase activity assay, circular dichroism assay and native polyacrylamide gel electrophoresis. These studies revealed that dominantly and recessively inherited STUB1 variants showed similar biochemical defects, including impaired ubiquitin ligase activity and altered oligomerization properties of the CHIP. Our findings expand the molecular understanding of SCA48 but also mean that assumptions concerning unaffected carriers of recessive STUB1 variants in SCAR16 families must be re-evaluated. More investigations are needed to verify the disease status of SCAR16 heterozygotes and elucidate the molecular relationship between SCA48 and SCAR16 diseases

Uncertainty Principle for Control of Ensembles of Oscillators Driven by Common Noise

We discuss control techniques for noisy self-sustained oscillators with a focus on reliability, stability of the response to noisy driving, and oscillation coherence understood in the sense of constancy of oscillation frequency. For any kind of linear feedback control--single and multiple delay feedback, linear frequency filter, etc.--the phase diffusion constant, quantifying coherence, and the Lyapunov exponent, quantifying reliability, can be efficiently controlled but their ratio remains constant. Thus, an "uncertainty principle" can be formulated: the loss of reliability occurs when coherence is enhanced and, vice versa, coherence is weakened when reliability is enhanced. Treatment of this principle for ensembles of oscillators synchronized by common noise or global coupling reveals a substantial difference between the cases of slightly non-identical oscillators and identical ones with intrinsic noise.Comment: 10 pages, 5 figure

Different references for valgus cut angle in Total Knee Arthroplasty

Background: The valgus cut angle (VCA) of the distal femur in Total Knee Arthroplasty (TKA) is measured preoperatively on three-joint alignment radiographs. The anatomical axis of the femur can be described as the anatomical axis of the full length of the femur or as the anatomical axis of the distal half of the femur, which may result in different angles in some cases. During TKA, the anatomical axis of the femur is determined by intramedullary femoral guides, which may follow the distal half or near full anatomical axis, based on the length of the femoral guide. The aim of this study was to compare using the anatomical axis of the full length of the femur versus the anatomical axis of the distal half of the femur for measuring VCA, in normal and varus aligned femurs. We hypothesized that the VCA would be different based upon these two definitions of the anatomical axis of the femur. Methods: Full-length weight bearing radiographs were used to determine three-joint alignment in normal aligned (Lateral Distal Femoral Angle; LDFA = 87° ± 2°) and varus aligned (LDFA > 89°) femurs. Full-length anatomical axismechanical axis angle (angle 1) and distal half anatomical axis-mechanical axis angle (angle 2) were measured in all subjects by two independent orthopedic surgeons using a DICOM viewer software (PACS). Angles 1 and 2 were compared in normal and varus aligned subjects to determine whether there was a significant difference. Results: Ninety-seven consecutive subjects with normally aligned femurs and 97 consecutive subjects with varus aligned femurs were included in this study. In normally aligned femurs, the mean value of angle 1 was 5.05° ± 0.76° and for angle 2 was 3.62° ± 1.19°, which were statistically different (P= 0.0001). In varus aligned femurs, the mean value of angle 1 was 5.42° ± 0.85° and for angle 2 was 4.23° ± 1.27°, which were also statistically different (P= 0.0047). Conclusion: The two different methods of outlining the anatomical axis of the femur lead to different results in both normal and varus-aligned femurs. This should be considered in determination of the valgus cut angle on preoperative radiographs and be adjusted according to the length of the intramedullary guide. © 2018 By The Archives of Bone and Joint Surgery

Asymptotic behaviour of neuron population models structured by elapsed-time

We study two population models describing the dynamics of interacting neurons, initially proposed by Pakdaman et al (2010 Nonlinearity 23 55–75) and Pakdaman et al (2014 J. Math. Neurosci. 4 1–26). In the first model, the structuring variable s represents the time elapsed since its last discharge, while in the second one neurons exhibit a fatigue property and the structuring variable is a generic 'state'. We prove existence of solutions and steady states in the space of finite, nonnegative measures. Furthermore, we show that solutions converge to the equilibrium exponentially in time in the case of weak nonlinearity (i.e. weak connectivity). The main innovation is the use of Doeblin's theorem from probability in order to show the existence of a spectral gap property in the linear (no-connectivity) setting. Relaxation to the steady state for the nonlinear models is then proved by a constructive perturbation argument.MTM2014-52056-P, MTM2017-85067-P, "la Caixa" Foundatio

The what and where of adding channel noise to the Hodgkin-Huxley equations

One of the most celebrated successes in computational biology is the Hodgkin-Huxley framework for modeling electrically active cells. This framework, expressed through a set of differential equations, synthesizes the impact of ionic currents on a cell's voltage -- and the highly nonlinear impact of that voltage back on the currents themselves -- into the rapid push and pull of the action potential. Latter studies confirmed that these cellular dynamics are orchestrated by individual ion channels, whose conformational changes regulate the conductance of each ionic current. Thus, kinetic equations familiar from physical chemistry are the natural setting for describing conductances; for small-to-moderate numbers of channels, these will predict fluctuations in conductances and stochasticity in the resulting action potentials. At first glance, the kinetic equations provide a far more complex (and higher-dimensional) description than the original Hodgkin-Huxley equations. This has prompted more than a decade of efforts to capture channel fluctuations with noise terms added to the Hodgkin-Huxley equations. Many of these approaches, while intuitively appealing, produce quantitative errors when compared to kinetic equations; others, as only very recently demonstrated, are both accurate and relatively simple. We review what works, what doesn't, and why, seeking to build a bridge to well-established results for the deterministic Hodgkin-Huxley equations. As such, we hope that this review will speed emerging studies of how channel noise modulates electrophysiological dynamics and function. We supply user-friendly Matlab simulation code of these stochastic versions of the Hodgkin-Huxley equations on the ModelDB website (accession number 138950) and http://www.amath.washington.edu/~etsb/tutorials.html.Comment: 14 pages, 3 figures, review articl