A kernel least mean square algorithm for fuzzy differential equations and its application in earth's energy balance model and climate

Abstract This paper concentrates on solving fuzzy dynamical differential equations (FDDEs) by use of unsupervised kernel least mean square (UKLMS). UKLMS is a nonlinear adaptive filter which works by applying kernel trick to LMS adaptive filter. UKLMS estimates multivariate function which is embedded to estimate the solution of FDDE. Adaptation mechanism of UKLMS helps for finding solution of FDDE in a recursive scenario. Without any desired response, UKLMS finds nonlinear functions. For this purpose, an approximate solution of FDDE is constructed based on adaptable parameters of UKLMS. An optimization algorithm, optimizes the values of adaptable parameters of UKLMS. The proposed algorithm is applied for solving Earth energy balance model (EBM) which is considered as a fuzzy differential equation for the first time. The method in comparison with the other existing approaches (such as numerical methods) has some advantages such as more accurate solution and also that the obtained solution has a functional form, thus the solution can be obtained at each time in training interval. Low error and applicability of developed algorithm are examined by applying it for solving several problems. After comparing the numerical results, with relative previous works, the superiority of the proposed method will be illustrated

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

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

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

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

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

Simple, Fast and Accurate Implementation of the Diffusion Approximation Algorithm for Stochastic Ion Channels with Multiple States

The phenomena that emerge from the interaction of the stochastic opening and closing of ion channels (channel noise) with the non-linear neural dynamics are essential to our understanding of the operation of the nervous system. The effects that channel noise can have on neural dynamics are generally studied using numerical simulations of stochastic models. Algorithms based on discrete Markov Chains (MC) seem to be the most reliable and trustworthy, but even optimized algorithms come with a non-negligible computational cost. Diffusion Approximation (DA) methods use Stochastic Differential Equations (SDE) to approximate the behavior of a number of MCs, considerably speeding up simulation times. However, model comparisons have suggested that DA methods did not lead to the same results as in MC modeling in terms of channel noise statistics and effects on excitability. Recently, it was shown that the difference arose because MCs were modeled with coupled activation subunits, while the DA was modeled using uncoupled activation subunits. Implementations of DA with coupled subunits, in the context of a specific kinetic scheme, yielded similar results to MC. However, it remained unclear how to generalize these implementations to different kinetic schemes, or whether they were faster than MC algorithms. Additionally, a steady state approximation was used for the stochastic terms, which, as we show here, can introduce significant inaccuracies. We derived the SDE explicitly for any given ion channel kinetic scheme. The resulting generic equations were surprisingly simple and interpretable - allowing an easy and efficient DA implementation. The algorithm was tested in a voltage clamp simulation and in two different current clamp simulations, yielding the same results as MC modeling. Also, the simulation efficiency of this DA method demonstrated considerable superiority over MC methods.Comment: 32 text pages, 10 figures, 1 supplementary text + figur

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

Monitoring lactoferrin iron levels by fluorescence resonance energy transfer: A combined chemical and computational study

Three forms of lactoferrin (Lf) that differed in their levels of iron loading (Lf, LfFe, and LfFe2) were simultaneously labeled with the fluorophores AF350 and AF430. All three resulting fluorescent lactoferrins exhibited fluorescence resonance energy transfer (FRET), but they all presented different FRET patterns. Whereas only partial FRET was observed for Lf and LfFe, practically complete FRET was seen for the holo form (LfFe2). For each form of metal-loaded lactoferrin, the AF350–AF430 distance varied depending on the protein conformation, which in turn depended on the level of iron loading. Thus, the FRET patterns of these lactoferrins were found to correlate with their iron loading levels. In order to gain greater insight into the number of fluorophores and the different FRET patterns observed (i.e., their iron levels), a computational analysis was performed. The results highlighted a number of lysines that have the greatest influence on the FRET profile. Moreover, despite the lack of an X-ray structure for any LfFe species, our study also showed that this species presents modified subdomain organization of the N-lobe, which narrows its iron-binding site. Complete domain rearrangement occurs during the LfFe to LfFe2 transition. Finally, as an example of the possible applications of the results of this study, we made use of the FRET fingerprints of these fluorescent lactoferrins to monitor the interaction of lactoferrin with a healthy bacterium, namely Bifidobacterium breve. This latter study demonstrated that lactoferrin supplies iron to this bacterium, and suggested that this process occurs with no protein internalization.This work was supported by MINECO and FEDER (projects CTQ2012-32236, CTQ2011-23336, and BIO2012-39682-C02-02) and BIOSEARCH SA. F.C. and V.M.R. are grateful to the Spanish MINECO for FPI fellowships

History-Dependent Excitability as a Single-Cell Substrate of Transient Memory for Information Discrimination

Neurons react differently to incoming stimuli depending upon their previous history of stimulation. This property can be considered as a single-cell substrate for transient memory, or context-dependent information processing: depending upon the current context that the neuron “sees” through the subset of the network impinging on it in the immediate past, the same synaptic event can evoke a postsynaptic spike or just a subthreshold depolarization. We propose a formal definition of History-Dependent Excitability (HDE) as a measure of the propensity to firing in any moment in time, linking the subthreshold history-dependent dynamics with spike generation. This definition allows the quantitative assessment of the intrinsic memory for different single-neuron dynamics and input statistics. We illustrate the concept of HDE by considering two general dynamical mechanisms: the passive behavior of an Integrate and Fire (IF) neuron, and the inductive behavior of a Generalized Integrate and Fire (GIF) neuron with subthreshold damped oscillations. This framework allows us to characterize the sensitivity of different model neurons to the detailed temporal structure of incoming stimuli. While a neuron with intrinsic oscillations discriminates equally well between input trains with the same or different frequency, a passive neuron discriminates better between inputs with different frequencies. This suggests that passive neurons are better suited to rate-based computation, while neurons with subthreshold oscillations are advantageous in a temporal coding scheme. We also address the influence of intrinsic properties in single-cell processing as a function of input statistics, and show that intrinsic oscillations enhance discrimination sensitivity at high input rates. Finally, we discuss how the recognition of these cell-specific discrimination properties might further our understanding of neuronal network computations and their relationships to the distribution and functional connectivity of different neuronal types