Wild oscillations in a nonlinear neuron model with resets: (II) Mixed-mode oscillations

This work continues the analysis of complex dynamics in a class of bidimensional nonlinear hybrid dynamical systems with resets modeling neuronal voltage dynamics with adaptation and spike emission. We show that these models can generically display a form of mixed-mode oscillations (MMOs), which are trajectories featuring an alternation of small oscillations with spikes or bursts (multiple consecutive spikes). The mechanism by which these are generated relies fundamentally on the hybrid structure of the flow: invariant manifolds of the continuous dynamics govern small oscillations, while discrete resets govern the emission of spikes or bursts, contrasting with classical MMO mechanisms in ordinary differential equations involving more than three dimensions and generally relying on a timescale separation. The decomposition of mechanisms reveals the geometrical origin of MMOs, allowing a relatively simple classification of points on the reset manifold associated to specific numbers of small oscillations. We show that the MMO pattern can be described through the study of orbits of a discrete adaptation map, which is singular as it features discrete discontinuities with unbounded left- and right-derivatives. We study orbits of the map via rotation theory for discontinuous circle maps and elucidate in detail complex behaviors arising in the case where MMOs display at most one small oscillation between each consecutive pair of spikes

Small ensemble of kriging models for optimization

The Efficient Global Optimization (EGO) algorithm uses a conditional Gaus-sian Process (GP) to approximate an objective function known at a finite number of observation points and sequentially adds new points which maximize the Expected Improvement criterion according to the GP. The important factor that controls the efficiency of EGO is the GP covariance function (or kernel) which should be chosen according to the objective function. Traditionally, a pa-rameterized family of covariance functions is considered whose parameters are learned through statistical procedures such as maximum likelihood or cross-validation. However, it may be questioned whether statistical procedures for learning covariance functions are the most efficient for optimization as they target a global agreement between the GP and the observations which is not the ultimate goal of optimization. Furthermore, statistical learning procedures are computationally expensive. The main alternative to the statistical learning of the GP is self-adaptation, where the algorithm tunes the kernel parameters based on their contribution to objective function improvement. After questioning the possibility of self-adaptation for kriging based optimizers, this paper proposes a novel approach for tuning the length-scale of the GP in EGO: At each iteration, a small ensemble of kriging models structured by their length-scales is created. All of the models contribute to an iterate in an EGO-like fashion. Then, the set of models is densified around the model whose length-scale yielded the best iterate and further points are produced. Numerical experiments are provided which motivate the use of many length-scales. The tested implementation does not perform better than the classical EGO algorithm in a sequential context but show the potential of the approach for parallel implementations

On the simulation of nonlinear bidimensional spiking neuron models

Bidimensional spiking models currently gather a lot of attention for their simplicity and their ability to reproduce various spiking patterns of cortical neurons, and are particularly used for large network simulations. These models describe the dynamics of the membrane potential by a nonlinear differential equation that blows up in finite time, coupled to a second equation for adaptation. Spikes are emitted when the membrane potential blows up or reaches a cutoff value. The precise simulation of the spike times and of the adaptation variable is critical for it governs the spike pattern produced, and is hard to compute accurately because of the exploding nature of the system at the spike times. We thoroughly study the precision of fixed time-step integration schemes for this type of models and demonstrate that these methods produce systematic errors that are unbounded, as the cutoff value is increased, in the evaluation of the two crucial quantities: the spike time and the value of the adaptation variable at this time. Precise evaluation of these quantities therefore involve very small time steps and long simulation times. In order to achieve a fixed absolute precision in a reasonable computational time, we propose here a new algorithm to simulate these systems based on a variable integration step method that either integrates the original ordinary differential equation or the equation of the orbits in the phase plane, and compare this algorithm with fixed time-step Euler scheme and other more accurate simulation algorithms

A Markovian event-based framework for stochastic spiking neural networks

In spiking neural networks, the information is conveyed by the spike times, that depend on the intrinsic dynamics of each neuron, the input they receive and on the connections between neurons. In this article we study the Markovian nature of the sequence of spike times in stochastic neural networks, and in particular the ability to deduce from a spike train the next spike time, and therefore produce a description of the network activity only based on the spike times regardless of the membrane potential process. To study this question in a rigorous manner, we introduce and study an event-based description of networks of noisy integrate-and-fire neurons, i.e. that is based on the computation of the spike times. We show that the firing times of the neurons in the networks constitute a Markov chain, whose transition probability is related to the probability distribution of the interspike interval of the neurons in the network. In the cases where the Markovian model can be developed, the transition probability is explicitly derived in such classical cases of neural networks as the linear integrate-and-fire neuron models with excitatory and inhibitory interactions, for different types of synapses, possibly featuring noisy synaptic integration, transmission delays and absolute and relative refractory period. This covers most of the cases that have been investigated in the event-based description of spiking deterministic neural networks

Runaway dilaton and equivalence principle violations

In a recently proposed scenario, where the dilaton decouples while cosmologically attracted towards infinite bare string coupling, its residual interactions can be related to the amplitude of density fluctuations generated during inflation, and are large enough to be detectable through a modest improvement on present tests of free-fall universality. Provided it has significant couplings to either dark matter or dark energy, a runaway dilaton can also induce time-variations of the natural "constants" within the reach of near-future experiments.Comment: 4 pages, minor change

On the equivalence principle and gravitational and inertial mass relation of classical charged particles

We show that the locally constant force necessary to get a stable hyperbolic motion regime for classical charged point particles, actually, is a combination of an applied external force and of the electromagnetic radiation reaction force. It implies, as the strong Equivalence Principle is valid, that the passive gravitational mass of a charged point particle should be slight greater than its inertial mass. An interesting new feature that emerges from the unexpected behavior of the gravitational and inertial mass relation, for classical charged particles, at very strong gravitational field, is the existence of a critical, particle dependent, gravitational field value that signs the validity domain of the strong Equivalence Principle. For electron and proton, these critical field values are $g_{c}\simeq 4.8\times 10^{31}m/s^{2}$ and $g_{c}\simeq 8.8\times 10^{34}m/s^{2}$, respectively

Quantum fluctuations for drag free geodesic motion

The drag free technique is used to force a proof mass to follow a geodesic motion. The mass is protected from perturbations by a cage, and the motion of the latter is actively controlled to follow the motion of the proof mass. We present a theoretical analysis of the effects of quantum fluctuations for this technique. We show that a perfect drag free operation is in principle possible at the quantum level, in spite of the back action exerted on the mass by the position sensor.Comment: 4 pages, 1 figure, RevTeX, minor change

Comparative evaluation by semiquantitative reverse transcriptase polymerase chain reaction of MDR1, MRP and GSTp gene expression in breast carcinomas.

Identification and quantitative evaluation of drug resistance markers are essential to assess the impact of multidrug resistance (MDR) in clinical oncology. The MDR1 gene confers pleiotropic drug resistance in tumour cells, but other molecular mechanisms are also involved in drug resistance. In particular, the clinical pattern of expression of the other MDR-related genes is unclear and their interrelationships are still unknown. Here, we report standardization of the procedures used to determine a reliable method of semiquantitative reverse transcriptase polymerase chain reaction (RT-PCR) using a standard series of drug-sensitive and increasingly resistant cell lines to evaluate the expression of three MDR-related genes, i.e. MDR1 (multidrug resistance gene 1), MRP (multidrug resistance related protein) and GSTp (glutathione-S-transferase p), reported to be endogenous standard genes for normalization of mRNAs. A total of 74 breast cancer surgical biopsies, obtained before any treatment, were evaluated by this method. When compared with classical clinical and laboratory findings, GSTp mRNA level was higher in diploid tumours. However, the main finding of our study suggests a clear relationship between two of these MDR-related gene expressions, namely GSTp and MRP. This finding provides new insight into human breast tumours, which may possibly be linked to the glutathione conjugate carrier function of MRP. Well defined semiquantitative RT-PCR procedures can therefore constitute a powerful tool to investigate MDR phenotype at mRNA levels of different related genes in small and precious tumour biopsy specimens

One-Year Risk of Stroke after Transient Ischemic Attack or Minor Stroke

BACKGROUND Previous studies conducted between 1997 and 2003 estimated that the risk of stroke or an acute coronary syndrome was 12 to 20% during the first 3 months after a transient ischemic attack (TIA) or minor stroke. The TIAregistry.org project was designed to describe the contemporary profile, etiologic factors, and outcomes in patients with a TIA or minor ischemic stroke who receive care in health systems that now offer urgent evaluation by stroke specialists. METHODS We recruited patients who had had a TIA or minor stroke within the previous 7 days. Sites were selected if they had systems dedicated to urgent evaluation of patients with TIA. We estimated the 1-year risk of stroke and of the composite outcome of stroke, an acute coronary syndrome, or death from cardiovascular causes. We also examined the association of the ABCD2 score for the risk of stroke (range, 0 [lowest risk] to 7 [highest risk]), findings on brain imaging, and cause of TIA or minor stroke with the risk of recurrent stroke over a period of 1 year. RESULTS From 2009 through 2011, we enrolled 4789 patients at 61 sites in 21 countries. A total of 78.4% of the patients were evaluated by stroke specialists within 24 hours after symptom onset. A total of 33.4% of the patients had an acute brain infarction, 23.2% had at least one extracranial or intracranial stenosis of 50% or more, and 10.4% had atrial fibrillation. The Kaplan–Meier estimate of the 1-year event rate of the composite cardiovascular outcome was 6.2% (95% confidence interval, 5.5 to 7.0). Kaplan–Meier estimates of the stroke rate at days 2, 7, 30, 90, and 365 were 1.5%, 2.1%, 2.8%, 3.7%, and 5.1%, respectively. In multivariable analyses, multiple infarctions on brain imaging, large-artery atherosclerosis, and an ABCD2 score of 6 or 7 were each associated with more than a doubling of the risk of stroke. CONCLUSIONS We observed a lower risk of cardiovascular events after TIA than previously reported. The ABCD2 score, findings on brain imaging, and status with respect to large-artery atherosclerosis helped stratify the risk of recurrent stroke within 1 year after a TIA or minor stroke. (Funded by Sanofi and Bristol-Myers Squibb.)Supported by an unrestricted grant from Sanofi and Bristol-Myers Squibb