Recent results of the searches for Supersymmetry in final states with one or two leptons at CMS are presented. Many Supersymmetry scenarios, including the Constrained Minimal Supersymmetric extension of the Standard Model (CMSSM), predict a substantial amount of events containing leptons, while the largest fraction of Standard Model background events -which are QCD interactions -gets strongly reduced by requiring isolated leptons. The analyzed data was taken in 2011 and corresponds to an integrated luminosity of approximately L = 1 fb −1 . The center-of-mass energy of the pp collisions was √ s = 7 TeV.

A dynamical equation is derived for the spike emission rate nu(t) of a homogeneous network of integrate-and-fire (IF) neurons in a mean-field theoretical framework, where the activity of the single cell depends both on the mean afferent current (the "field") and on its fluctuations. Finite-size effects are taken into account, by a stochastic extension of the dynamical equation for the nu; their effect on the collective activity is studied in detail. Conditions for the local stability of the collective activity are shown to be naturally and simply expressed in terms of (the slope of) the single neuron, static, current-to-rate transfer function. In the framework of the local analysis, we studied the spectral properties of the time-dependent collective activity of the finite network in an asynchronous state; finite-size fluctuations act as an ongoing self-stimulation, which probes the spectral structure of the system on a wide frequency range. The power spectrum of nu exhibits modes ranging from very high frequency (depending on spike transmission delays), which are responsible for instability, to oscillations at a few Hz, direct expression of the diffusion process describing the population dynamics. The latter "diffusion" slow modes do not contribute to the stability conditions. Their characteristic times govern the transient response of the network; these reaction times also exhibit a simple dependence on the slope of the neuron transfer function. We speculate on the possible relevance of our results for the change in the characteristic response time of a neural population during the learning process which shapes the synaptic couplings, thereby affecting the slope of the transfer function. There is remarkable agreement of the theoretical predictions with simulations of a network of IF neurons with a constant leakage term for the membrane potential.

The balance between excitation and inhibition is critical in the physiology of the cerebral cortex. To understand the influence of inhibitory control on the emergent activity of the cortical network, inhibition was progressively blocked in a slice preparation that generates spontaneous rhythmic up states at a similar frequency to those occurring in vivo during slow-wave sleep or anesthesia. Progressive removal of inhibition induced a parametric shortening of up state duration and elongation of the down states, the frequency of oscillations decaying. Concurrently, a gradual increase in the network firing rate during up states occurred. The slope of transitions between up and down states was quantified for different levels of inhibition. The slope of upward transitions reflects the recruitment of the local network and was progressively increased when inhibition was decreased, whereas the speed of activity propagation became faster. Removal of inhibition eventually resulted in epileptiform activity. Whereas gradual reduction of inhibition induced linear changes in up/down states and their propagation, epileptiform activity was the result of a nonlinear transformation. A computational network model showed that strong recurrence plus activity-dependent hyperpolarizing currents were sufficient to account for the observed up state modulations and predicted an increase in activity-dependent hyperpolarization following up states when inhibition was decreased, which was confirmed experimentally.

We analyze in detail the statistical properties of the spike emission process of a canonical integrate-and-fire neuron, with a linear integrator and a lower bound for the depolarization, as often used in VLSI implementations (Mead, 1989). The spike statistics of such neurons appear to be qualitatively similar to conventional (exponential) integrate-and-fire neurons, which exhibit a wide variety of characteristics observed in cortical recordings. We also show that, contrary to current opinion, the dynamics of a network composed of such neurons has two stable fixed points, even in the purely excitatory network, corresponding to two different states of reverberating activity. The analytical results are compared with numerical simulations and are found to be in good agreement.

Slow oscillations have been suggested as the default emergent activity of the cortical network. This is a low complexity state that integrates neuronal, synaptic, and connectivity properties of the cortex. Shaped by variations of physiological parameters, slow oscillations provide information about the underlying healthy or pathological network. We review how this default activity is shaped, how it acts as a powerful attractor, and how getting out of it is necessary for the brain to recover the levels of complexity associated with conscious states. We propose that slow oscillations provide a robust unifying paradigm for the study of cortical function.