Growing Critical: Self-Organized Criticality in a Developing Neural System

Experiments in various neural systems found avalanches: bursts of activity with characteristics typical for critical dynamics. A possible explanation for their occurrence is an underlying network that self-organizes into a critical state. We propose a simple spiking model for developing neural networks, showing how these may "grow into" criticality. Avalanches generated by our model correspond to clusters of widely applied Hawkes processes. We analytically derive the cluster size and duration distributions and find that they agree with those of experimentally observed neuronal avalanches.Comment: 6 pages, 4 figures, supplemental material: 10 pages, 7 figure

Predictability of extreme events in a branching diffusion model

We propose a framework for studying predictability of extreme events in complex systems. Major conceptual elements -- hierarchical structure, spatial dynamics, and external driving -- are combined in a classical branching diffusion with immigration. New elements -- observation space and observed events -- are introduced in order to formulate a prediction problem patterned after the geophysical and environmental applications. The problem consists of estimating the likelihood of occurrence of an extreme event given the observations of smaller events while the complete internal dynamics of the system is unknown. We look for premonitory patterns that emerge as an extreme event approaches; those patterns are deviations from the long-term system's averages. We have found a single control parameter that governs multiple spatio-temporal premonitory patterns. For that purpose, we derive i) complete analytic description of time- and space-dependent size distribution of particles generated by a single immigrant; ii) the steady-state moments that correspond to multiple immigrants; and iii) size- and space-based asymptotic for the particle size distribution. Our results suggest a mechanism for universal premonitory patterns and provide a natural framework for their theoretical and empirical study

Prospects of New Physics searches using High Lumi - LHC

After the observation of a Higgs boson near 125 GeV, the high energy physics community is investigating possible next steps for entering into a new era in particle physics. It is planned that the Large Hadron Collider will deliver an integrated luminosity of up to 3000/fb for the CMS and ATLAS experiments, requiring several upgrades for all detectors. The reach of various representative searches for supersymmetry and exotica physics with the upgraded detectors are discussed in this context, where a very high instantaneous luminosity will lead to a large number of pileup events in each bunch crossing. This note presents example benchmark studies for new physics prospects with the upgraded ATLAS and CMS detectors at a centre-of-mass energy of 14 TeV. Results are shown for an integrated luminosity of 300/fb and 3000/fb.Comment: Plenary talk presented at Next Steps in the Energy Frontier - Hadron Colliders Workshop, August 2014 - Fermi National Lab (FNAL). On behalf of the ATLAS and CMS Collaboration

Search for rare and exotic Higgs Boson decay modes

The latest results in the search for rare and exotic Higgs boson decays in proton-proton collision events collected with the CMS detector at the LHC are presented. The searches are performed for several decay modes of Higgs boson including $\mathrm{H}\rightarrow{\rm X (X \rightarrow2\ell)\gamma}$ ($X= {\rm Z}, \gamma^*$ and $\ell={\rm e},\mu$), $\mathrm{H}\rightarrow{ \mu\mu / {\rm e}{\rm e}}$, invisible decays, lepton flavour violating decays and Higgs decay to light scalars or pseudo-scalars. No hint for new physics has been found from the analyzed results with the full LHC run-1 data collected during 2011 and 2012 at $\sqrt{s}=7-8$ TeV and with the run-2 data at $\sqrt{s}=13$ TeV collected during 2015 and 2016. Limits are set for all the searches which have been performed by CMS.Comment: Presented at ICNFP2017 6th International Conference on new Frontiers in Physics 201

Lower large deviations for supercritical branching processes in random environment

Branching Processes in Random Environment (BPREs) $(Z\_n:n\geq0)$ are the generalization of Galton-Watson processes where in each generation the reproduction law is picked randomly in an i.i.d. manner. In the supercritical regime, the process survives with a positive probability and grows exponentially on the non-extinction event. We focus on rare events when the process takes positive values but lower than expected. More precisely, we are interested in the lower large deviations of $Z$, which means the asymptotic behavior of the probability $\{1 \leq Z\_n \leq \exp(n\theta)\}$ as $n\rightarrow \infty$. We provide an expression of the rate of decrease of this probability, under some moment assumptions, which yields the rate function. This result generalizes the lower large deviation theorem of Bansaye and Berestycki (2009) by considering processes where \P(Z\_1=0 \vert Z\_0=1)\textgreater{}0 and also much weaker moment assumptions.Comment: A mistake in the previous version has been corrected in the expression of the speed of decrease $P(Z\_n=1)$ in the case without extinctio

Bounds on the Speed and on Regeneration Times for Certain Processes on Regular Trees

We develop a technique that provides a lower bound on the speed of transient random walk in a random environment on regular trees. A refinement of this technique yields upper bounds on the first regeneration level and regeneration time. In particular, a lower and upper bound on the covariance in the annealed invariance principle follows. We emphasize the fact that our methods are general and also apply in the case of once-reinforced random walk. Durrett, Kesten and Limic (2002) prove an upper bound of the form $b/(b+\delta)$ for the speed on the $b$-ary tree, where $\delta$ is the reinforcement parameter. For $\delta>1$ we provide a lower bound of the form $\gamma^2 b/(b+\delta)$, where $\gamma$ is the survival probability of an associated branching process.Comment: 21 page