Convergence to a L\'evy process in the Skorohod M1M_1 and M2M_2 topologies for nonuniformly hyperbolic systems, including billiards with cusps

We prove convergence to a Levy process for a class of dispersing billiards with cusps. For such examples, convergence to a stable law was proved by Jung & Zhang. For the corresponding functional limit law, convergence is not possible in the usual Skorohod J_1 topology. Our main results yield elementary geometric conditions for convergence (i) in M_1, (ii) in M_2 but not M_1. In general, we show for a large class of nonuniformly hyperbolic systems how to deduce functional limit laws once convergence to the corresponding stable law is known.Comment: accepted versio

Particle interactions with single or multiple 3D solar reconnecting current sheets

The acceleration of charged particles (electrons and protons) in flaring solar active regions is analyzed by numerical experiments. The acceleration is modelled as a stochastic process taking place by the interaction of the particles with local magnetic reconnection sites via multiple steps. Two types of local reconnecting topologies are studied: the Harris-type and the X-point. A formula for the maximum kinetic energy gain in a Harris-type current sheet, found in a previous work of ours, fits well the numerical data for a single step of the process. A generalization is then given approximating the kinetic energy gain through an X-point. In the case of the multiple step process, in both topologies the particles' kinetic energy distribution is found to acquire a practically invariant form after a small number of steps. This tendency is interpreted theoretically. Other characteristics of the acceleration process are given, such as the mean acceleration time and the pitch angle distributions of the particles.Comment: 18 pages, 9 figures, Solar Physics, in pres

Inter-arrival times of message propagation on directed networks

One of the challenges in fighting cybercrime is to understand the dynamics of message propagation on botnets, networks of infected computers used to send viruses, unsolicited commercial emails (SPAM) or denial of service attacks. We map this problem to the propagation of multiple random walkers on directed networks and we evaluate the inter-arrival time distribution between successive walkers arriving at a target. We show that the temporal organization of this process, which models information propagation on unstructured peer to peer networks, has the same features as SPAM arriving to a single user. We study the behavior of the message inter-arrival time distribution on three different network topologies using two different rules for sending messages. In all networks the propagation is not a pure Poisson process. It shows universal features on Poissonian networks and a more complex behavior on scale free networks. Results open the possibility to indirectly learn about the process of sending messages on networks with unknown topologies, by studying inter-arrival times at any node of the network.Comment: 9 pages, 12 figure

Self-organization of structures and networks from merging and small-scale fluctuations

We discuss merging-and-creation as a self-organizing process for scale-free topologies in networks. Three power-law classes characterized by the power-law exponents 3/2, 2 and 5/2 are identified and the process is generalized to networks. In the network context the merging can be viewed as a consequence of optimization related to more efficient signaling.Comment: Physica A: Statistical Mechanics and its Applications, In Pres

Programmable parametric filter with noise generator and data acquisition

Audio filtering systems are used in commercial applications involving equalizers. However, some of the topologies used can be modified to be used in audio signal treatment applications. Parametric filter topologies allow the user to modify independently the central frequency of the filter, the bandwidth and the gain. Using a microprocessor and programmable components will allow the user to modify the parameters of the filter and to acquire the filtered signal so it can be processed in other stages. To improve the functionality of the system, a server will be implemented to process the data sent by the user, will be sent afterwards to the microcontroller. Finally, the results obtained will be thrown back to the user.Postprint (published version

Bayesian Structural Inference for Hidden Processes

We introduce a Bayesian approach to discovering patterns in structurally complex processes. The proposed method of Bayesian Structural Inference (BSI) relies on a set of candidate unifilar HMM (uHMM) topologies for inference of process structure from a data series. We employ a recently developed exact enumeration of topological epsilon-machines. (A sequel then removes the topological restriction.) This subset of the uHMM topologies has the added benefit that inferred models are guaranteed to be epsilon-machines, irrespective of estimated transition probabilities. Properties of epsilon-machines and uHMMs allow for the derivation of analytic expressions for estimating transition probabilities, inferring start states, and comparing the posterior probability of candidate model topologies, despite process internal structure being only indirectly present in data. We demonstrate BSI's effectiveness in estimating a process's randomness, as reflected by the Shannon entropy rate, and its structure, as quantified by the statistical complexity. We also compare using the posterior distribution over candidate models and the single, maximum a posteriori model for point estimation and show that the former more accurately reflects uncertainty in estimated values. We apply BSI to in-class examples of finite- and infinite-order Markov processes, as well to an out-of-class, infinite-state hidden process.Comment: 20 pages, 11 figures, 1 table; supplementary materials, 15 pages, 11 figures, 6 tables; http://csc.ucdavis.edu/~cmg/compmech/pubs/bsihp.ht