Error threshold in optimal coding, numerical criteria and classes of universalities for complexity

The free energy of the Random Energy Model at the transition point between ferromagnetic and spin glass phases is calculated. At this point, equivalent to the decoding error threshold in optimal codes, free energy has finite size corrections proportional to the square root of the number of degrees. The response of the magnetization to the ferromagnetic couplings is maximal at the values of magnetization equal to half. We give several criteria of complexity and define different universality classes. According to our classification, at the lowest class of complexity are random graph, Markov Models and Hidden Markov Models. At the next level is Sherrington-Kirkpatrick spin glass, connected with neuron-network models. On a higher level are critical theories, spin glass phase of Random Energy Model, percolation, self organized criticality (SOC). The top level class involves HOT design, error threshold in optimal coding, language, and, maybe, financial market. Alive systems are also related with the last class. A concept of anti-resonance is suggested for the complex systems.Comment: 17 page

Hamiltonian Monte Carlo Acceleration Using Surrogate Functions with Random Bases

For big data analysis, high computational cost for Bayesian methods often limits their applications in practice. In recent years, there have been many attempts to improve computational efficiency of Bayesian inference. Here we propose an efficient and scalable computational technique for a state-of-the-art Markov Chain Monte Carlo (MCMC) methods, namely, Hamiltonian Monte Carlo (HMC). The key idea is to explore and exploit the structure and regularity in parameter space for the underlying probabilistic model to construct an effective approximation of its geometric properties. To this end, we build a surrogate function to approximate the target distribution using properly chosen random bases and an efficient optimization process. The resulting method provides a flexible, scalable, and efficient sampling algorithm, which converges to the correct target distribution. We show that by choosing the basis functions and optimization process differently, our method can be related to other approaches for the construction of surrogate functions such as generalized additive models or Gaussian process models. Experiments based on simulated and real data show that our approach leads to substantially more efficient sampling algorithms compared to existing state-of-the art methods

Handover Management in Highly Dense Femtocellular Networks

For dense femtocells, intelligent integrated femtocell/macrocell network architecture, a neighbor cell list with a minimum number of femtocells, effective call admission control (CAC), and handover processes with proper signaling are the open research issues. An appropriate traffic model for the integrated femtocell/macrocell network is also not yet developed. In this paper, we present the major issue of mobility management for the integrated femtocell/macrocell network. We propose a novel algorithm to create a neighbor cell list with a minimum, but appropriate, number of cells for handover. We also propose detailed handover procedures and a novel traffic model for the integrated femtocell/macrocell network. The proposed CAC effectively handles various calls. The numerical and simulation results show the importance of the integrated femtocell/macrocell network and the performance improvement of the proposed schemes. Our proposed schemes for dense femtocells will be very effective for those in research and industry to implement

Sequential Bayesian inference for implicit hidden Markov models and current limitations

Hidden Markov models can describe time series arising in various fields of science, by treating the data as noisy measurements of an arbitrarily complex Markov process. Sequential Monte Carlo (SMC) methods have become standard tools to estimate the hidden Markov process given the observations and a fixed parameter value. We review some of the recent developments allowing the inclusion of parameter uncertainty as well as model uncertainty. The shortcomings of the currently available methodology are emphasised from an algorithmic complexity perspective. The statistical objects of interest for time series analysis are illustrated on a toy "Lotka-Volterra" model used in population ecology. Some open challenges are discussed regarding the scalability of the reviewed methodology to longer time series, higher-dimensional state spaces and more flexible models.Comment: Review article written for ESAIM: proceedings and surveys. 25 pages, 10 figure