Statistical Physics Analysis of Maximum a Posteriori Estimation for Multi-channel Hidden Markov Models

The performance of Maximum a posteriori (MAP) estimation is studied analytically for binary symmetric multi-channel Hidden Markov processes. We reduce the estimation problem to a 1D Ising spin model and define order parameters that correspond to different characteristics of the MAP-estimated sequence. The solution to the MAP estimation problem has different operational regimes separated by first order phase transitions. The transition points for $L$-channel system with identical noise levels, are uniquely determined by $L$ being odd or even, irrespective of the actual number of channels. We demonstrate that for lower noise intensities, the number of solutions is uniquely determined for odd $L$, whereas for even $L$ there are exponentially many solutions. We also develop a semi analytical approach to calculate the estimation error without resorting to brute force simulations. Finally, we examine the tradeoff between a system with single low-noise channel and one with multiple noisy channels.Comment: The paper has been submitted to Journal of Statistical Physics with submission number JOSS-S-12-0039

Flat Thomas-Fermi artificial atoms

We consider two-dimensional (2D) "artificial atoms" confined by an axially symmetric potential $V(\rho)$. Such configurations arise in circular quantum dots and other systems effectively restricted to a 2D layer. Using the semiclassical method, we present the first fully self-consistent and analytic solution yielding equations describing the density distribution, energy, and other quantities for any form of $V(\rho)$ and an arbitrary number of confined particles. An essential and nontrivial aspect of the problem is that the 2D density of states must be properly combined with 3D electrostatics. The solution turns out to have a universal form, with scaling parameters $\rho^2/R^2$ and $R/a_B^*$ ($R$ is the dot radius and $a_B^*$ is the effective Bohr radius)

Perspective: Size selected clusters for catalysis and electrochemistry

Size-selected clusters containing a handful of atoms may possess noble catalytic properties different from nano-sized or bulk catalysts. Size- and composition-selected clusters can also serve as models of the catalytic active site, where an addition or removal of a single atom can have a dramatic effect on their activity and selectivity. In this perspective, we provide an overview of studies performed under both ultra-high vacuum and realistic reaction conditions aimed at the interrogation, characterization, and understanding of the performance of supported size-selected clusters in heterogeneous and electrochemical reactions, which address the effects of cluster size, cluster composition, cluster–support interactions, and reaction conditions, the key parameters for the understanding and control of catalyst functionality. Computational modeling based on density functional theory sampling of local minima and energy barriers or ab initio molecular dynamics simulations is an integral part of this research by providing fundamental understanding of the catalytic processes at the atomic level, as well as by predicting new materials compositions which can be validated in experiments. Finally, we discuss approaches which aim at the scale up of the production of well-defined clusters for use in real world applications

A comparative property investigation of lithium phosphate glass melted in microwave and conventional heating

The present study addresses the application of microwave (MW) energy for melting lithium phosphate glass. A comparative analysis of the properties is presented with glasses melted in conventional resistance heating adopting standard methods of characterization. The density of the glass was found less in MW heating. The glass transition temperature was recorded as 3–10◦C lower in MW prepared glass than in conventional glass. Micro-hardness is found to be improved in case of MW heating. Maximum forward power was recorded less than 2 kW with an average power ∼1kW during melting of 40g glass in MW furnace. MW forward and reflected power measured during melting in the MW cavity was elaborated. Total melting time was within 2h 30 min in MW heating, whereas it was 6–7 h in resistive heating. Total power consumed was ∼5kWh in MW heating and ∼14kWh in resistance heating

Nanoassemblies of ultrasmall clusters with remarkable activity in carbon dioxide conversion into C1 fuels

Cu nanoassemblies formed transiently during reaction from size-selected subnanometer Cu4 clusters supported on amorphous OH-terminated alumina convert CO2 into methanol and hydrocarbons under near-atmospheric pressure at rates considerably higher than those of individually standing Cu4 clusters. An in situ characterization reveals that the clusters self-assemble into 2D nanoassemblies at higher temperatures which then disintegrate upon cooling down to room temperature. DFT calculations postulate a formation mechanism of these nanoassemblies by hydrogen-bond bridges between the clusters and H2O molecules, which keep the building blocks together while preventing their coalescence