Multilevel Monte Carlo in approximate Bayesian computation

In the following article, we consider approximate Bayesian computation (ABC) inference. We introduce a method for numerically approximating ABC posteriors using the multilevel Monte Carlo (MLMC). A sequential Monte Carlo version of the approach is developed and it is shown under some assumptions that for a given level of mean square error, this method for ABC has a lower cost than i.i.d. sampling from the most accurate ABC approximation. Several numerical examples are given.     

Design and Tuning of Photoswitches for Solar Energy Storage

Current energy demand makes it compulsory to explore alternative energy sources beyond fossil fuels. Molecular solar thermal (MOST) systems have been proposed as a suitable technology for the use and storage of solar energy. Compounds used for this application need to fulfil a long series of requirements, being the absorption of sunlight and the energy stored some of the most critical. In this paper, we study different families of well-known molecular photoswitches from the point of view of their potential use as MOST. Starting from basic structures, we use density functional theory (DFT) computational modelling to propose two different strategies to increase the energy difference between isomers and to tune the absorption spectrum. The inclusion of a mechanical lock in the structure, via an alkyl chain and the presence of a hydrogen bonding are shown to directly influence the energy difference and the absorption spectra. Results shown here prove that these two approaches could be relevant for the design of new compounds with improved performance for MOST applications.     

A novel analog fuzzy controller for intelligent sensors

A new analog fuzzy logic controller implemented in CMOS technology is described. The chosen membership function generator keeps the needed area for the inference engine very small while giving a big flexibility in the configuration of the membership function. The proposed solution for defuzzification gives an additional area reduction over earlier implementations. High speed, low power fuzzy controller hardware make the chip appropriate for intelligent sensor application. Simulation results as well as test measurements are presented and discussed to illustrate the properties and robustness of the proposed circuit.     

STM studies of cyclohexene hydrogenation/dehydrogenation and its poisoning by carbon monoxide on Pt(1 1 1)

A scanning tunneling microscope that can be operated in ultra high vacuum (<10⁻⁹ Torr) as well as at high pressures (1 − 10³ Torr) has been utilized to study the structures formed by cyclic C₆ hydrocarbons adsorbed on a platinum (1 1 1) crystal surface. Catalytic reactions of cyclohexene were also studied in the presence of hydrogen at pressures (up to 200 mTorr) and 300 K-350 K temperature range. Cyclohexane and cyclohexene produced the same adsorbed structure, which is attributed to the partially dehydrogenated π-allyl (C₆H₉). 1,3-Cyclohexadiene produced structures similar to those produced by benzene. In contrast 1,4-cyclohexadiene forms a structure that we attribute to intact molecular 1,4-cyclohexadiene. During reaction the STM images appear disordered, indicative of rapid diffusion of surface species. Addition of 5 mTorr of CO stops the catalytic activity and forms an ordered structure on the surface.     

A combinatorial perspective on the non-Radon partitions

Let E be a finite set of points in $\text{R}$^d. Then {A, E ? A} is a non-Radon partition of E iff there is a hyperplane H separating A strictly from E?A. Or equivalently iff ${}_{\mathrm{<mtext>A</mtext>}}\text{O}$ is an acyclic reorientation of (M_Aff(E), O), the oriented matroid canonically determined by E. If (M(E), O) is an oriented matroid without loops then the set $\text{NR(E, O) = {(A, E ? A):}{}_{\mathrm{<mtext>A</mtext>}}\text{O}\text{is acyclic}\text{}}$ determines (M(E), O). In particular the matroidal properties of a finite set of points in $\text{R}$^d are precisely the properties which can be formulated in non-Radon partitions terms. The Möbius function of the poset $\text{A = {A: A ? E,}{}_{\mathrm{<mtext>A</mtext>}}\text{O}\text{is acyclic}\text{}}$ and in a special case its homotopy type are computed. This paper generalizes recent results of P. Edelman (A partial order on the regions of $\text{R}$ⁿ dissected by hyperplanes     

Euler's relation,möbius functions and matroid identities

We give a short combinatorial proof of the Euler relation for convex polytopes in the context of oriented matroids. Using counting arguments we derive from the Euler relation several identities holding in the lattice of flats of an oriented matroid. These identities are proven for any matroid by Möbius inversion.