Effective Sample Size for Importance Sampling based on discrepancy measures

The Effective Sample Size (ESS) is an important measure of efficiency of Monte Carlo methods such as Markov Chain Monte Carlo (MCMC) and Importance Sampling (IS) techniques. In the IS context, an approximation $\widehat{ESS}$ of the theoretical ESS definition is widely applied, involving the inverse of the sum of the squares of the normalized importance weights. This formula, $\widehat{ESS}$, has become an essential piece within Sequential Monte Carlo (SMC) methods, to assess the convenience of a resampling step. From another perspective, the expression $\widehat{ESS}$ is related to the Euclidean distance between the probability mass described by the normalized weights and the discrete uniform probability mass function (pmf). In this work, we derive other possible ESS functions based on different discrepancy measures between these two pmfs. Several examples are provided involving, for instance, the geometric mean of the weights, the discrete entropy (including theperplexity measure, already proposed in literature) and the Gini coefficient among others. We list five theoretical requirements which a generic ESS function should satisfy, allowing us to classify different ESS measures. We also compare the most promising ones by means of numerical simulations

Group Importance Sampling for Particle Filtering and MCMC

Bayesian methods and their implementations by means of sophisticated Monte Carlo techniques have become very popular in signal processing over the last years. Importance Sampling (IS) is a well-known Monte Carlo technique that approximates integrals involving a posterior distribution by means of weighted samples. In this work, we study the assignation of a single weighted sample which compresses the information contained in a population of weighted samples. Part of the theory that we present as Group Importance Sampling (GIS) has been employed implicitly in different works in the literature. The provided analysis yields several theoretical and practical consequences. For instance, we discuss the application of GIS into the Sequential Importance Resampling framework and show that Independent Multiple Try Metropolis schemes can be interpreted as a standard Metropolis-Hastings algorithm, following the GIS approach. We also introduce two novel Markov Chain Monte Carlo (MCMC) techniques based on GIS. The first one, named Group Metropolis Sampling method, produces a Markov chain of sets of weighted samples. All these sets are then employed for obtaining a unique global estimator. The second one is the Distributed Particle Metropolis-Hastings technique, where different parallel particle filters are jointly used to drive an MCMC algorithm. Different resampled trajectories are compared and then tested with a proper acceptance probability. The novel schemes are tested in different numerical experiments such as learning the hyperparameters of Gaussian Processes, two localization problems in a wireless sensor network (with synthetic and real data) and the tracking of vegetation parameters given satellite observations, where they are compared with several benchmark Monte Carlo techniques. Three illustrative Matlab demos are also provided.Comment: To appear in Digital Signal Processing. Related Matlab demos are provided at https://github.com/lukafree/GIS.gi

Electron paramagnetic resonance g-tensors from state interaction spin-orbit coupling density matrix renormalization group

We present a state interaction spin-orbit coupling method to calculate electron paramagnetic resonance (EPR) $g$-tensors from density matrix renormalization group wavefunctions. We apply the technique to compute $g$-tensors for the \ce{TiF3} and \ce{CuCl4^2-} complexes, a [2Fe-2S] model of the active center of ferredoxins, and a \ce{Mn4CaO5} model of the S2 state of the oxygen evolving complex. These calculations raise the prospects of determining $g$-tensors in multireference calculations with a large number of open shells.Comment: 19 page

Parallel Metropolis chains with cooperative adaptation

Monte Carlo methods, such as Markov chain Monte Carlo (MCMC) algorithms, have become very popular in signal processing over the last years. In this work, we introduce a novel MCMC scheme where parallel MCMC chains interact, adapting cooperatively the parameters of their proposal functions. Furthermore, the novel algorithm distributes the computational effort adaptively, rewarding the chains which are providing better performance and, possibly even stopping other ones. These extinct chains can be reactivated if the algorithm considers necessary. Numerical simulations shows the benefits of the novel scheme

Orthogonal parallel MCMC methods for sampling and optimization

Monte Carlo (MC) methods are widely used for Bayesian inference and optimization in statistics, signal processing and machine learning. A well-known class of MC methods are Markov Chain Monte Carlo (MCMC) algorithms. In order to foster better exploration of the state space, specially in high-dimensional applications, several schemes employing multiple parallel MCMC chains have been recently introduced. In this work, we describe a novel parallel interacting MCMC scheme, called {\it orthogonal MCMC} (O-MCMC), where a set of "vertical" parallel MCMC chains share information using some "horizontal" MCMC techniques working on the entire population of current states. More specifically, the vertical chains are led by random-walk proposals, whereas the horizontal MCMC techniques employ independent proposals, thus allowing an efficient combination of global exploration and local approximation. The interaction is contained in these horizontal iterations. Within the analysis of different implementations of O-MCMC, novel schemes in order to reduce the overall computational cost of parallel multiple try Metropolis (MTM) chains are also presented. Furthermore, a modified version of O-MCMC for optimization is provided by considering parallel simulated annealing (SA) algorithms. Numerical results show the advantages of the proposed sampling scheme in terms of efficiency in the estimation, as well as robustness in terms of independence with respect to initial values and the choice of the parameters

Targeting Protein Synthesis in \u3ci\u3eClostridioides difficile\u3c/i\u3e to Develop Antimicrobial Candidate

Clostridioides difficile is a gram positive, spore forming, obligate anaerobic bacterium that causes Clostridioides difficile infection (CDI) which can result in pseudomembranous colitis and toxic megacolon. In the case of this research a focus on Protein synthesis is made since it is an essential metabolic process and is a validated target for antibiotics. Protein synthesis begins with Initiation which includes the three translation initiation factors. Through the NMR chemical shift assignments, the IF1 structure was determined, and it was found to be composed of a short α helix and five β helixes. A peptide was designed after the short α helix to test for inhibitory effects against gram positive bacteria using a Minimum Inhibition Concentration (MIC) Assay. From the MIC Assays the IF1 peptide showed an inhibitory affect against the bacteria tested which can aide in the process of drug discovery

Identifying wave packet fractional revivals by means of information entropy

Wave packet fractional revivals is a relevant feature in the long time scale evolution of a wide range of physical systems, including atoms, molecules and nonlinear systems. We show that the sum of information entropies in both position and momentum conjugate spaces is an indicator of fractional revivals by analyzing three different model systems: $(i)$ the infinite square well, $(ii)$ a particle bouncing vertically against a wall in a gravitational field, and $(iii)$ the vibrational dynamics of hydrogen iodide molecules. This description in terms of information entropies complements the usual one in terms of the autocorrelation function

Analisis Yuridis Pemindahan Tanah Wakaf Ditinjau dari Hukum Islam dan Undang-undang Nomor 41 Tahun 2004 Tentang Wakaf (Studi Putusan Ptun No: 98/g/2011/ptun.jkt)

In the opinion of Imam Syafi'i, wakaf property cannot be tranferred bu any reasons. Article 40 of law No.41/2004 on Wakaf states that wakaf property cannot be used a collateral, confiscated, given sold, bequeathed, changed, and transferred in the form of transfer of title. However, there is anexception in law No.41/2004 on Wakaf, for the sake of public interest according to RUTR (General Layout Plan), based on the regulations in forceand is not contrary to sharia. The process of transferring the wakaf land of Raudhatul Islam mosque is administratively defective and so are the Islamic provisions and law on wakaf. The verdict No. 98/G/2011/PTUN.JKT is contrary to legal provisions, the theory of justice, legal certainty, and social welfare

Memristors using solution-based IGZO nanoparticles

Solution-based indium-gallium-zinc oldde (IGZO) nanoparticles deposited by spin coating have been investigated as a resistive switching layer in metal-insulator-metal structures for nonvolatile memory applications. Optimized devices show a bipolar resistive switching behavior, low programming voltages of +/- 1 V, on/off ratios higher than 10, high endurance, and a retention time of up to 104 s. The better performing devices were achieved with annealing temperatures of 200 degrees C and using asymmetric electrode materials of titanium and silver. The physics behind the improved switching properties of the devices is discussed in terms of the oxygen deficiency of IGZO. Temperature analysis of the conductance states revealed a nonmetallic filamentary conduction. The presented devices are potential candidates for the integration of memory functionality into low-cost System-on-Panel technology.National Funds through FCT - Portuguese Foundation for Science and Technology [UID/CTM/50025/2013, SFRH/BDP/99136/2013]; FEDER [POCI-01-0145-FEDER-007688]info:eu-repo/semantics/publishedVersio

PIAFARc effects on physical condition and densitometry in obese

La obesidad es una enfermedad sistémica, crónica y multicausal que afecta a todas las edades, sexos y condiciones sociales. Las alteraciones a nivel músculo-esquelético son evidentes, repercutiendo en estructuras óseas, articulares y desencadenando enfermedades que conllevan un incremento destacado en el gasto sanitario. El objetivo del estudio fue comparar el efecto de dos programas de actividad física basado en actividades rítmicas con control nutricional (PIAFARC). El programa de actividad física tuvo una duración de 8 meses para cada uno de los dos estudios y se aplicó a dos muestras de 34 adultos obesos. Se midieron variables de condición física y densitometría. Los resultados de la comparativa muestran diferencias significativas para el equilibrio (p=0,018) y la fuerza en piernas (p=0,045) a favor del PIAFARC1 y PIAFARC2 respectivamente