Particle Filtering and Smoothing Using Windowed Rejection Sampling

"Particle methods" are sequential Monte Carlo algorithms, typically involving importance sampling, that are used to estimate and sample from joint and marginal densities from a collection of a, presumably increasing, number of random variables. In particular, a particle filter aims to estimate the current state $X_{n}$ of a stochastic system that is not directly observable by estimating a posterior distribution $\pi(x_{n}|y_{1},y_{2}, \ldots, y_{n})$ where the $\{Y_{n}\}$ are observations related to the $\{X_{n}\}$ through some measurement model $\pi(y_{n}|x_{n})$. A particle smoother aims to estimate a marginal distribution $\pi(x_{i}|y_{1},y_{2}, \ldots, y_{n})$ for $1 \leq i < n$. Particle methods are used extensively for hidden Markov models where $\{X_{n}\}$ is a Markov chain as well as for more general state space models. Existing particle filtering algorithms are extremely fast and easy to implement. Although they suffer from issues of degeneracy and "sample impoverishment", steps can be taken to minimize these problems and overall they are excellent tools for inference. However, if one wishes to sample from a posterior distribution of interest, a particle filter is only able to produce dependent draws. Particle smoothing algorithms are complicated and far less robust, often requiring cumbersome post-processing, "forward-backward" recursions, and multiple passes through subroutines. In this paper we introduce an alternative algorithm for both filtering and smoothing that is based on rejection sampling "in windows" . We compare both speed and accuracy of the traditional particle filter and this "windowed rejection sampler" (WRS) for several examples and show that good estimates for smoothing distributions are obtained at no extra cost

aristotle's demonstrative logic

Demonstrative logic, the study of demonstration as opposed to persuasion, is the subject of Aristotle's two-volume Analytics. Many examples are geometrical. Demonstration produces knowledge (of the truth of propositions). Persuasion merely produces opinion. Aristotle presented a general truth-and-consequence conception of demonstration meant to apply to all demonstrations. According to him, a demonstration, which normally proves a conclusion not previously known to be true, is an extended argumentation beginning with premises known to be truths and containing a chain of reasoning showing by deductively evident steps that its conclusion is a consequence of its premises. In particular, a demonstration is a deduction whose premises are known to be true. Aristotle's general theory of demonstration required a prior general theory of deduction presented in the Prior Analytics. His general immediate-deduction-chaining conception of deduction was meant to apply to all deductions. According to him, any deduction that is not immediately evident is an extended argumentation that involves a chaining of intermediate immediately evident steps that shows its final conclusion to follow logically from its premises. To illustrate his general theory of deduction, he presented an ingeniously simple and mathematically precise special case traditionally known as the categorical syllogisti

On the changes in the physical properties of the ionized region around the Weigelt structures in Eta Carinae over the 5.54-yr spectroscopic cycle

We present HST/STIS observations and analysis of two prominent nebular structures around the central source of Eta Carinae, the knots C and D. The former is brighter than the latter for emission lines from intermediate or high ionization potential ions. The brightness of lines from intermediate and high ionization potential ions significantly decreases at phases around periastron. We do not see conspicuous changes in the brightness of lines from low ionization potential (<13.6 eV) that the total extinction towards the Weigelt structures is that the total extinction towards the Weigelt structures is AsubV =2/0. that the total extinction towards the Weigelt structures is AV = 2.0. Weigelt C and D are characterized by an electron density of that the total extinction towards the Weigelt structures is AV = 2.0. Weigelt C and D are characterized by an electron density of 10exp6.9 cm-3 that does not significantly change throughout the orbital cycle. The electron temperature varies from 5500 K (around periastron) to 7200 K (around apastron). The relative changes in the brightness of He I lines are well reproduced by the variations in the electron temperature alone. We found that, at phases around periastron, the electron temperature seems to be higher for Weigelt C than that of D. The Weigelt structures are located close to the Homunculus equatorial plane, at a distance of about 1240 AU from the central source. From the analysis of proper motion and age, the Weigelt complex can be associated with the equatorial structure called the Butterfly Nebula surrounding the central binary system.Comment: 19 pages, 18 figure

Waiting in the Wings: Reflected X-ray Emission from the Homunculus Nebula

We report the first detection of X-ray emission associated with the Homunculus Nebula which surrounds the supermassive star Eta Carinae. The emission is characterized by a temperature in excess of 100 MK, and is consistent with scattering of the time-delayed X-ray flux associated with the star. The nebular emission is bright in the northwestern lobe and near the central regions of the Homunculus, and fainter in the southeastern lobe. We also report the detection of an unusually broad Fe K fluorescent line, which may indicate fluorescent scattering off the wind of a companion star or some other high velocity outflow. The X-ray Homunculus is the nearest member of the small class of Galactic X-ray reflection nebulae, and the only one in which both the emitting and reflecting sources are distinguishable.Comment: 17 pages, 5 figures, accepted by Ap

A spectral and spatial analysis of eta Carinae's diffuse X-ray emission using CHANDRA

The luminous unstable star (star system) eta Carinae is surrounded by an optically bright bipolar nebula, the Homunculus and a fainter but much larger nebula, the so-called outer ejecta. As images from the EINSTEIN and ROSAT satellites have shown, the outer ejecta is also visible in soft X-rays, while the central source is present in the harder X-ray bands. With our CHANDRA observations we show that the morphology and properties of the X-ray nebula are the result of shocks from fast clumps in the outer ejecta moving into a pre-existing denser circumstellar medium. An additional contribution to the soft X-ray flux results from mutual interactions of clumps within the ejecta. Spectra extracted from the CHANDRA data yield gas temperatures kT of 0.6-0.76 keV. The implied pre-shock velocities of 670-760 km/s are within the scatter of the velocities we measure for the majority of the clumps in the corresponding regions. Significant nitrogen enhancements over solar abundances are needed for acceptable fits in all parts of the outer ejecta, consistent with CNO processed material and non-uniform enhancement. The presence of a diffuse spot of hard X-ray emission at the S condensation shows some contribution of the highest velocity clumps and further underlines the multicomponent, non-equilibrium nature of the X-ray nebula. The detection of an X-ray ``bridge'' between the northern and southern part of the X-ray nebula and an X-ray shadow at the position of the NN bow can be attributed to a large expanding disk, which would appear as an extension of the equatorial disk. No soft emission is seen from the Homunculus, or from the NN bow or the ``strings''.Comment: 15 pages, 10 figures, accepted by A&A; paper including images with full resolution available at http://www.astro.ruhr-uni-bochum.de/kweis/publications.htm

Barriers to the Employment of Welfare Recipients

Dramatic reductions in welfare caseloads since passage of the Personal Responsibility and WorkOpportunity Reconciliation Act of 1996 have not allayed policy concerns about the employability of recipients remaining on the rolls. Analysis of potential barriers to employment can address whether current recipients have problems that either singly or in combination make it difficult for them to comply with the new requirements for getting and keeping jobs. In this paper, we explore the prevalence and work effects of 14 potential barriers in a new survey of a representative sample of 753 urban single-mother recipients. We report the prevalence of the barriers and how their number predicts employment rates, controlling for demographic characteristics. We also analyze which individual barriers are associated with employment and how a model inclusive of a comprehensive array of barriers improves upon a traditional human capital model of the work effects of education and work and welfare history. Single mothers who received welfare in 1997 had higher rates of personal health and mental health problems, domestic violence, and children’s health problems than do women in national samples, but they were no more likely than the general population to be drug or alcohol dependent. Only 15 percent of respondents had none of the barriers and almost two-thirds had two or more barriers. The numbers of multiple barriers were strongly and negatively associated with working, and among the individual barriers, low education, lack of access to transportation, poor health, having drug dependence or a major depressive disorder, and several experiences of workplace discrimination reduced employment. Welfare-to-work programs need to be more finely targeted with respect to exemptions and service provision, and states should consider providing longer-term and enhanced supports for those who face low prospects of leaving welfare for employment.

An equatorial wind from the massive young stellar object S140 IRS 1

The discovery of the second equatorial ionized stellar wind from a massive young stellar object is reported. High resolution radio continuum maps of S140 IRS 1 reveal a highly elongated source that is perpendicular to the larger scale bipolar molecular outflow. This picture is confirmed by location of a small scale monopolar near-IR reflection nebula at the base of the blueshifted lobe. A second epoch of observations over a five year baseline show little ordered outward proper motion of clumps as would have been expected for a jet. A third epoch, taken only 50 days after the second, did show significant changes in the radio morphology. These radio properties can all be understood in the context of an equatorial wind driven by radiation pressure from the central star and inner disc acting on the gas in the surface layers of the disc as proposed by Drew et al. (1998). This equatorial wind system is briefly compared with the one in S106IR, and contrasted with other massive young stellar objects that drive ionized jets.Comment: 19 pages, 5 figures, accepted by ApJ, minor changes in light of referees repor

Novel pyrrolobenzodiazepine benzofused hybrid molecules inhibit NF-κB activity and synergise with bortezomib and ibrutinib in hematological cancers

Chronic lymphocytic leukemia (CLL) and multiple myeloma (MM) are incurable hematological malignancies that are pathologically linked with aberrant NF-κB activation. In this study, we identified a group of novel C8-linked benzofused Pyrrolo[2,1-c][1,4]benzodiazepines (PBD) monomeric hybrids capable of sequence-selective inhibition of NF-κB with low nanomolar LD50 values in CLL (n=46) and MM cell lines (n=5). The lead compound, DC-1-192, significantly inhibited NF-κB DNA binding after just 4h exposure and demonstrating inhibitory effects on both canonical and non-canonical NF-κB subunits. In primary CLL cells, sensitivity to DC-1-192 was inversely correlated with RelA subunit expression (r2=0.2) and samples with BIRC3 or NOTCH1 mutations showed increased sensitivity (P=0.001). RNA-sequencing and gene set enrichment analysis confirmed the over-representation of NF-κB regulated genes in the down-regulated gene list. Furthermore, In vivo efficacy studies in NOD/SCID mice, using a systemic RPMI 8226 human multiple myeloma xenograft model, showed that DC-1-192 significantly prolonged survival (P=0.017). In addition, DC1-192 showed synergy with bortezomib and ibrutinib; synergy with ibrutinib was enhanced when CLL cells were co-cultured on CD40L-expressing fibroblasts in order to mimic the cytoprotective lymph node microenvironment (P = 0.01). Given that NF-κB plays a role in both bortezomib and ibrutinib resistance mechanisms, these data provide a strong rationale for the use of DC-1-192 in the treatment of NF-κB-driven cancers, particularly in the context of relapsed/refractory disease