Adapting the Number of Particles in Sequential Monte Carlo Methods through an Online Scheme for Convergence Assessment

Particle filters are broadly used to approximate posterior distributions of hidden states in state-space models by means of sets of weighted particles. While the convergence of the filter is guaranteed when the number of particles tends to infinity, the quality of the approximation is usually unknown but strongly dependent on the number of particles. In this paper, we propose a novel method for assessing the convergence of particle filters online manner, as well as a simple scheme for the online adaptation of the number of particles based on the convergence assessment. The method is based on a sequential comparison between the actual observations and their predictive probability distributions approximated by the filter. We provide a rigorous theoretical analysis of the proposed methodology and, as an example of its practical use, we present simulations of a simple algorithm for the dynamic and online adaption of the number of particles during the operation of a particle filter on a stochastic version of the Lorenz system

On the performance of particle filters with adaptive number of particles

We investigate the performance of a class of particle filters (PFs) that can automatically tune their computational complexity by evaluating online certain predictive statistics which are invariant for a broad class of state-space models. To be specific, we propose a family of block-adaptive PFs based on the methodology of Elvira et al. (IEEE Trans Signal Process 65(7):1781– 1794, 2017). In this class of algorithms, the number of Monte Carlo samples (known as particles) is adjusted periodically, and we prove that the theoretical error bounds of the PF actually adapt to the updates in the number of particles. The evaluation of the predictive statistics that lies at the core of the methodology is done by generating fictitious observations, i.e., particles in the observation space. We study, both analytically and numerically, the impact of the number K of these particles on the performance of the algorithm. In particular, we prove that if the predictive statistics with K fictitious observations converged exactly, then the particle approximation of the filtering distribution would match the first K elements in a series of moments of the true filter. This result can be understood as a converse to some convergence theorems for PFs. From this analysis, we deduce an alternative predictive statistic that can be computed (for some models) without sampling any fictitious observations at all. Finally, we conduct an extensive simulation study that illustrates the theoretical results and provides further insights into the complexity, performance and behavior of the new class of algorithms.This work was partially supported by Agence Nationale de la Recherche of France under PISCES Project (ANR-17-CE40-0031-01), the Office of Naval Research (Award No. N00014-19-1-2226), Agencia Estatal de Investigación of Spain (RTI2018-099655-B-I00 CLARA), and NSF through the award CCF-2021002

Dental Status of Victims from Batajnica’s Mass Graves

The aim of this paper is to present the post mortem dental evidence and dental health of the victims interred during 1999 in five grave pits at Batajnica near Belgrade. The investigated sample comprised 32 individuals with only maxillae preserved, 80 with mandible, and 260 individuals with both jaws. We have found high degree of enamel hypoplasia (25.89%), frequent signs of the severe forms of periodontal disease (18.55%), very high percent of antemortem tooth loss (31.48%), and evidence of edentate jaws in an early age of individuals. Amalgam was predominant material for tooth fillings; implants and non-metal ceramic crowns were not found, and three quaters of edentate individuals were found with full prostetic dentures. Despite the detailed postmortem dental analysis, antemortem dental charts were not collected. These individuals were identified by other forensic methods

Transcriptional profiling of putative human epithelial stem cells

<p>Abstract</p> <p>Background</p> <p>Human interfollicular epidermis is sustained by the proliferation of stem cells and their progeny, transient amplifying cells. Molecular characterization of these two cell populations is essential for better understanding of self renewal, differentiation and mechanisms of skin pathogenesis. The purpose of this study was to obtain gene expression profiles of alpha 6⁺/MHCI⁺, transient amplifying cells and alpha 6⁺/MHCI^-, putative stem cells, and to compare them with existing data bases of gene expression profiles of hair follicle stem cells. The expression of Major Histocompatibility Complex (MHC) class I, previously shown to be absent in stem cells in several tissues, and alpha 6 integrin were used to isolate MHCI positive basal cells, and MHCI low/negative basal cells.</p> <p>Results</p> <p>Transcriptional profiles of the two cell populations were determined and comparisons made with published data for hair follicle stem cell gene expression profiles. We demonstrate that presumptive interfollicular stem cells, alpha 6⁺/MHCI^-cells, are enriched in messenger RNAs encoding surface receptors, cell adhesion molecules, extracellular matrix proteins, transcripts encoding members of IFN-alpha family proteins and components of IFN signaling, but contain lower levels of transcripts encoding proteins which take part in energy metabolism, cell cycle, ribosome biosynthesis, splicing, protein translation, degradation, DNA replication, repair, and chromosome remodeling. Furthermore, our data indicate that the cell signaling pathways Notch1 and NF-κB are downregulated/inhibited in MHC negative basal cells.</p> <p>Conclusion</p> <p>This study demonstrates that alpha 6⁺/MHCI^-cells have additional characteristics attributed to stem cells. Moreover, the transcription profile of alpha 6⁺/MHCI^-cells shows similarities to transcription profiles of mouse hair follicle bulge cells known to be enriched for stem cells. Collectively, our data suggests that alpha 6⁺/MHCI^-cells may be enriched for stem cells. This study is the first comprehensive gene expression profile of putative human epithelial stem cells and their progeny that were isolated directly from neonatal foreskin tissue. Our study is important for understanding self renewal and differentiation of epidermal stem cells, and for elucidating signaling pathways involved in those processes. The generated data base may serve those working with other human epithelial tissue progenitors.</p