A generalization of Hausdorff dimension applied to Hilbert cubes and Wasserstein spaces

A Wasserstein spaces is a metric space of sufficiently concentrated probability measures over a general metric space. The main goal of this paper is to estimate the largeness of Wasserstein spaces, in a sense to be precised. In a first part, we generalize the Hausdorff dimension by defining a family of bi-Lipschitz invariants, called critical parameters, that measure largeness for infinite-dimensional metric spaces. Basic properties of these invariants are given, and they are estimated for a naturel set of spaces generalizing the usual Hilbert cube. In a second part, we estimate the value of these new invariants in the case of some Wasserstein spaces, as well as the dynamical complexity of push-forward maps. The lower bounds rely on several embedding results; for example we provide bi-Lipschitz embeddings of all powers of any space inside its Wasserstein space, with uniform bound and we prove that the Wasserstein space of a d-manifold has "power-exponential" critical parameter equal to d.Comment: v2 Largely expanded version, as reflected by the change of title; all part I on generalized Hausdorff dimension is new, as well as the embedding of Hilbert cubes into Wasserstein spaces. v3 modified according to the referee final remarks ; to appear in Journal of Topology and Analysi

A Number-Theoretic Error-Correcting Code

In this paper we describe a new error-correcting code (ECC) inspired by the Naccache-Stern cryptosystem. While by far less efficient than Turbo codes, the proposed ECC happens to be more efficient than some established ECCs for certain sets of parameters. The new ECC adds an appendix to the message. The appendix is the modular product of small primes representing the message bits. The receiver recomputes the product and detects transmission errors using modular division and lattice reduction

Evaluating implicit feedback models using searcher simulations

In this article we describe an evaluation of relevance feedback (RF) algorithms using searcher simulations. Since these algorithms select additional terms for query modification based on inferences made from searcher interaction, not on relevance information searchers explicitly provide (as in traditional RF), we refer to them as implicit feedback models. We introduce six different models that base their decisions on the interactions of searchers and use different approaches to rank query modification terms. The aim of this article is to determine which of these models should be used to assist searchers in the systems we develop. To evaluate these models we used searcher simulations that afforded us more control over the experimental conditions than experiments with human subjects and allowed complex interaction to be modeled without the need for costly human experimentation. The simulation-based evaluation methodology measures how well the models learn the distribution of terms across relevant documents (i.e., learn what information is relevant) and how well they improve search effectiveness (i.e., create effective search queries). Our findings show that an implicit feedback model based on Jeffrey's rule of conditioning outperformed other models under investigation

Multi-membership gene regulation in pathway based microarray analysis

This article is available through the Brunel Open Access Publishing Fund. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Background: Gene expression analysis has been intensively researched for more than a decade. Recently, there has been elevated interest in the integration of microarray data analysis with other types of biological knowledge in a holistic analytical approach. We propose a methodology that can be facilitated for pathway based microarray data analysis, based on the observation that a substantial proportion of genes present in biochemical pathway databases are members of a number of distinct pathways. Our methodology aims towards establishing the state of individual pathways, by identifying those truly affected by the experimental conditions based on the behaviour of such genes. For that purpose it considers all the pathways in which a gene participates and the general census of gene expression per pathway. Results: We utilise hill climbing, simulated annealing and a genetic algorithm to analyse the consistency of the produced results, through the application of fuzzy adjusted rand indexes and hamming distance. All algorithms produce highly consistent genes to pathways allocations, revealing the contribution of genes to pathway functionality, in agreement with current pathway state visualisation techniques, with the simulated annealing search proving slightly superior in terms of efficiency. Conclusions: We show that the expression values of genes, which are members of a number of biochemical pathways or modules, are the net effect of the contribution of each gene to these biochemical processes. We show that by manipulating the pathway and module contribution of such genes to follow underlying trends we can interpret microarray results centred on the behaviour of these genes.The work was sponsored by the studentship scheme of the School of Information Systems, Computing and Mathematics, Brunel Universit

Pulse Shape Analysis and Identification of Multipoint Events in a Large-Volume Proportional Counter in an Experimental Search for 2K Capture Kr-78

A pulse shape analysis algorithm and a method for suppressing the noise component of signals from a large copper proportional counter in the experiment aimed at searching for 2K capture of Kr-78 are described. These signals correspond to a compound event with different numbers of charge clusters due to from primary ionization is formed by these signals. A technique for separating single- and multipoint events and determining the charge in individual clusters is presented. Using the Daubechies wavelets in multiresolutional signal analysis, it is possible to increase the sensitivity and the resolution in extraction of multipoint events in the detector by a factor of 3-4.Comment: 10 pages, 8 figures. submitted to Instruments and Experimental Techniques; ISSN 0020/441

A novel method for engineering autologous non-thrombogenic in situ tissue-engineered blood vessels for arteriovenous grafting

The durability of prosthetic arteriovenous (AV) grafts for hemodialysis access is low, predominantly due to stenotic lesions in the venous outflow tract and infectious complications. Tissue engineered blood vessels (TEBVs) might offer a tailor-made autologous alternative for prosthetic grafts. We have designed a method in which TEBVs are grown in vivo, by utilizing the foreign body response to subcutaneously implanted polymeric rods in goats, resulting in the formation of an autologous fibrocellular tissue capsule (TC). One month after implantation, the polymeric rod is extracted, whereupon TCs (length 6 cm, diameter 6.8 mm) were grafted as arteriovenous conduit between the carotid artery and jugular vein of the same goats. At time of grafting, the TCs were shown to have sufficient mechanical strength in terms of bursting pressure (2382 +/- 129 mmHg), and suture retention strength (SRS: 1.97 +/- 0.49 N). The AV grafts were harvested at 1 or 2 months after grafting. In an ex vivo whole blood perfusion system, the lumen of the vascular grafts was shown to be less thrombogenic compared to the initial TCs and ePTFE grafts. At 8 weeks after grafting, the entire graft was covered with an endothelial layer and abundant elastin expression was present throughout the graft. Patency at 1 and 2 months was comparable with ePTFE AV-grafts. In conclusion, we demonstrate the remodeling capacity of cellularized in vivo engineered TEBVs, and their potential as autologous alternative for prosthetic vascular grafts.Vascular Surger

Local Difference Measures between Complex Networks for Dynamical System Model Evaluation

Acknowledgments We thank Reik V. Donner for inspiring suggestions that initialized the work presented herein. Jan H. Feldhoff is credited for providing us with the STARS simulation data and for his contributions to fruitful discussions. Comments by the anonymous reviewers are gratefully acknowledged as they led to substantial improvements of the manuscript.Peer reviewedPublisher PD

Plasma ACE2 predicts outcome of COVID-19 in hospitalized patients

AimsSevere acute respiratory syndrome coronavirus 2 (SARS-CoV-2) binds to angiotensin converting enzyme 2 (ACE2) enabling entrance of the virus into cells and causing the infection termed coronavirus disease of 2019 (COVID-19). Here, we investigate associations between plasma ACE2 and outcome of COVID-19.Methods and resultsThis analysis used data from a large longitudinal study of 306 COVID-19 positive patients and 78 COVID-19 negative patients (MGH Emergency Department COVID-19 Cohort). Comprehensive clinical data were collected on this cohort, including 28-day outcomes. The samples were run on the Olink® Explore 1536 platform which includes measurement of the ACE2 protein. High admission plasma ACE2 in COVID-19 patients was associated with increased maximal illness severity within 28 days with OR = 1.8, 95%-CI: 1.4-2.3 (P ConclusionThis study suggests that measuring plasma ACE2 is potentially valuable in predicting COVID-19 outcomes. Further, ACE2 could be a link between COVID-19 illness severity and its established risk factors hypertension, pre-existing heart disease and pre-existing kidney disease