Borel-Cantelli sequences

A sequence $\{x_{n}\}_1^\infty$ in $[0,1)$ is called Borel-Cantelli (BC) if for all non-increasing sequences of positive real numbers $\{a_n\}$ with $\underset{i=1}{\overset{\infty}{\sum}}a_i=\infty$ the set $$\underset{k=1}{\overset{\infty}{\cap}} \underset{n=k}{\overset{\infty}{\cup}} B(x_n, a_n))=\{x\in[0,1)\mid |x_n-x|<a_n \text{for} \infty \text{many}n\geq1\}$$ has full Lebesgue measure. (To put it informally, BC sequences are sequences for which a natural converse to the Borel-Cantelli Theorem holds). The notion of BC sequences is motivated by the Monotone Shrinking Target Property for dynamical systems, but our approach is from a geometric rather than dynamical perspective. A sufficient condition, a necessary condition and a necessary and sufficient condition for a sequence to be BC are established. A number of examples of BC and not BC sequences are presented. The property of a sequence to be BC is a delicate diophantine property. For example, the orbits of a pseudo-Anosoff IET (interval exchange transformation) are BC while the orbits of a "generic" IET are not. The notion of BC sequences is extended to more general spaces.Comment: 20 pages. Some proofs clarifie

Towards a method for rigorous development of generic requirements patterns

We present work in progress on a method for the engineering, validation and verification of generic requirements using domain engineering and formal methods. The need to develop a generic requirement set for subsequent system instantiation is complicated by the addition of the high levels of verification demanded by safety-critical domains such as avionics. Our chosen application domain is the failure detection and management function for engine control systems: here generic requirements drive a software product line of target systems. A pilot formal specification and design exercise is undertaken on a small (twosensor) system element. This exercise has a number of aims: to support the domain analysis, to gain a view of appropriate design abstractions, for a B novice to gain experience in the B method and tools, and to evaluate the usability and utility of that method.We also present a prototype method for the production and verification of a generic requirement set in our UML-based formal notation, UML-B, and tooling developed in support. The formal verification both of the structural generic requirement set, and of a particular application, is achieved via translation to the formal specification language, B, using our U2B and ProB tools

Second-Order Belief Hidden Markov Models

Hidden Markov Models (HMMs) are learning methods for pattern recognition. The probabilistic HMMs have been one of the most used techniques based on the Bayesian model. First-order probabilistic HMMs were adapted to the theory of belief functions such that Bayesian probabilities were replaced with mass functions. In this paper, we present a second-order Hidden Markov Model using belief functions. Previous works in belief HMMs have been focused on the first-order HMMs. We extend them to the second-order model

Heterotopic Ossification: A Comprehensive Review

Heterotopic ossification (HO) is a diverse pathologic process, defined as the formation of extraskeletal bone in muscle and soft tissues. HO can be conceptualized as a tissue repair process gone awry and is a common complication of trauma and surgery. This comprehensive review seeks to synthesize the clinical, pathoetiologic, and basic biologic features of HO, including nongenetic and genetic forms. First, the clinical features, radiographic appearance, histopathologic diagnosis, and current methods of treatment are discussed. Next, current concepts regarding the mechanistic bases for HO are discussed, including the putative cell types responsible for HO formation, the inflammatory milieu and other prerequisite “niche” factors for HO initiation and propagation, and currently available animal models for the study of HO of this common and potentially devastating condition. © 2019 The Authors. JBMR Plus published by Wiley Periodicals, Inc. on behalf of American Society for Bone and Mineral Research.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/149244/1/jbm410172_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/149244/2/jbm410172.pd

(Non)Invariance of dynamical quantities for orbit equivalent flows

We study how dynamical quantities such as Lyapunov exponents, metric entropy, topological pressure, recurrence rates, and dimension-like characteristics change under a time reparameterization of a dynamical system. These quantities are shown to either remain invariant, transform according to a multiplicative factor or transform through a convoluted dependence that may take the form of an integral over the initial local values. We discuss the significance of these results for the apparent non-invariance of chaos in general relativity and explore applications to the synchronization of equilibrium states and the elimination of expansions

Determination of six chemotherapeutic agents in municipal wastewater using online solid-phase extraction coupled to liquid chromatography-tandem mass spectrometry

• We analyzed six chemotherapy agents in wastewaters. • We used 1 ml injections and an 11 min SPE-LC-MS/MS. • Limits of detection ranged from 4 to 20 ng L − 1 . • Cyclophosphamide and methotrexate were found in wastewater at 17-60 ng L Due to the increased consumption of chemotherapeutic agents, their high toxicity, carcinogenicity, their occurrence in the aquatic environment must be properly evaluated. An analytical method based on online solid-phase extraction coupled to liquid chromatography-tandem mass spectrometry was developed and validated. A 1 mL injection volume was used to quantify six of the most widely used cytotoxic drugs (cyclophosphamide, gemcitabine, ifosfamide, methotrexate, irinotecan and epirubicin) in municipal wastewater. The method was validated using standard additions. The validation results in wastewater influent had coefficients of determination (R 2 ) between 0.983 and 0.998 and intra-day precision ranging from 7 to 13% (expressed as relative standard deviation %RSD), and from 9 to 23% for inter-day precision. Limits of detection ranged from 4 to 20 ng L −1 while recovery values were greater than 70% except for gemcitabine, which is the most hydrophilic compound in the selected group and had a recovery of 47%. Matrix effects were interpreted by signal suppression and ranged from 55 to 118% with cyclophosphamide having the highest value. Two of the target anticancer drugs (cyclophosphamide and methotrexate) were detected and quantified in wastewater (effluent and influent) and ranged from 13 to 60 ng L −1 . The proposed method thus allows proper monitoring of potential environmental releases of chemotherapy agents

Building a Open Source Framework for Virtual Medical Training

This paper presents a framework to build medical training applications by using virtual reality and a tool that helps the class instantiation of this framework. The main purpose is to make easier the building of virtual reality applications in the medical training area, considering systems to simulate biopsy exams and make available deformation, collision detection, and stereoscopy functionalities. The instantiation of the classes allows quick implementation of the tools for such a purpose, thus reducing errors and offering low cost due to the use of open source tools. Using the instantiation tool, the process of building applications is fast and easy. Therefore, computer programmers can obtain an initial application and adapt it to their needs. This tool allows the user to include, delete, and edit parameters in the functionalities chosen as well as storing these parameters for future use. In order to verify the efficiency of the framework, some case studies are presented

Current whole-body MRI applications in the neurofibromatoses

ObjectivesThe Response Evaluation in Neurofibromatosis and Schwannomatosis (REiNS) International Collaboration Whole-Body MRI (WB-MRI) Working Group reviewed the existing literature on WB-MRI, an emerging technology for assessing disease in patients with neurofibromatosis type 1 (NF1), neurofibromatosis type 2 (NF2), and schwannomatosis (SWN), to recommend optimal image acquisition and analysis methods to enable WB-MRI as an endpoint in NF clinical trials.MethodsA systematic process was used to review all published data about WB-MRI in NF syndromes to assess diagnostic accuracy, feasibility and reproducibility, and data about specific techniques for assessment of tumor burden, characterization of neoplasms, and response to therapy.ResultsWB-MRI at 1.5T or 3.0T is feasible for image acquisition. Short tau inversion recovery (STIR) sequence is used in all investigations to date, suggesting consensus about the utility of this sequence for detection of WB tumor burden in people with NF. There are insufficient data to support a consensus statement about the optimal imaging planes (axial vs coronal) or 2D vs 3D approaches. Functional imaging, although used in some NF studies, has not been systematically applied or evaluated. There are no comparative studies between regional vs WB-MRI or evaluations of WB-MRI reproducibility.ConclusionsWB-MRI is feasible for identifying tumors using both 1.5T and 3.0T systems. The STIR sequence is a core sequence. Additional investigation is needed to define the optimal approach for volumetric analysis, the reproducibility of WB-MRI in NF, and the diagnostic performance of WB-MRI vs regional MRI

In Vivo Mapping of Vascular Inflammation Using Multimodal Imaging

Plaque vulnerability to rupture has emerged as a critical correlate to risk of adverse coronary events but there is as yet no clinical method to assess plaque stability in vivo. In the search to identify biomarkers of vulnerable plaques an association has been found between macrophages and plaque stability--the density and pattern of macrophage localization in lesions is indicative of probability to rupture. In very unstable plaques, macrophages are found in high densities and concentrated in the plaque shoulders. Therefore, the ability to map macrophages in plaques could allow noninvasive assessment of plaque stability. We use a multimodality imaging approach to noninvasively map the distribution of macrophages in vivo. The use of multiple modalities allows us to combine the complementary strengths of each modality to better visualize features of interest. Our combined use of Positron Emission Tomography and Magnetic Resonance Imaging (PET/MRI) allows high sensitivity PET screening to identify putative lesions in a whole body view, and high resolution MRI for detailed mapping of biomarker expression in the lesions.Macromolecular and nanoparticle contrast agents targeted to macrophages were developed and tested in three different mouse and rat models of atherosclerosis in which inflamed vascular plaques form spontaneously and/or are induced by injury. For multimodal detection, the probes were designed to contain gadolinium (T1 MRI) or iron oxide (T2 MRI), and Cu-64 (PET). PET imaging was utilized to identify regions of macrophage accumulation; these regions were further probed by MRI to visualize macrophage distribution at high resolution. In both PET and MR images the probes enhanced contrast at sites of vascular inflammation, but not in normal vessel walls. MRI was able to identify discrete sites of inflammation that were blurred together at the low resolution of PET. Macrophage content in the lesions was confirmed by histology.The multimodal imaging approach allowed high-sensitivity and high-resolution mapping of biomarker distribution and may lead to a clinical method to predict plaque probability to rupture