Positive Alexander Duality for Pursuit and Evasion

Considered is a class of pursuit-evasion games, in which an evader tries to avoid detection. Such games can be formulated as the search for sections to the complement of a coverage region in a Euclidean space over a timeline. Prior results give homological criteria for evasion in the general case that are not necessary and sufficient. This paper provides a necessary and sufficient positive cohomological criterion for evasion in a general case. The principal tools are (1) a refinement of the Cech cohomology of a coverage region with a positive cone encoding spatial orientation, (2) a refinement of the Borel-Moore homology of the coverage gaps with a positive cone encoding time orientation, and (3) a positive variant of Alexander Duality. Positive cohomology decomposes as the global sections of a sheaf of local positive cohomology over the time axis; we show how this decomposition makes positive cohomology computable as a linear program.Comment: 19 pages, 6 figures; improvements made throughout: e.g. positive (co)homology generalized to arbitrary degrees; Positive Alexander Duality generalized from homological degrees 0,1; Morse and smoothness conditions generalized; illustrations of positive homology added. minor corrections in proofs, notation, organization, and language made throughout. variant of Borel-Moore homology now use

The Implementation, Interpretation, and Justification of Likelihoods in Cosmology

I discuss the formal implementation, interpretation, and justification of likelihood attributions in cosmology. I show that likelihood arguments in cosmology suffer from significant conceptual and formal problems that undermine their applicability in this context

Modelling Computing Devices and Processes by Information Operators

The concept of operator is exceedingly important in many areas as a tool of theoretical studies and practical applications. Here, we introduce the operator theory of computing, opening new opportunities for the exploration of computing devices, networks, and processes. In particular, the operator approach allows for the solving of many computing problems in a more general context of operating spaces. In addition, operator representation of computing devices and their networks allows for the construction of a variety of operator compositions and the development of new schemas of computation as well as network and computer architectures using operations with operators. Besides, operator representation allows for the efficient application of the axiomatic technique for the investigation of computation

Quantifying uncertainty in reliability block diagrams

Reliability analysis yields statistically derived technical system performance estimates. Traditional reliability analysis employs classical statistical techniques predicated upon asymptotic properties of large data sets. Not uncommonly, however, medium to small data sets constrain analysis efforts for high risk systems characterized by significant danger or cost. This paper outlines a general reliability analysis paradigm to contend with small to medium data sets. Preliminary sensitivity analysis using scatter plots and tests for non-randomness reveals component-level drivers in system-level performance measures. Comprehensive data collection efforts targeting all available, high-quality information sources decrease and allow analysts to estimate uncertainty in model parameters describing driving component performance. Bayesian analysis accumulates these data into posterior distributions summarizing all available performance knowledge about driving components. Sampling-based uncertainty propagation methods then transform component-level posterior distributions into system-level parent and sampling distributions. Reliability metric point-estimates and credible intervals estimate the system reliability and benchmark the quality of the estimates, respectively. An operational reliability assessment of the B-2 Radar Modernization Program (B2-RMP) modernized radar system demonstrates the mechanics of the analysis paradigm applied to real data. Results from analysis including uncertainty explicitly modeled in all B-2 RMP components benchmark results from analysis including uncertainty modeled for driving components only

Survey and Evaluate Uncertainty Quantification Methodologies

The Carbon Capture Simulation Initiative (CCSI) is a partnership among national laboratories, industry and academic institutions that will develop and deploy state-of-the-art computational modeling and simulation tools to accelerate the commercialization of carbon capture technologies from discovery to development, demonstration, and ultimately the widespread deployment to hundreds of power plants. The CCSI Toolset will provide end users in industry with a comprehensive, integrated suite of scientifically validated models with uncertainty quantification, optimization, risk analysis and decision making capabilities. The CCSI Toolset will incorporate commercial and open-source software currently in use by industry and will also develop new software tools as necessary to fill technology gaps identified during execution of the project. The CCSI Toolset will (1) enable promising concepts to be more quickly identified through rapid computational screening of devices and processes; (2) reduce the time to design and troubleshoot new devices and processes; (3) quantify the technical risk in taking technology from laboratory-scale to commercial-scale; and (4) stabilize deployment costs more quickly by replacing some of the physical operational tests with virtual power plant simulations. The goal of CCSI is to deliver a toolset that can simulate the scale-up of a broad set of new carbon capture technologies from laboratory scale to full commercial scale. To provide a framework around which the toolset can be developed and demonstrated, we will focus on three Industrial Challenge Problems (ICPs) related to carbon capture technologies relevant to U.S. pulverized coal (PC) power plants. Post combustion capture by solid sorbents is the technology focus of the initial ICP (referred to as ICP A). The goal of the uncertainty quantification (UQ) task (Task 6) is to provide a set of capabilities to the user community for the quantification of uncertainties associated with the carbon capture processes. As such, we will develop, as needed and beyond existing capabilities, a suite of robust and efficient computational tools for UQ to be integrated into a CCSI UQ software framework