Extending Set Functors To Generalised Metric Spaces, 2019 University Politehnica of Bucharest

#### Extending Set Functors To Generalised Metric Spaces, Adriana Balan, Alexander Kurz, Jiří Velebil

*Mathematics, Physics, and Computer Science Faculty Articles and Research*

For a commutative quantale V, the category V-cat can be perceived as a category of generalised metric spaces and non-expanding maps. We show that any type constructor T (formalised as an endofunctor on sets) can be extended in a canonical way to a type constructor T_{V} on V-cat. The proof yields methods of explicitly calculating the extension in concrete examples, which cover well-known notions such as the Pompeiu-Hausdorff metric as well as new ones.

Conceptually, this allows us to to solve the same recursive domain equation X ≅ TX in different categories (such as sets and metric spaces) and we ...

Enhancing Value-Based Healthcare With Reconstructability Analysis: Predicting Cost Of Care In Total Hip Replacement, 2018 Portland State University

#### Enhancing Value-Based Healthcare With Reconstructability Analysis: Predicting Cost Of Care In Total Hip Replacement, Cecily Corrine Froemke, Martin Zwick

*Systems Science Faculty Publications and Presentations*

Legislative reforms aimed at slowing growth of US healthcare costs are focused on achieving greater value per dollar. To increase value healthcare providers must not only provide high quality care, but deliver this care at a sustainable cost. Predicting risks that may lead to poor outcomes and higher costs enable providers to augment decision making for optimizing patient care and inform the risk stratification necessary in emerging reimbursement models. Healthcare delivery systems are looking at their high volume service lines and identifying variation in cost and outcomes in order to determine the patient factors that are driving this variation and ...

The Philosophical Foundations Of Plen: A Protocol-Theoretic Logic Of Epistemic Norms, 2018 The Graduate Center, City University of New York

#### The Philosophical Foundations Of Plen: A Protocol-Theoretic Logic Of Epistemic Norms, Ralph E. Jenkins

*All Dissertations, Theses, and Capstone Projects*

In this dissertation, I defend the protocol-theoretic account of epistemic norms. The protocol-theoretic account amounts to three theses: (i) There are norms of epistemic rationality that are procedural; epistemic rationality is at least partially defined by rules that restrict the possible ways in which epistemic actions and processes can be sequenced, combined, or chosen among under varying conditions. (ii) Epistemic rationality is ineliminably defined by procedural norms; procedural restrictions provide an irreducible unifying structure for even apparently non-procedural prescriptions and normative expressions, and they are practically indispensable in our cognitive lives. (iii) These procedural epistemic norms are best analyzed in ...

Fast Adjustable Npn Classification Using Generalized Symmetries, 2018 Fudan University

#### Fast Adjustable Npn Classification Using Generalized Symmetries, Xuegong Zhou, Lingli Wang, Peiyi Zhao, Alan Mishchenko

*Mathematics, Physics, and Computer Science Faculty Articles and Research*

NPN classification of Boolean functions is a powerful technique used in many logic synthesis and technology mapping tools in FPGA design flows. Computing the canonical form of a function is the most common approach of Boolean function classification. In this paper, a novel algorithm for computing NPN canonical form is proposed. By exploiting symmetries under different phase assignments and higher-order symmetries of Boolean functions, the search space of NPN canonical form computation is pruned and the runtime is dramatically reduced. The algorithm can be adjusted to be a slow exact algorithm or a fast heuristic algorithm with lower quality. For ...

The Rubbish Researchers Puzzle, 2018 Nil

#### The Rubbish Researchers Puzzle, Michael W. Lucht

*Journal of Humanistic Mathematics*

The Rubbish Researchers Puzzle is a humorous short story about the Blue-Eyed Islanders Puzzle, cultural insensitivity in logic problems, and the quality of research.

Second-Order Know-How Strategies, 2018 Lafayette College

#### Second-Order Know-How Strategies, Pavel Naumov, Jia Tao

*Faculty Research and Reports*

The fact that a coalition has a strategy does not mean that the coalition knows what the strategy is. If the coalition knows the strategy, then such a strategy is called a know-how strategy of the coalition. The paper proposes the notion of a second-order know-how strategy for the case when one coalition knows what the strategy of another coalition is. The main technical result is a sound and complete logical system describing the interplay between the distributed knowledge modality and the second-order coalition know-how modality.

Reconstructability & Dynamics Of Elementary Cellular Automata, 2018 Portland State University

#### Reconstructability & Dynamics Of Elementary Cellular Automata, Martin Zwick

*Systems Science Faculty Publications and Presentations*

Reconstructability analysis (RA) is a method to determine whether a multivariate relation, defined set- or information-theoretically, is decomposable with or without loss into lower ordinality relations. Set-theoretic RA (SRA) is used to characterize the mappings of elementary cellular automata. The decomposition possible for each mapping w/o loss is a better predictor than the λ parameter (Walker & Ashby, Langton) of chaos, & non-decomposable mappings tend to produce chaos. SRA yields not only the simplest lossless structure but also a vector of losses for all structures, indexed by parameter τ. These losses are analogous to transmissions in information-theoretic RA (IRA). IRA captures ...

Beyond Spatial Autocorrelation: A Novel Approach Using Reconstructability Analysis, 2018 Portland State University

#### Beyond Spatial Autocorrelation: A Novel Approach Using Reconstructability Analysis, David Percy, Martin Zwick

*Systems Science Faculty Publications and Presentations*

Raster data are digital representations of spatial phenomena that are organized into rows and columns that typically have the same dimensions in each direction. They are used to represent image data at any scale. Common raster data are medical images, satellite data, and photos generated by modern smartphones.

Satellites capture reflectance data in specific bands of wavelength that correspond to red, green, blue, and often some infrared and thermal bands. These composite vectors can then be classified into actual land use categories such as forest or water using automated techniques. These classifications are verified on the ground using hand-held sensors ...

Introduction To Reconstructability Analysis, 2018 Portland State University

#### Introduction To Reconstructability Analysis, Martin Zwick

*Systems Science Faculty Publications and Presentations*

This talk will introduce Reconstructability Analysis (RA), a data modeling methodology deriving from the 1960s work of Ross Ashby and developed in the systems community in the 1980s and afterwards. RA, based on information theory and graph theory, is a member of the family of methods known as ‘graphical models,’ which also include Bayesian networks and log-linear techniques. It is designed for exploratory modeling, although it can also be used for confirmatory hypothesis testing. RA can discover high ordinality and nonlinear interactions that are not hypothesized in advance. Its conceptual framework illuminates the relationships between wholes and parts, a subject ...

Preliminary Results Of Bayesian Networks And Reconstructability Analysis Applied To The Electric Grid, 2018 Portland State University

#### Preliminary Results Of Bayesian Networks And Reconstructability Analysis Applied To The Electric Grid, Marcus Harris, Martin Zwick

*Systems Science Faculty Publications and Presentations*

Reconstructability Analysis (RA) is an analytical approach developed in the systems community that combines graph theory and information theory. Graph theory provides the structure of relations (model of the data) between variables and information theory characterizes the strength and the nature of the relations. RA has three primary approaches to model data: variable based (VB) models without loops (acyclic graphs), VB models with loops (cyclic graphs) and state-based models (nearly always cyclic, individual states specifying model constraints). These models can either be directed or neutral. Directed models focus on a single response variable whereas neutral models focus on all relations ...

The Structure Of Models Of Second-Order Set Theories, 2018 The Graduate Center, City University of New York

#### The Structure Of Models Of Second-Order Set Theories, Kameryn J. Williams

*All Dissertations, Theses, and Capstone Projects*

This dissertation is a contribution to the project of second-order set theory, which has seen a revival in recent years. The approach is to understand second-order set theory by studying the structure of models of second-order set theories. The main results are the following, organized by chapter. First, I investigate the poset of T-realizations of a fixed countable model of ZFC, where T is a reasonable second-order set theory such as GBC or KM, showing that it has a rich structure. In particular, every countable partial order embeds into this structure. Moreover, we can arrange so that these embedding preserve ...

Coincidence Of Bargaining Solutions And Rationalizability In Epistemic Games, 2018 The Graduate Center, City University of New York

#### Coincidence Of Bargaining Solutions And Rationalizability In Epistemic Games, Todd Stambaugh

*All Dissertations, Theses, and Capstone Projects*

**Chapter 1**: In 1950, John Nash proposed the Bargaining Problem, for which a solution is a function that assigns to each space of possible utility assignments a single point in the space, in some sense representing the ’fair’ deal for the agents involved. Nash provided a solution of his own, and several others have been presented since then, including a notable solution by Ehud Kalai and Meir Smorodinsky. In chapter 1, a complete account is given for the conditions under which the two solutions will coincide for two player bargaining scenarios.

**Chapter 2**: In the same year, Nash presented one ...

Information Flow Under Budget Constraints, 2018 Lafayette College

#### Information Flow Under Budget Constraints, Pavel Naumov, Jia Tao

*Faculty Research and Reports*

Although first proposed in the database theory as properties of functional dependencies between attributes, Armstrong's axioms capture general principles of information flow by describing properties of dependencies between sets of pieces of information. This article generalizes Armstrong's axioms to a setting in which there is a cost associated with information. The proposed logical system captures general principles of dependencies between pieces of information constrained by a given budget.

Strategic Coalitions With Perfect Recall, 2018 Lafayette College

#### Strategic Coalitions With Perfect Recall, Pavel Naumov, Jia Tao

*Faculty Research and Reports*

The paper proposes a bimodal logic that describes an interplay between distributed knowledge modality and coalition know-how modality. Unlike other similar systems, the one proposed here assumes perfect recall by all agents. Perfect recall is captured in the system by a single axiom. The main technical results are the soundness and the completeness theorems for the proposed logical system.

Armstrong's Axioms And Navigation Strategies, 2018 Vassar College

#### Armstrong's Axioms And Navigation Strategies, Kaya Deuser, Pavel Naumov

*Faculty Research and Reports*

The paper investigates navigability with imperfect information. It shows that the properties of navigability with perfect recall are exactly those captured by Armstrong's axioms from database theory. If the assumption of perfect recall is omitted, then Armstrong's transitivity axiom is not valid, but it can be replaced by a weaker principle. The main technical results are soundness and completeness theorems for the logical systems describing properties of navigability with and without perfect recall.

Statistical Analysis Of Network Change, 2018 Portland State University

#### Statistical Analysis Of Network Change, Teresa D. Schmidt, Martin Zwick

*Systems Science Faculty Publications and Presentations*

Networks are rarely subjected to hypothesis tests for difference, but when they are inferred from datasets of independent observations statistical testing is feasible. To demonstrate, a healthcare provider network is tested for significant change after an intervention using Medicaid claims data. First, the network is inferred for each time period with (1) partial least squares (PLS) regression and (2) reconstructability analysis (RA). Second, network distance (i.e., change between time periods) is measured as the mean absolute difference in (1) coefficient matrices for PLS and (2) calculated probability distributions for RA. Third, the network distance is compared against a reference ...

What Makes A Theory Of Infinitesimals Useful? A View By Klein And Fraenkel, 2018 Bar-Ilan University

#### What Makes A Theory Of Infinitesimals Useful? A View By Klein And Fraenkel, Vladimir Kanovei, Karin Katz, Mikhail Katz, Thomas Mormann

*Journal of Humanistic Mathematics*

Felix Klein and Abraham Fraenkel each formulated a criterion for a theory of infinitesimals to be successful, in terms of the feasibility of implementation of the Mean Value Theorem. We explore the evolution of the idea over the past century, and the role of Abraham Robinson's framework therein.

Introduction To Game Theory: A Discovery Approach, 2018 Linfield College

#### Introduction To Game Theory: A Discovery Approach, Jennifer Firkins Nordstrom

*Linfield Authors Book Gallery*

Game theory is an excellent topic for a non-majors quantitative course as it develops mathematical models to understand human behavior in social, political, and economic settings. The variety of applications can appeal to a broad range of students. Additionally, students can learn mathematics through playing games, something many choose to do in their spare time! This text also includes an exploration of the ideas of game theory through the rich context of popular culture. It contains sections on applications of the concepts to popular culture. It suggests films, television shows, and novels with themes from game theory. The questions in ...

Inductive Certificate Synthesis For Control Design, 2018 University of Colorado at Boulder

#### Inductive Certificate Synthesis For Control Design, Hadi Ravanbakhsh

*Computer Science Graduate Theses & Dissertations*

The focus of this thesis is developing a framework for designing correct-by-construction controllers using control certificates. We use nonlinear dynamical systems to model the physical environment (plants). The goal is to synthesize controllers for these plants while guaranteeing formal correctness w.r.t. given specifications. We consider different fundamental specifications including stability, safety, and reach-while-stay. Stability specification states that the execution traces of the system remain close to an equilibrium state and approach it asymptotically. Safety specification requires the execution traces to stay in a safe region. Finally, for reach-while-stay specification, safety is needed until a target set is reached ...

Everyone Knows That Someone Knows: Quantifiers Over Epistemic Agents, 2018 Vassar College

#### Everyone Knows That Someone Knows: Quantifiers Over Epistemic Agents, Pavel Naumov, Jia Tao

*Faculty Research and Reports*

Modal logic S5 is commonly viewed as an epistemic logic that captures the most basic properties of knowledge. Kripke proved a completeness theorem for the first-order modal logic S5 with respect to a possible worlds semantics. A multiagent version of the propositional S5 as well as a version of the propositional S5 that describes properties of distributed knowledge in multiagent systems has also been previously studied. This article proposes a version of S5-like epistemic logic of distributed knowledge with quantifiers ranging over the set of agents, and proves its soundness and completeness with respect to a Kripke semantics.