Levels of Interoperability in Coalition Systems

Systems of different command centers that are brought together in a coalition operation must have some level of interoperability in order to work together. Bares [2000] has introduced a formalism of three interoperability domains that describe the ability of the systems to define their own level of interoperability within the coalition by assessing their own and the other systems’ ability to interact on actions of the coalition. The lowest domain, interconnectivity, reflects the ability to exchange messages; this level must already have been achieved in order for the systems to participate in the coalition. The second domain, interoperability, reflects a system’s ability to identify what tasks it is able to interoperate on. The third level, intercooperability, indicates that all systems have the ability to evaluate all other systems in the coalition. By describing the interoperability domains in this manner, the domains represent increasing levels of awareness of each system’s own capabilities and those of the other systems; it represents the transition from exchanging data to exchanging knowledge. This research looks particularly at the interoperability level and the ability of systems to evaluate their own interoperability on the coalition’s actions by using Bares’ formalism of interoperability to assign actions to systems participating in the coalition

On Stability and Consensus of Signed Networks: A Self-loop Compensation Perspective

Positive semidefinite is not an inherent property of signed Laplacians, which renders the stability and consensus of multi-agent system on undirected signed networks intricate. Inspired by the correlation between diagonal dominance and spectrum of signed Laplacians, this paper proposes a self-loop compensation mechanism in the design of interaction protocol amongst agents and examines the stability/consensus of the compensated signed networks. It turns out that self-loop compensation acts as exerting a virtual leader on these agents that are incident to negative edges, steering whom towards origin. Analytical connections between self-loop compensation and the collective behavior of the compensated signed network are established. Necessary and/or sufficient conditions for predictable cluster consensus of signed networks via self-loop compensation are provided. The optimality of self-loop compensation is discussed. Furthermore, we extend our results to directed signed networks where the symmetry of signed Laplacian is not free. Simulation examples are provided to demonstrate the theoretical results

Open Markov Processes and Reaction Networks

We define the concept of an `open' Markov process, a continuous-time Markov chain equipped with specified boundary states through which probability can flow in and out of the system. External couplings which fix the probabilities of boundary states induce non-equilibrium steady states characterized by non-zero probability currents flowing through the system. We show that these non-equilibrium steady states minimize a quadratic form which we call `dissipation.' This is closely related to Prigogine's principle of minimum entropy production. We bound the rate of change of the entropy of a driven non-equilibrium steady state relative to the underlying equilibrium state in terms of the flow of probability through the boundary of the process. We then consider open Markov processes as morphisms in a symmetric monoidal category by splitting up their boundary states into certain sets of `inputs' and `outputs.' Composition corresponds to gluing the outputs of one such open Markov process onto the inputs of another so that the probability flowing out of the first process is equal to the probability flowing into the second. We construct a `black-box' functor characterizing the behavior of an open Markov process in terms of the space of possible steady state probabilities and probability currents along the boundary. The fact that this is a functor means that the behavior of a composite open Markov process can be computed by composing the behaviors of the open Markov processes from which it is composed. We prove a similar black-boxing theorem for reaction networks whose dynamics are given by the non-linear rate equation. Along the way we describe a more general category of open dynamical systems where composition corresponds to gluing together open dynamical systems.Comment: 140 pages, University of California Riverside PhD Dissertatio

Hamiltonian cycles in symmetric graphs.

Let k be a positive integer. We define M[subscript]k to be the graph with a vertex set consisting of all binary strings of length 2k + 1 which have either k or k + 1 ones and edge set consisting of all pairs of these binary strings which differ in exactly one bit. Showing that the graph M[subscript]k is Hamiltonian for all k is known as the Middle Levels problem. This problem was first posed in the early 1980's and to this day remains unsolved. In this thesis we explore the symmetries of M[subscript]k and graphs related to it. We then use these symmetries to propose a method for finding Hamiltonian cycles in M[subscript]k when 2k + 1 and k are prime. We believe that our method is more efficient than methods proposed by previous authors.The original print copy of this thesis may be available here: http://wizard.unbc.ca/record=b159865

Finding common support through largest connected components and its implementation

Master of ScienceDepartment of ManagementMichael HigginsIn an observational study, the average treatment effect may only be reliably estimated for a subset of units under which the covariate space of both treatment and control units overlap. This is known as the common support assumption. In this report, we develop a method to find a region of common support. The method is as follows. Given a distance function to measure dissimilarity between any two units with differing treatment statuses, we can construct an adjacency list by drawing edges between each pair of treated and control units that have distance no larger than some pre-specified threshold. Then, all connected components of the graph are found. Finally, a region of common support is found by obtain- ing the largest connected components (LCC) (e.g. the connected components with the most treated units) of this graph. We implement the LCC algorithm by using binary search trees to find all the connected graphs from sample data and sorting them by size. This algorithm requires O(n²) runtime and O(n) memory (where n is the number of units in the observational study. We then create an R package implementing this LCC algorithm. Finally, we use our R package to compare the performance of LCC to that of other common support methods on simulated data

Path switching over multirate Benes network.

Mui Sze Wai.Thesis (M.Phil.)--Chinese University of Hong Kong, 2003.Includes bibliographical references (leaves 62-65).Abstracts in English and Chinese.Chapter 1. --- Introduction --- p.1Chapter 1.1 --- Evolution of Multirate Networks --- p.2Chapter 1.2 --- Some Results from Previous Work --- p.2Chapter 1.3 --- Multirate Traffic on Benes Network --- p.5Chapter 1.4 --- Organization --- p.7Chapter 2. --- Background Knowledge on Benes Network and Path Switching --- p.8Chapter 2.1 --- Benes Network --- p.9Chapter 2.1.1 --- Construction of Large Switching Fabrics --- p.9Chapter 2.1.2 --- Routing in Benes Network --- p.11Chapter 2.1.3 --- Performance when Operated as a Large Switch Fabric --- p.13Chapter 2.2 --- Path Switching --- p.14Chapter 2.2.1 --- Basic Concept of Path Switching --- p.14Chapter 2.2.2 --- Capacity Allocation and Route Assignment --- p.15Chapter 3. --- Path Switching over Benes Network --- p.20Chapter 3.1 --- The Model of path-switched Benes Network --- p.21Chapter 3.2 --- Module-to-Module Implementation --- p.21Chapter 3.2.1 --- The First Stage (Input Module) --- p.22Chapter 3.2.2 --- The Middle Stage (Central Module) --- p.23Chapter 3.2.3 --- The Last Stage (Output Module) --- p.24Chapter 3.3 --- Port-to-Port Implementation --- p.24Chapter 3.3.1 --- Uniform Traffic --- p.25Chapter 3.3.2 --- Mult irate Traffic --- p.26Chapter 3.4 --- Closing remarks --- p.29Chapter 4. --- Performance Analysis --- p.31Chapter 4.1 --- Traffic Constraints and Perform- ance Guarantees --- p.32Chapter 4.1.1 --- Arrival Curve and Service Curve --- p.33Chapter 4.1.2 --- Delay Bound and Backlog Bound --- p.36Chapter 4.2 --- Service Guarantees --- p.39Chapter 4.3 --- Deterministic Bounds --- p.42Chapter 4.3.1 --- Delay --- p.42Chapter 4.3.2 --- Backlog at Input Module --- p.44Chapter 4.3.3 --- Backlog at Output Module --- p.47Chapter 5. --- Simulation Results --- p.52Chapter 5.1 --- Uniform Traffic --- p.53Chapter 5.2 --- Multirate Traffic --- p.55Chapter 6. --- Conclusions and Future Research --- p.59Chapter 6.1 --- Suggestions for future research --- p.61Bibliography --- p.6

Quantum multipartite entangled states, classical and quantum error correction

Studying entanglement is essential for our understanding of such diverse areas as high-energy physics, condensed matter physics, and quantum optics. Moreover, entanglement allows us to surpass classical physics and technologies enabling better information processing, computation, and improved metrology. Recently, entanglement also played a prominent role in characterizing and simulating quantum many-body states and in this way deepened our understanding of quantum matter. While bipartite entanglement is well understood, multipartite entanglement is much richer and leads to stronger contradictions with classical physics. Among all possible entangled states, a special class of states has attracted attention for a wide range of tasks. These states are called k-uniform states and are pure multipartite quantum states of n parties and local dimension q with the property that all of their reductions to k parties are maximally mixed. Operationally, in a k-uniform state any subset of at most k parties is maximally entangled with the rest. The k = bn/2c-uniform states are called absolutely maximally entangled because they are maximally entangled along any splitting of the n parties into two groups. These states find applications in several protocols and, in particular, are the building blocks of quantum error correcting codes with a holographic geometry, which has provided valuable insight into the connections between quantum information theory and conformal field theory. Their properties and the applications are however intriguing, as we know little about them: when they exist, how to construct them, how they relate to other multipartite entangled states, such as graph states, or how they connect under local operations and classical communication. With this motivation in mind, in this thesis we first study the properties of k-uniform states and then present systematic methods to construct closed-form expressions of them. The structure of our methods proves to be particularly fruitful in understanding the structure of these quantum states, their graph-state representation and classification under local operations and classical communication. We also construct several examples of absolutely maximally entangled states whose existence was open so far. Finally, we explore a new family of quantum error correcting codes that generalize and improve the link between classical error correcting codes, multipartite entangled states, and the stabilizer formalism. The results of this thesis can have a role in characterizing and studying the following three topics: multipartite entanglement, classical error correcting codes and quantum error correcting codes. The multipartite entangled states can provide a link to find different resources for quantum information processing tasks and quantify entanglement. Constructing two sets of highly entangled multipartite states, it is important to know if they are equivalent under local operations and classical communication. By understanding which states belong to the same class of quantum resource, one may discuss the role they play in some certain quantum information tasks like quantum key distribution, teleportation and constructing optimum quantum error correcting codes. They can also be used to explore the connection between the Antide Sitter/Conformal Field Theory holographic correspondence and quantum error correction, which will then allow us to construct better quantum error correcting codes. At the same time, their roles in the characterization of quantum networks will be essential to design functional networks, robust against losses and local noise.El estudio del entrelazamiento cuántico es esencial para la comprensión de diversas áreas como la óptica cuántica, la materia condensada e incluso la física de altas energías. Además, el entrelazamiento nos permite superar la física y tecnologías clásicas llevando a una mejora en el procesado de la información, la computación y la metrología. Recientemente se ha descubierto que el entrelazamiento desarrolla un papel central en la caracterización y simulación de sistemas cuánticos de muchos cuerpos, de esta manera facilitando nuestra comprensión de la materia cuántica. Mientras que se tiene un buen conocimiento del entrelazamiento en estados puros bipartitos, nuestra comprensión del caso de muchas partes es mucho más limitada, a pesar de que sea un escenario más rico y que presenta un contraste más fuerte con la física clásica. De entre todos los posibles estados entrelazados, una clase especial ha llamado la atención por su amplia gama de aplicaciones. Estos estados se llaman k-uniformes y son los estados multipartitos de n cuerpos con dimensión local q con la propiedad de que todas las reducciones a k cuerpos son máximamente desordenadas. Operacionalmente, en un estado k-uniforme cualquier subconjunto de hasta k cuerpos está máximamente entrelazado con el resto. Los estados k = n/2 -uniformes se llaman estados absolutamente máximamente entrelazados porque son máximamente entrelazados respecto a cualquier partición de los n cuerpos en dos grupos. Estos estados encuentran aplicaciones en varios protocolos y, en particular, forman los elementos de base para la construcción de los códigos de corrección de errores cuánticos con geometría holográfica, los cuales han aportado intuición importante sobre la conexión entre la teoría de la información cuántica y la teoría conforme de campos. Las propiedades y aplicaciones de estos estados son intrigantes porque conocemos poco sobre las mismas: cuándo existen, cómo construirlos, cómo se relacionan con otros estados con entrelazamiento multipartito, cómo los estados grafo, o como se relacionan mediante operaciones locales y comunicación clásica. Con esta motivación en mente, en esta tesis primero estudiamos las propiedades de los estados k-uniformes y luego presentamos métodos sistemáticos para construir expresiones cerradas de los mismos. La naturaleza de nuestros métodos resulta ser muy útil para entender la estructura de estos estados cuánticos, su representación como estados grafo y su clasificación bajo operaciones locales y comunicación clásica. También construimos varios ejemplos de estados absolutamente máximamente entrelazados, cuya existencia era desconocida. Finalmente, exploramos una nueva familia de códigos de corrección de errores cuánticos que generalizan y mejoran la conexión entre los códigos de corrección de errores clásicos, los estados entrelazados multipartitos y el formalismo de estabilizadores. Los resultados de esta tesis pueden desarrollar un papel importante en la caracterización y el estudio de las tres siguientes áreas: entrelazamiento multipartito, códigos de corrección de errores clásicos y códigos de corrección de errores cuánticos. Los estados de entrelazamiento multipartito pueden aportar una conexión para encontrar diferentes recursos para tareas de procesamiento de la información cuántica y cuantificación del entrelazamiento. Al construir dos conjuntos de estados multipartitos altamente entrelazados, es importante saber si son equivalentes entre operaciones locales y comunicación clásica. Entendiendo qué estados pertenecen a la misma clase de recurso cuántico, se puede discutir qué papel desempeñan en ciertas tareas de información cuántica, como la distribución de claves criptográficas cuánticas, la teleportación y la construcción de códigos de corrección de errores cuánticos óptimos. También se pueden usar para explorar la conexión entre la correspondencia holográfica Anti-de Sitter/Conformal Field Theory y códigos de corrección de errores cuánticos, que nos permitiría construir mejores códigos de corrección de errores. A la vez, su papel en la caracterización de redes cuánticas será esencial en el diseño de redes funcionales, robustas ante pérdidas y ruidos locales

Algorithms for assessing the quality and difficulty of multiple choice exam questions

Multiple Choice Questions (MCQs) have long been the backbone of standardized testing in academia and industry. Correspondingly, there is a constant need for the authors of MCQs to write and refine new questions for new versions of standardized tests as well as to support measuring performance in the emerging massive open online courses, (MOOCs). Research that explores what makes a question difficult, or what questions distinguish higher-performing students from lower-performing students can aid in the creation of the next generation of teaching and evaluation tools. In the automated MCQ answering component of this thesis, algorithms query for definitions of scientific terms, process the returned web results, and compare the returned definitions to the original definition in the MCQ. This automated method for answering questions is then augmented with a model, based on human performance data from crowdsourced question sets, for analysis of question difficulty as well as the discrimination power of the non-answer alternatives. The crowdsourced question sets come from PeerWise, an open source online college-level question authoring and answering environment. The goal of this research is to create an automated method to both answer and assesses the difficulty of multiple choice inverse definition questions in the domain of introductory biology. The results of this work suggest that human-authored question banks provide useful data for building gold standard human performance models. The methodology for building these performance models has value in other domains that test the difficulty of questions and the quality of the exam takers