A Characterization Theorem for the K-functional Associated with the Algebraic Version of Trigonometric Jackson Integrals

2000 Mathematics Subject Classification: 41A25, 41A36.

A Note on the L2-norm of the Second Fundamental Form of Algebraic Manifolds

2000 Mathematics Subject Classification: 53C42, 53C55.

Neurophysiological investigations for the diagnosis of non-epileptic attack disorder in neuropsychiatry services:from safety standards to improved effectiveness

OBJECTIVE: The discipline of clinical neuropsychiatry currently provides specialised services for a number of conditions that cross the traditional boundaries of neurology and psychiatry, including non-epileptic attack disorder. Neurophysiological investigations have an important role within neuropsychiatry services, with video-electroencephalography (EEG) telemetry being the gold standard investigation for the differential diagnosis between epileptic seizures and non-epileptic attacks. This article reviews existing evidence on best practices for neurophysiology investigations, with focus on safety measures for video-EEG telemetry. METHODS: We conducted a systematic literature review using the PubMed database in order to identify the scientific literature on the best practices when using neurophysiological investigations in patients with suspected epileptic seizures or non-epileptic attacks. RESULTS: Specific measures need to be implemented for video-EEG telemetry to be safely and effectively carried out by neuropsychiatry services. A confirmed diagnosis of non-epileptic attack disorder following video-EEG telemetry carried out within neuropsychiatry units has the inherent advantage of allowing diagnosis communication and implementation of treatment strategies in a timely fashion, potentially improving clinical outcomes and cost-effectiveness significantly. CONCLUSION: The identified recommendations set the stage for the development of standardised guidelines to enable neuropsychiatry services to implement streamlined and evidence-based care pathways.

Algebraic duality theorems for infinite LP problems

In this paper we consider a primal-dual infinite linear programming problem-pair, i.e. LPs on infinite dimensional spaces with infinitely many constraints. We present two duality theorems for the problem-pair: a weak and a strong duality theorem. We do not assume any topology on the vector spaces, therefore our results are algebraic duality theorems. As an application, we consider transferable utility cooperative games with arbitrarily many players.

Algebraic theory of minimal nondeterministic finite automata with applications

Since the 1950s, the theory of deterministic and nondeterministic finite automata (DFAs and NFAs, respectively) has been a cornerstone of theoretical computer science. In this dissertation, our main object of study is minimal NFAs. In contrast with minimal DFAs, minimal NFAs are computationally challenging: first, there can be more than one minimal NFA recognizing a given language; second, the problem of converting an NFA to a minimal equivalent NFA is NP-hard, even for NFAs over a unary alphabet. Our study is based on the development of two main theories, inductive bases and partials, which in combination form the foundation for an incremental algorithm, ibas, to find minimal NFAs. An inductive basis is a collection of languages with the property that it can generate (through union) each of the left quotients of its elements. We prove a fundamental characterization theorem which says that a language can be recognized by an n-state NFA if and only if it can be generated by an n-element inductive basis. A partial is an incompletely-specified language. We say that an NFA recognizes a partial if its language extends the partial, meaning that the NFA’s behavior is unconstrained on unspecified strings; it follows that a minimal NFA for a partial is also minimal for its language. We therefore direct our attention to minimal NFAs recognizing a given partial. Combining inductive bases and partials, we generalize our characterization theorem, showing that a partial can be recognized by an n-state NFA if and only if it can be generated by an n-element partial inductive basis. We apply our theory to develop and implement ibas, an incremental algorithm that finds minimal partial inductive bases generating a given partial. In the case of unary languages, ibas can often find minimal NFAs of up to 10 states in about an hour of computing time; with brute-force search this would require many trillions of years.

Algebraic Theory of Minimal Nondeterministic Finite Automata with Applications

Since the 1950s, the theory of deterministic and nondeterministic finite automata (DFAs and NFAs, respectively) has been a cornerstone of theoretical computer science. In this dissertation, our main object of study is minimal NFAs. In contrast with minimal DFAs, minimal NFAs are computationally challenging: first, there can be more than one minimal NFA recognizing a given language; second, the problem of converting an NFA to a minimal equivalent NFA is NP-hard, even for NFAs over a unary alphabet. Our study is based on the development of two main theories, inductive bases and partials, which in combination form the foundation for an incremental algorithm, ibas, to find minimal NFAs. An inductive basis is a collection of languages with the property that it can generate (through union) each of the left quotients of its elements. We prove a fundamental characterization theorem which says that a language can be recognized by an n-state NFA if and only if it can be generated by an n-element inductive basis. A partial is an incompletely-specified language. We say that an NFA recognizes a partial if its language extends the partial, meaning that the NFA's behavior is unconstrained on unspecified strings; it follows that a minimal NFA for a partial is also minimal for its language. We therefore direct our attention to minimal NFAs recognizing a given partial. Combining inductive bases and partials, we generalize our characterization theorem, showing that a partial can be recognized by an n-state NFA if and only if it can be generated by an n-element partial inductive basis. We apply our theory to develop and implement ibas, an incremental algorithm that finds minimal partial inductive bases generating a given partial. In the case of unary languages, ibas can often find minimal NFAs of up to 10 states in about an hour of computing time; with brute-force search this would require many trillions of years.

Locally recurrent functions, density topologies and algebraic genericity

We study the algebraic and topological genericity of certain subsets of locally recurrent functions, obtaining (among other results) algebrability and spaceability within these classes.

Locally recurrent functions, density topologies and algebraic genericity

We study the algebraic and topological genericity of certain subsets of locally recurrent functions, obtaining (among other results) algebrability and spaceability within these classes.

Mitigate DoS and DDoS Attack in Ad Hoc Networks

This paper proposes a technique to defeat Denial of Service (DoS) and Distributed Denial of Service (DDoS) attacks in Ad Hoc Networks. The technique is divided into two main parts and with game theory and cryptographic puzzles. Introduced first is a new client puzzle to prevent DoS attacks in such networks. The second part presents a multiplayer game that takes place between the nodes of an ad hoc network and based on fundamental principles of game theory. By combining computational problems with puzzles, improvement occurs in the efficiency and latency of the communicating nodes and resistance in DoS and DDoS attacks. Experimental results show the effectiveness of the approach for devices with limited resources and for environments like ad hoc networks where nodes must exchange information quickly.

A monoidal algebraic model for rational SO(2)-spectra

The category of rational SO(2)--equivariant spectra admits an algebraic model. That is, there is an abelian category A(SO(2)) whose derived category is equivalent to the homotopy category of rational$SO(2)--equivariant spectra. An important question is: does this algebraic model capture the smash product of spectra? The category A(SO(2)) is known as Greenlees' standard model, it is an abelian category that has no projective objects and is constructed from modules over a non--Noetherian ring. As a consequence, the standard techniques for constructing a monoidal model structure cannot be applied. In this paper a monoidal model structure on A(SO(2)) is constructed and the derived tensor product on the homotopy category is shown to be compatible with the smash product of spectra. The method used is related to techniques developed by the author in earlier joint work with Roitzheim. That work constructed a monoidal model structure on Franke's exotic model for the K_(p)--local stable homotopy category. A monoidal Quillen equivalence to a simpler monoidal model category that has explicit generating sets is also given. Having monoidal model structures on the two categories removes a serious obstruction to constructing a series of monoidal Quillen equivalences between the algebraic model and rational SO(2)--equivariant spectra.

Oceans Deep: Lesson B (Shark Attack)

Teacher resources for Lesson B in the Discover Oceanography 'Scheme of Work' for use in schools.

Problems in Algebraic Vision

Thesis (Ph.D.)--University of Washington, 2016-08

Attack simulation based software protection assessment method

Software protection is an essential aspect of information security to withstand malicious activities on software, and preserving software assets. However, software developers still lacks a methodology for the assessment of the deployed protections. To solve these issues, we present a novel attack simulation based software protection assessment method to assess and compare various protection solutions. Our solution relies on Petri Nets to specify and visualize attack models, and we developed a Monte Carlo based approach to simulate attacking processes and to deal with uncertainty. Then, based on this simulation and estimation, a novel protection comparison model is proposed to compare different protection solutions. Lastly, our attack simulation based software protection assessment method is presented. We illustrate our method by means of a software protection assessment process to demonstrate that our approach can provide a suitable software protection assessment for developers and software companies.