We develop and test new machine learning methods for the prediction of topological representations of protein structures in the form of coarseor fine-grained contact or distance maps that are translation and rotation invariant. The methods are based on generalized input-output hidden Markov models (GIOHMMs) and generalized recursive neural networks (GRNNs). The methods are used to predict topol...

Recent interest in high frequency resonant converters has prompted this exploration of aspects that have not previously been studied carefully. More specifically, this thesis examines possible methods for deriving resonant converter topologies and show how to develop dynamic models for converter behavior, demonstrates the design and implementation of control schemes based on these models. Syste...

In the analysis of complex networks, the description of evolutionary processes, or investigations into dynamics on fitness or energy landscapes notions such as similarity, neighborhood, connectedness, or continuity of change appear in a natural way. These concepts are of an inherently topological nature. Nevertheless, the connection to the mathematical discipline of point set topology is rarely...

Both preorders and ordinary ultrametric spaces are instances of generalized ul-trametric spaces. Every generalized ultrametric space can be isometrically embedded in a (complete) function space by means of an ultrametric version of the categorical Yoneda Lemma. This simple fact gives naturally rise to: 1. a topology for generalized ultrametric spaces which for arbitrary preorders corresponds to...

The Bohr compactification and the Bohr topology are well known for groups, but they can easily be generalized to arbitrary structures. We prove a number of theorems about Bohr topologies in this general setting. Some of these results are new even for groups; for example, the weight of the Bohr compactification of a countable structure is either countable or continuum. In some cases, theorems ab...

Queueing networks with finite buffers, multiple servers, arbitrary acyclic, series-parallel topologies, and general service time distributions are considered in this paper. An approach to optimally allocate servers to series, merge, and split topologies and their combinations is demonstrated. The methodology builds upon two-moment approximations to the service time distribution embedded in the ...

Generalized metric spaces are a common generalization of preorders and ordinary metric spaces (Lawvere, 1973). Combining Lawvere’s (1973) enriched-categorical and Smyth’s (1988, 1991) topological view on generalized metric spaces, it is shown how to construct (1) completion, (2) two topologies, and (3) powerdomains for generalized metric spaces. Restricted to the special cases of preorders and ...

The power consumption for various opamps used in modulators are considered. We rst classify the diierent opamp topologies used in such modulators. We then develop a generalized in-tegrator model that allows us to compare the power consumption for all these topologies. We also derive an expression for the minimum theoretical bound on the power dissipation. We illustrate our results with two desi...

The main purpose of this paper is to introduce the compatibility of $M$-fuzzifying topologies and $M$-fuzzifying convexities, define an $M$-fuzzifying topological convex space, and give a method to generate an $M$-fuzzifying topological convex space. Some characterizations of $M$-fuzzifying topological convex spaces are presented. Finally, the notion of $M$-fuzzifying weak topologies is obtaine...

We show examples which reveal influences of spatial topologies to dynamics, using a class of spatially closed inhomogeneous cosmological models. The models, called the locally U(1)×U(1) symmetric models (or the generalized Gowdy models), are characterized by the existence of two commuting spatial local Killing vectors. For systematic investigations we first present a classification of possible ...