Aggregation operators on partially ordered sets and their categorical foundations

summary:In spite of increasing studies and investigations in the field of aggregation operators, there are two fundamental problems remaining unsolved: aggregation of $L$-fuzzy set-theoretic notions and their justification. In order to solve these problems, we will formulate aggregation operators and their special types on partially ordered sets with universal bounds, and introduce their categories. Furthermore, we will show that there exists a strong connection between the category of aggregation operators on partially ordered sets with universal bounds (Agop) and the category of partially ordered groupoids with universal bounds (Pogpu). Moreover, the subcategories of Agop consisting of associative aggregation operators, symmetric and associative aggregation operators and associative aggregation operators with neutral elements are, respectively, isomorphic to the subcategories of Pogpu formed by partially ordered semigroups, commutative partially ordered semigroups and partially ordered monoids in the sense of Birkhoff. As a justification of the present notions and results, some relevant examples for aggregations operators on partially ordered sets are given. Particularly, aggregation process in probabilistic metric spaces is also considered

Fuzzy Knowledge Based Reliability Evaluation and Its Application to Power Generating System

PhDThe method of using Fuzzy Sets Theory(FST) and Fuzzy Reasoning(FR) to aid reliability evaluation in a complex and uncertain environment is studied, with special reference to electrical power generating system reliability evaluation. Device(component) reliability prediction contributes significantly to a system's reliability through their ability to identify source and causes of unreliability. The main factors which affect reliability are identified in Reliability Prediction Process(RPP). However, the relation between reliability and each affecting factor is not a necessary and sufficient one. It is difficult to express this kind of relation precisely in terms of quantitative mathematics. It is acknowledged that human experts possesses some special characteristics that enable them to learn and reason in a vague and fuzzy environment based on their experience. Therefore, reliability prediction can be classified as a human engineer oriented decision process. A fuzzy knowledge based reliability prediction framework, in which speciality rather than generality is emphasised, is proposed in the first part of the thesis. For this purpose, various factors affected device reliability are investigated and the knowledge trees for predicting three reliability indices, i.e. failure rate, maintenance time and human error rate are presented. Human experts' empirical and heuristic knowledge are represented by fuzzy linguistic rules and fuzzy compositional rule of inference is employed as inference tool. Two approaches to system reliability evaluation are presented in the second part of this thesis. In first approach, fuzzy arithmetic are conducted as the foundation for system reliability evaluation under the fuzzy envimnment The objective is to extend the underlying fuzzy concept into strict mathematics framework in order to arrive at decision on system adequacy based on imprecise and qualitative information. To achieve this, various reliability indices are modelled as Trapezoidal Fuzzy Numbers(TFN) and are proceeded by extended fuzzy arithmetic operators. In second approach, the knowledge of system reliability evaluation are modelled in the form of fuzzy combination production rules and device combination sequence control algorithm. System reliability are evaluated by using fuzzy inference system. Comparison of two approaches are carried out through case studies. As an application, power generating system reliability adequacy is studied. Under the assumption that both unit reliability data and load data are subjectively estimated, these fuzzy data are modelled as triangular fuzzy numbers, fuzzy capacity outage model and fuzzy load model are developed by using fuzzy arithmetic operations. Power generating system adequacy is evaluated by convoluting fuzzy capacity outage model with fuzzy load model. A fuzzy risk index named "Possibility Of Load Loss" (POLL) is defined based on the concept of fuzzy containment The proposed new index is tested on IEEE Reliability Test System (RTS) and satisfactory results are obtained Finally, the implementation issues of Fuzzy Rule Based Expert System Shell (FRBESS) are reported. The application of ERBESS to device reliability prediction and system reliability evaluation is discussed

Unfolded, misfolded, and self-organized short alanine-rich peptides: implications for fundamental science, human disease, and biotechnology

Protein folding is the reversible transition by which an unordered polypeptide chain attains its functional 3-D native structure. A detailed understanding of the principles which govern the protein folding process, such as how sequence codes for structure, remains elusive. Achieving a complete picture of the folding process requires information regarding structural preferences in the unfolded state. Moreover, understanding the principles which govern protein aggregation is of significant biomedical and biotechnological importance. Herein, short alanine-based peptides are used as model systems for studying both the structural preferences in the unfolded state as well as protein aggregation in relation to human disease, and exploitation of the self-assembly process for various biotechnological applications.It is now a central dogma of protein science that the unfolded state is not conformationally random, as was originally believed, but that, instead, residual structure exists. Here, we elucidate the conformational propensities of alanine in the unfolded state using short alanine-rich peptides as model systems. The intrinsic conformational propensities of alanine, as well as nearest neighbor effects are illuminated using various vibrational spectroscopic methods, combined with NMR results.Protein and peptide aggregation is affiliated with various seemingly unrelated diseases, including several neurodegenerative diseases and the systemic amyloidoses. It is of current belief that aggregation is a general feature of the protein energy landscape, suggesting that the various unrelated human pathologies linked to protein aggregation are linked by common principles. Herein, fibril formation of a short alanine-based peptide with no known disease affiliation is probed by vibrational circular dichroism (VCD) spectroscopy. In particular, it is demonstrated that peptide fibrils give rise to VCD intensity enhancement, illustrating the use of the technique as a novel means to probe aggregation kinetics.In addition to the biomedical relevance, protein and peptide self-assembly can be exploited as a means of constructing biomaterials with inherent biofunctionality. In this regard, oligopeptide-based hydrogels have shown potential as drug delivery systems and tissue engineering scaffolds. Herein, the unique properties of a novel class of self-assembling alanine-rich oligoopeptides are presented. In particular, it is demonstrated that conformational instability can be exploited to tune the physicochemical properties of hydrogels formed by such systems, for the potential use in various biotechnological applications.Ph.D., Physical Chemistry -- Drexel University, 201

Nonstandard Mathematics and New Zeta and L-Functions

This Ph.D. thesis, prepared under the supervision of Professor Ivan Fesenko, defines new zeta functions in a nonstandard setting and their analytical properties are developed. Further, p-adic interpolation is presented within a nonstandard setting which enables the concept of interpolating with respect to two, or more, distinct primes to be defined. The final part of the dissertation examines the work of M. J. Shai Haran and makes initial attempts of viewing it from a nonstandard perspective.Comment: Ph.D. Thesis, University of Nottingham, 2007, 163 page

Development of advanced control strategies for Adaptive Optics systems

Atmospheric turbulence is a fast disturbance that requires high control frequency. At the same time, celestial objects are faint sources of light and thus WFSs often work in a low photon count regime. These two conditions require a trade-off between high closed-loop control frequency to improve the disturbance rejection performance, and large WFS exposure time to gather enough photons for the integrated signal to increase the Signal-to-Noise ratio (SNR), making the control a delicate yet fundamental aspect for AO systems. The AO plant and atmospheric turbulence were formalized as state-space linear time-invariant systems. The full AO system model is the ground upon which a model-based control can be designed. A Shack-Hartmann wavefront sensor was used to measure the horizontal atmospheric turbulence. The experimental measurements yielded to the Cn2 atmospheric structure parameter, which is key to describe the turbulence statistics, and the Zernike terms time-series. Experimental validation shows that the centroid extraction algorithm implemented on the Jetson GPU outperforms (i.e. is faster) than the CPU implementation on the same hardware. In fact, due to the construction of the Shack-Hartmann wavefront sensor, the intensity image captured from its camera is partitioned into several sub-images, each related to a point of the incoming wavefront. Such sub-images are independent each-other and can be computed concurrently. The AO model is exploited to automatically design an advanced linear-quadratic Gaussian controller with integral action. Experimental evidence shows that the system augmentation approach outperforms the simple integrator and the integrator filtered with the Kalman predictor, and that it requires less parameters to tune

Defining local order in the unfolded state using short peptide model systems and spectroscopic methods: conformational biases, mediation by solvation, and nearest neighbor effects!

This thesis describes conformational ensembles of amino acid residues in unfolded peptides, and how their dependence on solvation and nearest-neighbor interactions can be obtained by a combination of vibrational and NMR spectroscopies. To this end, short peptide model systems may be chosen ranging from dipeptides to blocked and unblocked tripeptides. The question then arises whether one type of model system is more suitable for studying conformational propensities. Results from our spectroscopic studies suggest that the conformational ensemble of trialanine and its high pPII content are independent of the peptide's protonation state. In addition, we find that the conformational ensemble of the alanine dipeptide, a classic peptide model system, resembles the unblocked GAG model peptide, as expected in the absence of any end effects. To explore the physical basis underlying residue-level conformational bias we utilized UVCD and NMR derived 3J coupling constants to decompose the Gibbs free energy landscape. We found that the thermodynamics underling conformational propensities of (1) trialanine in different binary solvents and (2) GxG peptides in water exhibit a near exact enthalpy-entropy compensation involving rarely observed isoequilibria. Their existence indicates peptide solvation as the common physical mechanism behind conformational preferences. Contrary to the isolated pair hypothesis, an ingredient of the classical random coil model, amino acid residues can not be considered as isolated from their neighbors in the unfolded state. To explore nearest neighbor (NN) interactions, we chose a series of "GxyG" host guest peptides, where x/y={A,K,LV}. Utilizing a six different NMR J- coupling constants in conjunction with amide I' (IR, VCD, Raman) band profiles we extracted the conformational distributions of x and y residues in the GxyG peptides. Our data reveal large changes in conformational distributions due to neighbor interactions, contrary to the isolated pair hypothesis. Interestingly, residues that have large intrinsic biases towards specific sub-populations tend to loose these preferences upon interaction with a given neighbor, indicating a degree of conformational randomization. Strong effects induced by residues with bulky side chains suggests that the underlying mechanism is the the disruption of neighboring residues' hydration shells.Ph.D., Chemistry -- Drexel University, 201

Command and Control in the Information Age: A Case Study of a Representative Air Power Command and Control Node

As operations command structures change, it is important to be able to explore and understand their fundamental nature; researchers should unearth the gestalt nature of the operational node. The organizational structure and the infrastructure can significantly affect overall command and control (C2) performance. Thus, it is necessary to develop understanding of effectiveness of the technical network and the people using the system as a whole. The purpose of this research is to conduct an analysis of a representative Air Power Operational C2 node, create and use a repeatable method, and present the results as a case study to elicit fundamental understanding. I posit that there is a recognizable (and discoverable) relationship between the social (human) network and technical supporting network. Examining the system under change can result in an understanding of this relationship. In this work, I enhanced an existing simulation tool to investigate the effects of organizational structure on task effectiveness. The primary research question examined is how a representative AOC system changes varying noise and system fragmentation when operating in two different organizational constructs. Network-Enabled Capability (as the term is used in NATO), Network Centric Operations, or Edge Organizations, is a core C2 transformation predicated upon a set of network-centric tenets. These tenets form the intellectual foundation for ongoing transformations. The secondary research question is to determine if these tenets are unbound, and what elucidation results if they are not. This research produces four significant contributions to Operational Command and Control and Engineering Management disciplines. First, I combined social networking theory and information theory into a single lens for evaluation. By using this new concept, I will be able to accomplish a quantitative evaluation by something other than mission treads, field exercise, historical evaluation, or actual combat. Second, I used both information theory and social networking concepts in a non-traditional setting. Third, I hope this research will start the process required to gain the knowledge to achieve some sort of future C2 structure. Fourth, this research suggests directions for future research to enhance understanding of core Operational Command and Control concepts

Analysing the role of public-private partnerships in global governance: institutional dynamics, variation and effects

While the promotion and growth of global public-private partnerships (PPPs) is indisputable, the same enthusiasm has not fuelled their disciplined study; thus, their potential to deliver on their promise of being effective and legitimate governance entities is far from established. Addressing this lack, this work investigates the universe of transnational PPPs in form, functioning and effects. It suggests that as PPPs are institutional innovations, partnership analysis can benefit from applying theoretical constructs from international regime research complemented with adjacent literature from management and organisational studies. Building an analytical framework based on the notions of input and output legitimacy, the work analyses how variation in partnership inputs (focus, actors involved, organisational dynamics and institutionalisation) interacts with varying internal management processes to result in varying outputs. The thesis utilises the operational notion of effects rather than the more subjective notion of partnership effectiveness, and considers effects related to goal attainment and problem solving. Applying a systematic methodology, the work also defines and describes the universe of PPPs, creating a transnational partnership database (TPD) which pulls together all existing sources, thus encompassing 757 partnerships. The resultant analysis reveals a marked variation across the universe of transnational partnerships as well as distinct differences in their operational capacity. It also highlights that while highly institutionalised PPPs are more likely to produce tangible outputs and effects, the extent of these is highly dependent upon internal management. By building a cumulative understanding of these institutional models, the work furthers debates regarding the role of PPPs as legitimate and effective governing actors