Results on singularities of pairs

Thesis (Ph.D.)--University of Washington, 2016-06

Leibniz on Rational Decision-Making

In this study I discuss G. W. Leibniz's (1646-1716) views on rational decision-making from the standpoint of both God and man. The Divine decision takes place within creation, as God freely chooses the best from an infinite number of possible worlds. While God's choice is based on absolutely certain knowledge, human decisions on practical matters are mostly based on uncertain knowledge. However, in many respects they could be regarded as analogous in more complicated situations. In addition to giving an overview of the divine decision-making and discussing critically the criteria God favours in his choice, I provide an account of Leibniz's views on human deliberation, which includes some new ideas. One of these concerns is the importance of estimating probabilities in making decisions one estimates both the goodness of the act itself and its consequences as far as the desired good is concerned. Another idea is related to the plurality of goods in complicated decisions and the competition this may provoke. Thirdly, heuristic models are used to sketch situations under deliberation in order to help in making the decision. Combining the views of Marcelo Dascal, Jaakko Hintikka and Simo Knuuttila, I argue that Leibniz applied two kinds of models of rational decision-making to practical controversies, often without explicating the details. The more simple, traditional pair of scales model is best suited to cases in which one has to decide for or against some option, or to distribute goods among parties and strive for a compromise. What may be of more help in more complicated deliberations is the novel vectorial model, which is an instance of the general mathematical doctrine of the calculus of variations. To illustrate this distinction, I discuss some cases in which he apparently applied these models in different kinds of situation. These examples support the view that the models had a systematic value in his theory of practical rationality.

A rational synthesis of vibration isolators

The paper deals with a rational approach to the development of general design criteria for non-dissipative vibration isolation systems. The study covers straight-through springmass systems as well as branched ones with dynamic absorbers. Various design options, such as the addition of another spring-mass pair, replacement of an existing system by one with more spring-mass pairs for the same space and material requirements, provision of one or more dynamic absorbers for the desired frequency range, etc., are investigated quantitatively by means of an algebraic algorithm which enables one to write down straightaway the velocity ratio and hence transmissibility of a linear dynamical system in terms of the constituent parameters.

Common Fixed Points of Generalized Rational Type Cocyclic Mappings in Multiplicative Metric Spaces

The aim of this paper is to present fixed point result of mappings satisfying a generalized rational contractive condition in the setup of multiplicative metric spaces. As an application, we obtain a common fixed point of a pair of weakly compatible mappings. Some common fixed point results of pair of rational contractive types mappings involved in cocyclic representation of a nonempty subset of a multiplicative metric space are also obtained. Some examples are presented to support the results proved herein. Our results generalize and extend various results in the existing literature.

From Rational Design of Drug Crystals to Understanding of Nucleic Acid Structures: Lamivudine Duplex

A DNA-like duplex of nucleosides is probable to exist even without the 5`-phosphate groups needed to assemble the chain backbone. However, double-stranded helical structures of nucleosides are unknown. Here, we report a duplex of nucleoside analogs that is spontaneously assembled due to stacking of the neutral and protonated molecules of lamivudine, a nucleoside reverse transcriptase inhibitor (NTRI) widely used in anti-HIV drug combinatory medication. The left-handed lamivudine duplex has features similar to those of i-motif DNA, as the face-to-face base stacking and the helix rise per base pair. Furthermore, the protonation pattern on alternate bases expected for it DNA-like duplex stabilized by pairing of neutral and protonated cytosine fragments was observed for the first time in the lamivudine double-stranded helix. This structure demonstrates that hydrogen bonds can substitute for covalent phosphodiester linkage in the stabilization of the duplex backbone. This interesting example of spontaneous molecular self-organization indicates that the 5`-phosphate group could not be a requirement for duplex assembly.

Sustainable Catalysis : Rational Pd Loading on MIL-101Cr-NH2 for More Efficient and Recyclable Suzuki-Miyaura Reactions

Palladium nanoparticles have been immobilized into an amino-functionalized metal-organic framework (MOF), MIL-101Cr-NH2, to form Pd@MIL-101Cr-NH2. Four materials with different loadings of palladium have been prepared (denoted as 4-, 8-, 12-, and 16wt%Pd@MIL-101Cr-NH2). The effects of catalyst loading and the size and distribution of the Pd nanoparticles on the catalytic performance have been studied. The catalysts were characterized by using scanning electron microscopy (SEM), transmission electron microscopy (TEM), Fourier-transform infrared (FTIR) spectroscopy, powder X-ray diffraction (PXRD), N-2-sorption isotherms, elemental analysis, and thermogravimetric analysis (TGA). To better characterize the palladium nanoparticles and their distribution in MIL-101Cr-NH2, electron tomography was employed to reconstruct the 3D volume of 8wt%Pd@MIL-101Cr-NH2 particles. The pair distribution functions (PDFs) of the samples were extracted from total scattering experiments using high-energy X-rays (60keV). The catalytic activity of the four MOF materials with different loadings of palladium nanoparticles was studied in the Suzuki-Miyaura cross-coupling reaction. The best catalytic performance was obtained with the MOF that contained 8wt% palladium nanoparticles. The metallic palladium nanoparticles were homogeneously distributed, with an average size of 2.6nm. Excellent yields were obtained for a wide scope of substrates under remarkably mild conditions (water, aerobic conditions, room temperature, catalyst loading as low as 0.15mol%). The material can be recycled at least 10times without alteration of its catalytic properties.

Cognitive behaviour therapy vs rational-emotive education : impact on children's self-talk, self-esteem and irrational beliefs

This study investigated the impact of Cognitive-Behavioural Therapy (CBT) and Rational~Emotive Education (REE) self-enhancement programs on children's self-talk, self-esteem and irrational beliefs. A total of 116 children (50.9% girls) with a mean age of 9.8 years attending Years 4 and 6 at two primary schools participated in the study. eBT resulted in a reduction in negative self-talk while REE seemed to enhance independence beliefs. Both programs were associated with increased positive self-talk and with having increased rationality in Conformity and Discomfort Intolerance beliefs.

Modeling corneal surfaces with rational functions for high-speed videokeratoscopy data compression

High-speed videokeratoscopy is an emerging technique that enables study of the corneal surface and tear-film dynamics. Unlike its static predecessor, this new technique results in a very large amount of digital data for which storage needs become significant. We aimed to design a compression technique that would use mathematical functions to parsimoniously fit corneal surface data with a minimum number of coefficients. Since the Zernike polynomial functions that have been traditionally used for modeling corneal surfaces may not necessarily correctly represent given corneal surface data in terms of its optical performance, we introduced the concept of Zernike polynomial-based rational functions. Modeling optimality criteria were employed in terms of both the rms surface error as well as the point spread function cross-correlation. The parameters of approximations were estimated using a nonlinear least-squares procedure based on the Levenberg-Marquardt algorithm. A large number of retrospective videokeratoscopic measurements were used to evaluate the performance of the proposed rational-function-based modeling approach. The results indicate that the rational functions almost always outperform the traditional Zernike polynomial approximations with the same number of coefficients.

Assessment of oral proficiency in EAP programs : a case for pair interaction

Reliability and validity in the testing of spoken language are essential in order to assess learners' English language proficiency as evidence of their readiness to begin courses in tertiary institutions. Research has indicated that the task chosen to elicit language samples can have a marked effect on both the nature of the interaction, including the power differential, and assessment, raising the issue of ethics. This exploratory studey, with a group of 32 students from the Peoples's Republic of China preparing for tertiary study in Singapore, compares test-takers' reactions to the use of an oral proficiency interview and a pair interaction.

Vulnerability assessment of reinforced concrete columns subjected to vehicular impacts

Columns are one of the key load bearing elements that are highly susceptible to vehicle impacts. The resulting severe damages to columns may leads to failures of the supporting structure that are catastrophic in nature. However, the columns in existing structures are seldom designed for impact due to inadequacies of design guidelines. The impact behaviour of columns designed for gravity loads and actions other than impact is, therefore, of an interest. A comprehensive investigation is conducted on reinforced concrete column with a particular focus on investigating the vulnerability of the exposed columns and to implement mitigation techniques under low to medium velocity car and truck impacts. The investigation is based on non-linear explicit computer simulations of impacted columns followed by a comprehensive validation process. The impact is simulated using force pulses generated from full scale vehicle impact tests. A material model capable of simulating triaxial loading conditions is used in the analyses. Circular columns adequate in capacity for five to twenty story buildings, designed according to Australian standards are considered in the investigation. The crucial parameters associated with the routine column designs and the different load combinations applied at the serviceability stage on the typical columns are considered in detail. Axially loaded columns are examined at the initial stage and the investigation is extended to analyse the impact behaviour under single axis bending and biaxial bending. The impact capacity reduction under varying axial loads is also investigated. Effects of the various load combinations are quantified and residual capacity of the impacted columns based on the status of the damage and mitigation techniques are also presented. In addition, the contribution of the individual parameter to the failure load is scrutinized and analytical equations are developed to identify the critical impulses in terms of the geometrical and material properties of the impacted column. In particular, an innovative technique was developed and introduced to improve the accuracy of the equations where the other techniques are failed due to the shape of the error distribution. Above all, the equations can be used to quantify the critical impulse for three consecutive points (load combinations) located on the interaction diagram for one particular column. Consequently, linear interpolation can be used to quantify the critical impulse for the loading points that are located in-between on the interaction diagram. Having provided a known force and impulse pair for an average impact duration, this method can be extended to assess the vulnerability of columns for a general vehicle population based on an analytical method that can be used to quantify the critical peak forces under different impact durations. Therefore the contribution of this research is not only limited to produce simplified yet rational design guidelines and equations, but also provides a comprehensive solution to quantify the impact capacity while delivering new insight to the scientific community for dealing with impacts.

Rational design of serine protease inhibitors

Proteases regulate a spectrum of diverse physiological processes, and dysregulation of proteolytic activity drives a plethora of pathological conditions. Understanding protease function is essential to appreciating many aspects of normal physiology and progression of disease. Consequently, development of potent and specific inhibitors of proteolytic enzymes is vital to provide tools for the dissection of protease function in biological systems and for the treatment of diseases linked to aberrant proteolytic activity. The studies in this thesis describe the rational design of potent inhibitors of three proteases that are implicated in disease development. Additionally, key features of the interaction of proteases and their cognate inhibitors or substrates are analysed and a series of rational inhibitor design principles are expounded and tested. Rational design of protease inhibitors relies on a comprehensive understanding of protease structure and biochemistry. Analysis of known protease cleavage sites in proteins and peptides is a commonly used source of such information. However, model peptide substrate and protein sequences have widely differing levels of backbone constraint and hence can adopt highly divergent structures when binding to a protease’s active site. This may result in identical sequences in peptides and proteins having different conformations and diverse spatial distribution of amino acid functionalities. Regardless of this, protein and peptide cleavage sites are often regarded as being equivalent. One of the key findings in the following studies is a definitive demonstration of the lack of equivalence between these two classes of substrate and invalidation of the common practice of using the sequences of model peptide substrates to predict cleavage of proteins in vivo. Another important feature for protease substrate recognition is subsite cooperativity. This type of cooperativity is commonly referred to as protease or substrate binding subsite cooperativity and is distinct from allosteric cooperativity, where binding of a molecule distant from the protease active site affects the binding affinity of a substrate. Subsite cooperativity may be intramolecular where neighbouring residues in substrates are interacting, affecting the scissile bond’s susceptibility to protease cleavage. Subsite cooperativity can also be intermolecular where a particular residue’s contribution to binding affinity changes depending on the identity of neighbouring amino acids. Although numerous studies have identified subsite cooperativity effects, these findings are frequently ignored in investigations probing subsite selectivity by screening against diverse combinatorial libraries of peptides (positional scanning synthetic combinatorial library; PS-SCL). This strategy for determining cleavage specificity relies on the averaged rates of hydrolysis for an uncharacterised ensemble of peptide sequences, as opposed to the defined rate of hydrolysis of a known specific substrate. Further, since PS-SCL screens probe the preference of the various protease subsites independently, this method is inherently unable to detect subsite cooperativity. However, mean hydrolysis rates from PS-SCL screens are often interpreted as being comparable to those produced by single peptide cleavages. Before this study no large systematic evaluation had been made to determine the level of correlation between protease selectivity as predicted by screening against a library of combinatorial peptides and cleavage of individual peptides. This subject is specifically explored in the studies described here. In order to establish whether PS-SCL screens could accurately determine the substrate preferences of proteases, a systematic comparison of data from PS-SCLs with libraries containing individually synthesised peptides (sparse matrix library; SML) was carried out. These SML libraries were designed to include all possible sequence combinations of the residues that were suggested to be preferred by a protease using the PS-SCL method. SML screening against the three serine proteases kallikrein 4 (KLK4), kallikrein 14 (KLK14) and plasmin revealed highly preferred peptide substrates that could not have been deduced by PS-SCL screening alone. Comparing protease subsite preference profiles from screens of the two types of peptide libraries showed that the most preferred substrates were not detected by PS SCL screening as a consequence of intermolecular cooperativity being negated by the very nature of PS SCL screening. Sequences that are highly favoured as result of intermolecular cooperativity achieve optimal protease subsite occupancy, and thereby interact with very specific determinants of the protease. Identifying these substrate sequences is important since they may be used to produce potent and selective inhibitors of protolytic enzymes. This study found that highly favoured substrate sequences that relied on intermolecular cooperativity allowed for the production of potent inhibitors of KLK4, KLK14 and plasmin. Peptide aldehydes based on preferred plasmin sequences produced high affinity transition state analogue inhibitors for this protease. The most potent of these maintained specificity over plasma kallikrein (known to have a very similar substrate preference to plasmin). Furthermore, the efficiency of this inhibitor in blocking fibrinolysis in vitro was comparable to aprotinin, which previously saw clinical use to reduce perioperative bleeding. One substrate sequence particularly favoured by KLK4 was substituted into the 14 amino acid, circular sunflower trypsin inhibitor (SFTI). This resulted in a highly potent and selective inhibitor (SFTI-FCQR) which attenuated protease activated receptor signalling by KLK4 in vitro. Moreover, SFTI-FCQR and paclitaxel synergistically reduced growth of ovarian cancer cells in vitro, making this inhibitor a lead compound for further therapeutic development. Similar incorporation of a preferred KLK14 amino acid sequence into the SFTI scaffold produced a potent inhibitor for this protease. However, the conformationally constrained SFTI backbone enforced a different intramolecular cooperativity, which masked a KLK14 specific determinant. As a consequence, the level of selectivity achievable was lower than that found for the KLK4 inhibitor. Standard mechanism inhibitors such as SFTI rely on a stable acyl-enzyme intermediate for high affinity binding. This is achieved by a conformationally constrained canonical binding loop that allows for reformation of the scissile peptide bond after cleavage. Amino acid substitutions within the inhibitor to target a particular protease may compromise structural determinants that support the rigidity of the binding loop and thereby prevent the engineered inhibitor reaching its full potential. An in silico analysis was carried out to examine the potential for further improvements to the potency and selectivity of the SFTI-based KLK4 and KLK14 inhibitors. Molecular dynamics simulations suggested that the substitutions within SFTI required to target KLK4 and KLK14 had compromised the intramolecular hydrogen bond network of the inhibitor and caused a concomitant loss of binding loop stability. Furthermore in silico amino acid substitution revealed a consistent correlation between a higher frequency of formation and the number of internal hydrogen bonds of SFTI-variants and lower inhibition constants. These predictions allowed for the production of second generation inhibitors with enhanced binding affinity toward both targets and highlight the importance of considering intramolecular cooperativity effects when engineering proteins or circular peptides to target proteases. The findings from this study show that although PS-SCLs are a useful tool for high throughput screening of approximate protease preference, later refinement by SML screening is needed to reveal optimal subsite occupancy due to cooperativity in substrate recognition. This investigation has also demonstrated the importance of maintaining structural determinants of backbone constraint and conformation when engineering standard mechanism inhibitors for new targets. Combined these results show that backbone conformation and amino acid cooperativity have more prominent roles than previously appreciated in determining substrate/inhibitor specificity and binding affinity. The three key inhibitors designed during this investigation are now being developed as lead compounds for cancer chemotherapy, control of fibrinolysis and cosmeceutical applications. These compounds form the basis of a portfolio of intellectual property which will be further developed in the coming years.

Rational avoidance of accountability

Anthony Downs public choice theory proposes that every rational person would try to meet their own desires in preference to those of others, and that such rational persons would attempt to obtain these desires in the most efficient manner possible. This paper will demonstrate that the application of this theory would mean that public servants and politicians would perform acts of corruption and maladministration in order to efficiently meet their desires. As such action is unavoidable, political parties must appear to meet the public demand for accountability systems, but must not make these systems viable lest they expose the corruption and maladministration that would threaten the government’s chance or re-election. It is therefore logical for governments to display a commitment for accountability whilst simultaneously ensuring the systems would not be able to interfere with government control or expose its flaws.

Roll the dice, rational agent : should extra-curial punishment mitigate an offender's sentence?

It was rugby league State of Origin night 2008 and a group of adults had descended upon a house in Eagleby, Brisbane to have some drinks and to celebrate the game. At 11pm that evening, Shane Thomas Davidson entered the bedroom of the homeowner’s 10-year-old son, TC. Davidson approached the bed and began to massage the boy’s penis under his clothing, which caused TC to wake. Davidson stated, ‘Show me how big your willy is and I’ll show you how big mine is’. TC refused the request and after a small period of time, left the bedroom and told his father what had happened...

Quantifying spatial structure in experimental observations and agent-based simulations using pair-correlation functions

We define a pair-correlation function that can be used to characterize spatiotemporal patterning in experimental images and snapshots from discrete simulations. Unlike previous pair-correlation functions, the pair-correlation functions developed here depend on the location and size of objects. The pair-correlation function can be used to indicate complete spatial randomness, aggregation or segregation over a range of length scales, and quantifies spatial structures such as the shape, size and distribution of clusters. Comparing pair-correlation data for various experimental and simulation images illustrates their potential use as a summary statistic for calibrating discrete models of various physical processes.