On the denominator values and barycentric weights of rational interpolants

We improve upon the method of Zhu and Zhu [A method for directly finding the denominator values of rational interpolants, J. Comput. Appl. Math. 148 (2002) 341-348] for finding the denominator values of rational interpolants, reducing considerably the number of arithmetical operations required for their computation. In a second stage, we determine the points (if existent) which can be discarded from the rational interpolation problem. Furthermore, when the interpolant has a linear denominator, we obtain a formula for the barycentric weights which is simpler than the one found by Berrut and Mittelmann [Matrices for the direct determination of the barycentric weights of rational interpolation, J. Comput. Appl. Math. 78 (1997) 355-370]. Subsequently, we give a necessary and sufficient condition for the rational interpolant to have a pole. (c) 2006 Elsevier B.V. All rights reserved.

Direct and Inverse Results on Row Sequences of Hermite-Pad, Approximants

We give necessary and sufficient conditions for the convergence with geometric rate of the common denominators of simultaneous rational interpolants with a bounded number of poles. The conditions are expressed in terms of intrinsic properties of the system of functions used to build the approximants. Exact rates of convergence for these denominators and the simultaneous rational approximants are provided.

Meromorphic continuation of functions and arbitrary distribution of interpolation points

We characterize the region of meromorphic continuation of an analytic function ff in terms of the geometric rate of convergence on a compact set of sequences of multi-point rational interpolants of ff. The rational approximants have a bounded number of poles and the distribution of interpolation points is arbitrary.

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.

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...

Rational design of artificial cellular niches for tissue engineering

Tissue Engineering is a promising emerging field that studies the intrinsic regenerative potential of the human body and uses it to restore functionality of damaged organs or tissues unable of self-healing due to illness or ageing. In order to achieve regeneration using Tissue Engineering strategies, it is first necessary to study the properties of the native tissue and determine the cause of tissue failure; second, to identify an optimum population of cells capable of restoring its functionality; and third, to design and manufacture a cellular microenvironment in which those specific cells are directed towards the desired cellular functions. The design of the artificial cellular niche has a tremendous importance, because cells will feel and respond to both its biochemical and biophysical properties very differently. In particular, the artificial niche will act as a physical scaffold for the cells, allowing their three-dimensional spatial organization; also, it will provide mechanical stability to the artificial construct; and finally, it will supply biochemical and mechanical cues to control cellular growth, migration, differentiation and synthesis of natural extracellular matrix. During the last decades, many scientists have made great contributions to the field of Tissue Engineering. Even though this research has frequently been accompanied by vast investments during extended periods of time, yet too often these efforts have not been enough to translate the advances into new clinical therapies. More and more scientists in this field are aware of the need of rational experimental designs before carrying out complex, expensive and time-consuming in vitro and in vivo trials. This review highlights the importance of computer modeling and novel biofabrication techniques as critical key players for a rational design of artificial cellular niches in Tissue Engineering.

An accuracy assessment of ASTER stereo images-derived digital elevation model by using rational polynomial coefficient model

The along-track stereo images of Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) sensor with 15 m resolution were used to generate Digital Elevation Model (DEM) on an area with low and near Mean Sea Level (MSL) elevation in Johor, Malaysia. The absolute DEM was generated by using the Rational Polynomial Coefficient (RPC) model which was run on ENVI 4.8 software. In order to generate the absolute DEM, 60 Ground Control Pointes (GCPs) with almost vertical accuracy less than 10 meter extracted from topographic map of the study area. The assessment was carried out on uncorrected and corrected DEM by utilizing dozens of Independent Check Points (ICPs). Consequently, the uncorrected DEM showed the RMSEz of ± 26.43 meter which was decreased to the RMSEz of ± 16.49 meter for the corrected DEM after post-processing. Overall, the corrected DEM of ASTER stereo images met the expectations.

Towards rational synthesis of inorganic solids

There have been major advances in the past couple of years in the rational synthesis of inorganic solids: synthesis of mercury-based superconducting cuprates showing transition temperatures up to 150 K; ZrP2-xVxO7 solid solutions showing zero or negative thermal expansion; copper oxides possessing ladder structures such as La1-xSrxCuO2.5; synthesis of mesoporous oxide materials having adjustable pore size in the range 15-100 Angstrom; and synthesis of a molecular ferromagnet showing a critical temperature of 18.6 K. Despite great advances in probing the structures of solids and measurement of their physical properties, the design and synthesis of inorganic solids possessing desired structures and properties remain a challenge today. With the availability of a variety of mild chemistry-based approaches, kinetic control of synthetic pathways is becoming increasingly possible, which, it is hoped, will eventually make rational design of inorganic solids a reality.

Stereochemical and steric control of enzymatic glucuronidation : A rational approach for the design of novel Inhibitors for the human UDP-glucuronosyltransferase 2B7

The UDP-glucuronosyltransferases (UGTs) are enzymes of the phase II metabolic system. These enzymes catalyze the transfer of α-D-glucuronic acid from UDP-glucuronic acid to aglycones bearing nucleophilic groups affording exclusively their corresponding β-D-glucuronides to render lipophilic endobiotics and xenobiotics more water soluble. This detoxification pathway aids in the urinary and biliary excretion of lipophilic compounds thus preventing their accumulation to harmful levels. The aim of this study was to investigate the effect of stereochemical and steric features of substrates on the glucuronidation catalyzed by UGTs 2B7 and 2B17. Furthermore, this study relates to the design and synthesis of novel, selective inhibitors that display high affinity for the key enzyme involved in drug glucuronidation, UGT2B7. The starting point for the development of inhibitors was to assess the influence of the stereochemistry of substrates on the UGT-catalyzed glucuronidation reaction. A set of 28 enantiomerically pure alcohols was subjected to glucuronidation assays employing the human UGT isoforms 2B7 and 2B17. Both UGT enzymes displayed high stereoselectivity, favoring the glucuronidation of the (R)-enantiomers over their respective mirror-image compounds. The spatial arrangement of the hydroxy group of the substrate determined the rate of the UGT-catalyzed reaction. However, the affinity of the enantiomeric substrates to the enzymes was not significantly influenced by the spatial orientation of the nucleophilic hydroxy group. Based on these results, a rational approach for the design of inhibitors was developed by addressing the stereochemical features of substrate molecules. Further studies showed that the rate of the enzymatic glucuronidation of substrates was also highly dependent on the steric demand in vicinity of the nucleophilic hydroxy group. These findings provided a rational approach to turn high-affinity substrates into true UGT inhibitors by addressing stereochemical and steric features of substrate molecules. The tricyclic sesquiterpenols longifolol and isolongifolol were identified as high-affinity substrates which displayed high selectivity for the UGT isoform 2B7. These compounds served therefore as lead structures for the design of potent and selective inhibitors for UGT2B7. Selective and potent inhibitors were prepared by synthetically modifying the lead compounds longifolol and isolongifolol taking stereochemical and steric features into account. The best inhibitor of UGT2B7, β-phenyllongifolol, displayed an inhibition constant of 0.91 nM.

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.