Linear Fractional PDE, Uniqueness of Global Solutions

Mathematics Subject Classification: 26A33, 47A60, 30C15.

Fractional Powers of Almost Non-Negative Operators

Mathematics Subject Classification: Primary 47A60, 47D06.

SHACC: a functional prototyper for a component calculus

Over the last decade component-based software development arose as a promising paradigm to deal with the ever increasing complexity in software design, evolution and reuse. SHACC is a prototyping tool for component-based systems in which components are modelled coinductively as generalized Mealy machines. The prototype is built as a HASKELL library endowed with a graphical user interface developed in Swing

Asymptotic limits of a self-dual Ginzburg-Landau functional in bounded domains

In the author's joint paper [HJS] with Jest and Struwe, we discuss asymtotic limits of a self-dual Ginzburg-Landau functional involving a section of a line bundle over a closed Riemann surface and a connection on this bundle. In this paper, the author generalizes the above results [HJS] to the case of bounded domains.

Two estimates concerning asymptotics of the minimizations of a Ginzburg-Landau functional

We prove two asymptotical estimates for minimizers of a Ginzburg-Landau functional of the form integral(Omega) [1/2 \del u\(2) + 1/4 epsilon(2) (1 - \u\(2))(2) W (x)] dx.

Large time behaviour for functional differential equations with dominant eigenvalues of arbitrary order

The spectral theory for linear autonomous neutral functional differential equations (FDE) yields explicit formulas for the large time behaviour of solutions. Our results are based on resolvent computations and Dunford calculus, applied to establish explicit formulas for the large time behaviour of solutions of FDE. We investigate in detail a class of two-dimensional systems of FDE. (C) 2009 Elsevier Inc. All rights reserved.

Functional Aesthetic Treatment of Patient With Phenytoin-Induced Gingival Overgrowth

Gingival overgrowth (GO) may be related to the frequent use of certain medications, such as cyclosporin, phenytoin (PHT), and nifedipine, and is therefore denominated drug-induced GO. This article reports a case of a patient who with chronic periodontitis made use of PHT and presented generalized GO. A 30-year-old man with GO was referred to the clinic of the Universidade Estadual Paulista, Brazil. The complaint was poor aesthetics because of the GO. The patient had a medical history of a controlled epileptic state, and PHT was administered as an anticonvulsant medication. The clinical examination showed generalized edematous gingival tissues and presence of bacterial plaque and calculus on the surfaces of the teeth. The diagnosis was GO associated with PHT because no other risk factors were identified. Treatment consisted of meticulous oral hygiene instruction, scaling, root surface instrumentation, prophylaxis, and daily chlorhexidine mouth rinses. After this stage, periodontal surgery was performed, and histopathologic evaluation was made. The patient has been under control for 3 years after the periodontal surgery, and up to the present time, there has been no recurrence. It can be concluded that PHT associated with the presence of irritants favored gingival growth and that the association of nonsurgical and surgical periodontal therapies was effective in the treatment of GO. Besides, motivating the patient to maintain oral hygiene is a prerequisite for the maintenance of periodontal health.

Problems in the classical calculus of variations

This dissertation concerns convergence analysis for nonparametric problems in the calculus of variations and sufficient conditions for weak local minimizer of a functional for both nonparametric and parametric problems. Newton's method in infinite-dimensional space is proved to be well-defined and converges quadratically to a weak local minimizer of a functional subject to certain boundary conditions. Sufficient conditions for global converges are proposed and a well-defined algorithm based on those conditions is presented and proved to converge. Finite element discretization is employed to achieve an implementable line-search-based quasi-Newton algorithm and a proof of convergence of the discretization of the algorithm is included. This work also proposes sufficient conditions for weak local minimizer without using the language of conjugate points. The form of new conditions is consistent with the ones in finite-dimensional case. It is believed that the new form of sufficient conditions will lead to simpler approaches to verify an extremal as local minimizer for well-known problems in calculus of variations.

Functional data analysis approaches for genotype-phenotype association studies from next-generation sequencing

Next-generation DNA sequencing platforms can effectively detect the entire spectrum of genomic variation and is emerging to be a major tool for systematic exploration of the universe of variants and interactions in the entire genome. However, the data produced by next-generation sequencing technologies will suffer from three basic problems: sequence errors, assembly errors, and missing data. Current statistical methods for genetic analysis are well suited for detecting the association of common variants, but are less suitable to rare variants. This raises great challenge for sequence-based genetic studies of complex diseases.^ This research dissertation utilized genome continuum model as a general principle, and stochastic calculus and functional data analysis as tools for developing novel and powerful statistical methods for next generation of association studies of both qualitative and quantitative traits in the context of sequencing data, which finally lead to shifting the paradigm of association analysis from the current locus-by-locus analysis to collectively analyzing genome regions.^ In this project, the functional principal component (FPC) methods coupled with high-dimensional data reduction techniques will be used to develop novel and powerful methods for testing the associations of the entire spectrum of genetic variation within a segment of genome or a gene regardless of whether the variants are common or rare.^ The classical quantitative genetics suffer from high type I error rates and low power for rare variants. To overcome these limitations for resequencing data, this project used functional linear models with scalar response to develop statistics for identifying quantitative trait loci (QTLs) for both common and rare variants. To illustrate their applications, the functional linear models were applied to five quantitative traits in Framingham heart studies. ^ This project proposed a novel concept of gene-gene co-association in which a gene or a genomic region is taken as a unit of association analysis and used stochastic calculus to develop a unified framework for testing the association of multiple genes or genomic regions for both common and rare alleles. The proposed methods were applied to gene-gene co-association analysis of psoriasis in two independent GWAS datasets which led to discovery of networks significantly associated with psoriasis.^

A syntactic and functional correspondence between reduction semantics and reduction-free full normalisers

Olivier Danvy and others have shown the syntactic correspondence between reduction semantics (a small-step semantics) and abstract machines, as well as the functional correspondence between reduction-free normalisers (a big-step semantics) and abstract machines. The correspondences are established by program transformation (so-called interderivation) techniques. A reduction semantics and a reduction-free normaliser are interderivable when the abstract machine obtained from them is the same. However, the correspondences fail when the underlying reduction strategy is hybrid, i.e., relies on another sub-strategy. Hybridisation is an essential structural property of full-reducing and complete strategies. Hybridisation is unproblematic in the functional correspondence. But in the syntactic correspondence the refocusing and inlining-of-iterate-function steps become context sensitive, preventing the refunctionalisation of the abstract machine. We show how to solve the problem and showcase the interderivation of normalisers for normal order, the standard, full-reducing and complete strategy of the pure lambda calculus. Our solution makes it possible to interderive, rather than contrive, full-reducing abstract machines. As expected, the machine we obtain is a variant of Pierre Crégut s full Krivine machine KN.

Existence Results for Fractional Functional Differential Inclusions with Infinite Delay and Applications to Control Theory

Mathematics Subject Classification: 26A33, 34A60, 34K40, 93B05

Impulsive Partial Hyperbolic Functional Differential Equations of Fractional Order with State-Dependent Delay

MSC 2010: 26A33, 34A37, 34K37, 34K40, 35R11

On Reasonable Space and Time Cost Models for the λ-Calculus

Slot and van Emde Boas Invariance Thesis states that a time (respectively, space) cost model is reasonable for a computational model C if there are mutual simulations between Turing machines and C such that the overhead is polynomial in time (respectively, linear in space). The rationale is that under the Invariance Thesis, complexity classes such as LOGSPACE, P, PSPACE, become robust, i.e. machine independent. In this dissertation, we want to find out if it possible to define a reasonable space cost model for the lambda-calculus, the paradigmatic model for functional programming languages. We start by considering an unusual evaluation mechanism for the lambda-calculus, based on Girard's Geometry of Interaction, that was conjectured to be the key ingredient to obtain a space reasonable cost model. By a fine complexity analysis of this schema, based on new variants of non-idempotent intersection types, we disprove this conjecture. Then, we change the target of our analysis. We consider a variant over Krivine's abstract machine, a standard evaluation mechanism for the call-by-name lambda-calculus, optimized for space complexity, and implemented without any pointer. A fine analysis of the execution of (a refined version of) the encoding of Turing machines into the lambda-calculus allows us to conclude that the space consumed by this machine is indeed a reasonable space cost model. In particular, for the first time we are able to measure also sub-linear space complexities. Moreover, we transfer this result to the call-by-value case. Finally, we provide also an intersection type system that characterizes compositionally this new reasonable space measure. This is done through a minimal, yet non trivial, modification of the original de Carvalho type system.

The Effect Of Celastrol, A Triterpene With Antitumorigenic Activity, On Conformational And Functional Aspects Of The Human 90kda Heat Shock Protein Hsp90α, A Chaperone Implicated In The Stabilization Of The Tumor Phenotype.

Hsp90 is a molecular chaperone essential for cell viability in eukaryotes that is associated with the maturation of proteins involved in important cell functions and implicated in the stabilization of the tumor phenotype of various cancers, making this chaperone a notably interesting therapeutic target. Celastrol is a plant-derived pentacyclic triterpenoid compound with potent antioxidant, anti-inflammatory and anticancer activities; however, celastrol's action mode is still elusive. In this work, we investigated the effect of celastrol on the conformational and functional aspects of Hsp90α. Interestingly, celastrol appeared to target Hsp90α directly as the compound induced the oligomerization of the chaperone via the C-terminal domain as demonstrated by experiments using a deletion mutant. The nature of the oligomers was investigated by biophysical tools demonstrating that a two-fold excess of celastrol induced the formation of a decameric Hsp90α bound throughout the C-terminal domain. When bound, celastrol destabilized the C-terminal domain. Surprisingly, standard chaperone functional investigations demonstrated that neither the in vitro chaperone activity of protecting against aggregation nor the ability to bind a TPR co-chaperone, which binds to the C-terminus of Hsp90α, were affected by celastrol. Celastrol interferes with specific biological functions of Hsp90α. Our results suggest a model in which celastrol binds directly to the C-terminal domain of Hsp90α causing oligomerization. However, the ability to protect against protein aggregation (supported by our results) and to bind to TPR co-chaperones are not affected by celastrol. Therefore celastrol may act primarily by inducing specific oligomerization that affects some, but not all, of the functions of Hsp90α. To the best of our knowledge, this study is the first work to use multiple probes to investigate the effect that celastrol has on the stability and oligomerization of Hsp90α and on the binding of this chaperone to Tom70. This work provides a novel mechanism by which celastrol binds Hsp90α.