Toward accurate polynomial evaluation in rounded arithmetic

Given a multivariate real (or complex) polynomial $p$ and a domain $\cal D$, we would like to decide whether an algorithm exists to evaluate $p(x)$ accurately for all $x \in {\cal D}$ using rounded real (or complex) arithmetic. Here ``accurately'' means with relative error less than 1, i.e., with some correct leading digits. The answer depends on the model of rounded arithmetic: We assume that for any arithmetic operator $op(a,b)$, for example $a+b$ or $a \cdot b$, its computed value is $op(a,b) \cdot (1 + \delta)$, where $| \delta |$ is bounded by some constant $\epsilon$ where $0 < \epsilon \ll 1$, but $\delta$ is otherwise arbitrary. This model is the traditional one used to analyze the accuracy of floating point algorithms.Our ultimate goal is to establish a decision procedure that, for any $p$ and $\cal D$, either exhibits an accurate algorithm or proves that none exists. In contrast to the case where numbers are stored and manipulated as finite bit strings (e.g., as floating point numbers or rational numbers) we show that some polynomials $p$ are impossible to evaluate accurately. The existence of an accurate algorithm will depend not just on $p$ and $\cal D$, but on which arithmetic operators and which constants are are available and whether branching is permitted. Toward this goal, we present necessary conditions on $p$ for it to be accurately evaluable on open real or complex domains ${\cal D}$. We also give sufficient conditions, and describe progress toward a complete decision procedure. We do present a complete decision procedure for homogeneous polynomials $p$ with integer coefficients, {\cal D} = \C^n, and using only the arithmetic operations $+$, $-$ and $\cdot$.Comment: 54 pages, 6 figures; refereed version; to appear in Foundations of Computational Mathematics: Santander 2005, Cambridge University Press, March 200

The relationship between milk, mammary adipocytes and ECM in regulating murine mammary gland involution

&nbsp;This thesis investigated the role of milk, extracellular matrix and mammary adipocytes in regulating mammary gland function during involution in mice and explored the use of an in vitro culture model, the mammosphere model system to study the same

Analysis of protein phosphorylation sites using affinity enrichment and mass spectrometry

Reversible modification of proteins by phosphorylation of serine, threonine and tyrosine residues is the most common post-translational modification, which is estimated to occur in 30-90% of the cellular expressed protein component at any one time. Phosphorylation can alter proteins' subcellular distribution, enzymatic activity and specificity. Altered protein phosphorylation may correlate with disease states such as cellular transformation. The analysis of phosphorylated proteins is therefore of vital importance to the field of biology and in particular signal transduction. Protein phosphorylation sites are increasingly investigated using mass spectrometric methods, exploiting the inherent accuracy and sensitivity of these methods. However, the presence of unphosphorylated peptides in enzymatic digests of proteins causes ion suppression of phosphopeptides, reducing the effective sensitivity of detection; this sensitivity is further decreased by the relative lability of the phosphate moiety in the mass spectrometer and the occurrence of sub-stoichiometric modification, which together further reduce the achievable sensitivity. This study has examined techniques for the analysis of protein phosphorylation sites, with particular emphasis upon mass spectrometry. The technique of immobilised metal ion affinity chromatography (IMAC) was investigated in detail as a method suited to phosphorylation site analysis. IMAC exploits the relatively specific affinity of phosphorylated peptides for metal ions, particularly Fe(III), to isolate phosphopeptides upon a solid-phase affinity matrix, separating the suppressing non- phosphorylated component and allowing improved detection of phosphorylated peptides. Conditions for the application of IMAC to phosphopeptide segregation have been established and applied. Using IMAC, protein phosphorylation site identification of both standards and signal transduction mediators has been carried out. Apparent sequence-specific binding of phosphorylated and non-phosphorylated peptides to IMAC resins has been found and investigated. IMAC methodology has been further improved to optimise phosphopeptide analysis using mass spectrometry. The developed methods have clear utility for phosphorylation site analysis, which is vital to the understanding of signal transduction

Human metabolic adaptations and prolonged expensive neurodevelopment: A review

1.&#x9;After weaning, human hunter-gatherer juveniles receive substantial (&#x2248;3.5-7 MJ day^-1^), extended (&#x2248;15 years) and reliable (kin and nonkin food pooling) energy provision.&#xd;&#xa;2.&#x9;The childhood (pediatric) and the adult human brain takes a very high share of both basal metabolic rate (BMR) (child: 50-70%; adult: &#x2248;20%) and total energy expenditure (TEE) (child: 30-50%; adult: &#x2248;10%).&#xd;&#xa;3.&#x9;The pediatric brain for an extended period (&#x2248;4-9 years-of-age) consumes roughly 50% more energy than the adult one, and after this, continues during adolescence, at a high but declining rate. Within the brain, childhood cerebral gray matter has an even higher 1.9 to 2.2-fold increased energy consumption. &#xd;&#xa;4.&#x9;This metabolic expensiveness is due to (i) the high cost of synapse activation (74% of brain energy expenditure in humans), combined with (ii), a prolonged period of exuberance in synapse numbers (up to double the number present in adults). Cognitive development during this period associates with volumetric changes in gray matter (expansion and contraction due to metabolic related size alterations in glial cells and capillary vascularization), and in white matter (expansion due to myelination). &#xd;&#xa;5.&#x9;Amongst mammals, anatomically modern humans show an unique pattern in which very slow musculoskeletal body growth is followed by a marked adolescent size/stature spurt. This pattern of growth contrasts with nonhuman primates that have a sustained fast juvenile growth with only a minor period of puberty acceleration. The existence of slow childhood growth in humans has been shown to date back to 160,000 BP. &#xd;&#xa;6.&#x9;Human children physiologically have a limited capacity to protect the brain from plasma glucose fluctuations and other metabolic disruptions. These can arise in adults, during prolonged strenuous exercise when skeletal muscle depletes plasma glucose, and produces other metabolic disruptions upon the brain (hypoxia, hyperthermia, dehydration and hyperammonemia). These are proportional to muscle mass.&#xd;&#xa;7.&#x9;Children show specific adaptations to minimize such metabolic disturbances. (i) Due to slow body growth and resulting small body size, they have limited skeletal muscle mass. (ii) They show other adaptations such as an exercise specific preference for free fatty acid metabolism. (iii) While children are generally more active than adolescents and adults, they avoid physically prolonged intense exertion. &#xd;&#xa;8.&#x9;Childhood has a close relationship to high levels of energy provision and metabolic adaptations that support prolonged synaptic neurodevelopment. &#xd;&#xa

Development and Validation of UPLC/MS/MS Methods for Quantification of Gangliosides in the Clinical Study of Ganglioside GM3 Synthase Deficiency

Gangliosides are a large subclass of glycosphingolipids that structurally characterized by the addition of mono- or poly-sialyated carbohydrate moieties onto the ceramide scaffold. They are presented at significant abundance in the central nervous system of vertebrates. Their interactions with trans-membrane receptors, especially receptor tyrosine kinase, are believed to play critical roles in modulating signal transduction events during cell proliferation, differentiation, migration, and adhesion. Furthermore, the disruption and dysfunction on their metabolism have been found to be associated with various neurodegenerative disorders, such as Alzheimer disease, Parkinson’s disease, and GM3 synthase deficiency. GM3 synthase deficiency (GSD) is a newly identified neurological disorder that has been prevalently found in the Amish population in the United States. Although the pathological mechanism remains to be understood, the condition is severe. It is characterized by infantile onset of severe irritability, developmental stagnation, profound intellectual disability and intractable seizures. In order to advance our understanding on the etiology of these neurodegenerative disorders, especially GSD, analytical assays with sufficient specificity, sensitivity, and throughput are urgently demanded to practically assist the implementation of relevant clinical studies. In this thesis, three projects have been conducted separately to benefit the clinical studies from individual aspects. In project 1, owing to the increased complexity of molecular assays in screening and diagnosing patients affected by GSD associated with increased numbers of identified nonsense/missense mutations, we have developed and validated a novel UPLC/MS/MS method with promising sensitivity, specificity, and throughput for four major ganglioside species, GM2, GM3, GD2, and GD3, in human plasma to facilitate the diagnosis and screening of GSD. In project 2, in order to obtain more informative results from GSD patients undergoing clinical trial in relation to the development of related therapeutic intervention, we have developed and validated a new UPLC/MS/MS method in human plasma for quantification of monosialogangliosides in combination with DMTMM&PAEA chemical derivatization for analysis with superior sensitivity and specificity. In project 3, we have implemented a clinical study aiming at developing a therapeutic intervention strategy based on oral administration of commercialized ganglioside-enrich formula to the affected patients

An extensive English language bibliography on graph theory and its applications

Bibliography on graph theory and its application

Development and Validation of UPLC/MS/MS Methods for Quantification of Gangliosides in the Clinical Study of Ganglioside GM3 Synthase Deficiency

Gangliosides are a large subclass of glycosphingolipids that structurally characterized by the addition of mono- or poly-sialyated carbohydrate moieties onto the ceramide scaffold. They are presented at significant abundance in the central nervous system of vertebrates. Their interactions with trans-membrane receptors, especially receptor tyrosine kinase, are believed to play critical roles in modulating signal transduction events during cell proliferation, differentiation, migration, and adhesion. Furthermore, the disruption and dysfunction on their metabolism have been found to be associated with various neurodegenerative disorders, such as Alzheimer disease, Parkinson’s disease, and GM3 synthase deficiency. GM3 synthase deficiency (GSD) is a newly identified neurological disorder that has been prevalently found in the Amish population in the United States. Although the pathological mechanism remains to be understood, the condition is severe. It is characterized by infantile onset of severe irritability, developmental stagnation, profound intellectual disability and intractable seizures. In order to advance our understanding on the etiology of these neurodegenerative disorders, especially GSD, analytical assays with sufficient specificity, sensitivity, and throughput are urgently demanded to practically assist the implementation of relevant clinical studies. In this thesis, three projects have been conducted separately to benefit the clinical studies from individual aspects. In project 1, owing to the increased complexity of molecular assays in screening and diagnosing patients affected by GSD associated with increased numbers of identified nonsense/missense mutations, we have developed and validated a novel UPLC/MS/MS method with promising sensitivity, specificity, and throughput for four major ganglioside species, GM2, GM3, GD2, and GD3, in human plasma to facilitate the diagnosis and screening of GSD. In project 2, in order to obtain more informative results from GSD patients undergoing clinical trial in relation to the development of related therapeutic intervention, we have developed and validated a new UPLC/MS/MS method in human plasma for quantification of monosialogangliosides in combination with DMTMM&PAEA chemical derivatization for analysis with superior sensitivity and specificity. In project 3, we have implemented a clinical study aiming at developing a therapeutic intervention strategy based on oral administration of commercialized ganglioside-enrich formula to the affected patients

Development and Validation of UPLC/MS/MS Methods for Quantification of Gangliosides in the Clinical Study of Ganglioside GM3 Synthase Deficiency

Gangliosides are a large subclass of glycosphingolipids that structurally characterized by the addition of mono- or poly-sialyated carbohydrate moieties onto the ceramide scaffold. They are presented at significant abundance in the central nervous system of vertebrates. Their interactions with trans-membrane receptors, especially receptor tyrosine kinase, are believed to play critical roles in modulating signal transduction events during cell proliferation, differentiation, migration, and adhesion. Furthermore, the disruption and dysfunction on their metabolism have been found to be associated with various neurodegenerative disorders, such as Alzheimer disease, Parkinson’s disease, and GM3 synthase deficiency. GM3 synthase deficiency (GSD) is a newly identified neurological disorder that has been prevalently found in the Amish population in the United States. Although the pathological mechanism remains to be understood, the condition is severe. It is characterized by infantile onset of severe irritability, developmental stagnation, profound intellectual disability and intractable seizures. In order to advance our understanding on the etiology of these neurodegenerative disorders, especially GSD, analytical assays with sufficient specificity, sensitivity, and throughput are urgently demanded to practically assist the implementation of relevant clinical studies. In this thesis, three projects have been conducted separately to benefit the clinical studies from individual aspects. In project 1, owing to the increased complexity of molecular assays in screening and diagnosing patients affected by GSD associated with increased numbers of identified nonsense/missense mutations, we have developed and validated a novel UPLC/MS/MS method with promising sensitivity, specificity, and throughput for four major ganglioside species, GM2, GM3, GD2, and GD3, in human plasma to facilitate the diagnosis and screening of GSD. In project 2, in order to obtain more informative results from GSD patients undergoing clinical trial in relation to the development of related therapeutic intervention, we have developed and validated a new UPLC/MS/MS method in human plasma for quantification of monosialogangliosides in combination with DMTMM&PAEA chemical derivatization for analysis with superior sensitivity and specificity. In project 3, we have implemented a clinical study aiming at developing a therapeutic intervention strategy based on oral administration of commercialized ganglioside-enrich formula to the affected patients

Glosarium Matematika

273 p.; 24 cm