On a Watson-like Uniqueness Theorem and Gevrey Expansions

We present a maximal class of analytic functions, elements of which are in one-to-one correspondence with their asymptotic expansions. In recent decades it has been realized (B. Malgrange, J. Ecalle, J.-P. Ramis, Y. Sibuya et al.), that the formal power series solutions of a wide range of systems of ordinary (even non-linear) analytic differential equations are in fact the Gevrey expansions for the regular solutions. Watson's uniqueness theorem belongs to the foundations of this new theory. This paper contains a discussion of an extension of Watson's uniqueness theorem for classes of functions which admit a Gevrey expansion in angular regions of the complex plane with opening less than or equal to (\frac \pi k,) where (k) is the order of the Gevrey expansion. We present conditions which ensure uniqueness and which suggest an extension of Watson's representation theorem. These results may be applied for solutions of certain classes of differential equations to obtain the best accuracy estimate for the deviation of a solution from a finite sum of the corresponding Gevrey expansion.Comment: 18 pages, 4 figure

Ignition conditions for inertial confinement fusion targets with a nuclear spin-polarized DT fuel

The nuclear fusion cross-section is modified when the spins of the interacting nuclei are polarized. In the case of deuterium?tritium it has been theoretically predicted that the nuclear fusion cross-section could be increased by a factor d = 1.5 if all the nuclei were polarized. In inertial confinement fusion this would result in a modification of the required ignition conditions. Using numerical simulations it is found that the required hot-spot temperature and areal density can both be reduced by about 15% for a fully polarized nuclear fuel. Moreover, numerical simulations of a directly driven capsule show that the required laser power and energy to achieve a high gain scale as d-0.6 and d-0.4 respectively, while the maximum achievable energy gain scales as d0.9

Toward an Ising Model of Cancer and Beyond

Theoretical and computational tools that can be used in the clinic to predict neoplastic progression and propose individualized optimal treatment strategies to control cancer growth is desired. To develop such a predictive model, one must account for the complex mechanisms involved in tumor growth. Here we review resarch work that we have done toward the development of an "Ising model" of cancer. The review begins with a description of a minimalist four-dimensional (three in space and one in time) cellular automaton (CA) model of cancer in which healthy cells transition between states (proliferative, hypoxic, and necrotic) according to simple local rules and their present states, which can viewed as a stripped-down Ising model of cancer. This model is applied to model the growth of glioblastoma multiforme, the most malignant of brain cancers. This is followed by a discussion of the extension of the model to study the effect on the tumor dynamics and geometry of a mutated subpopulation. A discussion of how tumor growth is affected by chemotherapeutic treatment is then described. How angiogenesis as well as the heterogeneous and confined environment in which a tumor grows is incorporated in the CA model is discussed. The characterization of the level of organization of the invasive network around a solid tumor using spanning trees is subsequently described. Then, we describe open problems and future promising avenues for future research, including the need to develop better molecular-based models that incorporate the true heterogeneous environment over wide range of length and time scales (via imaging data), cell motility, oncogenes, tumor suppressor genes and cell-cell communication. The need to bring to bear the powerful machinery of the theory of heterogeneous media to better understand the behavior of cancer in its microenvironment is presented.Comment: 55 pages, 21 figures and 3 tables. To appear in Physical Biology. Added reference

Cauchy's infinitesimals, his sum theorem, and foundational paradigms

Cauchy's sum theorem is a prototype of what is today a basic result on the convergence of a series of functions in undergraduate analysis. We seek to interpret Cauchy's proof, and discuss the related epistemological questions involved in comparing distinct interpretive paradigms. Cauchy's proof is often interpreted in the modern framework of a Weierstrassian paradigm. We analyze Cauchy's proof closely and show that it finds closer proxies in a different modern framework. Keywords: Cauchy's infinitesimal; sum theorem; quantifier alternation; uniform convergence; foundational paradigms.Comment: 42 pages; to appear in Foundations of Scienc

Measurement of XUV-absorption spectra of ZnS radiatively heated foils

Time-resolved absorption of zinc sulfide (ZnS) and aluminum in the XUV-range has been measured. Thin foils in conditions close to local thermodynamic equilibrium were heated by radiation from laser-irradiated gold spherical cavities. Analysis of the aluminum foil radiative hydrodynamic expansion, based on the detailed atomic calculations of its absorption spectra, showed that the cavity emitted flux that heated the absorption foils corresponds to a radiation temperature in the range 55 60 eV. Comparison of the ZnS absorption spectra with calculations based on a superconfiguration approach identified the presence of species Zn6+ - Zn8+ and S5+ - S6+. Based on the validation of the radiative source simulations, experimental spectra were then compared to calculations performed by post-processing the radiative hydrodynamic simulations of ZnS. Satisfying agreement is found when temperature gradients are accounted for

Mathematical and Statistical Techniques for Systems Medicine: The Wnt Signaling Pathway as a Case Study

The last decade has seen an explosion in models that describe phenomena in systems medicine. Such models are especially useful for studying signaling pathways, such as the Wnt pathway. In this chapter we use the Wnt pathway to showcase current mathematical and statistical techniques that enable modelers to gain insight into (models of) gene regulation, and generate testable predictions. We introduce a range of modeling frameworks, but focus on ordinary differential equation (ODE) models since they remain the most widely used approach in systems biology and medicine and continue to offer great potential. We present methods for the analysis of a single model, comprising applications of standard dynamical systems approaches such as nondimensionalization, steady state, asymptotic and sensitivity analysis, and more recent statistical and algebraic approaches to compare models with data. We present parameter estimation and model comparison techniques, focusing on Bayesian analysis and coplanarity via algebraic geometry. Our intention is that this (non exhaustive) review may serve as a useful starting point for the analysis of models in systems medicine.Comment: Submitted to 'Systems Medicine' as a book chapte

Divergent Perturbation Series

Various perturbation series are factorially divergent. The behavior of their high-order terms can be found by Lipatov's method, according to which they are determined by the saddle-point configurations (instantons) of appropriate functional integrals. When the Lipatov asymptotics is known and several lowest order terms of the perturbation series are found by direct calculation of diagrams, one can gain insight into the behavior of the remaining terms of the series. Summing it, one can solve (in a certain approximation) various strong-coupling problems. This approach is demonstrated by determining the Gell-Mann - Low functions in \phi^4 theory, QED, and QCD for arbitrary coupling constants. An overview of the mathematical theory of divergent series is presented, and interpretation of perturbation series is discussed. Explicit derivations of the Lipatov asymptotic forms are presented for some basic problems in theoretical physics. A solution is proposed to the problem of renormalon contributions, which hampered progress in this field in the late 1970s. Practical schemes for summation of perturbation series are described for a coupling constant of order unity and in the strong-coupling limit. An interpretation of the Borel integral is given for 'non-Borel-summable' series. High-order corrections to the Lipatov asymptotics are discussed.Comment: Review article, 45 pages, PD

Beak and feather disease virus in wild and captive parrots: an analysis of geographic and taxonomic distribution and methodological trends

Psittacine beak and feather disease (PBFD) has emerged in recent years as a major threat to wild parrot populations and is an increasing concern to aviculturists and managers of captive populations. Pathological and serological tests for screening for the presence of beak and feather disease virus (BFDV) are a critical component of efforts to manage the disease and of epidemiological studies. Since the disease was first reported in the mid-1970s, screening for BFDV has been conducted in numerous wild and captive populations. However, at present, there is no current and readily accessible synthesis of screening efforts and their results. Here, we consolidate information collected from 83 PBFD- and BFDV-based publications on the primary screening methods being used and identify important knowledge gaps regarding potential global disease hotspots. We present trends in research intensity in this field and critically discuss advances in screening techniques and their applications to both aviculture and to the management of threatened wild populations. Finally, we provide an overview of estimates of BFDV prevalence in captive and wild flocks alongside a complete list of all psittacine species in which the virus has been confirmed. Our evaluation highlights the need for standardised diagnostic tests and more emphasis on studies of wild populations, particularly in view of the intrinsic connection between global trade in companion birds and the spread of novel BFDV strains into wild populations. Increased emphasis should be placed on the screening of captive and wild parrot populations within their countries of origin across the Americas, Africa and Asia

Xnrs and Activin Regulate Distinct Genes during Xenopus Development: Activin Regulates Cell Division

BACKGROUND: The mesoderm of the amphibian embryo is formed through an inductive interaction in which vegetal cells of the blastula-staged embryo act on overlying equatorial cells. Candidate mesoderm-inducing factors include members of the transforming growth factor type β family such as Vg1, activin B, the nodal-related proteins and derrière. METHODOLOGY AND PRINCIPLE FINDINGS: Microarray analysis reveals different functions for activin B and the nodal-related proteins during early Xenopus development. Inhibition of nodal-related protein function causes the down-regulation of regionally expressed genes such as chordin, dickkopf and XSox17α/β, while genes that are mis-regulated in the absence of activin B tend to be more widely expressed and, interestingly, include several that are involved in cell cycle regulation. Consistent with the latter observation, cells of the involuting dorsal axial mesoderm, which normally undergo cell cycle arrest, continue to proliferate when the function of activin B is inhibited. CONCLUSIONS/SIGNIFICANCE: These observations reveal distinct functions for these two classes of the TGF-β family during early Xenopus development, and in doing so identify a new role for activin B during gastrulation

Graded Smad2/3 Activation Is Converted Directly into Levels of Target Gene Expression in Embryonic Stem Cells

The Transforming Growth Factor (TGF) β signalling family includes morphogens, such as Nodal and Activin, with important functions in vertebrate development. The concentration of the morphogen is critical for fate decisions in the responding cells. Smad2 and Smad3 are effectors of the Nodal/Activin branch of TGFβ signalling: they are activated by receptors, enter the nucleus and directly transcribe target genes. However, there have been no studies correlating levels of Smad2/3 activation with expression patterns of endogenous target genes in a developmental context over time. We used mouse Embryonic Stem (ES) cells to create a system whereby levels of activated Smad2/3 can be manipulated by an inducible constitutively active receptor (Alk4*) and an inhibitor (SB-431542) that blocks specifically Smad2/3 activation. The transcriptional responses were analysed by microarrays at different time points during activation and repression. We identified several genes that follow faithfully and reproducibly the Smad2/3 activation profile. Twenty-seven of these were novel and expressed in the early embryo downstream of Smad2/3 signalling. As they responded to Smad2/3 activation in the absence of protein synthesis, they were considered direct. These immediate responsive genes included negative intracellular feedback factors, like SnoN and I-Smad7, which inhibit the transcriptional activity of Smad2/3. However, their activation did not lead to subsequent repression of target genes over time, suggesting that this type of feedback is inefficient in ES cells or it is counteracted by mechanisms such as ubiquitin-mediated degradation by Arkadia. Here we present an ES cell system along with a database containing the expression profile of thousands of genes downstream of Smad2/3 activation patterns, in the presence or absence of protein synthesis. Furthermore, we identify primary target genes that follow proportionately and with high sensitivity changes in Smad2/3 levels over 15–30 hours. The above system and resource provide tools to study morphogen function in development