Generic Hypothesis Research Articles

Characterization of the nucleation barriers for protein aggregation and amyloid formation

Despite the complexity and the specificity of the amino acid code, a variety of peptides and proteins unrelated in sequence and function exhibit a common behavior and assemble into highly organized amyloid fibrils. The formation of such aggregates is often described by a nucleation and growth mechanism, in which the proteins involved also form intermediate oligomeric aggregates before they reorganize and grow into ordered fibrils with a characteristic cross-beta structure. It is extremely difficult to experimentally obtain an accurate description of the early stages of this phenomenon due to the transient nature and structural heterogeneity of the oligomeric precursors. We investigate here the phenomenon of ordered aggregation by using the recently introduced tube model of polypeptide chains in conjunction with the generic hypothesis of amyloid formation. Under conditions where oligomer formation is a rare event-the most common conditions for forming amyloid fibrils by experiment-we calculate directly the nucleation barriers associated with oligomer formation and conversion into cross-beta structure in order to reveal the nature of these species, determine the critical nuclei, and characterize their dependence on the hydrophobicity of the peptides and the thermodynamic parameters associated with aggregation and amyloid formation.

Consumer learning and its impact on store format selection

Although there has been a lot of research on learning and product/brand choice, there is a remarkable lack of linking this to store format selection. As both learning types may occur simultaneously, studying their similarity and interaction is called for. An embracing conceptual 3×3 grid is proposed, resulting from the combination of the classic stage model of Howard & Sheth with Bucklin's brand-store matrix. A set of generic hypotheses was tested empirically through an exploratory experiment involving storyboards, covering nine cognitive learning situations for a high involvement purchase. The results basically indicate that the typical product learning Howard & Sheth based hypotheses concerning cognitive effort and corresponding emotions, may also apply to store learning as well as to mixed store and product learning situations.

Degenerate bifurcations of nontwisted heterodimensional cycles with codimension 3

Bifurcations of heterodimensional cycles with highly degenerate conditions are studied by establishing a suitable local coordinate system in three-dimensional vector fields. The existence, coexistence and noncoexistence of the periodic orbit, homoclinic loop, heteroclinic loop and double periodic orbit are obtained under some generic hypotheses. The bifurcation surfaces and the existence regions are located; the number of the bifurcation surfaces exhibits variety and complexity of the bifurcation of degenerate heterodimensional cycles. The corresponding bifurcation graph is also drawn.

Geodesic laminations with closed ends on surfaces and Morse index; Kupka–Smale metrics

LetM2 be a closed orientable surface with curvatureK and γ ⊂ M a closed geodesic. The Morse index of γ is the index of the critical point γ for the length functional on the space of closed curves, i.e., the number of negative eigenvalues (counted with multiplicity) of the second derivative of length. Since the second derivative of length at γ in the direction of a normal variation un is − ∫ γ uLγ u where Lγ u = u′′ +Ku, the Morse index is the number of negative eigenvalues of Lγ . (By convention, an eigenfunction φ with eigenvalue λ of Lγ is a solution of Lγ φ + λφ = 0.) Note that if λ = 0, then φ (or φn) is a (normal) Jacobi field. γ is stable if the index is zero. The index of a noncompact geodesic is the dimension of a maximal vector space of compactly supported variations for which the second derivative of length is negative definite. We also say that such a geodesic is stable if the index is 0. We give in this paper bounds for the Morse indices of a large class of simple geodesics on a surface with a generic metric. To our knowledge these bounds are the first that use only the generic hypothesis on the metric.

Iterated Integrals, Gelfand—Leray Residue, and First Return Mapping

Recently, one of the authors gave an algorithm for calculating the first nonzero Poincare-Pontryagin function of a small polynomial perturbation of a polynomial Hamiltonian, under a generic hypothesis. We generalize this algorithm and show that any Poincare-Pontryagin function of order l, denoted by Ml, can be written as a sum of an iterated integral of length at most l and of a combination of all previous Poincare-Pontryagin functions, M1, M2,...,Ml-1, and their derivatives. This extends some results obtained recently and allows to identify the Bautin ideal with the ideal generated by iterated integrals.

{\rtf1\ansi\ansicpg1250\deff0\deflang1038\deflangfe1038\deftab708{\fonttbl{\f0\froman\fprq2\fcharset238{\*\fname Times New Roman;}Times New Roman CE;}} \viewkind4\uc1\pard\f0\fs24 Automated analysis of off-line measured gamma-spectra using \scaps UniSampo\scaps0 gamma-ray spectrum analysis software including criterias for alarming systems \par }

{\rtf1\ansi\ansicpg1250\deff0\deflang1038\deflangfe1038\deftab708{\fonttbl{\f0\froman\fprq2\fcharset238{\*\fname Times New Roman;}Times New Roman CE;}} \viewkind4\uc1\pard\lang2057\f0\fs24 In many laboratories the number of measured routine gamma-spectra can be significant and the labour work to review all the data is time consuming and expensive task. In many cases the routine sample does not normally contain radiation above a detectable level, and still the review of the spectra has to be performed. By introducing simple rules for emerging conditions, the review work can be significantly reduced. In one case the need to review the environmental measurement spectra was reduced to less than 1% compared to the original need, which in turn made the review personnel available for more useful functions. Using the \scaps UniSampo\scaps0 analysis system, the analysis results of spectra that are causing alarming conditions can be transmitted via e-mail to any address. Some systems are even equipped with the capability to forward these results to hand-portable telephones or pagers. This is a very practical solution for automated environmental monitoring, when the sample spectra are collected automatically and transmitted to central computer for further analysis. The paper describes how to set up an automatic analysis system, rules for the emerging conditions, technical solutions for an automated alarming system and a generic hypothesis test for the alarming system developed for \scaps UniSampo\scaps0 analysis software. \par }

Quantitative estimates on the normal form around a non-semi-simple 1:−1 resonant periodic orbit

The purpose of this work is to give precise estimates for the size of the remainder of the normalized Hamiltonian around a non-semi-simple 1: −1 resonant periodic orbit, as a function of the distance to the orbit.We consider a periodic orbit of a real analytic three-degrees of freedom Hamiltonian system having a pairwise collision of its non-trivial characteristic multipliers on the unit circle. Under generic hypotheses of non-resonance and non-degeneracy of the collision, we present a constructive methodology to reduce the Hamiltonian around the orbit to its (integrable) normal form, up to any given order. This constructive process allows to obtain quantitative estimates for the size of the remainder of the normal form, as a function of the normalizing order. By selecting appropriately this order in terms of the distance R to the resonant orbit (measured using suitable coordinates), r = ropt(R) := 2+⌊exp(W(log(1/R1/(τ+1+ε))))⌋, we have proved that the size of the remainder can be bounded (for small R) by . Here, W(·) stands for Lambert's W function and verifies that W(z)exp(W(z)) = z, τ ⩾ 1 is the exponent of the required Diophantine condition and ε > 0 is any small quantity. The reasons leading to this bound instead of classical exponentially small estimates are also discussed.

Index theorems for holomorphic self-maps

Let $M$ be a complex manifold and $S\subset M$ a (possibly singular) subvariety of $M$. Let $f\colon M\to M$ be a holomorphic map such that $f$ restricted to $S$ is the identity. We show that one can associate to $f$ a holomorphic section $X_f$ of a sheaf related to the embedding of $S$ in $M$ and that such a section reads the dynamical behavior of $f$ along $S$. In particular we prove that under generic hypotheses the canonical section $X_f$ induces a holomorphic action in the sense of Bott on the normal bundle of (the regular part of) $S$ in $M$ and this allows to obtain for holomorphic self-maps with non- isolated fixed points index theorems similar to Camacho-Sad, Baum-Bott and variation index theorems for holomorphic foliations. Finally we apply our index theorems to obtain information about topology and dynamics of holomorphic self-maps of surfaces with a compact curve of fixed points.

Decay estimates for weighted oscillatory integrals in R^2

In this paper, we study decay estimates for a two-dimensional scalar oscillatory integral with degenerate real-analytic phase and amplitude. Integrals such as these form a model for certain higher-dimensional degenerate oscillatory integrals, for which it is known that many of the two-dimensional results fail. We define an analogue of the Newton distance in the weighted case, and prove that this gives the optimal rate of decay for the weighted oscillatory integral under certain generic hypotheses. When these hypotheses fail, we provide counterexamples to show that the optimal rate of decay may be faster in general. We have obtained bounds for the rate of decay in some of these exceptional cases.

Seasonality, density dependence, and population cycles in Hokkaido voles.

Voles and lemmings show extensive variation in population dynamics regulated across and within species. In an attempt to develop and test generic hypotheses explaining these differences, we studied 84 populations of the gray-sided vole (Clethrionomys rufocanus) in Hokkaido, Japan. We show that these populations are limited by a combination of density-independent factors (such as climate) and density-dependent processes (such as specialist predators). We show that density-dependent regulation primarily occurs in winter months, so that populations experiencing longer winters tend to have a stronger delayed density-dependence and, as a result, exhibit regular density cycles. Altogether, we demonstrate that seasonality plays a key role in determining whether a vole population is cyclic or not.

Complex vector fields having orbits with bounded geometry

Germs of holomorphic vector fields at the origin $0\in \co^{\kern1pt2}$ and polynomial vector fields on $\co^{\kern1pt2}$ are studied. Our aim is to classify these vector fields whose orbits have bounded geometry in a certain sense. Namely, we consider the following situations: (i) the volume of orbits is an integrable function, (ii) the orbits have sub-exponential growth, (iii) the total curvature of orbits is finite. In each case we classify these vector fields under some generic hypothesis on singularities. Applications to questions, concerning polynomial vector fields having closed orbits and complete polynomial vector fields, are given. We also give some applications to the classical theory of compact foliations.

The Views of Family Companies on Venture Capital: Empirical Evidence from the UK Small to Medium-Size Enterprising Economy

This explorative research paper draws evidence from a database of small to medium-size unquoted private companies (n = 240) in the UK and reports on the family business and venture capital relationship from the demand side. Following the review of literature relating to financial affairs of private companies, the main research inquiries are outlined and a set of generic hypotheses is elicited based on the pecking order theory—that is, private companies, including family-controlled ventures, have a propensity to finance their operations in a hierarchical fashion, first using internally available funds, followed by debt and, finally, external equity (Petitt & Singer, 1985). Univariate statistical analyses confirm that family companies adhere strongly to the pecking order principles of financial development. The paper explores factors governing the rationale of owner-managing directors of private and family companies for considering venture capital dealings as well as main areas of concern about the deal structures. The paper then concludes with a discussion of the policy implications from the perspective of the owner-manager, financier, and enterprise policy maker. To encourage equity development of smaller privately held companies, particularly family firms, there is room for policy initiatives that respect the financial philosophy of private companies.

Uncertainty in the Specification of Surface Characteristics, Part ii: Hierarchy of Interaction-Explicit Statistical Analysis

The uncertainty in the specification of surface characteristics in soil-vegetation- atmosphere-transfer (SVAT) schemes within planetary boundary-layer (PBL) or mesoscale models is addressed. The hypothesis to be tested is whether the errors in the specification of the individual parameters are accumulative or whether they tend to balance each other in the overall sense for the system. A hierarchy of statistical applications is developed: classical one-at-a-time (OAT) approach, level 1; linear analysis of variance (ANOVA), level 1.5; fractional factorial (FF), or level 2; two-factor interaction (TFI) technique, or level 2.5; and a non-linear response surface methodology (RSM), or level 3. Using the First ISLSCP Field Experiment (FIFE) observations for June 6, 1987 as the initial condition for a SVAT scheme dynamically coupled to a PBL model, the interactions between uncertainty errors are analyzed. A secondary objective addresses the temporal changes in the uncertainty pattern using data for morning, afternoon, and evening conditions. It is found that the outcome from the level 1 OAT-like studies can be considered as the limiting uncertainty values for the majority of mesoscale cases. From the higher-level analyses, it is concluded that for most of the moderate surface scenarios, the effective uncertainty from the individual parameters is balanced and thus lowered. However, for the extreme cases, such as near wilting or saturation soil moisture, the uncertainties add up synergistically and these effects can be even greater than those from the outcomes of the OAT-like studies. Thus, parameter uncertainty cannot be simply related to its deviation alone, but is also dependent on other parameter settings. Also, from the temporal changes in the interaction pattern studies, it is found that, for the morning case soil texture is the important parameter, for afternoon vegetation parameters are crucial, while for the evening case soil moisture is capable of propagating maximum uncertainty in the SVAT processes. Finally, a generic hypothesis is presented that an appropriate question for analysis has to be rephrased from the previous 'which parameters are significant?’ to 'what scenarios make a particular parameter significant?’

Bifurcations of cuspidal loops

A cuspidal loop for a planar vector field X consists of a homoclinic orbit through a singular point p, at which X has a nilpotent cusp. This is the simplest non-elementary singular cycle (or graphic) in the sense that its singularities are not elementary (i.e. hyperbolic or semihyperbolic). Cuspidal loops appear persistently in three-parameter families of planar vector fields. The bifurcation diagrams of unfoldings of cuspidal loops are studied here under mild genericity hypotheses: the singular point p is of Bogdanov - Takens type and the derivative of the first return map along the orbit is different from 1. An analytic and geometric method based on the blowing up for unfoldings is proposed here to justify the two essentially different models for generic bifurcation diagrams presented in this work. This method can be applied for the study of a large class of complex multiparametric bifurcation problems involving non-elementary singularities, of which the cuspidal loop is the simplest representative. The proofs are complete in a large part of parameter space and can be extended to the complete parameter space modulo a conjecture on the time function of certain quadratic planar vector fields. In one of the cases we can prove that the generic cuspidal loop bifurcates into four limit cycles that are close to it in the Hausdorff sense.

Temporal diagnostic reasoning based on time-objects

Time is essential in diagnostic problem-solving. However, as with other commonsense tasks, time representation and reasoning is not a trivial undertaking. This probably explains why time has either been ignored or implicitly represented and used in the majority of diagnostic systems, medical or otherwise. Durations, temporal uncertainty and multiple temporal granularities are necessary requirements for medical problem-solving. Most general theories of time proposed in the literature do not address all these requirements, and some do not address any. The paper discusses time representation and reasoning in medical diagnostic problem-solving, building from a generic temporal ontology which covers the above temporal requirements. Much of what is discussed, however, is applicable to non-medical domains as well. It is argued that the diagnostic concepts (patient data, disorders, therapeutic-actions) are naturally modelled as time-objects. The resulting representation treats time as an integral dimension to these concepts, with special status. Time-object-based representations for generic hypotheses (disorders, actions) are discussed and illustrated; in the case of disorders the representation covers both an associational model and a causal-associational model. A central function of diagnostic problem-solving is deciding the compatibility of hypotheses with regard to a patient model. In this respect the paper discusses temporal and contextual screening of triggered hypotheses as well as accountings and conflicts between time-objects.

The Fallacy of the Latest Word: The Case of "Pietism and Science"

The resiliency exhibited by some theories or derived hypotheses, despite their periodically conclusive refutation, is examined by taking the generic hypothesis on the connection between ascetic Protestantism and the emergence of modern science as a case in point. Refutations proposed in the Becker critique of the specific instance of Pietism and science strengthen rather than weaken the grounds for deepened interest in exploring both the generic and specific hypothesese insofar as the critique exhibits the fallacy of the latest word. That fallacy rests on three common but untenable tacit assumptions: (1) that latest word correctly formulates the essentials of the preceding word while being immune to the failures of observation and inference imputed to what went before, (2) that each succeeding work improves on its knowledge base, and (3) that theoretically derived hypotheses are to be abandoned as soon as they seem to be empirically falsified. An Appendix examines evidence on the sociohistorical particu...

TOPICS IN LOCAL BIFURCATION THEORY

Abstract : Suppose Lambda, X, Z are Banach spaces, M: Lambda x X yields Z is a mapping continuous together with derivatives up through some order r. A Bifurcation surface for the equation (1) M(lambda,x) = 0 is a surface in parameter space Lambda for which the number of solutions x of (1) changes as lambda crosses this surface. Under certain generic hypotheses on M, it is shown that one can systematically determine the bifurcation surfaces by elementary scaling techniques and the implicit function theorem. This document gives a summary of these results for the case of bifurcation near an isolated solution or families of solutions of the equation M(lambda sub 0, x) = 0. The results have applications of the buckling theory of plates and shells under the effect of external forces, imperfections, curvature and variations in shape. The results on bifurcation near families has applications in nonlinear oscillations and the theory of homoclinic orbits.

Generic bifurcation with application to the von Kármán equations

We examine the possible types of generic bifurcation than can occur for a three-parameter family of mappings from a Banach space into itself. Specifically, the general form of the bifurcation equations arising from the von Kármán equations for the buckling of a rectangular plate is investigated. Chow, Hale, and Mallet-Paret (Applications of generic bifurcation. II, Arch. Rational Mech. Anal. 67 (1976)) studied the bifurcation of solutions to these equations in a two-parameter setting. These parameters were related to the normal loading and to the compressive thrust applied at the ends of the plate. We introduce a third bifurcation parameter by considering the length of the plate as variable. The generic hypotheses of Chow et al. no longer apply in this three-parameter setting, but modifications and extensions of these hypotheses permit a characterization of the three-parameter bifurcation diagram. The bifurcation sheets of this diagram appear as a natural generalization of the finite collection of arcs comprising the two-parameter diagram. As an example of this theory, an actual three-parameter bifurcation diagram is constructed for a specific form of the von Kármán equations.

Determination of Baum–Bott residues of higher codimensional foliations

Let $\mathscr{F}$ be a singular holomorphic foliation, of codimension $k$, on a complex compact manifold such that its singular set has codimension $\geq k+1$. In this work we determinate Baum-Bott residues for $\mathscr{F}$ with respect to homogeneous symmetric polynomials of degree $k+1$. We drop the Baum-Bott's generic hypothesis and we show that the residues can be expressed in terms of the Grothendieck residue of an one-dimensional foliation on a $(k+1)$-dimensional disc transversal to a $(k+1)$-codimensional component of the singular set of $\mathscr{F}$. Also, we show that Cenkl's algorithm for non-expected dimensional singularities holds dropping the Cenkl's regularity assumption.