Minimal Hypothesis Research Articles

A selfdual variational principle with minimal hypothesis and applications to stationary, dynamic and stochastic equations

We revisit the self-dual variational approach to the resolution of non-linear stationary, parabolic and stochastic partial differential equations involving a monotone non-linearity, by relaxing the hypothesis under which it is applicable, in two directions: The prohibitive coercivity condition which was problematic for applications to evolution equations, be them deterministic or stochastic, and the restrictive “regularity” property that required the domain of the non-linear operator under study to be large. The new principle is applied to give more direct proofs for the existence of weak solutions for incompressible Navier-Stokes equations in their stationary, dynamic or stochastic versions.

The Minimal Astration Hypothesis—a Necessity for Solving the Dust Budget Crisis?

Abstract Assuming that gas and dust separate in the interstellar medium (ISM) so that high-density regions, where stars can form, are almost devoid of dust, the amount of metals being removed from the ISM can be significantly reduced (minimized astration). Here, it is shown by simple analytical models that this may increase the total metal budget of a galaxy considerably. It is suggested that these extra metals may increase the mass of dust such that the “dust budget crisis”, i.e., the fact that there seems to be more dust at high redshifts than can be accounted for, can be ameliorated. Reducing the amount of astration, the metal budget can be more than doubled, in particular for systems that evolve under continuous gas accretion.

Electroweak phase transition with composite Higgs models: calculability, gravitational waves and collider searches

We study the strong first order electroweak phase transition (SFOEWPT) with the SO(6)/SO(5) composite Higgs model, whose scalar sector contains one Higgs doublet and one real singlet. Six benchmark models are built with fermion embeddings in 1, 6, and 15 of SO(6). We show that SFOEWPT cannot be triggered under the minimal Higgs potential hypothesis, which assumes the scalar potential is dominated by the form factors from the lightest composite resonances. To get a SFOEWPT, the contributions from local operators induced by physics above the cutoff scale are needed. We take the 6 + 6 model as an example to investigate the gravitational waves prediction and the related collider phenomenology.

Localization for Anderson models on metric and discrete tree graphs

We establish spectral and dynamical localization for several Anderson models on metric and discrete radial trees. The localization results are obtained on compact intervals contained in the complement of discrete sets of exceptional energies. All results are proved under the minimal hypothesis on the type of disorder: the random variables generating the trees assume at least two distinct values. This level of generality, in particular, allows us to treat radial trees with disordered geometry as well as Schrodinger operators with Bernoulli-type singular potentials. Our methods are based on an interplay between graph-theoretical properties of radial trees and spectral analysis of the associated random differential and difference operators on the half-line.

Stochastic Near-Optimal Singular Controls for Jump Diffusions: Necessary and Sufficient Conditions

This paper studies the necessary and sufficient conditions for near-optimal singular stochastic controls for the systems driven by non-linear stochastic differential equations with jump processes. The proof of our result is based on Ekeland's variational principle and some delicate estimates of the state and adjoint processes. We apply convex perturbation for continuous and singular components of the control. It is shown that optimal singular controls may fail to exist even in simple cases. This justifies the use of near-optimal stochastic singular controls, which exist under minimal hypothesis and are sufficient in most practical cases. Moreover, since there are many near-optimal singular controls, it is possible to choose suitable ones that are convenient for implementation. The set of controls under consideration is necessarily convex. We prove that under an additional hypothesis, the near-maximum condition on the Hamiltonian function is a sufficient condition for near optimality.

SHAPING THE BROWN DWARF DESERT: PREDICTING THE PRIMORDIAL BROWN DWARF BINARY DISTRIBUTIONS FROM TURBULENT FRAGMENTATION

The formation of brown dwarfs (BDs) poses a key challenge to star formation theory. The observed dearth of nearby ($\leq 5$ AU) brown dwarf companions to solar-mass stars, known as the brown dwarf desert, as well as the tendency for low-mass binary systems to be more tightly-bound than stellar binaries, have been cited as evidence for distinct formation mechanisms for brown dwarfs and stars. In this paper, we explore the implications of the minimal hypothesis that brown dwarfs in binary systems originate via the same fundamental fragmentation mechanism as stars, within isolated, turbulent giant molecular cloud cores. We demonstrate analytically that the scaling of specific angular momentum with turbulent core mass naturally gives rise to the brown dwarf desert, as well as wide brown-dwarf binary systems. Further, we show that the turbulent core fragmentation model also naturally predicts that very low-mass (VLM) binary and BD/BD systems are more tightly-bound than stellar systems. In addition, in order to capture the stochastic variation intrinsic to turbulence, we generate $10^4$ model turbulent cores with synthetic turbulent velocity fields to show that the turbulent fragmentation model accommodates a small fraction of binary brown dwarfs with wide separations, similar to observations. Indeed, the picture which emerges from the turbulent fragmentation model is that a single fragmentation mechanism may largely shape both stellar and brown dwarf binary distributions during formation.

Evolutionary history of black grouse major histocompatibility complex class IIB genes revealed through single locus sequence-based genotyping

BackgroundGene duplications are frequently observed in the Major Histocompatibility Complex (MHC) of many species, and as a consequence loci belonging to the same MHC class are often too similar to tell apart. In birds, single locus genotyping of MHC genes has proven difficult due to concerted evolution homogenizing sequences at different loci. But studies on evolutionary history, mode of selection and heterozygosity correlations on the MHC cannot be performed before it is possible to analyse duplicated genes separately. In this study we investigate the architecture and evolution of the MHC class IIB genes in black grouse. We developed a sequence-based genotyping method for separate amplification of the two black grouse MHC class IIB genes BLB1 and BLB2. Based on this approach we are able to study differences in structure and selection between the two genes in black grouse and relate these results to the chicken MHC structure and organization.ResultsSequences were obtained from 12 individuals and separated into alleles using the software PHASE. We compared nucleotide diversity measures and employed selection tests for BLB1 and BLB2 to explore their modes of selection. Both BLB1 and BLB2 are transcribed and display classic characteristics of balancing selection as predicted for expressed MHC class IIB genes. We found evidence for both intra- and interlocus recombination or gene conversion, as well as indication for positive but differential selection at both loci. Moreover, the two loci appear to be linked. Phylogenetic analyses revealed orthology of the black grouse MHC class IIB genes to the respective BLB loci in chicken.ConclusionsThe results indicate that the duplication of the BLB gene occurred before the species divergence into black grouse, chicken and pheasant. Further, we conclude that BLB1 and BLB2 in black grouse are subjected to homogenizing concerted evolution due to interlocus genetic exchange after species divergence. The loci are in linkage disequilibrium, which is in line with the theory of tightly coevolving genes within the MHC under the minimal essential MHC hypothesis. Our results support the conclusion that MHC form and function in birds derived from studies on the domesticated chicken are not artefacts of the domestication process.

Discovering Arabic structures from texts: what a formal analysis can tell us

We present a new approach to discover Arabic language structures from electronic texts. The method is based on a distributional analysis inspired from Arabic Grammatical Tradition (AGT) and Harris, and uses a minimum knowledge about the Arabic language. The idea underlying this research is that in the absence of a formal model of Arabic language and freely usable Natural Language Processing (NLP) tools for this language, what we can learn about the structures of this language only by a formal analysis of raw corpora written in it. By the word 'formal' we mean, here, that the analysis is based only on the form of the written texts and uses only a minimum knowledge about the language. This knowledge consists in some minimal hypothesis inspired from AGT and that never refers to the meaning of words, utterances and texts. On the contrary, we do not yet know these structures, but we want to discover them formally by automatic algorithms.

Growth Cones As Sensing, Amplifying And Filtering Modules

Sensitivity to weak directional signals is a striking feature of chemotactic systems. In eukaryotic cells, it is often attributed to spatial amplification in the detection of the gradient of guidance cues due to an asymmetric distribution of signaling molecules of the signaling pathway. By combining single-quantum dot imaging with a guidance assay, we probed the dynamics of GABAA receptors (GABAARs) in nerve growth cones. In presence of a GABA gradient, we observed a lateral redistribution of the receptors towards the GABA source. This effect was both reversible and specific of GABA signals. Its functional implication was established by calcium imaging which showed that the redistribution was accompanied by an enhanced asymmetry of the calcium response. Furthermore, single quantum-dot tracking of GABAARs revealed a “conveyor-belt” type of motion in which receptors randomly alternated between periods of free diffusion and of microtubule-dependent directed movement.We therefore propose a model in which an asymmetric activation by the signaling gradient leads to oriented growth of the MTs which, in turn, contributes to an asymmetric distribution of the receptors and amplification in gradient sensing. This simple model for the formation of polarity at the cell membrane is supported by numerical simulations that describe with minimal hypothesis the results of our experiments. These simulations also provide predictions on the dependence of the formation of polarity as a function of gradient parameters. We will finally show our current effort to place neurons in microfluidic devices, to generate controlled gradients and to characterize the growth cone as a sensing, amplifying and filtering module.

Harnack inequality and smoothness for quasilinear degenerate elliptic equations

We prove local and global regularity for the positive solutions of a quasilinear variational degenerate equation, assuming minimal hypothesis on the coefficients of the lower order terms. As an application we obtain Hölder continuity for the gradient of solutions to nonvariational quasilinear equations.

Interior Multiplications and Deformations with Meson Algebras

A meson algebra is involved in the Duffin wave equation for mesons in the same way as a Clifford algebra is involved in the Dirac wave equation for electrons. Therefore meson algebras too should have geometrical properties after the manner of Grassmann. Actually it is possible to define interior multiplications with similar properties, and deformations too. Every meson algebra is a deformation of a neutral meson algebra, in the same way as (almost) every Clifford algebra is a deformation of an exterior algebra. Some applications follow: the PBW-property is proved for all meson algebras, the injectiveness of Jacobson’s diagonal morphism is proved with the minimal hypothesis, and the existence of Lipschitz monoids is established at least for meson algebras over fields.

Courbes algébriques et équations multiplicatives

We study the intersection of an algebraic curve C lying in a multiplicative torus over \({\bar{\mathbb{Q}}}\) with the union of all algebraic subgroups of codimension 2. Finiteness of this set has already been proved by Bombieri, Masser and Zannier under the assumption that C is not contained in a translate of a proper subtorus. Following this result, the question of the minimal hypothesis implying finiteness has been raised by these authors, giving rise to the conjecture~: finiteness holds precisely when C is not contained in a proper subgroup. We prove here this statement which is also a special case of more general conjectures stated independently by Zilber and Pink. Our proof takes its inspiration from an article by Remond and Viada concerning the Zilber-Pink conjecture for curves lying in a power of an elliptic curve. Hence, it relies on a uniform version of the Vojta inequality proven via the generalized Vojta inequality of Remond. The main task is to establish a lower bound for some intersection numbers, here on a whole family of surfaces obtained by blowing up a compactification of C × C.

The Dry Sliding Wear Behavior of Interpenetrating Titanium Trialuminide/Aluminium Composites

Owing to the brittle reinforced phase are introduced into ductile matrix phase, metal–intermetallic interpenetrating composites exhibit various types of wear mechanism such as adhesive, abrasive, and fatigue wear. In present work, the wear model has been proposed according to the mixing rule. Many factors such as special topology structure characteristic of reinforcement and elastic module were discussed in this model. The model based on the maximal and minimal hypothesis posts the mathematic relation among volume content of reinforcement, elastic module and wear rate. Increase in the volume fraction of reinforcement leads to improvement in the wear resistance. Unlike the Khruschov model and Zum-Gahr model, the proposed model was no longer follow linear rule. One kind of Al3Ti/Al composite with different volume content was fabricated and many wear test data were obtained to validate the correctness and universality of the model.

MAXIMALLY SYMMETRIC MINIMAL UNIFICATION MODEL SO(32) WITH THREE FAMILIES IN TEN-DIMENSIONAL SPACETIME

Based on a maximally symmetric minimal unification hypothesis and a quantum charge-dimension correspondence principle, it is demonstrated that each family of quarks and leptons belongs to the Majorana–Weyl spinor representation of 14 dimensions that relate to quantum spin-isospin-color charges. Families of quarks and leptons attribute to a spinor structure of extra six dimensions that relate to quantum family charges. Of particular, it is shown that ten dimensions relating to quantum spin-family charges form a motional ten-dimensional quantum spacetime with a generalized Lorentz symmetry SO (1, 9), and ten dimensions relating to quantum isospin-color charges become a motionless ten-dimensional quantum intrinsic space. Its corresponding 32-component fermions in the spinor representation possess a maximal gauge symmetry SO (32). As a consequence, a maximally symmetric minimal unification model SO (32) containing three families in ten-dimensional quantum spacetime is naturally obtained by choosing a suitable Majorana–Weyl spinor structure into which quarks and leptons are directly embedded. Both resulting symmetry and dimensions coincide with those of type I string and heterotic string SO (32) in string theory.

Cosmological implications of a minimal length hypothesis

One of the firm predictions of inflationary cosmology is the consistency relation between scalar and tensor spectra. It has been argued that such a relation — if experimentally confirmed — would offer strong support for the idea of inflation. We examine the possibility that trans-Planckian physics violates the consistency relation in the framework of inflation with a cutoff proposed in astro-ph/0009209. We find that despite the ambiguity that exists in choosing the action, Planck-scale physics modifies the consistency relation considerably. It also leads to the running of the spectral index. For modes that are larger than our current horizon, the tensor spectral index is positive. For a window of k values with amplitudes of the same order as the modes that are the precursors to structure formation, the behavior of the tensor spectral index is oscillatory about the standard Quantum field theory result, taking both positive and negative values. There is a hope that in the light of future experiments, this scenario of short distance physics, can be verified.PACS Nos.: 98.80.Cq , 98.80.-k, 98.80.Qc

Brain activations during letter-by-letter reading: A follow-up study

Lesions affecting the ventral cortex of the left temporal lobe commonly yield a selective reading impairment known as pure alexia. It is thought to result from the disruption or deafferentation of the Visual Word Form Area (VWFA), a region in the left lateral occipitotemporal sulcus activated whenever normal subjects are viewing alphabetic strings. Most pure alexic patients retain the ability to identify single letters, and develop a strategy of letter-by-letter (LBL) reading. We recently studied fMRI activations in LBL readers and clarified the underlying mechanisms. However, LBL reading is a dynamic process which may improve over months or years of practice, although the cerebral bases of this continuing improvement are currently unknown. We had the opportunity to run the same behavioural testing and fMRI experiment a second time in an alexic patient, 8 months after collecting the data reported by Cohen et al. [Cohen, L., Henry, C., Dehaene, S., Molko, N., Lehéricy, S., Martinaud, O., Lemer, C., & Ferrieux, S. (2004). The pathophysiology of letter-by-letter reading. Neuropsychologia, 42, 1768–1780]. We analyze the changes that occurred over this period in the pattern of reading-related activations, while the patient's LBL reading improved. The activation level decreased in most of the overall network between the two sessions. This general trend contrasted with a focal increase restricted to specific left frontal and parietal areas. When studying the contrast between words and consonant strings, which may be taken as a correlate of LBL reading, we also found a general decrease, except for similar left frontal and parietal regions, which showed a significant increase. We suggest that the pattern of evolution fits with the minimal hypothesis of normal strategic abilities and skill learning, associated with perceptual tuning in right-hemispheric structures able to substitute the disrupted VWFA.

A Neuronal Model of a Global Workspace in Effortful Cognitive Tasks

Abstract: A minimal hypothesis is proposed concerning the brain processes underlying effortful tasks. It distinguishes two main computational spaces: a unique global workspace composed of distributed and heavily interconnected neurons with long‐range axons, and a set of specialized and modular perceptual, motor, memory, evaluative, and attentional processors. Workspace neurons are mobilized in effortful tasks for which the specialized processors do not suffice. They selectively mobilize or suppress, through descending connections, the contribution of specific processor neurons. In the course of task performance, workspace neurons become spontaneously coactivated, forming discrete though variable spatio‐temporal patterns subject to modulation by vigilance signals and to selection by reward signals. A computer simulation of the Stroop task shows workspace activation to increase during acquisition of a novel task, effortful execution, and after errors. We outline predictions for spatio‐temporal activation patterns during brain imaging, particularly about the contribution of dorsolateral prefrontal cortex and anterior cingulate to the workspace.

Where are the minimal trees? Evidence from early Zulu L2 subordination

The Minimal Trees Hypothesis (Vainikka and Young-Scholten 1994; 1996a; 1996b) proposes that second language (L2) initial state grammars lack functional categories because functional categories are not subject to transfer effects. The aim of this article is to argue that, to some extent, functional categories instantiated in the learner's first language (L1) transfer to the initial state of L2 syntactic development. On the basis of Zulu interlanguage (IL) data on the acquisition of the obligatory declarative complementizer ukuthi(‘that’) by English native speakers, it is argued that Comp contains a null complementizer system which has sufficient syntactic content to generate subordination in the learners' initial Zulu IL grammar. Regarding transfer of functional categories, it is suggested that null Comp evident at the Zulu L2 initial state is transferred from English, the subjects' L1.

Explaining risk regulation regimes: Exploring the ‘minimal feasible response’ hypothesis

This paper provides an analytic description of four health-related risk regulation regimes in the UK (governing radon in the home, dangerous dogs outside the home, pesticide residues in food and water, and ambient benzene). It compares observed state activity for information-gathering, standard-setting and behaviour modification or enforcement in those four regimes with what would be expected from the standpoint of a ‘minimal feasible response’ hypothesis. Such a hypothesis assumes state activity will consist of the minimal level of intervention needed to correct specific failures in market or tort-law processes (where the costs of informing oneself about risks or opting out of risks through market or civil law methods are very high). Only one out of the four cases (dogs) fits the minimal feasible response hypothesis (and even that not completely), and observed regimes differ from the minimal feasible response pattern in terms of both greater-than-expected and lesser-than-expected regulation. These variations allow the influence of two different shapers of risk regulation regimes ('responsive government', reflecting public and media opinion, and ‘client politics', reflecting the best-organized interest groups) to be explored. Both factors appear to shape observed risk regulation regimes, though in some cases they pull in opposite directions.

From SOV to SVO: the grammar of interlanguage word order

This paper analyses the grammatical outcome of the conflict speakers of a head-final L1 (Southern Quechua) face when learning a head-initial target (Standard Spanish) in a naturalistic setting. It proposes that interlanguage sentential word orders reflect a transfer of two independent parameters from the L1: the possibility of having null objects with definite/specific antecedents and a feature triggering object movement for sentential focus. The second parameter can be successfully reset through contradictory evidence; the first one, however, cannot, since target evidence is compatible with the L1 setting. This data can better be accounted for in Schwartz and Sprouse's full-access/full-transfer model (Schwartz and Sprouse, 1994; 1996) than in other alternatives such as Vainikka and Young-Scholten's (1994) minimal trees hypothesis and Eubank's (1994; 1996) valueless features hypothesis.