Dislocation core field. I. Modeling in anisotropic linear elasticity theory

Aside from the Volterra field, dislocations create a core field, which can be modeled in linear anisotropic elasticity theory with force and dislocation dipoles. We derive an expression of the elastic energy of a dislocation taking full account of its core field and show that no cross term exists between the Volterra and the core fields. We also obtain the contribution of the core field to the dislocation interaction energy with an external stress, thus showing that dislocation can interact with a pressure. The additional force that derives from this core field contribution is proportional to the gradient of the applied stress. Such a supplementary force on dislocations may be important in high stress gradient regions, such as close to a crack tip or in a dislocation pile-up

Constructive Dimension and Turing Degrees

This paper examines the constructive Hausdorff and packing dimensions of Turing degrees. The main result is that every infinite sequence S with constructive Hausdorff dimension dim_H(S) and constructive packing dimension dim_P(S) is Turing equivalent to a sequence R with dim_H(R) <= (dim_H(S) / dim_P(S)) - epsilon, for arbitrary epsilon > 0. Furthermore, if dim_P(S) > 0, then dim_P(R) >= 1 - epsilon. The reduction thus serves as a *randomness extractor* that increases the algorithmic randomness of S, as measured by constructive dimension. A number of applications of this result shed new light on the constructive dimensions of Turing degrees. A lower bound of dim_H(S) / dim_P(S) is shown to hold for the Turing degree of any sequence S. A new proof is given of a previously-known zero-one law for the constructive packing dimension of Turing degrees. It is also shown that, for any regular sequence S (that is, dim_H(S) = dim_P(S)) such that dim_H(S) > 0, the Turing degree of S has constructive Hausdorff and packing dimension equal to 1. Finally, it is shown that no single Turing reduction can be a universal constructive Hausdorff dimension extractor, and that bounded Turing reductions cannot extract constructive Hausdorff dimension. We also exhibit sequences on which weak truth-table and bounded Turing reductions differ in their ability to extract dimension.Comment: The version of this paper appearing in Theory of Computing Systems, 45(4):740-755, 2009, had an error in the proof of Theorem 2.4, due to insufficient care with the choice of delta. This version modifies that proof to fix the error

Concentric double hollow grid cathode discharges

A new cathode system, consisting of two concentric spherical hollow grids with two aligned orifices, is investigated by space-resolved Langmuir probe measurements and non-linear dynamics analysis. Negative biases of this spherical hollow grids arrangement lead to the formation of two complex space charge structures in the regions of the orifices. The overall dynamics of the current-voltage characteristic (I–V characteristic) of each discharge is characterized by strong oscillatory behaviour with various waveforms correlated with jumps in the static I–V characteristics. Space-resolved measurements through the two aligned orifices of the two grids show a peak increase of the electron temperature and particle density in the regions of the two space-charge structures. The effects of the biases and Ar pressure on the overall spatial distribution of all plasma parameters are investigated. Two important working points of the concentric double hollow grid cathode discharges are revealed which could make this configuration suitable as an electron source

Sensitive periods for the effect of childhood adversity on DNA methylation: Results from a prospective, longitudinal study

Background: Exposure to "early life" adversity is known to predict DNA methylation (DNAm) patterns that may be related to psychiatric risk. However, few studies have investigated whether adversity has time-dependent effects based on the age at exposure.Methods: Using a two-stage structured life course modeling approach (SLCMA), we tested the hypothesis that there are sensitive periods when adversity induced greater DNAm changes. We tested this hypothesis in relation to two alternatives: an accumulation hypothesis, in which the effect of adversity increases with the number of occasions exposed, regardless of timing, and a recency model, in which the effect of adversity is stronger for more proximal events. Data came from the Accessible Resource for Integrated Epigenomics Studies (ARIES), a subsample of mother-child pairs from the Avon Longitudinal Study of Parents and Children (ALSPAC; n=691-774).Results: After covariate adjustment and multiple testing correction, we identified 38 CpG sites that were differentially methylated at age 7 following exposure to adversity. Most loci (n=35) were predicted by the timing of adversity, namely exposures before age 3. Neither theaccumulation nor recency of the adversity explained considerable variability in DNAm. A standard EWAS of lifetime exposure (vs. no exposure) failed to detect these associations.Conclusions: The developmental timing of adversity explains more variability in DNAm than the accumulation or recency of exposure. Very early childhood appears to be a sensitive period when exposure to adversity predicts differential DNAm patterns. Classification of individuals as exposed vs. unexposed to “early life” adversity may dilute observed effects

A Hierarchy of Polynomial Kernels

In parameterized algorithmics, the process of kernelization is defined as a polynomial time algorithm that transforms the instance of a given problem to an equivalent instance of a size that is limited by a function of the parameter. As, afterwards, this smaller instance can then be solved to find an answer to the original question, kernelization is often presented as a form of preprocessing. A natural generalization of kernelization is the process that allows for a number of smaller instances to be produced to provide an answer to the original problem, possibly also using negation. This generalization is called Turing kernelization. Immediately, questions of equivalence occur or, when is one form possible and not the other. These have been long standing open problems in parameterized complexity. In the present paper, we answer many of these. In particular, we show that Turing kernelizations differ not only from regular kernelization, but also from intermediate forms as truth-table kernelizations. We achieve absolute results by diagonalizations and also results on natural problems depending on widely accepted complexity theoretic assumptions. In particular, we improve on known lower bounds for the kernel size of compositional problems using these assumptions

PU.1 controls fibroblast polarization and tissue fibrosis

Fibroblasts are polymorphic cells with pleiotropic roles in organ morphogenesis, tissue homeostasis and immune responses. In fibrotic diseases, fibroblasts synthesize abundant amounts of extracellular matrix, which induces scarring and organ failure. By contrast, a hallmark feature of fibroblasts in arthritis is degradation of the extracellular matrix because of the release of metalloproteinases and degrading enzymes, and subsequent tissue destruction. The mechanisms that drive these functionally opposing pro-fibrotic and pro-inflammatory phenotypes of fibroblasts remain unknown. Here we identify the transcription factor PU.1 as an essential regulator of the pro-fibrotic gene expression program. The interplay between transcriptional and post-transcriptional mechanisms that normally control the expression of PU.1 expression is perturbed in various fibrotic diseases, resulting in the upregulation of PU.1, induction of fibrosis-associated gene sets and a phenotypic switch in extracellular matrix-producing pro-fibrotic fibroblasts. By contrast, pharmacological and genetic inactivation of PU.1 disrupts the fibrotic network and enables reprogramming of fibrotic fibroblasts into resting fibroblasts, leading to regression of fibrosis in several organs

Bounding Helly numbers via Betti numbers

We show that very weak topological assumptions are enough to ensure the existence of a Helly-type theorem. More precisely, we show that for any non-negative integers $b$ and $d$ there exists an integer $h(b,d)$ such that the following holds. If $\mathcal F$ is a finite family of subsets of $\mathbb R^d$ such that $\tilde\beta_i\left(\bigcap\mathcal G\right) \le b$ for any $\mathcal G \subsetneq \mathcal F$ and every $0 \le i \le \lceil d/2 \rceil-1$ then $\mathcal F$ has Helly number at most $h(b,d)$. Here $\tilde\beta_i$ denotes the reduced $\mathbb Z_2$-Betti numbers (with singular homology). These topological conditions are sharp: not controlling any of these $\lceil d/2 \rceil$ first Betti numbers allow for families with unbounded Helly number. Our proofs combine homological non-embeddability results with a Ramsey-based approach to build, given an arbitrary simplicial complex $K$, some well-behaved chain map $C_*(K) \to C_*(\mathbb R^d)$.Comment: 29 pages, 8 figure

Influência do uso e ocupação da terra no ciclo hidrológico no Município de Viçosa - MG.

O ciclo hidrológico é um dos processos biogeoquímicos mais afetados pela ação antrópica. Objetivou-se com esse trabalho analisar a influência do uso e ocupação da terra nas etapas de infiltração e escoamento superficial do ciclo hidrológico no município de Viçosa ? Minas Gerais. O mapa de uso e ocupação foi gerado com a partir de imagens ópticas do sensor Multispectral Instrument (MSI) acoplado na constelação de satélites Sentinel-2, considerando, a partir da classificação supervisionada de máxima verossimilhança, quatro classes de uso e ocupação da terra, que são: ?área florestal/agricultura?, ?pastagem?, ?solo exposto? e ?área construída?. Para validação da acurácia da classificação foi utilizada a estatística do coeficiente Kappa e o Índice de Exatidão Global. Considerando, sobretudo, a grande área de ?pastagem? (66%), é possível afirmar que o uso e ocupação da terra local, considerando as classes analisadas, possibilita maior potencial para o escoamento superficial que infiltração da água no solo

On the strength of the finite intersection principle

We study the logical content of several maximality principles related to the finite intersection principle (F\IP) in set theory. Classically, these are all equivalent to the axiom of choice, but in the context of reverse mathematics their strengths vary: some are equivalent to \ACA over \RCA, while others are strictly weaker, and incomparable with \WKL. We show that there is a computable instance of F\IP all of whose solutions have hyperimmune degree, and that every computable instance has a solution in every nonzero c.e.\ degree. In terms of other weak principles previously studied in the literature, the former result translates to F\IP implying the omitting partial types principle ($\mathsf{OPT}$). We also show that, modulo $\Sigma^0_2$ induction, F\IP lies strictly below the atomic model theorem ($\mathsf{AMT}$).Comment: This paper corresponds to section 3 of arXiv:1009.3242, "Reverse mathematics and equivalents of the axiom of choice", which has been abbreviated and divided into two pieces for publicatio