All functions g:N-->N which have a single-fold Diophantine representation are dominated by a limit-computable function f:N\{0}-->N which is implemented in MuPAD and whose computability is an open problem

Let E_n={x_k=1, x_i+x_j=x_k, x_i \cdot x_j=x_k: i,j,k \in {1,...,n}}. For any integer n \geq 2214, we define a system T \subseteq E_n which has a unique integer solution (a_1,...,a_n). We prove that the numbers a_1,...,a_n are positive and max(a_1,...,a_n)>2^(2^n). For a positive integer n, let f(n) denote the smallest non-negative integer b such that for each system S \subseteq E_n with a unique solution in non-negative integers x_1,...,x_n, this solution belongs to [0,b]^n. We prove that if a function g:N-->N has a single-fold Diophantine representation, then f dominates g. We present a MuPAD code which takes as input a positive integer n, performs an infinite loop, returns a non-negative integer on each iteration, and returns f(n) on each sufficiently high iteration.Comment: 17 pages, Theorem 3 added. arXiv admin note: substantial text overlap with arXiv:1309.2605. text overlap with arXiv:1404.5975, arXiv:1310.536

Multiple dietary supplements do not affect metabolic and cardio-vascular health

Dietary supplements are widely used for health purposes. However, little is known about the metabolic and cardiovascular effects of combinations of popular over-the-counter supplements, each of which has been shown to have anti-oxidant, anti-inflammatory and pro-longevity properties in cell culture or animal studies. This study was a 6-month randomized, single-blind controlled trial, in which 56 non-obese (BMI 21.0-29.9 kg/m(2)) men and women, aged 38 to 55 yr, were assigned to a dietary supplement (SUP) group or control (CON) group, with a 6-month follow-up. The SUP group took 10 dietary supplements each day (100 mg of resveratrol, a complex of 800 mg each of green, black, and white tea extract, 250 mg of pomegranate extract, 650 mg of quercetin, 500 mg of acetyl-l-carnitine, 600 mg of lipoic acid, 900 mg of curcumin, 1 g of sesamin, 1.7 g of cinnamon bark extract, and 1.0 g fish oil). Both the SUP and CON groups took a daily multivitamin/mineral supplement. The main outcome measures were arterial stiffness, endothelial function, biomarkers of inflammation and oxidative stress, and cardiometabolic risk factors. Twenty-four weeks of daily supplementation with 10 dietary supplements did not affect arterial stiffness or endothelial function in nonobese individuals. These compounds also did not alter body fat measured by DEXA, blood pressure, plasma lipids, glucose, insulin, IGF-1, and markers of inflammation and oxidative stress. In summary, supplementation with a combination of popular dietary supplements has no cardiovascular or metabolic effects in non-obese relatively healthy individuals

Degree spectra for transcendence in fields

We show that for both the unary relation of transcendence and the finitary relation of algebraic independence on a field, the degree spectra of these relations may consist of any single computably enumerable Turing degree, or of those c.e. degrees above an arbitrary fixed $\Delta^0_2$ degree. In other cases, these spectra may be characterized by the ability to enumerate an arbitrary $\Sigma^0_2$ set. This is the first proof that a computable field can fail to have a computable copy with a computable transcendence basis

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

Universal fluctuations in subdiffusive transport

Subdiffusive transport in tilted washboard potentials is studied within the fractional Fokker-Planck equation approach, using the associated continuous time random walk (CTRW) framework. The scaled subvelocity is shown to obey a universal law, assuming the form of a stationary Levy-stable distribution. The latter is defined by the index of subdiffusion alpha and the mean subvelocity only, but interestingly depends neither on the bias strength nor on the specific form of the potential. These scaled, universal subvelocity fluctuations emerge due to the weak ergodicity breaking and are vanishing in the limit of normal diffusion. The results of the analytical heuristic theory are corroborated by Monte Carlo simulations of the underlying CTRW

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

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

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

The Argyre Region as a Prime Target for in situ Astrobiological Exploration of Mars

At the time before ∼3.5 Ga that life originated and began to spread on Earth, Mars was a wetter and more geologically dynamic planet than it is today. The Argyre basin, in the southern cratered highlands of Mars, formed from a giant impact at ∼3.93 Ga, which generated an enormous basin approximately 1800 km in diameter. The early post-impact environment of the Argyre basin possibly contained many of the ingredients that are thought to be necessary for life: abundant and long-lived liquid water, biogenic elements, and energy sources, all of which would have supported a regional environment favorable for the origin and the persistence of life. We discuss the astrobiological significance of some landscape features and terrain types in the Argyre region that are promising and accessible sites for astrobiological exploration. These include (i) deposits related to the hydrothermal activity associated with the Argyre impact event, subsequent impacts, and those associated with the migration of heated water along Argyre-induced basement structures; (ii) constructs along the floor of the basin that could mark venting of volatiles, possibly related to the development of mud volcanoes; (iii) features interpreted as ice-cored mounds (open-system pingos), whose origin and development could be the result of deeply seated groundwater upwelling to the surface; (iv) sedimentary deposits related to the formation of glaciers along the basin's margins, such as evidenced by the ridges interpreted to be eskers on the basin floor; (v) sedimentary deposits related to the formation of lakes in both the primary Argyre basin and other smaller impact-derived basins along the margin, including those in the highly degraded rim materials; and (vi) crater-wall gullies, whose morphology points to a structural origin and discharge of (wet) flows

VARIABILITY OF YIELD AND FEW QUALITY COMPONENTS TO SOME MUTANT/RECOMBINANT LINES OF WINTER WHEAT

Ten DH mutant/recombinant wheat lines viz. Ai-II 126, Ai-II 131, Ai-II 152, Ai-II 172, Ai-II 183, Ai-II 193, Ai-II 201, Ai-II 223, Bi-I 3, Bi-I 40 and their parental forms Izvor and F00628-34 were analyzed for yield and some grain quality parameters (protein and starch content, TKW, hectolitre mass and moisture content). These lines were cultivated in Southern Romania, on chernozen soil in 2015-2017 period. Lines with higher yield potential were identified and of quality. Average yield of 6757 Kg/ha (Ai-II 152) and 6724 Kg/ha (Ai-II 193) were obtained and protein content of 13.35% (Ai-II 126) and 13.10% (Ai-II 172) were realized. Higher variability for TKW was identified and smaller for starch and HM. Significant positive correlation between TKW and protein content and negative correlation between protein and starch and yield was found. The results of this study conclude that on the basis of the analyzed characters there are some lines which can be selected as one of best genotypes.