Minimal Castelnuovo-Mumford regularity for a given Hilbert polynomial

Let $K$ be an algebraically closed field of null characteristic and $p(z)$ a Hilbert polynomial. We look for the minimal Castelnuovo-Mumford regularity $m_{p(z)}$ of closed subschemes of projective spaces over $K$ with Hilbert polynomial $p(z)$. Experimental evidences led us to consider the idea that $m_{p(z)}$ could be achieved by schemes having a suitable minimal Hilbert function. We give a constructive proof of this fact. Moreover, we are able to compute the minimal Castelnuovo-Mumford regularity $m_p(z)^{\varrho}$ of schemes with Hilbert polynomial $p(z)$ and given regularity $\varrho$ of the Hilbert function, and also the minimal Castelnuovo-Mumford regularity $m_u$ of schemes with Hilbert function $u$. These results find applications in the study of Hilbert schemes. They are obtained by means of minimal Hilbert functions and of two new constructive methods which are based on the notion of growth-height-lexicographic Borel set and called ideal graft and extended lifting.Comment: 21 pages. Comments are welcome. More concise version with a slight change in the title. A further revised version has been accepted for publication in Experimental Mathematic

Rotation of Low-mass Stars in Taurus with K2

We present an analysis of K2 light curves (LCs) from Campaigns 4 and 13 for members of the young (~3 Myr) Taurus association, in addition to an older (~30 Myr) population of stars that is largely in the foreground of the Taurus molecular clouds. Out of 156 of the highest-confidence Taurus members, we find that 81% are periodic. Our sample of young foreground stars is biased and incomplete, but nearly all stars (37/38) are periodic. The overall distribution of rotation rates as a function of color (a proxy for mass) is similar to that found in other clusters: the slowest rotators are among the early M spectral types, with faster rotation toward both earlier FGK and later M types. The relationship between period and color/mass exhibited by older clusters such as the Pleiades is already in place by Taurus age. The foreground population has very few stars but is consistent with the USco and Pleiades period distributions. As found in other young clusters, stars with disks rotate on average slower, and few with disks are found rotating faster than ~2 days. The overall amplitude of the LCs decreases with age, and higher-mass stars have generally lower amplitudes than lower-mass stars. Stars with disks have on average larger amplitudes than stars without disks, though the physical mechanisms driving the variability and the resulting LC morphologies are also different between these two classes

Analysis of GPS, VLBI and DORIS input time series for ITRF2014

In this work we have compared the Up component time series reprocessed in view of the new ITRF2014. The solutions that we have considered are the combinations of individual submissions of the Operational Analysis Centers (ACs) as o- cial IVS, IGS and IDS products.We have modelled time series as discrete-time Marcov processes, we have detected and removed discontinuities from data time series and estimated trends (long term signals). A frequency analysis making research of residual periodic signals and identification of the common ones to all the three space geodetic techniques has been performed. Preliminary results on co-located sites are shown

Borel Degenerations of Arithmetically Cohen-Macaulay curves in P^3

We investigate Borel ideals on the Hilbert scheme components of arithmetically Cohen-Macaulay (ACM) codimension two schemes in P^n. We give a basic necessary criterion for a Borel ideal to be on such a component. Then considering ACM curves in P^3 on a quadric we compute in several examples all the Borel ideals on their Hilbert scheme component. Based on this we conjecture which Borel ideals are on such a component, and for a range of Borel ideals we prove that they are on the component.Comment: 20 pages, shorter and more effective versio

Shintaido in the elderly: the new way for physical and psychological health

The research aims to investigate the effects of a Shintaido practice in terms of physical and psychological functioning in a group of elderly. Forty seniors, of both gender, with a mean age of (69 ± 6) years, self-sufficient and without highly invalidating diseases participated in the study. The experimental group (EG) attended the Shintaido physical training of 20 weeks (1 hour per session, twice a week), while the control group (CG) maintained his usual routine. The exercise protocol included specific activities of joint mobility, balance and breathing. At the begin and at the end of intervention were administered to both groups the following validated instruments: 1) One-leg Stance test for the measure of monopodalic static balance; 2) 6-Minutes Walking test for the endurance assessment; 3) Self-Efficacy Perception in Physical Activity (APEF) questionnaire for the selfefficacy evaluation. Data were treated with the not-parametric test for paired and unpaired samples, the Spearman correlation and the linear regression. The results show that: 1) the EG improves the endurance in walking and the monopodalic balance as well as his self-efficacy after the Shintaido program; 2) there are strong associations among Shintaido physical activity and physical/psychological variables; 3) there is a mediating effect of walking endurance between the participation to Shintaido training and the self-efficacy. The results suggest that a well structured Shintaido training can help to maintain a good level of physical and psychological functioning in old people

Preventive Effect of Cow's Milk Fermented with Lactobacillus paracasei CBA L74 on Common Infectious Diseases in Children: A Multicenter Randomized Controlled Trial

Background: Fermented foods have been proposed to prevent common infectious diseases (CIDs) in children attending day care or preschool

Congruences of lines in P5\mathbb{P}^5, quadratic normality, and completely exceptional Monge-Amp\`ere equations

The existence is proved of two new families of locally Cohen-Macaulay sextic threefolds in $\mathbb{P}^5$, which are not quadratically normal. These threefolds arise naturally in the realm of first order congruences of lines as focal loci and in the study of the completely exceptional Monge-Amp\`ere equations. One of these families comes from a smooth congruence of multidegree $(1,3,3)$ which is a smooth Fano fourfold of index two and genus 9.Comment: 16 page

The Genome of the Toluene-Degrading Pseudomonas veronii Strain 1YdBTEX2 and Its Differential Gene Expression in Contaminated Sand.

The natural restoration of soils polluted by aromatic hydrocarbons such as benzene, toluene, ethylbenzene and m- and p-xylene (BTEX) may be accelerated by inoculation of specific biodegraders (bioaugmentation). Bioaugmentation mainly involves introducing bacteria that deploy their metabolic properties and adaptation potential to survive and propagate in the contaminated environment by degrading the pollutant. In order to better understand the adaptive response of cells during a transition to contaminated material, we analyzed here the genome and short-term (1 h) changes in genome-wide gene expression of the BTEX-degrading bacterium Pseudomonas veronii 1YdBTEX2 in non-sterile soil and liquid medium, both in presence or absence of toluene. We obtained a gapless genome sequence of P. veronii 1YdBTEX2 covering three individual replicons with a total size of 8 Mb, two of which are largely unrelated to current known bacterial replicons. One-hour exposure to toluene, both in soil and liquid, triggered massive transcription (up to 208-fold induction) of multiple gene clusters, such as toluene degradation pathway(s), chemotaxis and toluene efflux pumps. This clearly underlines their key role in the adaptive response to toluene. In comparison to liquid medium, cells in soil drastically changed expression of genes involved in membrane functioning (e.g., lipid composition, lipid metabolism, cell fatty acid synthesis), osmotic stress response (e.g., polyamine or trehalose synthesis, uptake of potassium) and putrescine metabolism, highlighting the immediate response mechanisms of P. veronii 1YdBTEX2 for successful establishment in polluted soil