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

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

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

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

Term-ordering free involutive bases

In this paper, we consider a monomial ideal J in P := A[x1,...,xn], over a commutative ring A, and we face the problem of the characterization for the family Mf(J) of all homogeneous ideals I in P such that the A-module P/I is free with basis given by the set of terms in the Groebner escalier N(J) of J. This family is in general wider than that of the ideals having J as initial ideal w.r.t. any term-ordering, hence more suited to a computational approach to the study of Hilbert schemes. For this purpose, we exploit and enhance the concepts of multiplicative variables, complete sets and involutive bases introduced by Janet and we generalize the construction of J-marked bases and term-ordering free reduction process introduced and deeply studied for the special case of a strongly stable monomial ideal J. Here, we introduce and characterize for every monomial ideal J a particular complete set of generators F(J), called stably complete, that allows an explicit description of the family Mf(J). We obtain stronger results if J is quasi stable, proving that F(J) is a Pommaret basis and Mf(J) has a natural structure of affine scheme. The final section presents a detailed analysis of the origin and the historical evolution of the main notions we refer to

Dynamics of SNARE Assembly and Disassembly during Sperm Acrosomal Exocytosis

The dynamics of SNARE assembly and disassembly during membrane recognition and fusion is a central issue in intracellular trafficking and regulated secretion. Exocytosis of sperm's single vesicle—the acrosome—is a synchronized, all-or-nothing process that happens only once in the life of the cell and depends on activation of both the GTP-binding protein Rab3 and of neurotoxin-sensitive SNAREs. These characteristics make acrosomal exocytosis a unique mammalian model for the study of the different phases of the membrane fusion cascade. By using a functional assay and immunofluorescence techniques in combination with neurotoxins and a photosensitive Ca(2+) chelator we show that, in unactivated sperm, SNAREs are locked in heterotrimeric cis complexes. Upon Ca(2+) entry into the cytoplasm, Rab3 is activated and triggers NSF/α-SNAP-dependent disassembly of cis SNARE complexes. Monomeric SNAREs in the plasma membrane and the outer acrosomal membrane are then free to reassemble in loose trans complexes that are resistant to NSF/α-SNAP and differentially sensitive to cleavage by two vesicle-associated membrane protein (VAMP)–specific neurotoxins. Ca(2+) must be released from inside the acrosome to trigger the final steps of membrane fusion that require fully assembled trans SNARE complexes and synaptotagmin. Our results indicate that the unidirectional and sequential disassembly and assembly of SNARE complexes drive acrosomal exocytosis