A combinatorial description of finite O-sequences and aCM genera

The goal of this paper is to explicitly detect all the arithmetic genera of arithmetically Cohen-Macaulay projective curves with a given degree $d$. It is well-known that the arithmetic genus $g$ of a curve $C$ can be easily deduced from the $h$-vector of the curve; in the case where $C$ is arithmetically Cohen-Macaulay of degree $d$, $g$ must belong to the range of integers $\big\{0,\ldots,\binom{d-1}{2}\big\}$. We develop an algorithmic procedure that allows one to avoid constructing most of the possible $h$-vectors of $C$. The essential tools are a combinatorial description of the finite O-sequences of multiplicity $d$, and a sort of continuity result regarding the generation of the genera. The efficiency of our method is supported by computational evidence. As a consequence, we single out the minimal possible Castelnuovo-Mumford regularity of a curve with Cohen-Macaulay postulation and given degree and genus.Comment: Final versio

Upgraded methods for the effective computation of marked schemes on a strongly stable ideal

Let $J\subset S=K[x_0,...,x_n]$ be a monomial strongly stable ideal. The collection \Mf(J) of the homogeneous polynomial ideals $I$, such that the monomials outside $J$ form a $K$-vector basis of $S/I$, is called a {\em $J$-marked family}. It can be endowed with a structure of affine scheme, called a {\em $J$-marked scheme}. For special ideals $J$, $J$-marked schemes provide an open cover of the Hilbert scheme \hilbp, where $p(t)$ is the Hilbert polynomial of $S/J$. Those ideals more suitable to this aim are the $m$-truncation ideals $\underline{J}_{\geq m}$ generated by the monomials of degree $\geq m$ in a saturated strongly stable monomial ideal $\underline{J}$. Exploiting a characterization of the ideals in \Mf(\underline{J}_{\geq m}) in terms of a Buchberger-like criterion, we compute the equations defining the $\underline{J}_{\geq m}$-marked scheme by a new reduction relation, called {\em superminimal reduction}, and obtain an embedding of \Mf(\underline{J}_{\geq m}) in an affine space of low dimension. In this setting, explicit computations are achievable in many non-trivial cases. Moreover, for every $m$, we give a closed embedding \phi_m: \Mf(\underline{J}_{\geq m})\hookrightarrow \Mf(\underline{J}_{\geq m+1}), characterize those $\phi_m$ that are isomorphisms in terms of the monomial basis of $\underline{J}$, especially we characterize the minimum integer $m_0$ such that $\phi_m$ is an isomorphism for every $m\geq m_0$.Comment: 28 pages; this paper contains and extends the second part of the paper posed at arXiv:0909.2184v2[math.AG]; sections are now reorganized and the general presentation of the paper is improved. Final version accepted for publicatio

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

Segments and Hilbert schemes of points

Using results obtained from the study of homogeneous ideals sharing the same initial ideal with respect to some term order, we prove the singularity of the point corresponding to a segment ideal with respect to the revlex term order in the Hilbert scheme of points in $\mathbb{P}^n$. In this context, we look inside properties of several types of "segment" ideals that we define and compare. This study led us to focus our attention also to connections between the shape of generators of Borel ideals and the related Hilbert polynomial, providing an algorithm for computing all saturated Borel ideals with the given Hilbert polynomial.Comment: 19 pages, 2 figures. Comments and suggestions are welcome

Projections of climate extremes under potential climate change as represented by changing equator to pole temperature gradient and land ocean temperature contrast.

Under climate variability and anthropogenic forcing, the Equator-to-Pole Temperature Gradient (EPG) and the Ocean-Land Temperature Contrast (OLC) undergo systematic changes, which can be associated with the equatorial pacific circulation patterns via teleconnections, and with the Atlantic Meridional Overturning Circulation (AMOC) via ocean-atmosphere coupling. We couple the Lorenz ’84 atmospheric model, a Box AMOC model (after Roebber 1994), and an ENSO coupled ocean-atmosphere model (Tziperman et al, 1994) to explore the sensitivity of the strength, position and other statistics of the mid-latitude wind components to changes in the aforementioned systems and components. Sea ice and water balances are not explicitly modeled. We then develop and discuss projections of the changes in persistence, low frequency variability, and frequency of extremes in key climatic parameters, as specific climate changes, anticipated under anthropogenic forcing in the 21st century, are postulated

Effect of somatosensory amplification and trait anxiety on experimentally induced orthodontic pain

The perception of pain varies considerably across individuals and is affected by psychological traits. This study aimed to investigate the combined effects of somatosensory amplification and trait anxiety on orthodontic pain. Five-hundred and five adults completed the State Trait Anxiety Inventory (STAI) and the Somatosensory Amplification Scale (SSAS). Individuals with combined STAI and SSAS scores below the 20th percentile (LASA group: five men and 12 women; mean age ± SD = 22.4 ± 1.3 yr) or above the 80th percentile (HASA group: 13 men and seven women; mean age ± SD = 23.7 ± 1.0 yr) were selected and filled in the Oral Behaviors Checklist (OBC). Orthodontic separators were placed for 5 d in order to induce experimental pain. Visual analog scales (VAS) were administered to collect ratings for occlusal discomfort, pain, and perceived stress. Pressure pain thresholds (PPT) were measured. A mixed regression model was used to evaluate pain and discomfort ratings over the 5-d duration of the study. At baseline, the LASA group had statistically significantly higher PPT values for the masseter muscle than did the HASA group. During the experimental procedure, the HASA group had statistically significantly higher discomfort and pain. A significant difference in pain ratings during the 5 d of the study was found for subjects in the HASA group. Higher OBC values were statistically significantly positively associated with pain. Somatosensory amplification and trait anxiety substantially affect experimentally induced orthodontic pain

CRT-175 Old Saphenous Vein Grafts with Important Degeneration Treated with Self-Expandable Stents: Our Experience

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