177,384 research outputs found
A classification of one-dimensional local domains based on the invariant (c-delta)r-delta
No full textLet (R, m) be a one-dimensional, local, Noetherian domain
and let R' be the integral closure of R in its quotient field K. We assume that R is not regular, analitycally irreducible and residually rational. The usual valuation v : K\longrightarrow Z \cup \infty associated to R' defines the numerical semigroup
v (R)= { v (a), a in R, a\neq 0} \subseteq N.
The aim of the paper is to study the non-negative invariant b:=(c- delta)r- delta , where c, delta, r denote respectively the conductor, the length of R'/R and the Cohen Macaulay type of R. In particular, the classification of the semigroups v(R) for rings R having b\leq 2(r-1) is realized. This method of classification might be successfully utilized with similar arguments but more boring computations in the cases b \leq q(r-1), for reasonably low values of q . The main tools are type sequences and the invariant k which estimates the number of elements in v(R) belonging to the interval [c-e,c-1], e being the multiplicity of R
RADICAL PROSTATECTOMY: ONCOLOGIC RISK OF THE BLADDER NECK SPARING PROCEDURES F. Oneto, U. Repetto, A Curotto, M. Cussotto, R.. Franchini, R. Banchero, A. Simonato, G. Carmignani ABSTRACTS XXIITH EAU PARIGI, 1 -4 SETTEMRE 1996
No full textInvariants associated with ideals in one-dimensional local domains
No full textLet R be a one-dimensional local Noetherian domain with maximal ideal \m, quotient field K and residue field R/\m:=k . We assume that the integral closure \R of R in its quotient field K is a DVR and a finite R- module. We assume also that the field k is isomorphic to the residue field of \R . For I a proper ideal of R, denote the inverse of I by I*; that is, I* is the set (R:_K I) of
elements of K that multiply I into R. We investigate two numerical invariants associated to a proper ideal I of R that have previously come up in the literature from
various points of view. The two invariants are:\ (1)
the difference between the composition
lengths of I*/R and R/I, and (2) the difference between the
product, when the composition length of
R/I is multiplied by the composition length of \m*/R, and the length of I*/R. We show that these two differences can be expressed in terms of the type sequence of R, a finite sequence of positive integers related to the natural valuation
inherited from \R
Distribution-Dependent Weighted Union Bound
No full textIn this paper, we deal with the classical Statistical Learning Theory’s problem of bounding, with high probability, the true risk R(h) of a hypothesis h chosen from a set H of m hypotheses. The Union Bound (UB) allows one to state that PLR^(h),δqh≤R(h)≤UR^(h),δph≥1−δ where R^(h) is the empirical errors, if it is possible to prove that P{R(h)≥L(R^(h),δ)}≥1−δ and P{R(h)≤U(R^(h),δ)}≥1−δ, when h, qh, and ph are chosen before seeing the data such that qh,ph∈[0,1] and ∑h∈H(qh+ph)=1. If no a priori information is available qh and ph are set to 12m, namely equally distributed. This approach gives poor results since, as a matter of fact, a learning procedure targets just particular hypotheses, namely hypotheses with small empirical error, disregarding the others. In this work we set the qh and ph in a distribution-dependent way increasing the probability of being chosen to function with small true risk. We will call this proposal Distribution-Dependent Weighted UB (DDWUB) and we will retrieve the sufficient conditions on the choice of qh and ph that state that DDWUB outperforms or, in the worst case, degenerates into UB. Furthermore, theoretical and numerical results will show the applicability, the validity, and the potentiality of DDWUB
An application of type sequences to the blowing-up
No full textLet I be an \m -primary ideal of a
one-dimensional, analytically irreducible and
residually rational local Noetherian
domain R. Given the blowing-up of R
along I, we establish connections between the type-sequence of R and classical invariants like multiplicity, genus
and reduction exponent of I
Syzygies of GS monomial curves and Weierstrass property.
No full textWe find a resolution for the coordinate ring R of an algebraic monomial curve associated to a G numerical semigroup (i.e. generated by a generalized arithmetic sequence), by extending a previous paper (Gimenez, Sengupta, Srinivasan) on arithmetic sequences . A consequence is the determinantal description of the first syzygy module of R. By this fact, via suitable deformations of the defining matrices, we can prove the smoothability of the curves associated to a large class of semigroups generated by arithmetic sequences, that is the Weierstrass property for such semigroups
Fairness and accountability of machine learning models in railway market: Are applicable railway laws up to regulate them?
No full textThis paper discusses whether the law is up to regulate machine learning (”ML”) model-based decision-making in the context of the railways. We especially deal with the fairness and accountability of these models when exploited in the context of train traffic management (”TTM”). Railway sector-specific regulation, in their quality as network industry, hereby serves as a pilot. We show that, even where technological solutions are available, the law needs to keep up to support and accurately regulate the use of the technological solutions and we identify stumble points in this regard
On semigroup rings with decreasing Hilbert function
No full textGiven a one-dimensional semigroup ring R=k[[S]], in this article we study the behaviour of the Hilbert function HR. By means of the notion of support of the elements in S, for some classes of semigroup rings we give conditions on the generators of S in order to have decreasing HR. When the embedding dimension v and the multiplicity e verify v+3â¤eâ¤v+4, the decrease of HRgives an explicit description of the Apéry set of S. In particular for e=v+3, we prove that HRis non-decreasing if eâ¤12 and we classify the semigroups with e=13 and HRdecreasing. Finally we deduce that HRis non-decreasing for every Gorenstein semigroup ring with eâ¤v+4. This fact is not true in general: through numerical duplication and some of the above results another recent paper shows the existence of infinitely many one-dimensional Gorenstein rings with decreasing Hilbert function
INdAM meeting: International meeting on numerical semigroups Cortona 2018
No full textIn this article we study the Hilbert function HR of one-dimensional semigroup rings R = k[[S]], with embedding dimension four over an infinite field k. Let S =< e, n2, n3, n4 > and let M = S ?{0}. Consider the Apéry set of S with respect to the multiplicity e and its subsets Ah = {s ? Apéry(S) | s ? hM ? (h + 1)M}, h ≥ 2. Further let D2 ?{n3, n4} be the set of generators with torsion order 1. We prove that HR is non-decreasing at level ≤ 3 and that HR is non decreasing in each of the following cases: if A2 has cardinality ≤ 4, if A3 has cardinality ≤ 3, if A4 = ?, if D2 has cardinality 2, if S has multiplicity ≤ 13
Lo status di conservazione della testuggine palustre Emys trinacris negli ambienti umidi della Sicilia: un approccio integrato
No full textThe research turned to the Sicilian pond turtle, Emys trinacris, recently distinguished from the congener Emys orbicularis (FRITZ et al., 2005; 2006). It is an endemism of Sicily spread throughout the region in a fragmented way (DI CERBO, 2011), from sea level up to about 1000 m asl (MARRONE et al., 2016), which colonizes a good variety of environments (marshes and lagoons, ponds in agro-pastoral context, mountain ponds, artificial reservoirs) (TURRISI, 2008).
With regard to the study of the trophism of this species, the analysis of trophic niches is particularly relevant in this specific case to determine the level of competition between species (BALZANI et al., 2016) and the effects on the target species. Studies on fecal contents are traditionally applied which, however, although easy to apply, do not provide information on the long term and on how the diet changes over time (BOECKLEN et al., 2011). On the contrary, the analysis of the stable isotopes (SIA) of carbon (δ13C) and nitrogen (δ15N) provides information on the trophic resources actually used as well as on trophic behavior (MIDDELBURG, 2014).
The study was conducted in two areas identified on the Sicilian territory and characterized from an environmental point of view:
1. WWF Nature Reserve “Lago Preola - Gorghi Tondi” (TP);
2. Wetlands in the Bosco della Ficuzza nature reserve, Rocca Busambra, Bosco del Cappelliere and Gorgo del Drago (PA).
The research was carried out through periodic captures of terrapins operated in colonized habitats, using methodologies widely tested in other populations of E. orbicularis in mainland Italy (CANESSA et al., 2016) and on E. trinacris in Sicily (OTTONELLO et al. , 2016), and shared at ministerial level (LO VALVO et al., 2016). The individuals were therefore captured with the aid of primed pots and pots of the "bertovelli" type (without bait) depending on the type of environment. The same pots were also used to capture the alien species present in cohabitation with Emys (mainly fish, shrimp). The animals were temporarily housed for the collection of morphological parameters and tissue and sexing samples. Blood and horn samples are taken from all animals for subsequent dietary analysis. The overlap of isotopic niches has been studied by applying recent investigation methodologies that involve the use of stable isotopes of Nitrogen and Carbon, through blood and horny material samples (PEARSON et al., 2013; BALZANI et al., 2016) from marsh terrapins and potentially competing species. The analysis was carried out through a collaboration with the Department of Earth and Sea Sciences of the University of Palermo.
All analyzes were carried out with the help of the packages available in the R4.04 software (R CORE TEAM 2021). Information on inter- and intraspecific variability in isotopic niche size and trophic diversity was obtained using the metrics proposed by LAYMAN et al. (2007) with the package R SIAR - Stable Isotope Analysis in R (Parnell et al. 2010) and SIBER (Stable Isotope Bayesian Ellipses in R).
During the sessions held in 2018 (2) and 2019 (3), 109 terrapins were captured respectively in the Lago Preola Reserve - Gorghi Tondi and 42 terrapins in the Bosco Ficuzza Reserve.
In the Lago Preola - Gorghi Tondi Reserve, 84 allochthonous fish were also caught: 44 Cyprinus carpio and 40 Gambusia holbrooki. As reported by OTTONELLO et al., (2021), also in this study the fishes appear to colonize exclusively the Gorgo Medio - Gorgo Alto system, while there are no fish in the Gorgo Basso. In the Gorgo Lungo pond, no fish or other species of alien terrapins have been found.
The trophic strategy of the Sicilian terrapin populations in the investigated areas reflects what has already been indicated for Emys orbicularis (FICETOLA et al., 2006; OTTONELLO et al., 2021), following a substantially opportunistic and generalist scheme. The main preys are aquatic invertebrates, while terrestrial ones are rarer (OTTONELLO et al., 2021).
In the case of the population of the Lago Preola and Gorghi Tondi Reserve, as already described by OTTONELLO et al., (2017), the individuals of terrapins captured in the 3 Gorghi present significant differences especially as regards the Body Condition Index (BCI), therefore it is possible to distinguish on the one hand the individuals coming from the Gorgo Basso and on the other hand those coming from the Gorgo Medio-Gorgo Alto system.
By comparing the biometric data collected in the two study areas, considering BCI, SCL and weight, the individuals of the Gorgo Lungo are significantly different compared to the individuals of the Lago Preola and Gorghi Tondi Reserve for all the variables considered, with terrapins of the Gorgo Lungo on average larger than those from coastal sites.
Analyzing the isotopic contents of the blood of males and females of Emys no significant differences were detected by comparing the sites and periods of capture. On the other hand, comparing the isotopic contents of the horny material of Emys, Gorgo Basso would differ from both Gorgo Alto and Gorgo Medio, while Alto and Medio would be similar. This would be valid above all for δ15N, while the variability for δ13C is less evident.
OTTONELLO et al. (2016) hypothesize that the evident differences both biometric and in the productivity and growth of terrapins detectable between Gorgo Basso and the Gorgo Alto and Gorgo Medio systems can be traced back to the presence only in the Gorgo Alto and Gorgo Medio of fish species such as carp and gambusia , species that can have a significant impact on the macrobenthic component of colonized water bodies (CAGLE, 1946; GIBBONS, 1982; MACCULLOCH & SECOY, 1983; DUNHAM & GIBBONS, 1990, OTTONELLO et al., 2016). For this reason, the isotopic content of the fish species present was also tested, to evaluate their position in the trophic chain.
Applying the metrics proposed by LAYMAN et al. (2007a), considering the isotopic traces of Emys nails, it is observed that the NR and CR values are substantially comparable in the terrapins coming from the single site. Comparing terrapins and fishes, the NR values would be slightly higher in Emys than in carp and allies with gambusia, indicating a similar ability to exploit resources at different trophic levels, also the CR values would be substantially similar between Emys and fish. The values of TA and CD in the terrapins of the Gorgo Medio e Alto are lower than especially in the Gorgo Alto indicating a greater amplitude, albeit slight, of the trophic niche in the fish. Comparing the data obtained between Gorgo Basso and Gorgo Medio / Alto, also in this case Gorgo Basso confirms that it has a different trend compared to the other two, with overall higher values attesting to trophic niches and availability of greater resources than Gorgo Alto and Medio.
The corrected standard ellipse (SEAc), in the case of the isotopic traces of Emys nails, visually confirms what has been described, reporting a substantial overlap between the isotopic niches of the terrapins in the different sites, with a much wider niche for those coming from Gorgo Basso . These ellipses overlap only partially with those of the Gorgo Alto and Medio terrapins.
Analyzing the isotopic niches and their overlap in males and females of the Gorgo Lungo, the values of the Layman metrics are substantially similar if we consider the samples derived from the nails, with a greater variability of basal sources in males (male CR> female CR) and on the contrary, a greater capacity of females to exploit the available resources (NR male
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