A note on the computation of the Frobenius number of a numerical semigroup

In this note we observe that the Frobenius number and therefore the conductor of a numerical semigroup can be obtained from the maximal socle degree of the quotient of the corresponding semigroup algebra by the ideal generated by the biggest generator of the semigroup.Comment: Some typos in the introduction have been correcte

Computation with narrow CTCs

We examine some variants of computation with closed timelike curves (CTCs), where various restrictions are imposed on the memory of the computer, and the information carrying capacity and range of the CTC. We give full characterizations of the classes of languages recognized by polynomial time probabilistic and quantum computers that can send a single classical bit to their own past. Such narrow CTCs are demonstrated to add the power of limited nondeterminism to deterministic computers, and lead to exponential speedup in constant-space probabilistic and quantum computation. We show that, given a time machine with constant negative delay, one can implement CTC-based computations without the need to know about the runtime beforehand.Comment: 16 pages. A few typo was correcte

Betti numbers for numerical semigroup rings

We survey results related to the magnitude of the Betti numbers of numerical semigroup rings and of their tangent cones.Comment: 22 pages; v2: updated references. To appear in Multigraded Algebra and Applications (V. Ene, E. Miller Eds.

On Weierstra{\ss} semigroups at one and two points and their corresponding Poincar\'e series

The aim of this paper is to introduce and investigate the Poincar\'e series associated with the Weierstra{\ss} semigroup of one and two rational points at a (not necessarily irreducible) non-singular projective algebraic curve defined over a finite field, as well as to describe their functional equations in the case of an affine complete intersection.Comment: Beginning of Section 3 and Subsection 3.1 were modifie

Oral contraceptive use and anterior cruciate ligament injury: comparison of active comparator new user cohort and case-control study designs

Background: This study further investigates a protective association between oral contraceptive (OC) use and anterior cruciate ligament (ACL) injury noted in prior case-control studies. Methods: Active comparator new user cohort analysis of women aged 13–45 years in the United States from the IBM MarketScan Commercial Claims and Encounters database who newly-initiated low-dose OCs (exposed) or underwent intrauterine device (IUD) insertion (comparison group) from 2000 to 2014. Women were followed for ACL injury starting 90 days after OC initiation or IUD insertion until OC or IUD discontinuation or end of continuous enrollment. Adjusted hazard ratios (adjHR) and 95% confidence intervals (CI) were estimated controlling for age. Secondary analysis replicated previously-published case-control studies assessing “ever” versus “never” OC use over 1- and 5-year periods among women who underwent ACL reconstruction compared to age-matched controls. Results: In the cohort analysis, 2,370,286 women initiated OCs and 621,798 underwent IUD insertion. There were 3571 (0.15%) ACL injuries during an average 370.6 days of continuous OC use and 1620 (0.26%) during an average 590.5 days of IUD use. No difference in risk of ACL injury was observed between OC initiators and IUD users (adjHR = 0.95; 95%CI 0.89, 1.01). The case-control analysis replicated the slight protective association observed in prior studies over a 5-year period (OR = 0.90; 95%CI 0.85, 0.94). Conclusions: This cohort study suggests no association between OC use and ACL injury, while the case-control study suggested bias from uncontrolled confounding and selection factors may have influenced previous findings that suggested a protective association between OC use and ACL injury

Ultrafast carrier relaxation in GaN, In_(0.05)Ga_(0.95)N and an In_(0.05)Ga_(0.95)/In_(0.15)Ga_(0.85)N Multiple Quantum Well

Room temperature, wavelength non-degenerate ultrafast pump/probe measurements were performed on GaN and InGaN epilayers and an InGaN multiple quantum well structure. Carrier relaxation dynamics were investigated as a function of excitation wavelength and intensity. Spectrally-resolved sub-picosecond relaxation due to carrier redistribution and QW capture was found to depend sensitively on the wavelength of pump excitation. Moreover, for pump intensities above a threshold of 100 microJ/cm2, all samples demonstrated an additional emission feature arising from stimulated emission (SE). SE is evidenced as accelerated relaxation (< 10 ps) in the pump-probe data, fundamentally altering the re-distribution of carriers. Once SE and carrier redistribution is completed, a slower relaxation of up to 1 ns for GaN and InGaN epilayers, and 660 ps for the MQW sample, indicates carrier recombination through spontaneous emission.Comment: submitted to Phys. Rev.

The discontinuous nature of chromospheric activity evolution

Chromospheric activity has been thought to decay smoothly with time and, hence, to be a viable age indicator. Measurements in solar type stars in open clusters seem to point to a different conclusion: chromospheric activity undergoes a fast transition from Hyades level to that of the Sun after about 1 Gyr of main--sequence lifetime and any decaying trend before or after this transition must be much less significant than the short term variations.Comment: 6 pages, 1 figure, to be published in Astrophysics and Space Scienc

The prediction of preference for unfamiliar urban places

Preferences for unfamiliar urban environments were studied as a function of urban categories, viewing time, and four predictor variables: complexity, coherence, identifiability, and mystery. A nonmetric factor analysis of the preference ratings for the longest viewing-time condition yielded five dimensions: Contemporary Life, Alley/Factory, Urban Nature, Unusual Architecture, and Older Buildings. The five categories differed significantly in preference, with Urban Nature by far the most preferred and Alley/Factory distinctly disliked. The combination of low coherence and high complexity characterizes the least liked Alley/Factory category, while the role of mystery in the urban setting is highlighted by the most preferred Urban Nature category. The results point to various ways in which the urban environment could be more responsive to people's preferences.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43513/1/11111_2005_Article_BF01359051.pd

How Coupling Determines the Entrainment of Circadian Clocks

Autonomous circadian clocks drive daily rhythms in physiology and behaviour. A network of coupled neurons, the suprachiasmatic nucleus (SCN), serves as a robust self-sustained circadian pacemaker. Synchronization of this timer to the environmental light-dark cycle is crucial for an organism's fitness. In a recent theoretical and experimental study it was shown that coupling governs the entrainment range of circadian clocks. We apply the theory of coupled oscillators to analyse how diffusive and mean-field coupling affects the entrainment range of interacting cells. Mean-field coupling leads to amplitude expansion of weak oscillators and, as a result, reduces the entrainment range. We also show that coupling determines the rigidity of the synchronized SCN network, i.e. the relaxation rates upon perturbation. %(Floquet exponents). Our simulations and analytical calculations using generic oscillator models help to elucidate how coupling determines the entrainment of the SCN. Our theoretical framework helps to interpret experimental data