Irreducibility of Random Hilbert Schemes

We prove that a random Hilbert scheme that parametrizes the closed subschemes with a fixed Hilbert polynomial in some projective space is irreducible and nonsingular with probability greater than $0.5$. To consider the set of nonempty Hilbert schemes as a probability space, we transform this set into a disjoint union of infinite binary trees, reinterpreting Macaulay's classification of admissible Hilbert polynomials. Choosing discrete probability distributions with infinite support on the trees establishes our notion of random Hilbert schemes. To bound the probability that random Hilbert schemes are irreducible and nonsingular, we show that at least half of the vertices in the binary trees correspond to Hilbert schemes with unique Borel-fixed points.

The Poincaré polynomial for the Hilbert scheme of points of C^2

Questo lavoro prende in esame lo schema di Hilbert di punti di C^2, il quale viene descritto assieme ad alcune sue proprietà, ad esempio la sua struttura hyper-kahleriana. Lo scopo della tesi è lo studio del polinomio di Poincaré di tale schema di Hilbert: ciò che si ottiene è una espressione del tipo serie di potenze, la quale è un caso particolare di una formula molto più generale, nota con il nome di formula di Goettsche.

Moduli spaces of (G,h)-constellations

Given a reductive group G acting on an affine scheme X over C and a Hilbert function h: Irr G → N_0, we construct the moduli space M_Ө(X) of Ө-stable (G,h)-constellations on X, which is a common generalisation of the invariant Hilbert scheme after Alexeev and Brion and the moduli space of Ө-stable G-constellations for finite groups G introduced by Craw and Ishii. Our construction of a morphism M_Ө(X) → X//G makes this moduli space a candidate for a resolution of singularities of the quotient X//G. Furthermore, we determine the invariant Hilbert scheme of the zero fibre of the moment map of an action of Sl_2 on (C²)⁶ as one of the first examples of invariant Hilbert schemes with multiplicities. While doing this, we present a general procedure for the realisation of such calculations. We also consider questions of smoothness and connectedness and thereby show that our Hilbert scheme gives a resolution of singularities of the symplectic reduction of the action.

Borcherds products and arithmetic intersection theory on Hilbert modular surfaces

We prove an arithmetic version of a theorem of Hirzebruch and Zagier saying that Hirzebruch-Zagier divisors on a Hilbert modular surface are the coefficients of an elliptic modular form of weight 2. Moreover, we determine the arithmetic selfintersection number of the line bundle of modular forms equipped with its Petersson metric on a regular model of a Hilbert modular surface, and we study Faltings heights of arithmetic Hirzebruch-Zagier divisors.

Estimating losses in teleportation schemes using the phenomenological operator approach to dissipation in cavity quantum electrodynamics

In this paper, we estimate the losses during teleportation processes requiring either two high-Q cavities or a single bimodal cavity. The estimates were carried out using the phenomenological operator approach introduced by de Almeida et al. [Phys. Rev. A 62, 033815 (2000)].

HORMONAL RESPONSES TO DIFFERENT RESISTANCE EXERCISE SCHEMES OF SIMILAR TOTAL VOLUME

Uchida, MC, Crewther, BT, Ugrinowitsch, C, Bacurau, RFP, Moriscot, AS, and Aoki, MS. J Strength Cond Res 23(7): 2003-2008, 2009-This study assessed the effect of different resistance exercise scheme (RES) designs of similar total of load lifted on the responses of testosterone, cortisol, and creatine kinase (CK). Twenty-seven healthy males performed 1 of 4 bench press workouts described by the 1 repetition maximum (1RM) load: 4 sets of maximum repetitions at 50%-1RM (50%-1RM RES), 5 sets of maximum repetitions at 75%-1RM (75%-1RM RES), 10 sets of maximum repetitions at 90%-1RM (90%1RM RES), or 8 sets of maximum repetitions at 110%-1RM (110%-1RM RES). Each RES was equated by the total volume of load lifted (repetitions x sets x load). Blood samples, collected pre-exercise (Pre) and post-exercise (Post) at 1 and 24 hours (24 h), were analyzed for total and free testosterone, total cortisol, and CK. In general, testosterone and cortisol showed little change within or between the different RES (p > 0.05), possibly because of the relatively low volume lifted and/ or the small muscle mass activated by the bench press exercise. Cortisol was elevated after the 75%-1RM RES at the Post sample, with this response also exceeding the other RES (p < 0.05). The 24 h CK response was also elevated after the 75%-1RM RES (p < 0.05), thereby suggesting greater training strain for the same volume of load. These results confirm previous recommendations regarding the prescription of resistance exercise and the importance of total volume as a stimulus for activating the endocrine system and achieving long-term adaptation.

SALIVARY HORMONE AND IMMUNE RESPONSES TO THREE RESISTANCE EXERCISE SCHEMES IN ELITE FEMALE ATHLETES

Nunes, JA, Crewther, BT, Ugrinowitsch, C, Tricoli, V, Viveiros, L, de Rose Jr, D, and Aoki, MS. Salivary hormone and immune responses to three resistance exercise schemes in elite female athletes J Strength Cond Res 25(8): 2322-2327, 2011-This study examined the salivary hormone and immune responses of elite female athletes to 3 different resistance exercise schemes. Fourteen female basketball players each performed an endurance scheme (ES-4 sets of 12 reps, 60% of 1 repetition maximum (1RM) load, 1-minute rest periods), a strength-hypertrophy scheme (SHS-1 set of 5RM, 1 set of 4RM, 1 set of 3RM, 1 set of 2RM, and 1set of 1RM with 3-minute rest periods, followed by 3 sets of 10RM with 2-minute rest periods) and a power scheme (PS-3 sets of 10 reps, 50% 1RM load, 3-minute rest periods) using the same exercises (bench press, squat, and biceps curl). Saliva samples were collected at 07:30 hours, pre-exercise (Pre) at 09:30 hours, postexercise (Post), and at 17:30 hours. Matching samples were also taken on a nonexercising control day. The samples were analyzed for testosterone, cortisol (C), and immunoglobulin A concentrations. The total volume of load lifted differed among the 3 schemes (SHS > ES > PS, p < 0.05). Postexercise C concentrations increased after all schemes, compared to control values (p < 0.05). In the SHS, the postexercise C response was also greater than pre-exercise data (p < 0.05). The current findings confirm that high-volume resistance exercise schemes can stimulate greater C secretion because of higher metabolic demand. In terms of practical applications, acute changes in C may be used to evaluate the metabolic demands of different resistance exercise schemes, or as a tool for monitoring training strain.

Online Mammographic Images Database for Development and Comparison of CAD Schemes

Considering the difficulties in finding good-quality images for the development and test of computer-aided diagnosis (CAD), this paper presents a public online mammographic images database free for all interested viewers and aimed to help develop and evaluate CAD schemes. The digitalization of the mammographic images is made with suitable contrast and spatial resolution for processing purposes. The broad recuperation system allows the user to search for different images, exams, or patient characteristics. Comparison with other databases currently available has shown that the presented database has a sufficient number of images, is of high quality, and is the only one to include a functional search system.

A Geometric Approach for Turbo Decoding of Reed-Solomon Codes in QAM Modulation Schemes

This work studies the turbo decoding of Reed-Solomon codes in QAM modulation schemes for additive white Gaussian noise channels (AWGN) by using a geometric approach. Considering the relations between the Galois field elements of the Reed-Solomon code and the symbols combined with their geometric dispositions in the QAM constellation, a turbo decoding algorithm, based on the work of Chase and Pyndiah, is developed. Simulation results show that the performance achieved is similar to the one obtained with the pragmatic approach with binary decomposition and analysis.

Quantum mechanics as an approximation to classical mechanics in Hilbert space

Classical mechanics is formulated in complex Hilbert space with the introduction of a commutative product of operators, an antisymmetric bracket and a quasidensity operator that is not positive definite. These are analogues of the star product, the Moyal bracket, and the Wigner function in the phase space formulation of quantum mechanics. Quantum mechanics is then viewed as a limiting form of classical mechanics, as Planck's constant approaches zero, rather than the other way around. The forms of semiquantum approximations to classical mechanics, analogous to semiclassical approximations to quantum mechanics, are indicated.

Strain-dependent fluid flow defined through rock mass classification schemes

Strain-dependent hydraulic conductivities are uniquely defined by an environmental factor, representing applied normal and shear strains, combined with intrinsic material parameters representing mass and component deformation moduli, initial conductivities, and mass structure. The components representing mass moduli and structure are defined in terms of RQD (rock quality designation) and RMR (rock mass rating) to represent the response of a whole spectrum of rock masses, varying from highly fractured (crushed) rock to intact rock. These two empirical parameters determine the hydraulic response of a fractured medium to the induced-deformations The constitutive relations are verified against available published data and applied to study one-dimensional, strain-dependent fluid flow. Analytical results indicate that both normal and shear strains exert a significant influence on the processes of fluid flow and that the magnitude of this influence is regulated by the values of RQD and RMR.

Two-link approximation schemes for loss networks with linear structure and trunk reservation

Loss networks have long been used to model various types of telecommunication network, including circuit-switched networks. Such networks often use admission controls, such as trunk reservation, to optimize revenue or stabilize the behaviour of the network. Unfortunately, an exact analysis of such networks is not usually possible, and reduced-load approximations such as the Erlang Fixed Point (EFP) approximation have been widely used. The performance of these approximations is typically very good for networks without controls, under several regimes. There is evidence, however, that in networks with controls, these approximations will in general perform less well. We propose an extension to the EFP approximation that gives marked improvement for a simple ring-shaped network with trunk reservation. It is based on the idea of considering pairs of links together, thus making greater allowance for dependencies between neighbouring links than does the EFP approximation, which only considers links in isolation.

Quantification of endocrine disruptors and pesticides in water by gas chromatography–tandem mass spectrometry. Method validation using weighted linear regression schemes

Amulti-residue methodology based on a solid phase extraction followed by gas chromatography–tandem mass spectrometry was developed for trace analysis of 32 compounds in water matrices, including estrogens and several pesticides from different chemical families, some of them with endocrine disrupting properties. Matrix standard calibration solutions were prepared by adding known amounts of the analytes to a residue-free sample to compensate matrix-induced chromatographic response enhancement observed for certain pesticides. Validation was done mainly according to the International Conference on Harmonisation recommendations, as well as some European and American validation guidelines with specifications for pesticides analysis and/or GC–MS methodology. As the assumption of homoscedasticity was not met for analytical data, weighted least squares linear regression procedure was applied as a simple and effective way to counteract the greater influence of the greater concentrations on the fitted regression line, improving accuracy at the lower end of the calibration curve. The method was considered validated for 31 compounds after consistent evaluation of the key analytical parameters: specificity, linearity, limit of detection and quantification, range, precision, accuracy, extraction efficiency, stability and robustness.