1,721,071 research outputs found
Hilbert curves of conic fibrations over smooth surfaces
No full textLet (X, L) be a complex polarized threefold which is a conic fibration over a smooth surface. The complex affine cubic Γ representing the Hilbert curve of (X, L) is studied, paying special attention to its reducibility. In particular, Γ contains a specific line l 0 if and only if X has no singular fibers. This leads to characterize the existence of a triple point simply in terms of numerical invariants of X. Other lines may cause the reducibility of Γ, which in this case depends also on the polarization. This situation is analyzed for a special class of conic fibrations
‘Beauty Contested. How much of Keynes’ remains in Behavioural Economics’ Beauty Contests?, COREP Papers, Turin
No full text"What is Behavioural Economics About? Loss Aversion, Endowment Effect and some Unanswered Questions about Realisticness and the Relationship with Mainstream", SEMeQ Working Paper 22/2007, November
No full textEstimating multi-index models with response-conditional least squares
No full textThe multi-index model is a simple yet powerful high-dimensional regression model which circumvents the curse of dimensionality assuming E[Y |X] = g(A⊤X) for some unknown index space A and link function g. In this paper we introduce a method for the estimation of the index space, and study the propagation error of an index space estimate in the regression of the link function. The proposed method approximates the index space by the span of linear regression slope coefficients computed over level sets of the data. Being based on ordinary least squares, our approach is easy to implement and computationally efficient. We prove a tight concentration bound that shows N−1/2-convergence, but also faithfully describes the dependence on the chosen partition of level sets, hence providing guidance on the hyperparameter tuning. The estimator’s competitiveness is confirmed by extensive comparisons with state-of-the-art methods, both on synthetic and real data sets. As a second contribution, we establish minimax optimal generalization bounds for k-nearest neighbors and piecewise polynomial regression when trained on samples projected onto any N−1/2-consistent estimate of the index space, thus providing complete and provable estimation of the multi-index model
Semipolarized nonruled surfaces with sectional genus two
No full textComplex projective nonruled surfaces S endowed with a numerically effective line bundle L of arithmetic genus g(S, L) = 2 are investigated. In view of existing results on elliptic surfaces we focus on surfaces of Kodaira dimension κ(S) = 0 and 2. Structure results for (S, L) are provided in both cases, according to the values of L2. When S is not minimal we describe explicitly the structure of any birational morphism from S to its minimal model S0, reducing the study of (S, L) to that of (S0, L 0), where L0 is a numerically effective line bundle with g(S0, L0) = 2 or 3. Our description of (S, L) when S is minimal, as well as that of the pair (S0, L0) when g(S0, L0) = 3, relies on several results concerning linear systems, mainly on surfaces of Kodaira dimension 0. Moreover, several examples are provided, especially to enlighten the case in which S is a minimal surface of general type, (S, L) having Iitaka dimension
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