We give an effective upper bound of |Bir(X)| for the birational automorphism group of an irregular n-fold (with n = 3) of general type in terms of the volume V = V (X) under an ”albanese smoothness and simplicity” condition. To be precise, |Bir(X)| ≤ d3V . An optimum linear bound |Bir(X)| ≤ 1 3 ×42V is obtained for those 3-folds with non-maximal albanese dimension. For all n ≥ 3, a bound |Bir(X...

Source: Hacker, Eddy and Lewis (2002) A visual appreciation of Keane’s two-dimensional (m=2) bump function may be obtained from the graphical presentation (Fig.-1; Hacker et al., 2002). As the dimension (m) grows larger, the optimum value of the function becomes more and more difficult to obtain. Keane (1994) observed that for m=20 the value of min[f(x)] could be about -0.76 and for m=50 it cou...

This paper is devoted to noisy optimization in case of a noise with standard deviation as large as variations of the fitness values, specifically when the variance does not decrease to zero around the optimum. We focus on comparing methods for choosing the number of resamplings. Experiments are performed on the differential evolution algorithm. By mathematical analysis, we design a new rule for...

Pulse deposition of 2.4 T Co37Fe63 alloy in photoresist features with 40 nm critical dimension and high aspect ratio is presented. The design of the pulse deposition parameters is described in terms of the transport limitations through the diffusion layer, electrochemical interface stability with respect to Fe(OH)3 precipitation, and the optimum conditions for additive (Saccharin) adsorption. T...

There are described methods used to minimize data files dimension. There are defined indicators for measuring size of files and databases. The storage optimization process is based on selecting from a multitude of data storage models the one that satisfies the propose problem objective, maximization or minimization of the optimum criterion that is mapped on the size of used disk memory. The pap...

We apply the method of complexity regularization to learn concepts from large concept classes. The method is shown to automatically find a good balance between the approximation error and the estimation error. In particular, the error probability of the obtained classifier is shown to decrease as O(dm) to the achievable optimum, for large nonparametric classes of distributions, as the sample si...

An analytical framework is established to dimension the pilot grid for MIMO-OFDM operating in time-variant frequency selective channels. The optimum placement of pilot symbols in terms of overhead and power allocation is identified that maximizes the training-based capacity for MIMO-OFDM schemes without channel knowledge at the transmitter. For pilot-aided channel estimation (PACE) with perfect...

We consider optimization problems with polynomial inequality constraints in non-commuting variables. These non-commuting variables are viewed as bounded operators on a Hilbert space whose dimension is not fixed and the associated polynomial inequalities as semidefinite positivity constraints. Such problems arise naturally in quantum theory and quantum information science. To solve them, we intr...

A proof is presented that shows how the neighborhood structure that is induced under a Gray Code representation repeats under shifting. Convergence proofs are also presented for steepest ascent using a local search bit climber and a Gray code representation: for unimodal 1-D functions and multimodal functions that are separable and unimodal in each dimension, the worst case number of steps need...

We review recent results obtained by the authors on the approximability of a family of combinatorial problems arising in optimal experimental design. We first recall a result based on submodularity, which states that the greedy approach always gives a design within 1 − 1/e of the optimal solution. Then, we present a new result on the design found by rounding the solution of the continuous relax...