Matrix algebras in quasi-newtonian algorithms for optimal learning in multi-layer perceptrons

In this work the authors implement in a Multi-Layer Perceptron (MLP) environment a new class of quasi-newtonian (QN) methods. The algorithms proposed in the present paper use in the iterative scheme of a generalized BFGS-method a family of matrix algebras, recently introduced for displacement decompositions and for optimal preconditioning. This novel approach allows to construct methods having an O(n log_2 n) complexity. Numerical experiences compared with the performances of the best QN-algorithms known in the literature confirm the effectiveness of these new optimization techniques

Comparison of the TaqMan and LightCycler systems in pharmacogenetic testing: evaluation of the CYP2C9*2/*3 polymorphisms.

Background: Pharmacogenetic testing for drugmetabolizing enzymes is not yet widely used in clinical practice. Methods: In an attempt to facilitate the application of this procedure, we have compared two real-time PCRbased methods, the TaqMan_ and the LightCycler_ for the pharmacogenetic evaluation of CYP2C9*2/*3 polymorphisms. Results and Conclusion: Both procedures are suitable for pharmacogenetic studies. The TaqMan procedure was less expensive in terms of cost per sample, but the TaqMan apparatus is more expensive than the LightCycler apparatus

A variation of Broyden Class methods using Householder adaptive transforms

In this work we introduce and study novel Quasi Newton minimization methods based on a Hessian approximation Broyden Class-\textit{type} updating scheme, where a suitable matrix $\tilde{B}_k$ is updated instead of the current Hessian approximation $B_k$. We identify conditions which imply the convergence of the algorithm and, if exact line search is chosen, its quadratic termination. By a remarkable connection between the projection operation and Krylov spaces, such conditions can be ensured using low complexity matrices $\tilde{B}_k$ obtained projecting $B_k$ onto algebras of matrices diagonalized by products of two or three Householder matrices adaptively chosen step by step. Extended experimental tests show that the introduction of the adaptive criterion, which theoretically guarantees the convergence, considerably improves the robustness of the minimization schemes when compared with a non-adaptive choice; moreover, they show that the proposed methods could be particularly suitable to solve large scale problems where $L$-$BFGS$ performs poorly

Low complexity secant quasi-Newton minimization algorithms for nonconvex functions

In this work some interesting relations between results on basic optimization and algorithms for nonconvex functions (such as BFGS and secant methods) are pointed out. In particular, some innovative tools for improving our recent secant BFGS-type and LQN algorithms are described in detail

On the best least squares fit to a matrix and its applications

The best least squares fit L_A to a matrix A in a space L can be useful to improve the rate of convergence of the conjugate gradient method in solving systems Ax=b as well as to define low complexity quasi-Newton algorithms in unconstrained minimization. This is shown in the present paper with new important applications and ideas. Moreover, some theoretical results on the representation and on the computation of L_A are investigated

Testicular endocrine activity is upregulated by D-Aspartic acid in the green frog Rana esculenta

This study investigated the involvement of D-aspartic acid (D-Asp) in testicular steroidogenesis of the green frog Rana esculenta and its effect on stimulation of thumb pad morphology and glandular activity, a typical testosterone-dependent secondary sexual characteristic in this amphibian species. In the testis, D-Asp concentrations vary significantly during the reproductive cycle: they are low in pre- and post-reproductive periods, but reach peak levels in the reproductive period (140-236 nmol/g wet tissue). Moreover, the concentrations of D-Asp in the testis through the sexual cycle positively match the testosterone levels in the gonad and the plasma. The racemase activity evaluated during the cycle expresses its peak when D-Asp and testosterone levels are highest, that is, during the reproductive period, confirming the synthesis of D-Asp from L-Asp by an aspartate racemase. Short-term in vivo experiments consisting of a single injection of D-Asp (2.0 micro mol/g body weight) demonstrated that this amino acid accumulates significantly in the testis, and after 3 h its uptake is coupled with a testosterone increase in both testis and plasma. Moreover, within 18 h of amino acid administration, the D-Asp concentration in the testis decreased along with the testosterone titer to prestimulation levels. Other amino acids (L-Asp, D-Glu and L-Glu) used instead of D-Asp were ineffective, confirming that the significant increase in testicular testosterone was a specific feature of this amino acid. In long-term experiments, D-Asp had been administered chronically to frogs caught during the three phases of the reproductive cycle, inducing testosterone increase and 17beta-estradiol decrease in the gonad during the pre- and post-reproductive period, and vice versa during the reproductive period

Adaptive matrix algebras in unconstrained minimization

In this paper we study adaptive L(k)QNmethods, involving special matrix algebras of low complexity, to solve general (non-structured) unconstrained minimization problems. These methods, which generalize the classical BFGS method, are based on an iterative formula which exploits, at each step, an ad hocchosen matrix algebra L(k). A global convergence result is obtained under suitable assumptions on f

Earth modeling and estimation of the local seismic ground motion due to site geology in complex volcanoclastic areas

Volcanic areas often show complex behaviour as far as seismic waves propagation and seismic motion at surface are concerned. In fact, the finite lateral extent of surface layers such as lava flows, blocks, differential welding and/or zeolitization within pyroclastic deposits, introduces in the propagation of seismic waves effects such as the generation of surface waves at the edge, resonance in lateral direction, diffractions and scattering of energy, which tend to modify the amplitude as well as the duration of the ground motion. The irregular topographic surface, typical of volcanic areas, also strongly influences the seismic site response. Despite this heterogeneity, it is unfortunately a common geophysical and engineering practice to evaluate even in volcanic environments the subsurface velocity field with monodimensional investigation method (i.e. geognostic soundings, refraction survey, down-hole, etc.) prior to the seismic site response computation which in a such cases is obviously also made with 1D algorithms. This approach often leads to highly inaccurate results. In this paper we use a different approach, i.e. a fully 2D P-wave Çturning rayÈ tomographic survey followed by 2D seismic site response modeling. We report here the results of this approach in three sites located at short distance from Mt. Vesuvius and Campi Flegrei and characterized by overburdens constituted by volcanoclastic deposits with large lateral and vertical variations of their elastic properties. Comparison between 1D and 2D Dynamic Amplification Factor shows in all reported cases entirely different results, both in terms of peak period and spectral contents, as expected from the clear bidimensionality of the geological section. Therefore, these studies suggest evaluating carefully the subsoil geological structures in areas characterized by possible large lateral and vertical variations of the elastic properties in order to reach correct seismic site response curves to be used for engineering projects

Six Years of ScoX-1 Monitoring with BeppoSAX Wide Field Cameras

We performed a systematic analysis of 54 Wide Field Camera (WFC) observations of ScoX-1 available in the BeppoSAX public archive. Observations span over the six years of BeppoSAX mission lifetime and include 690 hr of data. We searched for shifts and shape changes of the Z pattern in the color-color diagrams. We find that the Z pattern occupies most of the time the same locus in the color-color diagram. There are however a few exceptions, which are discussed in detail.Comment: 4 Pages, 4 figures. To appear in Proc. of the BeppoSAX Symposium: "The Restless High-Energy Universe", E.P.J. van den Heuvel, J.J.M. in 't Zand, and R.A.M.J. Wijers (Eds

Examples of application of tensorial resistivity probability tomography to architectonic and archaeological targets

We present the results of the application of the tensor resistivity method to the assessment of the state of conservation of some architectonic features of the S.Giovanni a Carbonara monumental monastery (Naples, Italy) and to the recognition of buried remains in the archaeological site of the roman Port of Claudius at Fiumicino (Rome, Italy). The 3D tomographic approach, based on the concept of resistivity anomaly source occurrence probability, has been used for the analysis of the invariant parameter related to the trace of the determinant of the apparent resistivity tensor