Generalized Schmidt decomposition and classification of three-quantum-bit states

We prove for any pure three-quantum-bit state the existence of local bases which allow one to build a set of five orthogonal product states in terms of which the state can be written in a unique form. This leads to a canonical form which generalizes the two-quantum-bit Schmidt decomposition. It is uniquely characterized by the five entanglement parameters. It leads to a complete classification of the three-quantum-bit states. It shows that the right outcome of an adequate local measurement always erases all entanglement between the other two parties.

Magnetic field scaling of relaxation curves in small particle systems

We study the effects of the magnetic field on the relaxation of the magnetization of smallmonodomain noninteracting particles with random orientations and distribution of anisotropyconstants. Starting from a master equation, we build up an expression for the time dependence of themagnetization which takes into account thermal activation only over barriers separating energyminima, which, in our model, can be computed exactly from analytical expressions. Numericalcalculations of the relaxation curves for different distribution widths, and under different magneticfields H and temperatures T, have been performed. We show how a T ln(t/t0) scaling of the curves,at different T and for a given H, can be carried out after proper normalization of the data to theequilibrium magnetization. The resulting master curves are shown to be closely related to what wecall effective energy barrier distributions, which, in our model, can be computed exactly fromanalytical expressions. The concept of effective distribution serves us as a basis for finding a scalingvariable to scale relaxation curves at different H and a given T, thus showing that the fielddependence of energy barriers can be also extracted from relaxation measurements.

Classification of indian classical vocal styles from melodic contours

A prominent categorization of Indian classical music is the Hindustani and Carnatic traditions, the two styleshaving evolved under distinctly different historical andcultural influences. Both styles are grounded in the melodicand rhythmic framework of raga and tala. The styles differ along dimensions such as instrumentation,aesthetics and voice production. In particular, Carnatic music is perceived as being more ornamented. The hypothesisthat style distinctions are embedded in the melodic contour is validated via subjective classification tests. Melodic features representing the distinctive characteristicsare extracted from the audio. Previous work based on the extent of stable pitch regions is supported by measurements of musicians’ annotations of stable notes. Further, a new feature is introduced that captures thepresence of specific pitch modulations characteristic ofornamentation in Indian classical music. The combined features show high classification accuracy on a database of vocal music of prominent artistes. The misclassifications are seen to match actual listener confusions.

A Classification of Tools for Learning Logic

A table showing a comparison and classification of tools (intelligent tutoring systems) for e-learning of Logic at a college level.

Prediction of crude protein and classification of the growth stage of wheat plant samples from NIR spectra

Near-infrared spectroscopy (NIRS) was used to analyse the crude protein content of dried and milled samples of wheat and to discriminate samples according to their stage of growth. A calibration set of 72 samples from three growth stages of wheat (tillering, heading and harvest) and a validation set of 28 samples was collected for this purpose. Principal components analysis (PCA) of the calibration set discriminated groups of samples according to the growth stage of the wheat. Based on these differences, a classification procedure (SIMCA) showed a very accurate classification of the validation set samples : all of them were successfully classified in each group using this procedure when both the residual and the leverage were used in the classification criteria. Looking only at the residuals all the samples were also correctly classified except one of tillering stage that was assigned to both tillering and heading stages. Finally, the determination of the crude protein content of these samples was considered in two ways: building up a global model for all the growth stages, and building up local models for each stage, separately. The best prediction results for crude protein were obtained using a global model for samples in the two first growth stages (tillering and heading), and using a local model for the harvest stage samples.

Volcanoes of l-isogenies of elliptic curves over finite fields: the case l=3

This paper is devoted to the study of the volcanoes of l-isogenies of elliptic curves over a finite field, focusing on their height as well as on the location of curves across its different levels. The core of the paper lies on the relationship between the l-Sylow subgroup of an elliptic curve and the level of the volcano where it is placed. The particular case l = 3 is studied in detail, giving an algorithm to determine the volcano of 3-isogenies of a given elliptic curve. Experimental results are also provided.

Genotypic classification of patients with Wolfram syndrome: insights into the natural history of the disease and correlation with phenotype

Purpose: Wolfram syndrome is a degenerative, recessive rare disease with an onset in childhood. It is caused by mutations in WFS1 or CISD2 genes. More than 200 different variations in WFS1 have been described in patients with Wolfram syndrome, which complicates the establishment of clear genotype-phenotype correlation. The purpose of this study was to elucidate the role of WFS1 mutations and update the natural history of the disease. Methods: This study analyzed clinical and genetic data of 412 patients with Wolfram syndrome published in the last 15 years. Results: (i) 15% of published patients do not fulfill the current ­inclusion criterion; (ii) genotypic prevalence differences may exist among countries; (iii) diabetes mellitus and optic atrophy might not be the first two clinical features in some patients; (iv) mutations are nonuniformly distributed in WFS1; (v) age at onset of diabetes mellitus, hearing defects, and diabetes insipidus may depend on the patient"s genotypic class; and (vi) disease progression rate might depend on genotypic class. Conclusion: New genotype-phenotype correlations were established, disease progression rate for the general population and for the genotypic classes has been calculated, and new diagnostic criteria have been proposed. The conclusions raised could be important for patient management and counseling as well as for the development of treatments for Wolfram syndrome.

Classification of textures seen from different distances and under varying illumination direction

Changes in the angle of illumination incident upon a 3D surface texture can significantly alter its appearance, implying variations in the image texture. These texture variations produce displacements of class members in the feature space, increasing the failure rates of texture classifiers. To avoid this problem, a model-based texture recognition system which classifies textures seen from different distances and under different illumination directions is presented in this paper. The system works on the basis of a surface model obtained by means of 4-source colour photometric stereo, used to generate 2D image textures under different illumination directions. The recognition system combines coocurrence matrices for feature extraction with a Nearest Neighbour classifier. Moreover, the recognition allows one to guess the approximate direction of the illumination used to capture the test image

A new approach to the classification of mammographic masses and normal breast tissue

A new approach to mammographic mass detection is presented in this paper. Although different algorithms have been proposed for such a task, most of them are application dependent. In contrast, our approach makes use of a kindred topic in computer vision adapted to our particular problem. In this sense, we translate the eigenfaces approach for face detection/classification problems to a mass detection. Two different databases were used to show the robustness of the approach. The first one consisted on a set of 160 regions of interest (RoIs) extracted from the MIAS database, being 40 of them with confirmed masses and the rest normal tissue. The second set of RoIs was extracted from the DDSM database, and contained 196 RoIs containing masses and 392 with normal, but suspicious regions. Initial results demonstrate the feasibility of using such approach with performances comparable to other algorithms, with the advantage of being a more general, simple and cost-effective approach

Fermat's treatise on quadrature: A new reading

The Treatise on Quadrature of Fermat (c. 1659), besides containing the first known proof of the computation of the area under a higher parabola, R x+m/n dx, or under a higher hyperbola, R x-m/n dx with the appropriate limits of integration in each case , has a second part which was not understood by Fermat s contemporaries. This second part of the Treatise is obscure and difficult to read and even the great Huygens described it as'published with many mistakes and it is so obscure (with proofs redolent of error) that I have been unable to make any sense of it'. Far from the confusion that Huygens attributes to it, in this paper we try to prove that Fermat, in writing the Treatise, had a very clear goal in mind and he managed to attain it by means of a simple and original method. Fermat reduced the quadrature of a great number of algebraic curves to the quadrature of known curves: the higher parabolas and hyperbolas of the first part of the paper. Others, he reduced to the quadrature of the circle. We shall see how the clever use of two procedures, quite novel at the time: the change of variables and a particular case of the formulaof integration by parts, provide Fermat with the necessary tools to square very easily curves as well-known as the folium of Descartes, the cissoid of Diocles or the witch of Agnesi.

Inverse Problems for multiple invariant curves

Planar polynomial vector fields which admit invariant algebraic curves, Darboux integrating factors or Darboux first integrals are of special interest. In the present paper we solve the inverse problem for invariant algebraic curves with a given multiplicity and for integrating factors, under generic assumptions regarding the (multiple) invariant algebraic curves involved. In particular we prove, in this generic scenario, that the existence of a Darboux integrating factor implies Darboux integrability. Furthermore we construct examples where the genericity assumption does not hold and indicate that the situation is different for these.

Equations of hyperelliptic Shimura curves

We describe an algorithm that computes explicit models of hyperelliptic Shimura curves attached to an indefinite quaternion algebra over Q and Atkin-Lehner quotients of them. It exploits Cerednik-Drinfeld’s nonarchimedean uniformisation of Shimura curves, a formula of Gross and Zagier for the endomorphism ring of Heegner points over Artinian rings and the connection between Ribet’s bimodules and the specialization of Heegner points, as introduced in [21]. As an application, we provide a list of equations of Shimura curves and quotients of them obtained by our algorithm that had been conjectured by Kurihara.

Incorporating features of distribution and progression for automatic Makam classification

Automatic classification of makams from symbolic data is a rarely studied topic. In this paper, first a review of an n-gram based approach is presented using various representations of the symbolic data. While a high degree of precision can be obtained, confusion happens mainly for makams using (almost) the same scale and pitch hierarchy but differ in overall melodic progression, seyir. To further improve the system, first n-gram based classification is tested for various sections of the piece to take into account a feature of the seyir that melodic progression starts in a certain region of the scale. In a second test, a hierarchical classification structure is designed which uses n-grams and seyir features in different levels to further improve the system.

The glasses of the transept's rosette of the Cathedral of Tarragona: characterization, classification and decay.

The glasses of the rosette forming the main window of the transept of the Gothic Cathedral of Tarragona have been characterised by means of SEM/EDS, XRD, FTIR and electronic microprobe. The multivariate statistical treatment of these data allow to establish a classification of the samples forming groups having an historical significance and reflecting ancient restorations. Furthermore, the decay patterns and mechanisms have been determined and the weathering by-products characterised. It has been demonstrated a clear influence of the bioactivity in the decay of these glasses, which activity is partially controlled by the chemical composition of the glasses.

The glasses of the transept's rosette of the Cathedral of Tarragona: characterization, classification and decay.

The glasses of the rosette forming the main window of the transept of the Gothic Cathedral of Tarragona have been characterised by means of SEM/EDS, XRD, FTIR and electronic microprobe. The multivariate statistical treatment of these data allow to establish a classification of the samples forming groups having an historical significance and reflecting ancient restorations. Furthermore, the decay patterns and mechanisms have been determined and the weathering by-products characterised. It has been demonstrated a clear influence of the bioactivity in the decay of these glasses, which activity is partially controlled by the chemical composition of the glasses.