Introduction to Machine learning covering Statistical Inference (Bayes, EM, ML/MaxEnt duality), algebraic and spectral methods (PCA, LDA, CCA, Clustering), and PAC learning (the Formal model, VC dimension, Double Sampling theorem).

In this paper, we investigate the double covering of modular ${\mathrm{\ensuremath{\Gamma}}}_{5}\ensuremath{\simeq}{A}_{5}$ group and derive all forms weight one for first time. The higher weights are also explicitly given by decomposing direct products weight-one forms. For double-covering ${\mathrm{\ensuremath{\Gamma}}}_{5}^{\ensuremath{'}}\ensuremath{\simeq}{A}_{5}^{\ensuremath{'}}$, there e...

A new method based on the concept of virtual optics for both encryption and decryption is proposed. The technique shows the possibility to encode/decode any digital information. A virtual wavelength and a pseudo-random covering mask (PRCM) are used to design "double locks" and "double keys" for image encryption. Numerical experiments are presented to test the sensitivity of the virtual waveleng...

We describe the first analytically tractable example of an instability of a nonorientable minimal surface under parametric variation of its boundary. A one-parameter family of incomplete Meeks Möbius surfaces is defined and shown to exhibit an instability threshold as the bounding curve is opened up from a double-covering of the circle. Numerical and analytical methods are used to determine the...

A new planar antenna with double access and three separated bands is presented in this article. The first access operates over two bands, a narrow band for GPS standard (1.575 GHz), and a wideband covering PCS (1.85-1.99 GHZ) and UMTS (1.92-2.17 GHz) standards and also six sub bands of the new norm 3GPP (LTE). The second access operates over a wideband covering WLAN applications (2.4-2.484 GHz)...

We study real lines on certain Moishezon threefolds which are potentially twistor spaces of 3CP. Here, line means a smooth rational curve whose normal bundle is O(1) and the reality implies the invariance under an anti-holomorphic involution on the threefolds. Our threefolds are birational to double covering of CP branched along a singular quartic surface. On these threefolds we find families o...

1. The cell membrane of the spermatid of the grasshopper Melanoplus differentialis is shown to be composed of a double-layered membrane 10 mmicro thick. Closely applied to this is an additional outer covering 25 to 35 mmicro thick which has a regular geometrical pattern. 2. Models of cell membrane structure are discussed briefly. It is suggested that the pattern results from preferential adsorp...

Graph coverings are known to induce surjections of their critical groups. Here we describe the kernels of these morphisms in terms of data parametrizing the covering. Regular coverings are parametrized by voltage graphs, and the above kernel can be identified with a naturally defined voltage graph critical group. For double covers, the voltage graph is a signed graph, and the theory takes a par...

We investigate the covering problem in RT spaces induced by the RosenbloomTsfasman metric, extending the classical covering problem in Hamming spaces. Some connections between coverings in RT spaces and coverings in Hamming spaces are derived. Several lower and upper bounds are established for the smallest cardinality of a covering code in an RT space, generalizing results by Carnielli, Chen an...