On Suboptimal LCS-alignments for Independent Bernoulli Sequences with Asymmetric Distributions

Let X = X ₁ ... X _n and Y = Y ₁ ... Y _n be two binary sequences with length n. A common subsequence of X and Y is any subsequence of X that at the same time is a subsequence of Y; The common subsequence with maximal length is called the longest common subsequence (LCS) of X and Y. LCS is a common tool for measuring the closeness of X and Y. In this note, we consider the case when X and Y are both i.i.d. Bernoulli sequences with the parameters ϵ and 1 − ϵ, respectively. Hence, typically the sequences consist of large and short blocks of different colors. This gives an idea to the so-called block-by-block alignment, where the short blocks in one sequence are matched to the long blocks of the same color in another sequence. Such and alignment is not necessarily a LCS, but it is computationally easy to obtain and, therefore, of practical interest. We investigate the asymptotical properties of several block-by-block type of alignments. The paper ends with the simulation study, where the of block-by-block type of alignments are compared with the LCS.     

On the structure of the Bochner–Martinelli residue currents

The paper presents a survey of the main results of I.M. Vinogradov.     

Crystal habit modifications of imatinib mesylate under various precipitation conditions

Abstract  

Crystals of the α-form of imatinib mesylate with various habits (e.g., polyhedral-like and plate-like) were prepared from various organic solvents (e.g., butyl lactate, 4-methyl-2-pentanone, 2-methyl-2-butanol, 2-isopropoxyethanol, propyl ether) by several precipitation methods. The methods provide imatinib mesylate in a non-needle-shaped crystalline α-form. The crystal modification was identified by hot-stage microscopy, scanning electron microscopy, differential scanning calorimetry (DSC), Fourier transform infrared spectroscopy (FTIR), and X-ray powder diffraction (XRPD). The analyses by DSC, IR, and XRPD indicate that imatinib mesylate crystals with various habits have the same crystal structure. The plate-like habit has been also observed in the system where the organic solvent acts as a precipitant.     

Pore size distribution of micelle-templated silicas studied by thermoporosimetry using water and n-heptane

Thermoporosimetry, i.e., DSC measurements of melting point depression of water and heptane confined in mesopores, has been used for determination the pore size distribution of several mesoporous silicas synthesized with the use of micelle templates. Porosity of these materials was additionally characterized by low-temperature nitrogen adsorption and quasi-equilibrated thermodesorption of nonane. The pore size distributions obtained using the water thermoporosimetry were similar to those determined using the other methods, but the pore size values found for the narrow pore materials were underestimated by ca 1?nm. Too large pore sizes obtained for the wide pore silica from heptane thermoporosimetry were attributed to nonlinear dependence of the melting point depression on the reciprocal of the pore size.     

A Fractal Representation of the Complex Clifford Algebra Equivalent to the Fock Representation

We construct a representation of the infinite dimensional complex Clifford algebra on the Hilbert space of square-integrable complex-valued functions on the Cantor set, which we show to be equivalent to the classical Fock representation.