"Minesweeper" and spectrum of discrete Laplacians

The paper is devoted to a problem inspired by the "Minesweeper" computer game. It is shown that certain configurations of open cells guarantee the existence and the uniqueness of solution. Mathematically the problem is reduced to some spectral properties of discrete differential operators. It is shown how the uniqueness can be used to create a new game which preserves the spirit of "Minesweeper" but does not require a computer.Comment: We add consideration of tables based on the triangle tiling of the plane. Its paper version encounters situations typical for the computer "Minesweeper" gam

A SEARCHING ALGORITHM FOR TEXT WITH MISTAKES

The paper contains a new text searching method representing modification of the Boyer-Moore algorithm and enabling a user to find the places in the text where the given substring occurs maybe with possible errors, that is the string in text and a query may not coincide but nevertheless are identical. The idea consists in division of the searching process in two phases: at the first phase a fuzzy variant of the Boyer–Moore algorithm is performed; at the second phase the Dice metrics is used. The advantage of suggested technique in comparison with the known methods using the fixed value of the mistakes number is that it 1) does not perform precomputation of the auxiliary table of the sizes comparable to the original text sizes and 2) it more flexibly catches the semantics of the erroneous text substrings even for a big number of mistakes. This circumstance extends possibilities of the Boyer–Moore method by addmitting a bigger amount of possible mistakes in text and preserving text semantics. The suggested method provides also more accurate regulation of the upper boundary for the text mistakes which differs it from the known methods with fixed value of the maximum number of mistakes not depending on the text sizes. Moreover, this upper boundary is defined as Levenshtein distance not suitable for evaluating a relevance of the founded text and a query, while the Dice metrics provides such a relevance. In fact, if maximum Levenshtein distanse is 3 then how one can judge if this value is big or small to provide relevance of the search results. Consequently, the suggested method is more flexible, enables one to find relevant answers even in case of a big number of mistakes in text. The efficiency of the suggested method in the worst case is O(nc) with constant c defining the biggest allowable number of mistakes.The paper contains a new text searching method representing modification of the Boyer-Moore algorithm and enabling a user to find the places in the text where the given substring occurs maybe with possible errors, that is the string in text and a query may not coincide but nevertheless are identical. The idea consists in division of the searching process in two phases: at the first phase a fuzzy variant of the Boyer–Moore algorithm is performed; at the second phase the Dice metrics is used. The advantage of suggested technique in comparison with the known methods using the fixed value of the mistakes number is that it 1) does not perform precomputation of the auxiliary table of the sizes comparable to the original text sizes and 2) it more flexibly catches the semantics of the erroneous text substrings even for a big number of mistakes. This circumstance extends possibilities of the Boyer–Moore method by addmitting a bigger amount of possible mistakes in text and preserving text semantics. The suggested method provides also more accurate regulation of the upper boundary for the text mistakes which differs it from the known methods with fixed value of the maximum number of mistakes not depending on the text sizes. Moreover, this upper boundary is defined as Levenshtein distance not suitable for evaluating a relevance of the founded text and a query, while the Dice metrics provides such a relevance. In fact, if maximum Levenshtein distanse is 3 then how one can judge if this value is big or small to provide relevance of the search results. Consequently, the suggested method is more flexible, enables one to find relevant answers even in case of a big number of mistakes in text. The efficiency of the suggested method in the worst case is O(nc) with constant c defining the biggest allowable number of mistakes

Argentaffin carcinoma of the terminal ileum

The purpose of this paper is to emphasise the importance of routine exploration of the abdominal viscera in all patients undergoing elective abdominal surgical procedures. We report here a case in which an unsuspected and asymptomatic argentaffin carcinoma of the small bowel was discovered in the course of hysterectomy carried out for intractable metrorrhagia. The operative procedure consisted of total hysterectomy and bilateral salpingo-oophorectomy. This was followed by resection of part of the terminal ileum 10 cm. on each side of the tumour together with a wedge of mesentery which included the infiltrated area.peer-reviewe

Realizing the consciousness in artificial intelligence

A new two-unit model of a "concious" neuron is presented to be realised in AL-based systems/ The main difference from the known paradigms is the admission of the phenomenon of self-perception by the neuron of its own state, displayed by its electromagnetic cloud. This phenomenoncreates in given representation the nature of consciusness. Some consequences of the hypothesis are considered

Effect of a confining surface on a mixture with spontaneous inhomogeneities

A binary self-assembling mixture near a planar wall is studied by theory and Monte Carlo simulations. The grand potential functional of the local concentration and the local volume fraction of all particles is developed in the framework of the density functional and field-theoretic methods. We obtain ordinary differential Euler–Lagrange equations for the concentration and the volume fraction, and solve them analytically in the perturbation expansion. The obtained exponentially damped oscillations of the concentration, with the characteristic lengths the same as in the concentration-concentration correlation function, agree very well with simulations. For the excess volume fraction we obtain a monotonic decay superimposed on the exponentially damped oscillations with a fair agreement with simulations. The period of the density oscillations is equal to half the period of the concentration oscillations in both the theory and simulations. Simulations show local ordering in the layers parallel to the wall that are rich in one of the two components. Bubbles, stripes and clusters appear in the subsequent layers for increasing distance from the wall. Between these almost one-component layers the density takes minima, and a bulk-like structure with clusters of different particles being nearest neighbors appears.Fil: Patsahan, O.. National Academy of Sciences of Ukraine; UcraniaFil: Meyra, Ariel German. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física de Líquidos y Sistemas Biológicos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física de Líquidos y Sistemas Biológicos; ArgentinaFil: Ciach, A.. Polish Academy of Sciences; Argentin

Correlation functions in mixtures with energetically favoured nearest neighbours of different kind: A size-asymmetric case

Binary mixtures of hard spheres with different diameters and square-well attraction between different particles are studied by theory and Monte Carlo simulations. In our mesoscopic theory, local fluctuations of the volume fraction of the two components are taken into account. Semi-quantitative agreement between the simulation and theoretical results is obtained, except from very small distances. The correlation functions exhibit exponentially damped oscillations, with the period determined by the interaction potential, and both the amplitude and the correlation length increasing significantly with increasing diameter ratio. Increasing size asymmetry leads also to decreasing fluctuations of the number of the smaller particles in the attractive shell of the bigger ones. For small size asymmetry, the strongest correlations occur for comparable volume fraction of the two components. When the size ratio increases, the maximum of the structure factor moves to a larger volume fraction of the bigger particles, and for the size ratio as large as 4, the maximum goes beyond the accessible range of volume fractions. Our results show that when the neighbourhood of different particles is energetically favoured, the particles are much more uniformly distributed than in the random distribution even at relatively high temperature, especially for large size asymmetry.Fil: Patsahan, O.. National Academy of Sciences of Ukraine. Institute for Condensed Matter Physics; UcraniaFil: Meyra, Ariel German. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física de Líquidos y Sistemas Biológicos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física de Líquidos y Sistemas Biológicos; ArgentinaFil: Ciach, A.. Polish Academy of Sciences; Argentin

Effects of fluctuations on correlation functions in inhomogeneous mixtures

Approximate expressions for correlation functions in binary inhomogeneous mixtures are derived in a framework of the mesoscopic theory [Ciach A., Mol. Phys., 2011, 109, 1101]. Fluctuation contribution is taken into account in a Brazovskii-type approximation. Explicit results are obtained for two model systems. In the two models, the diameters of the hard cores of particles are equal, and the interactions favour a periodic arrangement of alternating species A and B. However, the optimal distance between the species A and B is much different in the two models. Theoretical results for different temperature and volume fractions of the two components are compared with the results of Monte Carlo simulations, and the structure is illustrated by simulation snapshots. Despite different interaction potentials and different length scale of the local ordering, properties of the correlation functions in the two models are very similar.Fil: Ciach, null. Polish Academy of Sciences; ArgentinaFil: Patsahan, O.. National Academy of Sciences of Ukraine; UcraniaFil: Meyra, Ariel German. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física de Líquidos y Sistemas Biológicos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física de Líquidos y Sistemas Biológicos; Argentina. Universidad Tecnológica Nacional; Argentin