Orofacial granulomatosis: A diagnostic problem for the unwary and a management dilemma. Case reports

Orofacial granulomatosis is a condition that, may be difficult to diagnose for those unfamiliar with the entity. This paper describes two cases and addresses the presentation, pathogenesis and treatment. The clinical recognition of his condition is important as is the subsequent investigation by an appropriate specialist. Management of patients needs to take into account the results of further investigations, the patient's expectations, and the severity of the condition.

Spatiotemporal solitons in multidimensional optical media with a quadratic nonlinearity

We consider solutions to the second-harmonic generation equations in two-and three-dimensional dispersive media in the form of solitons localized in space and time. As is known, collapse does not take place in these models, which is why the solitons may be stable. The general solution is obtained in an approximate analytical form by means of a variational approach, which also allows the stability of the solutions to be predicted. Then, we directly simulate the two-dimensional case, taking the initial configuration as suggested by the variational approximation. We thus demonstrate that spatiotemporal solitons indeed exist and are stable. Furthermore, they are not, in the general case, equivalent to the previously known cylindrical spatial solitons. Direct simulations generate solitons with some internal oscillations. However, these oscillations neither grow nor do they exhibit any significant radiative damping. Numerical solutions of the stationary version of the equations produce the same solitons in their unperturbed form, i.e., without internal oscillations. Strictly stable solitons exist only if the system has anomalous dispersion at both the fundamental harmonic and second harmonic (SH), including the case of zero dispersion at SH. Quasistationary solitons, decaying extremely slowly into radiation, are found in the presence of weak normal dispersion at the second-harmonic frequency.

The application of adaptive partitioned random search in feature selection problem

Feature selection is one of important and frequently used techniques in data preprocessing. It can improve the efficiency and the effectiveness of data mining by reducing the dimensions of feature space and removing the irrelevant and redundant information. Feature selection can be viewed as a global optimization problem of finding a minimum set of M relevant features that describes the dataset as well as the original N attributes. In this paper, we apply the adaptive partitioned random search strategy into our feature selection algorithm. Under this search strategy, the partition structure and evaluation function is proposed for feature selection problem. This algorithm ensures the global optimal solution in theory and avoids complete randomness in search direction. The good property of our algorithm is shown through the theoretical analysis.

The mu-way intersection problem for m-cycle systems

An m-cycle system of order upsilon is a partition of the edge-set of a complete graph of order upsilon into m-cycles. The mu -way intersection problem for m-cycle systems involves taking mu systems, based on the same vertex set, and determining the possible number of cycles which can be common to all mu systems. General results for arbitrary m are obtained, and detailed intersection values for (mu, m) = (3, 4), (4, 5),(4, 6), (4, 7), (8, 8), (8, 9). (For the case (mu, m)= (2, m), see Billington (J. Combin. Des. 1 (1993) 435); for the case (Cc,m)=(3,3), see Milici and Quattrochi (Ars Combin. A 24 (1987) 175. (C) 2001 Elsevier Science B.V. All rights reserved.

On the intersection problem for 1-factorizations and near 1-factorizations of K-v

The number of 1-factors (near 1-factors) that mu 1-factorizations (near 1-factorizations) of the complete graph K-v, v even (v odd), can have in common, is studied. The problem is completely settled for mu = 2 and mu = 3.