Generalising Hrushovski's fusion technique we construct the free fusion of two strongly minimal theories T1; T2 intersecting in a totally categorical sub-theory T0. We show that if, e.g. T0 is the theory of in nite vector spaces over a nite eld then the fusion theory T! exists, is complete and !stable of rank !. We give a detailed geometrical analysis of T! , proving that if both T1; T2 are 1-b...

In this article, we generalize the Wasserstein distance to measures with di erent masses. We study the properties of such distance. In particular, we show that it metrizes weak convergence for tight sequences. We use this generalized Wasserstein distance to study a transport equation with source, in which both the vector eld and the source depend on the measure itself. We prove existence and un...

In this paper, we show that an n-dimensional connected noncompact Ricci soliton isometrically immersed in the ‡at complex space form (C n+1 2 ; J; h; i), with potential vector …eld of the Ricci soliton is the characteristic vector …eld of the real hypersurface is an Einstein manifold. We classify connected Hopf hypersurfaces in the ‡at complex space form (C n+1 2 ; J; h; i) and also obtain a ch...

We study the supersingular curves on Picard modular surfaces modulo a prime p which is inert in the underlying quadratic imaginary ...eld. We analyze the automorphic vector bundles in characteristic p; and as an application derive a formula relating the number of irreducible components in the supersingular locus to the second Chern class of the surface. The characteristic p ...bers of Shimura v...

The dimensionality of visual motion analysis can be reduced by analyzing directional components (projections) of ow elds. In contrast to vector elds, these lower-dimensional spaces exhibit two simple geometric properties which are invariant to the scene structure and depend only on the camera motion. Using these properties, structure and motion can be separated. The approach is closely related ...

We discuss metric perturbations produced during a period of innation in the early universe where two scalar elds evolve. The nal scalar perturbation spectrum can be calculated in terms of the perturbed expansion along neighbouring trajectories in eld-space. In the usual single eld case this is xed by the values of the elds at horizon-crossing, but in the presence of more than one eld there is n...

Orientation selective cells in the primary visual cortex of monkeys and cats are often characterized by an orientation-tuning width that is invariant under stimulus contrast. At the same time their contrast response function saturates or even super-saturates for high values of contrast. When two bar stimuli are presented within their classical receptive eld, the neuronal response decreases with...

background two-dimensional (2d) strain is a new reproducible technique for assessing regional myocardial function; however, its application for evaluation of left atrium (la) function is less studied. objectives we sought to assess la function in heart failure patients using velocity vector imaging (vvi). patients and methods thirty five patients (mean age: 43.34 ± 18.1 years, 59.3% male) with ...

We study the topology of 3-D symmetric tensor elds. The goal is to represent their complex structure by a simple set of carefully chosen points and lines analogous to vector eld topology. The basic constituents of tensor topology are the degenerate points, or points where eigenvalues are equal to each other. First, we introduce a new method for locating 3-D degenerate points. We then extract th...

The paper is devoted to the rigorous proof of the universality conjecture of the random matrix theory, according to which the limiting eigenvalue statistics of n n random matrices within spectral intervals of the order O(n ) is determined by the type of matrices (real symmetric, Hermitian or quaternion real) and by the density of states. We prove this conjecture for a certain class of the Hermi...