Related papers: The boundary motive: definition and basic properti…
Let A be a line arrangement in the complex projective plane CP2. We define and describe the inclusion map of the boundary manifold --the boundary of a close regular neighborhood of A-- in the exterior of the arrangement. We obtain two…
Let G be a semisimple affine algebraic group over a field F. Assuming that G becomes of inner type over some finite field extension of F of degree a power of a prime p, we investigate the structure of the Chow motives with coefficients in a…
We examine two central regularization strategies for monotone variational inequalities, the first a direct regularization of the operative monotone mapping, and the second via regularization of the associated dual gap function. A key link…
The problem of 3D object recognition is of immense practical importance, with the last decade witnessing a number of breakthroughs in the state of the art. Most of the previous work has focused on the matching of textured objects using…
This paper describes an integrated solution to the problem of describing and interpreting goals for robots in open uncertain domains. Given a formal specification of a desired situation, in which objects are described only by their…
Let A and B be normal matrices with coefficients that are continuous complex-valued functions on a topological space X that has the homotopy type of a CW complex, and suppose these matrices have the same distinct eigenvalues at each point…
We consider generic families $X_\param$ of smooth dynamical systems depending on parameters $\param\in P$ where $P$ is a 2-dimensional simply connected domain and assume that each $X_\param$ only has a finite number of restpoints and…
The notion of causal boundary $\partial M$ for a strongly causal spacetime $M$ has been a controversial topic along last decades: on one hand, some attempted definitions were not fully consistent, on the other, there were simple examples…
In this paper certain Chow weight structures on the "big" triangulated motivic categories $DM_R^{eff}\subset DM_R$ are defined in terms of motives of all smooth varieties over the base field. This definition allows studying basic properties…
We define and compare two different definitions of Chow motives for Deligne-Mumford stacks, associated with two definitions of Chow rings. The main result we prove is that both categories of motives are equivalent to the usual category of…
The space of human goals is tremendously vast; and yet, from just a few moments of watching a scene or reading a story, we seem to spontaneously infer a range of plausible motivations for the people and characters involved. What explains…
In this survey article we discuss a framework of noncommutative geometry with differential graded categories as models for spaces. We outline a construction of the category of noncommutative spaces and also include a discussion on…
The computation of amoebas has been a challenging open problem for the last dozen years. The most natural approach, namely to compute an amoeba via its boundary, has not been practical so far since only a superset of the boundary, the…
Making a survey of recent constructions of universal cohomologies we suggest a new framework for a theory of motives in algebraic geometry.
Building on earlier work concerning the motives of $G$-bundles, we study the structure of motives associated with certain classes of $G$-varieties. In particular, we show that the corresponding motives lie within the category of mixed-Tate…
We consider a nonlocal problem involving the fractional laplacian and the Hardy potential, in bounded smooth domains. Exploiting the moving plane method and some weak and strong comparison principles, we deduce symmetry and monotonicity…
Let $X$ be a smooth proper scheme over an algebraically closed field $k$ in characteristic $p$. In this short note, by interpreting $\mathcal{D}_{X}$-modules as $F$-divided sheaves and establishing a cohomological boundedness property for…
We describe a three-stage procedure to analyze the dependence of Poisson Boltzmann calculations on the shape, size and geometry of the boundary between solute and solvent. Our study is carried out within the boundary element formalism, but…
Measuring comodules are defined and shown to provide a useful generalization of the set of maps between modules with a broad range of applications. Three applications are described. Connections on bundles are described in terms of measuring…
A general setup for deterministic system identification problems on graphs with Dirichlet and Neumann boundary conditions is introduced. When control nodes are available along the boundary, we apply a discretize-then-optimize method to…