Related papers: Evolution variational inequalities with general co…
We prove a new extremal inequality, motivated by the vector Gaussian broadcast channel and the distributed source coding with a single quadratic distortion constraint problems. As a corollary, this inequality yields a generalization of the…
Assuming a-priori a smooth generating vector field, we introduce a generally covariant measure of the flow geometry called the referential gradient of the flow. The main result is the explicit relation between the referential gradient and…
We analyze gradient flows with jumps generated by a finite set of complete vector fields in involution using some Radon measures $u\in \mathcal{U}_a$ as admissible perturbations. Both the evolution of a bounded gradient flow $\{x^u(t,\l)\in…
We offer a new point of view on the (Modified) Log-Sobolev inequality and lower bounds on the Ricci-curvature in the setting where the dynamics are obtained as the limit of Markov processes. In this setting, the large deviation rate…
We link regularity and smoothness analysis of multivariate vector subdivision schemes with network flow theory and with special linear optimization problems. This connection allows us to prove the existence of what we call optimal…
Equivariance is central to graph generative models, as it ensures the model respects the permutation symmetry of graphs. However, strict equivariance can increase computational cost due to added architectural constraints, and can slow down…
We provide a novel existence result for energy-variational solutions to a general class of evolutionary partial differential equations. Compared to previous works on this solution concept, the generalization is mainly twofold: a relaxation…
This paper introduces a new method to build linear flows, by taking the exponential of a linear transformation. This linear transformation does not need to be invertible itself, and the exponential has the following desirable properties: it…
We provide in this article a new proof of the uniqueness of the flow solution to ordinary differential equations with $BV$ vector-fields that have divergence in $L^\infty$ (or in $L^1$) and that are nearly incompressible (see the text for…
We develop a gradient-flow theory for time-dependent functionals defined in abstract metric spaces. Global well-posedness and asymptotic behavior of solutions are provided. Conditions on functionals and metric spaces allow to consider the…
George Williams defined an evolutionary unit as hereditary information for which the selection bias between competing units dominates the informational decay caused by imperfect transmission. In this article, I extend Williams' approach to…
We use the vorticity transportation equation as the start point--with the help of stream function for two-dimensional planar incompressible flows--to obtain exact solutions that characterize evolution and dynamics of the flows. These…
Many large-scale and distributed optimization problems can be brought into a composite form in which the objective function is given by the sum of a smooth term and a nonsmooth regularizer. Such problems can be solved via a proximal…
Eastern Boundary Upwelling Systems (EBUS) are characterized by wind-triggered upwelling of deep waters along the coast. They are hotspots of biological productivity and diversity and therefore have a high economic, ecological and social…
We discuss a possible theoretical interpretation of the self scaling property of turbulent flows (Extended Self Similarity). Our interpretation predicts that, even in cases when ESS is not observed, a generalized self scaling, must be…
In this paper, we consider a class of initial-boundary value problems governed by pseudo-parabolic total variation flows. The principal characteristic of our problem lies in the velocity term of the diffusion flux, a feature that can bring…
Given a graph with non-negative edge weights, there are various ways to interpret the edge weights and induce a metric on the vertices of the graph. A few examples are shortest-path, when interpreting the weights as lengths; resistance…
In a series of recent papers and in a book, this author put forward a mathematical model capable of embracing the search for extra-terrestrial intelligence (SETI), Darwinian Evolution and Human History into a single, unified statistical…
The dynamics of complex systems in nature often occurs in terms of punctuations, or avalanches, rather than following a smooth, gradual path. A comprehensive theory of avalanche dynamics in models of growth, interface depinning, and…
We consider open multi-class queueing networks with general arrival processes, general processing time sequences and Bernoulli routing. The network is assumed to be operating under an arbitrary work-conserving scheduling policy that makes…