לוח שנה משולב

A tangent vector field on a surface is the generator of a smooth family of maps from the surface to itself, known as the flow. Given a scalar function on the surface, it can be transported, or advected, by composing it with a vector field's flow. Such transport is exhibited by many physical phenomena, e.g., in fluid dynamics. In this paper, we are interested in the inverse problem: given source and target functions, compute a vector field whose flow advects the source to the target. We propose a method for addressing this problem, by minimizing an energy given by the advection constraint together with a regularizing term for the vector field. Our approach is inspired by a similar method in computational anatomy, known as LDDMM, yet leverages the recent framework of functional vector fields for discretizing the advection and the flow as operators on scalar functions. The latter allows us to efficiently generalize LDDMM to curved surfaces, without explicitly computing the flow lines of the vector field we are optimizing for. We show two approaches for the solution: using linear advection with multiple vector fields, and using non-linear advection with a single vector field. We additionally derive an approximated gradient of the corresponding energy, which is based on a novel vector field transport operator. Finally, we demonstrate applications of our machinery to intrinsic symmetry analysis, function interpolation and map improvement.

: Recurrent neural networks are an important class of models for explaining neural computations. Recently, there has been progress both in training these networks to perform various tasks, and in relating their activity to that recorded in the brain. Despite this progress, there are many fundamental gaps towards a theory of these networks. Neither the conditions for successful learning, nor the dynamics of trained networks are fully understood. I will present the rationale for using such networks for neuroscience research, and a detailed analysis of very simple tasks as an approach to build a theory of general trained recurrent neural networks.

Devices that combined electricity with moving parts were crucial to the very earliest electronic communications. Today, electromechanical structures are ubiquitous yet under-appreciated signal processing elements. Because the speed of sound is so slow compared to the speed of light, they are used to create compact filter and clock elements. Moreover they convert force and acceleration signals into more easily processed electrical signals. Can these humble, apparently classical, objects exhibit genuinely quantum behavior? Indeed—by strongly coupling the vibrations of a micromechanical oscillator to microwave frequency electrical signals, a mechanical oscillator can inherit a quantum state from an electrical signal. This recent and exciting result heralds the development of a quantum processors or quantum enhanced sensors that exploit the unique properties of mechanical systems. Furthermore, quantum electromechanics provides a powerful and versatile way to bring ever larger, more tangible objects into non-classical regimes.