Related papers: An uncertainty principle underlying the pinwheel s…
Heisenberg's uncertainty principle is usually taken to express a limitation of operational possibilities imposed by quantum mechanics. Here we demonstrate that the full content of this principle also includes its positive role as a…
We use coarse-grained molecular dynamics simulations to study the motility of a 2D vesicle containing self-propelled rods, as a function of the vesicle bending rigidity and the number density, length, and activity of the enclosed rods.…
The structure and quantitative composition of the cerebral cortex are interrelated with its computational capacity. Empirical data analyzed here indicate a certain hierarchy in local cortical composition. Specifically, neural wire, i.e.,…
Neurons in cortical areas often integrate signals from different origins. In the primary visual cortex (V1), neural responses are modulated by non-visual context such as the animal's position. However, the spatial profile of these position…
The present phase of Machine Learning is characterized by supervised learning algorithms relying on large sets of labeled examples ($n \to \infty$). The next phase is likely to focus on algorithms capable of learning from very few labeled…
Navigating our physical environment requires changing directions and turning. Despite its ecological importance, we do not have a unified theoretical account of non-straight-line human movement. Here, we present a unified optimality…
Treating neural network inputs and outputs as random variables, we characterize the structure of neural networks that can be used to model data that are invariant or equivariant under the action of a compact group. Much recent research has…
Learning and interpreting the structure of the environment is an innate feature of biological systems, and is integral to guiding flexible behaviours for evolutionary viability. The concept of a cognitive map has emerged as one of the…
A number of psychological and physiological evidences suggest that early visual attention works in a coarse-to-fine way, which lays a basis for the reverse hierarchy theory (RHT). This theory states that attention propagates from the top…
The complexity of neural dynamics stems in part from the complexity of the underlying anatomy. Yet how the organization of white matter architecture constrains how the brain transitions from one cognitive state to another remains unknown.…
We have developed an efficient information-maximization method for computing the optimal shapes of tuning curves of sensory neurons by optimizing the parameters of the underlying feedforward network model. When applied to the problem of…
We develop a unified theory of designs for controlled experiments that balance baseline covariates a priori (before treatment and before randomization) using the framework of minimax variance and a new method called kernel allocation. We…
For modelling the location of pyramidal cells in the human cerebral cortex we suggest a hierarchical point process in $\mathbb{R}^3$ that exhibits anisotropy in the form of cylinders extending along the $z$-axis. The model consists first of…
Animals move smoothly and reliably in unpredictable environments. Models of sensorimotor control have assumed that sensory information from the environment leads to actions, which then act back on the environment, creating a single,…
We propose a macroscopic description of the superconducting state in presence of an applied external magnetic field in terms of first order differential equations. They describe a corrugated two-component order parameter intertwined with a…
We introduce a model for image morphing in the primary visual cortex V1 to perform completion of missing images in time. We model the output of simple cells through a family of Gabor filters and the propagation of the neural signal…
This work addresses the problem of vehicle path planning in the presence of obstacles and uncertainties, which is a fundamental problem in robotics. While many path planning algorithms have been proposed for decades, many of them have dealt…
The problem of optimal motion planing and control is fundamental in robotics. However, this problem is intractable for continuous-time stochastic systems in general and the solution is difficult to approximate if non-instantaneous nonlinear…
Diffusion-driven patterns appear on curved surfaces in many settings, initiated by unstable modes of an underlying Laplacian operator. On a flat surface or perfect sphere, the patterns are degenerate, reflecting translational/rotational…
Recently introduced inpainting algorithms using a combination of applied harmonic analysis and compressed sensing have turned out to be very successful. One key ingredient is a carefully chosen representation system which provides…