Related papers: On the scaling law for cortical magnification fact…

We study the structure of representations, defined as approximations of minimal sufficient statistics that are maximal invariants to nuisance factors, for visual data subject to scaling and occlusion of line-of-sight. We derive analytical…

Slow Feature Analysis is a unsupervised representation learning method that extracts slowly varying features from temporal data and can be used as a basis for subsequent reinforcement learning. Often, the behavior that generates the data on…

Adaptive Cluster Sampling (ACS) is introduced as a technique to use when "natural" groupings are evident in a spatially distributed population, especially sparsely distributed populations. An ACS sampling design will allow efficient…

One of the limitations of transformer networks is the sequence length due to the quadratic nature of the attention matrix. Classical self attention uses the entire sequence length, however, the actual attention being used is sparse. Humans…

The Zipf's law establishes that if the words of a (large) text are ordered by decreasing frequency, the frequency versus the rank decreases as a power law with exponent close to $-1$. Previous work has stressed that this pattern arises from…

We consider the centralized optimal estimation problem in spatially distributed systems. We use the setting of spatially invariant systems as an idealization for which concrete and detailed results are given. Such estimators are known to…

Two colour photometry of the cluster A1689 reveals a `relative magnification-bias' between lensed blue and red background galaxies, arising from a dependence of the faint galaxy count-slope on colour. The colour distribution is skewed…

The process of dynamic state estimation (filtering) based on point process observations is in general intractable. Numerical sampling techniques are often practically useful, but lead to limited conceptual insight about optimal…

We report new results for the gravitational microlensing target OGLE-2011-BLG-0950 from adaptive optics (AO) images using the Keck observatory. The original analysis by Choi et al. 2012 reports degenerate solutions between planetary and…

Exploration is a fundamental problem in robotics. While sampling-based planners have shown high performance, they are oftentimes compute intensive and can exhibit high variance. To this end, we propose to directly learn the underlying…

Sampling from unnormalized densities presents a fundamental challenge with wide-ranging applications, from posterior inference to molecular dynamics simulations. Continuous flow-based neural samplers offer a promising approach, learning a…

Scaling law for geometrical and dynamical quantities of biological molecules is an interesting topic. According to Flory's theory, a power law between radius of gyration and the length of homopolymer chain is found, with exponent 3/5 for…

We study the scaling laws of diffusion in two-dimensional media with long-range correlated disorder through exact enumeration of random walks. The disordered medium is modelled by percolation clusters with correlations decaying with the…

Many physical systems share the property of scale invariance. Most of them show ordinary power-law scaling, where quantities can be expressed as a leading power law times a scaling function which depends on scaling-invariant ratios of the…

To adapt their behaviour in changing environments, cells sense concentrations by binding external ligands to their receptors. However, incorrect ligands may bind nonspecifically to receptors, and when their concentration is large, this…

Human mobility patterns deeply affect the dynamics of many social systems. In this paper, we empirically analyze the real-world human movements based GPS records, and observe rich scaling properties in the temporal-spatial patterns as well…

Performance of optimization on quadratic problems sensitively depends on the low-lying part of the spectrum. For large (effectively infinite-dimensional) problems, this part of the spectrum can often be naturally represented or approximated…

We propose a stochastic model of a fragmentation process, developed by taking into account fragment lifetime as a function of their size based on the Gibrat process. If lifetime is determined by a power function of fragment size, numerical…

The properties of clusters of galaxies offer key insights into the assembly process of structure in the universe. Numerical simulations of cosmic structure formation in a hierarchical, dark matter dominated universe suggest that galaxy…

The visual systems of many mammals, including humans, is able to integrate the geometric information of visual stimuli and to perform cognitive tasks already at the first stages of the cortical processing. This is thought to be the result…