Related papers: Behavioral Metrics via Functor Lifting
In this note we study the behavior of the size of Furstenberg sets with respect to the size of the set of directions defining it. For any pair $\alpha,\beta\in(0,1]$, we will say that a set $E\subset \R^2$ is an $F_{\alpha\beta}$-set if…
We use Kolmogorov complexity methods to give a lower bound on the effective Hausdorff dimension of the point (x, ax+b), given real numbers a, b, and x. We apply our main theorem to a problem in fractal geometry, giving an improved lower…
Research on human social interactions has traditionally relied on self-reports. Despite their widespread use, self-reported accounts of behaviour are prone to biases and necessarily reduce the range of behaviours, and the number of…
Only a few states in high-dimensional systems can be identified as (un)steerable using existing theoretical or experimental methods. We utilize semidefinite programming (SDP) to construct a dataset for steerability detection in…
Collective motion is found in various animal systems, active suspensions and robotic or virtual agents. This is often understood using high level models that directly encode selected empirical features, such as co-alignment and cohesion.…
Simulation and bisimulation metrics for stochastic systems provide a quantitative generalization of the classical simulation and bisimulation relations. These metrics capture the similarity of states with respect to quantitative…
Let $P$ and $Q$ be polynomials in one variable over an algebraically closed field $k$ of characteristic zero. Let $f$ and $g$ be elements of a function field $\K$ over $k$ such that $P(f)=Q(g).$ We give conditions on $P$ and $Q$ such that…
Dirichlet Process mixture models (DPMM) in combination with Gaussian kernels have been an important modeling tool for numerous data domains arising from biological, physical, and social sciences. However, this versatility in applications…
Offline RL algorithms aim to improve upon the behavior policy that produces the collected data while constraining the learned policy to be within the support of the dataset. However, practical offline datasets often contain examples with…
Recovering probability measures from moments is a central theme in statistics and optimization. In particular, we focus on the recovery of measures from moments and pseudo-moments, which may come from solving the moment-SOS hierarchy in one…
Models and simulations of collective behaviours are often based on considering them as assumed by interactive particle systems. The focus is then on behavioural and interaction rules by using approaches based on artificial agents designed…
Single-cell omics enable the profiles of cells, which contain large numbers of biological features, to be quantified. Cluster analysis, a dimensionality reduction process, is used to reduce the dimensions of the data to make it…
Performative prediction, as introduced by Perdomo et al, is a framework for studying social prediction in which the data distribution itself changes in response to the deployment of a model. Existing work in this field usually hinges on…
According to the Language Familiarity Effect (LFE), people are better at discriminating between speakers of their native language. Although this cognitive effect was largely studied in the literature, experiments have only been conducted on…
We expound on some known lower bounds of the quadratic Wasserstein distance between random vectors in $\mathbb{R}^n$ with an emphasis on affine transformations that have been used in manifold learning of data in Wasserstein space. In…
The one-dimensional long-range voter model, where an agent takes the opinion of another at distance $r$ with probability $\propto r^{-\alpha}$, is studied analytically. The model displays rich and diverse features as $\alpha$ is changed.…
Hilbert space structure is assumed as a valid geometric description for neurodynamics, i.e., for applying any kind of quantum formalism in brain dynamics. The orientation selectivity of the neurons is used as a justification to construct a…
We provide a variable metric stochastic approximation theory. In doing so, we provide a convergence theory for a large class of online variable metric methods including the recently introduced online versions of the BFGS algorithm and its…
Determinantal processes provide mathematical modeling of repulsion among points. In quantum mechanics, Slater determinant states generate such processes, reflecting Fermionic behavior. This note exploits the connections between the former…
The classification of random objects within metric spaces without a vector structure has attracted increasing attention. However, the complexity inherent in such non-Euclidean data often restricts existing models to handle only a limited…