Related papers: Distributive Mereotopology: Extended distributive …
This article proposes a formal rapprochement between cognitive load theory and embodied cognition by reconceptualizing psychological representations as dynamic multiscale attractors within a temporal-hierarchical prediction architecture.…
We develop a unified geometric framework for dissipative mechanical systems based on uniform $q$-contact manifolds, which provide an extended phase space equipped with multiple contact $1$-forms. Within this setting, we construct both…
In recent research, some of the present authors introduced the concept of an n-dimensional Boolean algebra and its corresponding propositional logic nCL, generalising the Boolean propositional calculus to n>= 2 perfectly symmetric truth…
We give a constructive account of the de Groot duality of stably compact spaces in the setting of strong proximity lattice, a point-free representation of a stably compact space. To this end, we introduce a notion of strong continuous…
Deep Reinforcement learning (DRL) has achieved remarkable success in domains with well-defined reward structures, such as Atari games and locomotion. In contrast, dexterous manipulation lacks general-purpose reward formulations and…
The correlation matrix is a central representation of functional brain networks in neuroimaging. Traditional analyses often treat pairwise interactions independently in a Euclidean setting, overlooking the intrinsic geometry of correlation…
In discrete signal and image processing, many dilations and erosions can be written as the max-plus and min-plus product of a matrix on a vector. Previous studies considered operators on symmetrical, unbounded complete lattices, such as…
In this article we introduce theory and algorithms for learning discrete representations that take on a lattice that is embedded in an Euclidean space. Lattice representations possess an interesting combination of properties: a) they can be…
Generalizing Weyl's tube formula and building on Chern's work, Alesker reinterpreted the Lipschitz-Killing curvature integrals as a family of valuations (finitely-additive measures with good analytic properties), attached canonically to any…
A connected Fano complex-contact manifold is isomorphic to the kaehlerian C-space of Boothby type with a natural complex-contact structure corresponding to a non-abelian simple complex Lie algebra if the contact line bundle is very ample.…
Constructing an extension of Newton's theory which is defined on a non-Euclidean topology (in the sense of Thurston's decomposition), called a non-Euclidean Newtonian theory, corresponding to the zeroth order of a non-relativistic limit of…
The main purpose of this article is to classify contact structures on some 3-manifolds, namely lens spaces, most torus bundles over a circle, the solid torus, and the thickened torus T^2 x [0,1]. This classification completes earlier work…
Parallel transport as dictated by a gauge field determines a collection of local reference systems. Comparing local reference systems in overlapping regions leads to an ensemble of algebras of relational kinematical observables for gauge…
We demonstrate that the functorial properties of the symplectic field theory under strong cobordisms and surgery cobordisms can produce finite algebraic (planar) torsions from simple examples, which gives a unified treatment of most of the…
We extend the equations of motion that describe non-relativistic elastic collision of two particles in one dimension to an arbitrary associative algebra. Relativistic elastic collision equations turn out to be a particular case of these…
We construct C-algebras for a class of surfaces that are inverse images of certain polynomials of arbitrary degree. By using the directed graph associated to a matrix, the representation theory can be understood in terms of ``loop'' and…
Attention mechanisms are developing into a viable alternative to convolutional layers as elementary building block of NNs. Their main advantage is that they are not restricted to capture local dependencies in the input, but can draw…
We study entanglement entropy (EE) for a Maxwell field in 2+1 dimensions. We do numerical calculations in two dimensional lattices. This gives a concrete example of the general results of our recent work on entropy for lattice gauge fields…
The main purpose of this article is to introduce a comprehensive, unified theory of the geometry of all connections. We show that one can study a connection via a certain, closely associated second-order differential equation. One of the…
A regular contact manifold is a manifold $M$ equipped with a globally defined contact form $\eta$ such that the topological space $M/\mathcal{R}$ of orbits (trajectories) of the Reeb vector field $\mathcal{R}$ of $\eta$ carries a smooth…