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We introduce an algebraic analogue of dynamical systems, based on term rewriting. We show that a recursive function applied to the output of an iterated rewriting system defines a formal class of models into which all the main architectures…
Among (conformal) quantum field theories, the rational conformal field theories are singled out by the fact that their correlators can be constructed from a modular tensor category C with a distinguished object, a symmetric special…
Application of the so-called refined algebraic quantization scheme for constrained systems to the relativistic particle provides an inner product that defines a unique Fock representation for a scalar field in curved space-time. The…
In holographic duality an eternal AdS black hole is described by two copies of the boundary CFT in the thermal field double state. In this paper we provide explicit constructions in the boundary theory of infalling time evolutions which can…
Second-order superintegrable systems in dimensions two and three are essentially classified. With increasing dimension, however, the non-linear partial differential equations employed in current methods become unmanageable. Here we propose…
In algebra, atomicity is the study of divisibility by and factorizations into atoms (also called irreducibles). In one side of the spectrum of atomicity we find the antimatter algebraic structures, inside which there are no atoms and,…
We provide a full realization of the electromagnetic duality at the boundary by extending the phase space of Maxwell's theory through the introduction of edge modes and their conjugate momenta. We show how such extension, which follows from…
We are interested in shapes of real algebraic curves in the plane and regions surrounded by them: they are named refined algebraic domains by the author. As characteristic finite sets, we consider points contained in two curves and the sets…
Artificial neural networks used for reinforcement learning are structurally rigid, meaning that each optimized parameter of the network is tied to its specific placement in the network structure. It also means that a network only works with…
Automated theorem provers (ATPs) can disprove conjectures by saturating a set of clauses, but the resulting saturated sets are opaque certificates. In the unit equational fragment, a saturated set can in fact be read as a convergent rewrite…
Semigroup algebras admit certain `coherent' deformations which, in the special case of a path algebra, may associate a periodic function to an evolving path; for a particle moving freely on a straight line after an initial impulse, the wave…
The purpose of this article is to study extrapolation of solvability for boundary value problems of elliptic systems in divergence form on the upper half-space assuming De Giorgi type conditions. We develop a method allowing to treat each…
We analyze $2+1d$ and $3+1d$ Bosonic Symmetry Protected Topological (SPT) phases of matter protected by onsite symmetry group $G$ by using dual bulk and boundary approaches. In the bulk we study an effective field theory which upon coupling…
Many biochemical measurements define state spaces that are bounded, absorbing, and physically irreversible, yet are routinely analysed using linear and Euclidean frameworks that assume global invertibility, symmetry, and translation…
In this work we study gapped boundary states of $\mathbb{Z}_N$ bosonic symmetry-protected topological (SPT) phases in 4+1d, which are characterized by mixed $\mathbb{Z}_N$-gravity response, and the closely related phases protected by $C_N$…
Merging the two cultures of deep and statistical learning provides insights into structured high-dimensional data. Traditional statistical modeling is still a dominant strategy for structured tabular data. Deep learning can be viewed…
An axiomatic approach to signal reconstruction is formulated, involving a sample consistent set and a guiding set, describing desired reconstructions. New frame-less reconstruction methods are proposed, based on a novel concept of a…
Topological phases of matter are commonly understood as emerging either from crystalline symmetry and intrinsic spin-orbit coupling or from disorder-driven electronic renormalization. In realistic materials, however, structural defects…
Phase separation in confined environments is a fundamental process underlying geological flows, porous filtration, emulsions, and intracellular organization. Yet, how confinement and activity jointly govern coarsening kinetics and…
Calculating perturbation response properties of materials from first principles provides a vital link between theory and experiment, but is bottlenecked by the high computational cost. Here a general framework is proposed to perform density…