Related papers: Hypercurrents
In this work, we present the Grounded Recurrent Neural Network (GRNN), a recurrent neural network architecture for multi-label prediction which explicitly ties labels to specific dimensions of the recurrent hidden state (we call this…
Persistent currents in annular geometries have played an important role in disclosing the quantum phase coherence of superconductors and mesoscopic electronic systems. Ultracold atomic gases in multiply connected traps also exhibit…
We study the possible stationary persistent supercurrents flowing on a cylindrical sample supporting a two-dimensional charged fluid. The internal dynamics of the fluid is obtained by means of an effective theory in which the fluid…
Graphs and hypergraphs are foundational structures in discrete mathematics. They have many practical applications, including the rapidly developing field of bioinformatics, and more generally, biomathematics. They are also a source of…
We use the framework of "props" to study electrical circuits, signal-flow diagrams, and bond graphs. A prop is a strict symmetric monoidal category where the objects are natural numbers, with the tensor product of objects given by addition.…
Research on high-$T_c$ superconductors has generally not focused on analysis of the topological structure of electronic bands in these materials. In this article we collate and discuss several well-known experimental observables that signal…
The interval graph for a set of intervals on a line consists of one vertex for each interval, and an edge for each intersecting pair of intervals. A probe interval graph is a variant that is motivated by an application to genomics, where…
We describe a class of parity- and time-reversal-invariant topological states of matter which can arise in correlated electron systems in 2+1-dimensions. These states are characterized by particle-like excitations exhibiting exotic braiding…
We describe a class of topological vector spaces admitting a mixing uniformly continuous operator group ${T_t}_{t\in\C^n}$ with holomorphic dependence on the parameter $t$. This result covers those existing in the literature. We also…
This paper proves that labelled flows are expressive enough to contain all process algebras which are a standard model for concurrency. More precisely, we construct the space of execution paths and of higher dimensional homotopies between…
A new high-level interface to multi-threading in Prolog, implemented in hProlog, is described. Modern CPUs often contain multiple cores and through high-level multi-threading a programmer can leverage this power without having to worry…
Multicore parallel programming has some very difficult problems such as deadlocks during synchronizations and race conditions brought by concurrency. Added to the difficulty is the lack of a simple, well-accepted computing model for…
Textual documents are commonly connected in a hierarchical graph structure where a central document links to others with an exponentially growing connectivity. Though Hyperbolic Graph Neural Networks (HGNNs) excel at capturing such graph…
We introduce the calculus of Classical Transitions (CT), which extends the research line on the relationship between linear logic and processes to labelled transitions. The key twist from previous work is registering parallelism in typing…
Many complex systems exhibit interactions that depend not only on pairwise connections, but also group structures and memory effects. To capture such effects, we develop a unified tensor framework for modeling higher-order Markov chains…
We define a hierarchy of systems with topological completely positive entropy in the context of continuous countable amenable group actions on compact metric spaces. For each countable ordinal we construct a dynamical system on the…
We classify the topological terms (in a sense to be made precise) that may appear in a non-linear sigma model based on maps from an arbitrary worldvolume manifold to a homogeneous space $G/H$ (where $G$ is an arbitrary Lie group and $H…
In this paper we study the persistent homology associated with topological crackle generated by distributions with an unbounded support. Persistent homology is a topological and algebraic structure that tracks the creation and destruction…
We develop a method of driving a Markov processes through a continuous flow. In particular, at the level of the transition functions we investigate an approach of adding a first order operator to the generator of a Markov process, when the…
Each rule $f$ that assigns a vector $f(G)$ to an $(n+1)$-graph $G$ determines a class (or property) of $n$-manifold invariants. An invariant $v=v(M)$ is in this class if, for any triangulated manifold $|G|=M$, one has that $v(M)$ is a…