Related papers: Acyclic Solos and Differential Interaction Nets
We study the relationship between singularities of finite-dimensional integrable systems and singularities of the corresponding spectral curves. For the large class of integrable systems on matrix polynomials, which is a general framework…
The dynamics of large complex systems are predominately modeled through pairwise interactions, the principle underlying structure being a network of the form of a digraph or quiver. Significant success has been obtained in applying the…
The $\rho$-calculus (Reflective Higher-Order Calculus) of Meredith and Radestock is a $\pi$-calculus-like language with some unusual features, notably, structured names, runtime generation of free names, and the lack of an operator for…
Synchrony patterns describe network states in which nodes of a coupled dynamical system are grouped into clusters based on synchronization between nodes. Beyond simple synchrony, synchronized clusters may also exhibit active or inactive…
The function of a real network depends not only on the reliability of its own components, but is affected also by the simultaneous operation of other real networks coupled with it. Robustness of systems composed of interdependent network…
This paper considers the problem of estimating the structure of multiple related directed acyclic graph (DAG) models. Building on recent developments in exact estimation of DAGs using integer linear programming (ILP), we present an ILP…
Often in language and other areas of cognition, whether two components of an object are identical or not determines if it is well formed. We call such constraints identity effects. When developing a system to learn well-formedness from…
Distributions on integers are ubiquitous in probabilistic modeling but remain challenging for many of today's probabilistic programming languages (PPLs). The core challenge comes from discrete structure: many of today's PPL inference…
Equality saturation, a technique for program optimisation and reasoning, has gained attention due to the resurgence of equality graphs (e-graphs). E-graphs represent equivalence classes of terms under rewrite rules, enabling simultaneous…
We investigate a property that extends the Danos-Regnier correctness criterion for linear logic proof-structures. The property applies to the correctness graphs of a proof-structure: it states that any such graph is acyclic and the number…
This paper deals with the design of Excitation and Measurement Patterns (EMPs) for the identification of dynamical networks, when the objective is to identify only a subnetwork embedded in a larger network. Recent results have shown how to…
Modern society is dependent on distributed software systems and to verify them different modelling languages such as mobile ambients were developed. To analyse the quality of mobile ambients as a good foundational model for distributed…
We exhibit an encoding of knots into processes in the {\pi}-calculus such that knots are ambient isotopic if and only their encodings are weakly bisimilar.
Treating neural network inputs and outputs as random variables, we characterize the structure of neural networks that can be used to model data that are invariant or equivariant under the action of a compact group. Much recent research has…
The statement in the title was proved in \cite{Cao23} by introducing dominant sets of seeds, which are analogs of torsion classes in representation theory. In this note, we observe a short proof by the existence of consistent cluster…
The recently introduced series of description logics under the common moniker DL-Lite has attracted attention of the description logic and semantic web communities due to the low computational complexity of inference, on the one hand, and…
Formalising the pi-calculus is an illuminating test of the expressiveness of logical frameworks and mechanised metatheory systems, because of the presence of name binding, labelled transitions with name extrusion, bisimulation, and…
Motivated by very large-scale communication networks, we newly introduce exponentiation of graphs. Using the exponential operation on graphs, we can construct various graphs of multi-exponential order with logarithmic diameter. We show that…
The infinite reduction of couplings is a tool to consistently renormalize a wide class of non-renormalizable theories with a reduced, eventually finite, set of independent couplings, and classify the non-renormalizable interactions. Several…
We introduce the (private) entropy of a directed graph (in a new network coding sense) as well as a number of related concepts. We show that the entropy of a directed graph is identical to its guessing number and can be bounded from below…