Related papers: Stream Differential Equations: Specification Forma…
Subject of research is complex networks and network systems. The network system is defined as a complex network in which flows are moved. Classification of flows in the network is carried out on the basis of ordering and continuity. It is…
Assignment flows denote a class of dynamical models for contextual data labeling (classification) on graphs. We derive a novel parametrization of assignment flows that reveals how the underlying information geometry induces two processes…
In this study, we propose a new scheme named as complete flux scheme (CFS) based on the finite volume method for solving singularly perturbed differential-difference equations (SPDDEs) of elliptic type. An alternate integral representation…
Stochastic diffusion equations are crucial for modeling a range of physical phenomena influenced by uncertainties. We introduce the generalized finite difference method for solving these equations. Then, we examine its consistency,…
A delayed term in a differential equation reflects the fact that information takes significant time to travel from one place to another within a process being studied. Despite de apparent similarity with ordinary differential equations,…
Many time series are effectively generated by a combination of deterministic continuous flows along with discrete jumps sparked by stochastic events. However, we usually do not have the equation of motion describing the flows, or how they…
We derive and analyze a broad class of finite element methods for numerically simulating the stationary, low Reynolds number flow of concentrated mixtures of several distinct chemical species in a common thermodynamic phase. The underlying…
We consider a two-dimensional, two-layer, incompressible, steady flow, with vorticity which is constant in each layer, in an infinite channel with rigid walls. The velocity is continuous across the interface, there is no surface tension or…
Differential equations are widely used to describe complex dynamical systems with evolving parameters in nature and engineering. Effectively learning a family of maps from the parameter function to the system dynamics is of great…
Recently, the nonlinearity continuation method has been used to numerically solve boundary value problems for steady-state Richards equation. The method can be considered as a predictor-corrector procedure with the simplest form which has…
Over the years, RDF streaming was explored in research and practice from many angles, resulting in a wide range of RDF stream definitions. This variety presents a major challenge in discussing and integrating streaming systems, due to the…
Digital circuits, despite having been studied for nearly a century and used at scale for about half that time, have until recently evaded a fully compositional theoretical in which arbitrary circuits may be freely composed together without…
Longstanding problems regarding the causality of the diffusion equation are resolved through a class of exact solutions. A universal differential solution for diffusive processes is derived that is causal and exact at any analytic point in…
This paper shows that the topological structures of particle orbits generated by a generic class of vector fields on spherical surfaces, called {\it the flow of finite type}, are in one-to-one correspondence with discrete structures such as…
Consistency requirements for state-of-the-art stream processing systems are defined in terms of delivery guarantees. Exactly-once is the strongest one and the most desirable for end-user. However, there are several issues regarding this…
Nonlinearity continuation method, applied to boundary value problems for steady-state Richards equation, gradually approaches the solution through a series of intermediate problems. Originally, the Newton method with simple line search…
Two finite volume methods are derived and applied to the solution of problems of incompressible flow. In particular, external inviscid flows and boundary-layer flows are examined. The firstmethod analyzed is a cell-centered finite volume…
Coinductive reasoning about infinitary structures such as streams is widely applicable. However, practical frameworks for developing coinductive proofs and finding reasoning principles that help structure such proofs remain a challenge,…
The analytic solution for the two-streams discrete ordinates equations is carried out on the spatial domain in one-dimensional spherical geometry. The solution satisfies all the physical and the geometric conditions, namely: the natural…
Whether listening to overlapping conversations in a crowded room or recording the simultaneous electrical activity of millions of neurons, the natural world abounds with sparse measurements of complex overlapping signals that arise from…