Related papers: Stream Differential Equations: Specification Forma…
In the pursuit of autonomous learning systems, the foundational assumption of stationarity, the premise that data distributions and model behaviors remain constant, is fundamentally untenable. Historically, the research community has…
We are concerned with demonstrating productivity of specifications of infinite streams of data, based on orthogonal rewrite rules. In general, this property is undecidable, but for restricted formats computable sufficient conditions can be…
The signature is an infinite graded sequence of statistics known to characterise a stream of data up to a negligible equivalence class. It is a transform which has previously been treated as a fixed feature transformation, on top of which a…
We study equations with infinitely many derivatives. Equations of this type form a new class of equations in mathematical physics. These equations originally appeared in p-adic and later in fermionic string theories and their investigation…
This paper investigates the well posedness of ordinary differential equations and more precisely the existence (or uniqueness) of a flow through explicit compactness estimates. Instead of assuming a bounded divergence condition on the…
Data stream learning has been largely studied for extracting knowledge structures from continuous and rapid data records. In the semantic Web, data is interpreted in ontologies and its ordered sequence is represented as an ontology stream.…
In most fluid dynamics problems, the governing equations are nonlinear because of the presence of convective terms. Nevertheless, existence of solutions can be shown by direct sum provided one identifies, in the relevant Banach space of…
Graph stream summarization refers to the process of processing a continuous stream of edges that form a rapidly evolving graph. The primary challenges in handling graph streams include the impracticality of fully storing the ever-growing…
The steady streaming flow pattern caused by a no-slip sphere oscillating in an unbounded viscous incompressible fluid is calculated exactly to second order in the amplitude. The pattern depends on a dimensionless scale number, determined by…
Exact representations of real numbers such as the signed digit representation or more generally linear fractional representations or the infinite Gray code represent real numbers as infinite streams of digits. In earlier work by the first…
The spectra of parallel flows (that is, flows governed by first-order differential operators parallel to one direction) are investigated, on both $L^2$ spaces and weighted-$L^2$ spaces. As a consequence, an example of a flow admitting a…
Incompressible Euler flows in narrow domains, in which the horizontal length scale is much larger than other scales, play an important role in applications, and their leading-order behavior can be described by the hydrostatic Euler…
The numerical methods for differential equation solution allow obtaining a discrete field that converges towards the solution if the method is applied to the correct problem. Nevertheless, the numerical methods have the restricted class of…
Abstractive dialogue summarization is to generate a concise and fluent summary covering the salient information in a dialogue among two or more interlocutors. It has attracted great attention in recent years based on the massive emergence…
Graph processing has become an important part of various areas of computing, including machine learning, medical applications, social network analysis, computational sciences, and others. A growing amount of the associated graph processing…
Smooth parametrization consists in a subdivision of the mathematical objects under consideration into simple pieces, and then parametric representation of each piece, while keeping control of high order derivatives. The main goal of the…
In this paper, we propose a numerical method to approximate the solution of partial differential equations in irregular domains with no-flux boundary conditions by means of spectral methods. The main features of this method are its…
The calculus of finite differences is a solid foundation for the development of operations such as the derivative and the integral for infinite sequences. Here we showed a way to extend it for finite sequences. We could then define…
This survey paper is a structured concise summary of four of our recent papers on the stochastic regularity of diffusions that are associated to regular strongly local (but not necessarily symmetric) Dirichlet forms. Here by stochastic…
In this paper, we study non-Newtonian fluids in a class of unbounded domains with noncompact boundaries. With respect to the resulting mathematical problems, we establish the global existence of solutions with arbitrary large flux under…