相关论文: Streams and Lazy Evaluation Applied to Integrable …
We identify a common scheme in several existing algorithms addressing computational problems on linear differential equations with polynomial coefficients. These algorithms reduce to computing a linear relation between vectors obtained as…
In this paper, we consider operator realizations of quadratic algebras generated by second-order superintegrable systems in 2D. At least one such realization is given for each set of St\"ackel equivalent systems for both degenerate and…
An implicit purification scheme is proposed for calculation of the temperature-dependent, grand canonical single-particle density matrix, given as a Fermi operator expansion in terms of the Hamiltonian. The computational complexity is shown…
Complex systems are composed of a large number of simple components connected to each other in the form of a network. It is shown that, for some network configurations, the equivalent dynamic behavior of the system is governed by an…
We present a theoretical framework for analyzing linear attention models through matrix-valued state space models (SSMs). Our approach, Parallel Flows, provides a perspective that systematically decouples temporal dynamics from…
Stream computing is the use of multiple autonomic and parallel modules together with integrative processors at a higher level of abstraction to embody "intelligent" processing. The biological basis of this computing is sketched and the…
We propose the Sparse Abstract Machine (SAM), an abstract machine model for targeting sparse tensor algebra to reconfigurable and fixed-function spatial dataflow accelerators. SAM defines a streaming dataflow abstraction with sparse…
The paper introduces a generalization for known probabilistic models such as log-linear and graphical models, called here multiplicative models. These models, that express probabilities via product of parameters are shown to capture…
We discuss the deal of imperfectness of atomic actions in reality with the background of process algebras. And we show the applications of the imperfect actions in verification of computational systems.
Classification algorithms to mine data stream have been extensively studied in recent years. However, a lot of these algorithms are designed for supervised learning which requires labeled instances. Nevertheless, the labeling of the data is…
Inference algorithms in probabilistic programming languages (PPLs) can be thought of as interpreters, since an inference algorithm traverses a model given evidence to answer a query. As with interpreters, we can improve the efficiency of…
The well-known Turing machine is an example of a theoretical digital computer, and it was the logical basis of constructing real electronic computers. In the present paper we propose an alternative, namely, by formalising arithmetic…
We investigate how large language models can be used as research tools in scientific computing while preserving mathematical rigor. We propose a human-in-the-loop workflow for interactive theorem proving and discovery with LLMs. Human…
In this work we develop implicit Active Flux schemes for the scalar advection equation. At every cell interface we approximate the solution by a polynomial in time. This allows to evolve the point values using characteristics and to update…
Machine learning pipelines often rely on optimization procedures to make discrete decisions (e.g., sorting, picking closest neighbors, or shortest paths). Although these discrete decisions are easily computed, they break the…
Large Language Models (LLMs) have a natural role in answering complex queries about data streams, but the high computational cost of LLM inference makes them infeasible in many such tasks. We propose online cascade learning, the first…
We review the definition and main properties of differential subresultants in order to achieve their implementation in Maple, using the DEtools package. The focus is on computing GCRDs of ordinary differential operators with non necessarily…
Lagrangian averaging plays an important role in the analysis of wave--mean-flow interactions and other multiscale fluid phenomena. The numerical computation of Lagrangian means, e.g. from simulation data, is however challenging. Typical…
In this paper we introduced an algebraic semantics for process algebra in form of abstract data types. For that purpose, we developed a particular type of algebra, the seed algebra, which describes exactly the behavior of a process within a…
This draft suggests a new counterexample guided abstraction refinement (CEGAR) framework that uses the combination of numerical simulation for nonlinear differential equations with linear programming for linear hybrid automata (LHA) to…