Related papers: Multithreading for the expression-dag-based number…
In many choice modeling applications, people demand is frequently characterized as multiple discrete, which means that people choose multiple items simultaneously. The analysis and prediction of people behavior in multiple discrete choice…
Although the Turing-machine model of computation is widely used in computer science it is fundamentally inadequate as a foundation for the theory of modern scientific computation. The real-number model is described as an alternative.…
Though many safety-critical software systems use floating point to represent real-world input and output, programmers usually have idealized versions in mind that compute with real numbers. Significant deviations from the ideal can cause…
In studying the complexity of iterative processes it is usually assumed that the arithmetic operations of addition, multiplication, and division can be performed in certain constant times. This assumption is invalid if the precision…
A new deterministic floating-point arithmetic called precision arithmetic is developed to track precision for arithmetic calculations. It uses a novel rounding scheme to avoid excessive rounding error propagation of conventional…
We consider algorithmic approaches to the D-optimality problem for cases where the input design matrix is large and highly structured, in particular implicitly specified as a full quadratic or linear response-surface model in several levels…
In this paper we present several novel efficient techniques and multidimensional data structures which can improve the decision making process in many domains. We consider online range aggregation, range selection and range weighted median…
Dual numbers and their higher order version are important tools for numerical computations, and in particular for finite difference calculus. Based upon the relevant algebraic rules and matrix realizations of dual numbers, we will present a…
Distributed Computation has been a recent trend in engineering research. Parallel Computation is widely used in different areas of Data Mining, Image Processing, Simulating Models, Aerodynamics and so forth. One of the major usage of…
Modern computer architectures support low-precision arithmetic, which present opportunities for the adoption of mixed-precision algorithms to achieve high computational throughput and reduce energy consumption. As a growing number of…
Recent commercial hardware platforms for embedded real-time systems feature heterogeneous processing units and computing accelerators on the same System-on-Chip. When designing complex real-time application for such architectures, the…
We describe various computational models based initially, but not exclusively, on that of the Turing machine, that are generalized to allow for transfinitely many computational steps. Variants of such machines are considered that have…
Given the stringent requirements of energy efficiency for Internet-of-Things edge devices, approximate multipliers, as a basic component of many processors and accelerators, have been constantly proposed and studied for decades, especially…
Traditional computers work with finite numbers. Situations where the usage of infinite or infinitesimal quantities is required are studied mainly theoretically. In this paper, a recently introduced computational methodology (that is not…
The purpose of this paper is to explore the question "to what extent could we produce formal, machine-verifiable, proofs in real algebraic geometry?" The question has been asked before but as yet the leading algorithms for answering such…
This paper presents a novel attention-based algorithm for achieving adaptive computation called DACT, which, unlike existing ones, is end-to-end differentiable. Our method can be used in conjunction with many networks; in particular, we…
Parallel real-time embedded applications can be modelled as directed acyclic graphs (DAGs) whose nodes model subtasks and whose edges model precedence constraints among subtasks. Efficiently scheduling such parallel tasks can be challenging…
Block Floating Point (BFP) arithmetic is currently seeing a resurgence in interest because it requires less power, less chip area, and is less complicated to implement in hardware than standard floating point arithmetic. This paper explores…
Inspired by computer assisted proofs in analysis, we present an interval approach to real-number computations.
We introduce AccurateRAG -- a novel framework for constructing high-performance question-answering applications based on retrieval-augmented generation (RAG). Our framework offers a pipeline for development efficiency with tools for raw…