相关论文: A symbolic algebra for the computation of expected…
The paper deals with the process of mathematical modeling representations of exponential and logarithmic functions hypercomplex number system of generalized quaternions via determining a linear differential equation with hypercomplex…
In this paper, inspired by the work of Megiddo on the formation of preferences and strategic analysis, we consider an early market model studied in the field of economic theory, in which each trader's utility may be influenced by the…
Additive utility function models are widely used in multiple criteria decision analysis. In such models, a numerical value is associated to each alternative involved in the decision problem. It is computed by aggregating the scores of the…
We consider the problem of expected cost analysis over nondeterministic probabilistic programs, which aims at automated methods for analyzing the resource-usage of such programs. Previous approaches for this problem could only handle…
A model of computation that is widely used in the formal analysis of reactive systems is symbolic algorithms. In this model the access to the input graph is restricted to consist of symbolic operations, which are expensive in comparison to…
In this paper we provide, first, a general symbolic algorithm for computing the symmetries of a given rational surface, based on the classical differential invariants of surfaces, i.e. Gauss curvature and mean curvature. In practice, the…
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…
An efficient structural identifiability analysis algorithm is developed in this study for a broad range of network structures. The proposed method adopts the Wright's path coefficient method to generate identifiability equations in forms of…
So far, the scope of computer algebra has been needlessly restricted to exact algebraic methods. Its possible extension to approximate analytical methods is discussed. The entangled roles of functional analysis and symbolic programming,…
Many real-world domains can be expressed as graphs and, more generally, as multi-relational knowledge graphs. Though reasoning and learning with knowledge graphs has traditionally been addressed by symbolic approaches, recent methods in…
We survey and unify recent results on the existence of accurate algorithms for evaluating multivariate polynomials, and more generally for accurate numerical linear algebra with structured matrices. By "accurate" we mean that the computed…
We assume some standard choices for the branch cuts of a group of functions and consider the problem of then calculating the branch cuts of expressions involving those functions. Typical examples include the addition formulae for inverse…
Structured matrices with symbolic sizes appear frequently in the literature, especially in the description of algorithms for linear algebra. Recent work has treated these symbolic structured matrices themselves as computational objects,…
We introduce the concept of a \textbf{neuro-symbolic pair} -- neural and symbolic approaches that are linked through a common knowledge representation. Next, we present \textbf{taxonomic networks}, a type of discrimination network in which…
Student appreciation of a function is enhanced by understanding the graphical representation of that function. From the real graph of a polynomial, students can identify real-valued solutions to polynomial equations that correspond to the…
Geometry constitutes a core set of intuitions present in all humans, regardless of their language or schooling [1]. Could brain's built in machinery for processing geometric information take part in uncertainty representation? For decades…
Complex analyses involving multiple, dependent random quantities often lead to graphical models - a set of nodes denoting variables of interest, and corresponding edges denoting statistical interactions between nodes. To develop statistical…
Graphical models use graphs to compactly capture stochastic dependencies amongst a collection of random variables. Inference over graphical models corresponds to finding marginal probability distributions given joint probability…
Probabilistic conceptual network is a knowledge representation scheme designed for reasoning about concepts and categorical abstractions in utility-based categorization. The scheme combines the formalisms of abstraction and inheritance…
In this paper we report on an application of computer algebra in which mathematical puzzles are generated of a type that had been widely used in mathematics contests by a large number of participants worldwide. The algorithmic aspect of our…