Related papers: Properties of pattern matrices with applications t…
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,…
Observability is a modelling property that describes the possibility of inferring the internal state of a system from observations of its output. A related property, structural identifiability, refers to the theoretical possibility of…
Mathematical modelling is a widely used approach to understand and interpret clinical trial data. This modelling typically involves fitting mechanistic mathematical models to data from individual trial participants. Despite the widespread…
System Gramian matrices are a well-known encoding for properties of input-output systems such as controllability, observability or minimality. These so-called system Gramians were developed in linear system theory for applications such as…
Probabilistic graphical models combine the graph theory and probability theory to give a multivariate statistical modeling. They provide a unified description of uncertainty using probability and complexity using the graphical model.…
Matrix factorization exploits the idea that, in complex high-dimensional data, the actual signal typically lies in lower-dimensional structures. These lower dimensional objects provide useful insight, with interpretability favored by sparse…
Inferring control parameters in non-linear dynamical systems is an important task in analysing general dynamical behaviours, particularly in the presence of inherently deterministic chaos. Traditional approaches often rely on…
In finance, economics and many other fields, observations in a matrix form are often observed over time. For example, many economic indicators are obtained in different countries over time. Various financial characteristics of many…
We address the problem of merging graph and feature-space information while learning a metric from structured data. Existing algorithms tackle the problem in an asymmetric way, by either extracting vectorized summaries of the graph…
A large family of linear codes with flexible parameters from almost bent functions and perfect nonlinear functions are constructed and their parameters are determined. Some constructed linear codes and their related codes are optimal in the…
Pattern matching is a powerful tool which is part of many functional programming languages as well as computer algebra systems such as Mathematica. Among the existing systems, Mathematica offers the most expressive pattern matching.…
In the context of dynamical systems, nonlinearity measures quantify the strength of nonlinearity by means of the distance of their input-output behaviour to a set of linear input-output mappings. In this paper, we establish a framework to…
Patterns are fundamental to human cognition, enabling the recognition of structure and regularity across diverse domains. In this work, we focus on structural repeats, patterns that arise from the repetition of hierarchical relations within…
Given a real symmetric $n\times n$ matrix, the sepr-sequence $t_1\cdots t_n$ records information about the existence of principal minors of each order that are positive, negative, or zero. This paper extends the notion of the sepr-sequence…
Large scale dynamical systems (e.g. many nonlinear coupled differential equations) can often be summarized in terms of only a few state variables (a few equations), a trait that reduces complexity and facilitates exploration of behavioral…
A foundational question in the theory of linear compartmental models is how to assess whether a model is structurally identifiable -- that is, whether parameter values can be inferred from noiseless data -- directly from the combinatorics…
A real matrix is said to be positive if its every entry is positive, and a real square matrix A is algebraically positive if there exists a real polynomial f such that f(A) is a positive matrix. A sign pattern matrix A is said to require a…
High-throughput data analyses are becoming common in biology, communications, economics and sociology. The vast amounts of data are usually represented in the form of matrices and can be considered as knowledge networks. Spectra-based…
When we speak about parametric programming, sensitivity analysis, or related topics, we usually mean the problem of studying specified perturbations of the data such that for a given optimization problem some optimality criterion remains…
Parameter inference and uncertainty quantification are important steps when relating mathematical models to real-world observations, and when estimating uncertainty in model predictions. However, methods for doing this can be…