Related papers: Structural Identifiability of Series-Parallel LCR …
An explicit formula for the resistance between two nodes in a network with a non-symmetric Laplacian matrix L is obtained. This is of great advantage e.g. in electronic circuit fault analysis, where non-linear systems have to be solved…
The exact parameter values of mathematical models are often uncertain or even unknown. Nevertheless, we may have access to crude information about the parameters, e.g., that some of them are nonzero. Such information can be captured by…
Linear Complementary Dual codes (LCD) are binary linear codes that meet their dual trivially. We construct LCD codes using orthogonal matrices, self-dual codes, combinatorial designs and Gray map from codes over the family of rings $R_k$.…
Network models are used to study interconnected systems across many physical, biological, and social disciplines. Such models often assume a particular network-generating mechanism, which when fit to data produces estimates of…
We study recursive-cube-of-rings (RCR), a class of scalable graphs that can potentially provide rich inter-connection network topology for the emerging distributed and parallel computing infrastructure. Through rigorous proof and validating…
In this paper we introduce the notion of nonlinear resistance forms. We define a $1$-parameter family of nonlinear resistance metrics and show their additivity over serial circuits. Moreover, we prove that resistance forms and…
Accurate trajectory tracking is an essential characteristic for the safe navigation of a quadrotor in cluttered or disturbed environments. In this paper, we present in detail two state-of-the-art model-based control frameworks for…
In this paper, we study diagnosabilities of multiprocessor systems under two diagnosis models: the PMC model and the comparison model. In each model, we further consider two different diagnosis strategies: the precise diagnosis strategy…
The study of multiplicative noise models has a long history in control theory but is re-emerging in the context of complex networked systems and systems with learning-based control. We consider linear system identification with…
The article continues the work on the description of integrable nonlinear chains with three independent variables of the following form $u^j_{n+1,x}=u^j_{n,x}+f(u^{j+1}_{n}, u^{j}_n,u^j_{n+1 },u^{j-1}_{n+1})$ by the presence of a hierarchy…
Layer normalization (LN) is a ubiquitous technique in deep learning but our theoretical understanding to it remains elusive. This paper investigates a new theoretical direction for LN, regarding to its nonlinearity and representation…
*Automated circuit discovery* is a central tool in mechanistic interpretability for identifying the internal components of neural networks responsible for specific behaviors. While prior methods have made significant progress, they…
Learning latent structure in complex networks has become an important problem fueled by many types of networked data originating from practically all fields of science. In this paper, we propose a new non-parametric Bayesian…
We consider optical response in multi-band, multi-layer two-dimensional superconductors. Within a simple model, we show that linear response to AC gating can detect collective modes of the condensate, such as Leggett and clapping modes. We…
High-dimensional feature vectors are likely to contain sets of measurements that are approximate replicates of one another. In complex applications, or automated data collection, these feature sets are not known a priori, and need to be…
We describe a type system with mixed linear and non-linear recursive types called LNL-FPC (the linear/non-linear fixpoint calculus). The type system supports linear typing, which enhances the safety properties of programs, but also supports…
Cycles, which can be found in many different kinds of networks, make the problems more intractable, especially when dealing with dynamical processes on networks. On the contrary, tree networks in which no cycle exists, are simplifications…
A recent development in data-driven modelling addresses the problem of identifying dynamic models of interconnected systems, represented as linear dynamic networks. For these networks the notion network identifiability has been introduced…
Complex networks have become essential tools for understanding diverse phenomena in social systems, traffic systems, biomolecular systems, and financial systems. Identifying critical nodes is a central theme in contemporary research,…
Parameter identifiability describes whether, for a given differential model, one can determine parameter values from model equations. Knowing global or local identifiability properties allows construction of better practical experiments to…