Related papers: Fifty Years of Stiffness
Complex systems thinking is applied to a wide variety of domains, from neuroscience to computer science and economics. The wide variety of implementations has resulted in two key challenges: the progenation of many domain-specific…
With the advent of high-performance computing, Bayesian methods are increasingly popular tools for the quantification of uncertainty throughout science and industry. Since these methods impact the making of sometimes critical decisions in…
[Connelly and Servatius, 1994] shows the difficulty of properly defining n-th order rigidity and flexiblity of a bar-and-joint framework for higher order (n >= 3) through the introduction of a cusp mechanism. The author proposes a "proper"…
Users of program analyses expect that results change predictably in response to changes in their programs, but many analyses fail to provide such robustness. This paper introduces a theoretical framework that provides a unified language to…
Better representation of the uncertainty in a data visualisation is a focus of recent research activity. A problem with the current literature is that there is a lack of clarity about the definition of uncertainty and what it means to…
We introduce the notion of a stable instance for a discrete optimization problem, and argue that in many practical situations only sufficiently stable instances are of interest. The question then arises whether stable instances of NP--hard…
Localized patterns are coherent structures embedded in a quiescent state and occur in both discrete and continuous media across a wide range of applications. While it is well-understood how domain covering patterns (for example stripes and…
Economic transformation -- change in what an economy produces -- is foundational to development and rising standards of living. Our understanding of this process has been propelled recently by two branches of work in the field of economic…
Solid modeling is a technique underlying CAD software as we see it today, and its theories and algorithms are among the most fundamental milestones in the historical development of CAD. Basically, it has answered the question of what…
High-dimensional computational challenges are frequently explained via the curse of dimensionality, i.e., increasing the number of dimensions leads to exponentially growing computational complexity. In this commentary, we argue that…
Following Stolarsky, we say that a natural number n is flimsy in base b if some positive multiple of n has smaller digit sum in base b than n does; otherwise it is sturdy. We develop algorithmic methods for the study of sturdy and flimsy…
Verification of discrete time or continuous time dynamical systems over the reals is known to be undecidable. It is however known that undecidability does not hold for various classes of systems: if robustness is defined as the fact that…
The purpose of this essay is to bring out the unique role of Mathematics in providing a base to the diverse sciences which conform to its rigid structure. Of these the physical and economic sciences are so intimately linked with…
We introduce a logical approach to formalizing statistical properties of machine learning. Specifically, we propose a formal model for statistical classification based on a Kripke model, and formalize various notions of classification…
In the last two decades, the popularity of self-adaptive systems in the field of software and systems engineering has drastically increased. However, despite the extensive work on self-adaptive systems, the literature still lacks a common…
In the first part of this paper, we present a unified framework for analyzing the algorithmic complexity of any optimization problem, whether it be continuous or discrete in nature. This helps to formalize notions like "input", "size" and…
We look at intensionality from the perspective of computation. In particular, we review how game semantics has been used to characterize the sequential functional processes, leading to powerful and flexible methods for constructing fully…
We consider the systematic force on a heavy probe induced by interaction with an overdamped diffusive medium where particles undergo a rotating force around a fixed center. The stiffness matrix summarizes the stability of the probe around…
Building software-driven systems that are easily understood becomes a challenge, with their ever-increasing complexity and autonomy. Accordingly, recent research efforts strive to aid in designing explainable systems. Nevertheless, a common…
In order to work with mathematical content in computer systems, it is necessary to represent it in formal languages. Ideally, these are supported by tools that verify the correctness of the content, allow computing with it, and produce…