Graphical criteria for positive solutions to linear systems

We study linear systems of equations with coefficients in a generic partially ordered ring $R$ and a unique solution, and seek conditions for the solution to be nonnegative, that is, every component of the solution is a quotient of two nonnegative elements in $R$. The requirement of a nonnegative solution arises typically in applications, such as in biology and ecology, where quantities of interest are concentrations and abundances. We provide novel conditions on a labeled multidigraph associated with the linear system that guarantee the solution to be nonnegative. Furthermore, we study a generalization of the first class of linear systems, where the coefficient matrix has a specific block form and provide analogous conditions for nonnegativity of the solution, similarly based on a labeled multidigraph. The latter scenario arises naturally in chemical reaction network theory, when studying full or partial parameterizations of the positive part of the steady state variety of a polynomial dynamical system in the concentrations of the molecular species

A comparison of linear and calendar travel itinerary visualizations for personal digital assistants

Various graphical travel itinerary visualization systems have in recent years been developed to allow making easier references between different events such as flights and hotel bookings on a travel itinerary, thereby addressing a problem with tabular itineraries which list travel events in a chronological order of date and time, and only allow referencing consecutive events. These graphical travel itinerary systems are based on a linear visualization of travel events. Although this linear visualization deals with some of the problems associated with tabular itineraries, it is not the only form of visualization which might be capable of addressing these issues. This paper introduces a new visualization of travel itineraries, called the calendar visualization, which relies on a more familiar concept of calendars to depict the relationships between travel events. This paper also describes an empirical study undertaken to compare the calendar and linear itinerary visualizations

Visualising Discourse Coherence in Non-Linear Documents

To produce coherent linear documents, Natural Language Generation systems have traditionally exploited the structuring role of textual discourse markers such as relational and referential phrases. These coherence markers of the traditional notion of text, however, do not work in non-linear documents: a new set of graphical devices is needed together with formation rules to govern their usage, supported by sound theoretical frameworks. If in linear documents graphical devices such as layout and formatting complement textual devices in the expression of discourse coherence, in non-linear documents they play a more important role. In this paper, we present our theoretical and empirical work in progress, which explores new possibilities for expressing coherence in the generation of hypertext documents

Hierarchical Decomposition of Nonlinear Dynamics and Control for System Identification and Policy Distillation

The control of nonlinear dynamical systems remains a major challenge for autonomous agents. Current trends in reinforcement learning (RL) focus on complex representations of dynamics and policies, which have yielded impressive results in solving a variety of hard control tasks. However, this new sophistication and extremely over-parameterized models have come with the cost of an overall reduction in our ability to interpret the resulting policies. In this paper, we take inspiration from the control community and apply the principles of hybrid switching systems in order to break down complex dynamics into simpler components. We exploit the rich representational power of probabilistic graphical models and derive an expectation-maximization (EM) algorithm for learning a sequence model to capture the temporal structure of the data and automatically decompose nonlinear dynamics into stochastic switching linear dynamical systems. Moreover, we show how this framework of switching models enables extracting hierarchies of Markovian and auto-regressive locally linear controllers from nonlinear experts in an imitation learning scenario.Comment: 2nd Annual Conference on Learning for Dynamics and Contro

Mikhailov Stability Criterion for Time-delayed Systems

The valid and invalid application of the Mikhailov criterion to linear, time-invariant systems with time delays is discussed. The Mikhailov criterion is a graphical procedure which was developed to examine the stability of linear, time-invariant systems with no time delays. Two equivalent formulations of the criterion are discussed. Results indicate that the first formulation remains valid for time-delayed systems of the retared type, with the understanding that the Mikhailov curve need not necessarily always rotate in the counterclockwise direction for a stable system. Erroneous results in the second formulation are formed when there are time delays in the systems

Teaching, Analyzing, Designing and Interactively Simulating of Sliding Mode Control

This paper introduces an interactive methodology to analize, design, and simulate sliding model controllers for R2 linear systems. This paper reviews sliding mode basic concepts and design methodologies and describes an interactive tool which has been developed to support teaching in this field. The tool helps students by generating a nice graphical and interactive display of most relevant concepts. This fact can be used so that students build their own intuition about the role of different parameters in a sliding mode controller. Described application has been coded with Sysquake using an event-driven solver technique. The Sysquake allows using precise integration methods in real time and handling interactivity in a simple manner.Peer ReviewedPostprint (published version

Bipolar Proof Nets for MALL

In this work we present a computation paradigm based on a concurrent and incremental construction of proof nets (de-sequentialized or graphical proofs) of the pure multiplicative and additive fragment of Linear Logic, a resources conscious refinement of Classical Logic. Moreover, we set a correspon- dence between this paradigm and those more pragmatic ones inspired to transactional or distributed systems. In particular we show that the construction of additive proof nets can be interpreted as a model for super-ACID (or co-operative) transactions over distributed transactional systems (typi- cally, multi-databases).Comment: Proceedings of the "Proof, Computation, Complexity" International Workshop, 17-18 August 2012, University of Copenhagen, Denmar

Teaching Differential Equations with Graphics and without Linear Algebra

We present our approach to teaching the Method of Eigenvectors to solve linear systems of ODEs without assuming a prerequisite course in Linear Algebra. Rather we depend heavily on a graphical approach to systems in two dimensions to motivate the eigenvalue equation

Teaching, Analyzing, Designing and Interactively Simulating of Sliding Mode Control

This paper introduces an interactive methodology to analize, design, and simulate sliding model controllers for R2 linear systems. This paper reviews sliding mode basic concepts and design methodologies and describes an interactive tool which has been developed to support teaching in this field. The tool helps students by generating a nice graphical and interactive display of most relevant concepts. This fact can be used so that students build their own intuition about the role of different parameters in a sliding mode controller. Described application has been coded with Sysquake using an event-driven solver technique. The Sysquake allows using precise integration methods in real time and handling interactivity in a simple manner.Peer ReviewedPostprint (published version