15,823 research outputs found
Control theoretic models of pointing
This article presents an empirical comparison of four models from manual control theory on their ability to model targeting behaviour by human users using a mouse: McRuer’s Crossover, Costello’s Surge, second-order lag (2OL), and the Bang-bang model. Such dynamic models are generative, estimating not only movement time, but also pointer position, velocity, and acceleration on a moment-to-moment basis. We describe an experimental framework for acquiring pointing actions and automatically fitting the parameters of mathematical models to the empirical data. We present the use of time-series, phase space, and Hooke plot visualisations of the experimental data, to gain insight into human pointing dynamics. We find that the identified control models can generate a range of dynamic behaviours that captures aspects of human pointing behaviour to varying degrees. Conditions with a low index of difficulty (ID) showed poorer fit because their unconstrained nature leads naturally to more behavioural variability. We report on characteristics of human surge behaviour (the initial, ballistic sub-movement) in pointing, as well as differences in a number of controller performance measures, including overshoot, settling time, peak time, and rise time. We describe trade-offs among the models. We conclude that control theory offers a promising complement to Fitts’ law based approaches in HCI, with models providing representations and predictions of human pointing dynamics, which can improve our understanding of pointing and inform design
Controllability Metrics, Limitations and Algorithms for Complex Networks
This paper studies the problem of controlling complex networks, that is, the
joint problem of selecting a set of control nodes and of designing a control
input to steer a network to a target state. For this problem (i) we propose a
metric to quantify the difficulty of the control problem as a function of the
required control energy, (ii) we derive bounds based on the system dynamics
(network topology and weights) to characterize the tradeoff between the control
energy and the number of control nodes, and (iii) we propose an open-loop
control strategy with performance guarantees. In our strategy we select control
nodes by relying on network partitioning, and we design the control input by
leveraging optimal and distributed control techniques. Our findings show
several control limitations and properties. For instance, for Schur stable and
symmetric networks: (i) if the number of control nodes is constant, then the
control energy increases exponentially with the number of network nodes, (ii)
if the number of control nodes is a fixed fraction of the network nodes, then
certain networks can be controlled with constant energy independently of the
network dimension, and (iii) clustered networks may be easier to control
because, for sufficiently many control nodes, the control energy depends only
on the controllability properties of the clusters and on their coupling
strength. We validate our results with examples from power networks, social
networks, and epidemics spreading
Counting Steiner triple systems with classical parameters and prescribed rank
By a famous result of Doyen, Hubaut and Vandensavel \cite{DHV}, the 2-rank of
a Steiner triple system on points is at least , and equality
holds only for the classical point-line design in the projective geometry
. It follows from results of Assmus \cite{A} that, given any integer
with , there is a code containing
representatives of all isomorphism classes of STS with 2-rank at most
. Using a mixture of coding theoretic, geometric, design
theoretic and combinatorial arguments, we prove a general formula for the
number of distinct STS with 2-rank at most contained
in this code. This generalizes the only previously known cases, , proved
by Tonchev \cite{T01} in 2001, , proved by V. Zinoviev and D. Zinoviev
\cite{ZZ12} in 2012, and (V. Zinoviev and D. Zinoviev \cite{ZZ13},
\cite{ZZ13a} (2013), D. Zinoviev \cite{Z16} (2016)), while also unifying and
simplifying the proofs. This enumeration result allows us to prove lower and
upper bounds for the number of isomorphism classes of STS with 2-rank
exactly (or at most) . Finally, using our recent systematic
study of the ternary block codes of Steiner triple systems \cite{JT}, we obtain
analogous results for the ternary case, that is, for STS with 3-rank at
most (or exactly) . We note that this work provides the first
two infinite families of 2-designs for which one has non-trivial lower and
upper bounds for the number of non-isomorphic examples with a prescribed
-rank in almost the entire range of possible ranks.Comment: 27 page
Group theoretic, Lie algebraic and Jordan algebraic formulations of the SIC existence problem
Although symmetric informationally complete positive operator valued measures
(SIC POVMs, or SICs for short) have been constructed in every dimension up to
67, a general existence proof remains elusive. The purpose of this paper is to
show that the SIC existence problem is equivalent to three other, on the face
of it quite different problems. Although it is still not clear whether these
reformulations of the problem will make it more tractable, we believe that the
fact that SICs have these connections to other areas of mathematics is of some
intrinsic interest. Specifically, we reformulate the SIC problem in terms of
(1) Lie groups, (2) Lie algebras and (3) Jordan algebras (the second result
being a greatly strengthened version of one previously obtained by Appleby,
Flammia and Fuchs). The connection between these three reformulations is
non-trivial: It is not easy to demonstrate their equivalence directly, without
appealing to their common equivalence to SIC existence. In the course of our
analysis we obtain a number of other results which may be of some independent
interest.Comment: 36 pages, to appear in Quantum Inf. Compu
- …