23,230 research outputs found
Modelling and identification of non-linear deterministic systems in the delta-domain
This paper provides a formulation for using the delta-operator in the modelling of non-linear systems. It is shown that a unique representation of a deterministic non-linear auto-regressive with exogenous input (NARX) model can be obtained for polynomial basis functions using the delta-operator and expressions are derived to convert between the shift- and delta- domain. A delta-NARX model is applied to the identification of a test problem (a Van-der-Pol oscillator): a comparison is made with the standard shift operator non-linear model and it is demonstrated that the delta-domain approach improves the numerical properties of structure detection, leads to a parsimonious description and provides a model that is closely linked to the continuous-time non-linear system in terms of both parameters and structure
Violator Spaces: Structure and Algorithms
Sharir and Welzl introduced an abstract framework for optimization problems,
called LP-type problems or also generalized linear programming problems, which
proved useful in algorithm design. We define a new, and as we believe, simpler
and more natural framework: violator spaces, which constitute a proper
generalization of LP-type problems. We show that Clarkson's randomized
algorithms for low-dimensional linear programming work in the context of
violator spaces. For example, in this way we obtain the fastest known algorithm
for the P-matrix generalized linear complementarity problem with a constant
number of blocks. We also give two new characterizations of LP-type problems:
they are equivalent to acyclic violator spaces, as well as to concrete LP-type
problems (informally, the constraints in a concrete LP-type problem are subsets
of a linearly ordered ground set, and the value of a set of constraints is the
minimum of its intersection).Comment: 28 pages, 5 figures, extended abstract was presented at ESA 2006;
author spelling fixe
Estimating the effect of joint interventions from observational data in sparse high-dimensional settings
We consider the estimation of joint causal effects from observational data.
In particular, we propose new methods to estimate the effect of multiple
simultaneous interventions (e.g., multiple gene knockouts), under the
assumption that the observational data come from an unknown linear structural
equation model with independent errors. We derive asymptotic variances of our
estimators when the underlying causal structure is partly known, as well as
high-dimensional consistency when the causal structure is fully unknown and the
joint distribution is multivariate Gaussian. We also propose a generalization
of our methodology to the class of nonparanormal distributions. We evaluate the
estimators in simulation studies and also illustrate them on data from the
DREAM4 challenge.Comment: 30 pages, 3 figures, 45 pages supplemen
Regions of linearity, Lusztig cones and canonical basis elements for the quantized enveloping algebra of type A_4
Let U_q be the quantum group associated to a Lie algebra g of rank n. The
negative part U^- of U has a canonical basis B with favourable properties,
introduced by Kashiwara and Lusztig. The approaches of Kashiwara and Lusztig
lead to a set of alternative parametrizations of the canonical basis, one for
each reduced expression for the longest word in the Weyl group of g. We show
that if g is of type A_4 there are close relationships between the Lusztig
cones, canonical basis elements and the regions of linearity of
reparametrization functions arising from the above parametrizations. A graph
can be defined on the set of simplicial regions of linearity with respect to
adjacency, and we further show that this graph is isomorphic to the graph with
vertices given by the reduced expressions of the longest word of the Weyl group
modulo commutation and edges given by long braid relations.
Keywords: Quantum group, Lie algebra, Canonical basis, Tight monomials, Weyl
group, Piecewise-linear functions.Comment: 61 pages, 17 figures, uses picte
Quantum Programming Made Easy
We present IQu, namely a quantum programming language that extends Reynold's
Idealized Algol, the paradigmatic core of Algol-like languages. IQu combines
imperative programming with high-order features, mediated by a simple type
theory. IQu mildly merges its quantum features with the classical programming
style that we can experiment through Idealized Algol, the aim being to ease a
transition towards the quantum programming world. The proposed extension is
done along two main directions. First, IQu makes the access to quantum
co-processors by means of quantum stores. Second, IQu includes some support for
the direct manipulation of quantum circuits, in accordance with recent trends
in the development of quantum programming languages. Finally, we show that IQu
is quite effective in expressing well-known quantum algorithms.Comment: In Proceedings Linearity-TLLA 2018, arXiv:1904.0615
Separable and Low-Rank Continuous Games
In this paper, we study nonzero-sum separable games, which are continuous
games whose payoffs take a sum-of-products form. Included in this subclass are
all finite games and polynomial games. We investigate the structure of
equilibria in separable games. We show that these games admit finitely
supported Nash equilibria. Motivated by the bounds on the supports of mixed
equilibria in two-player finite games in terms of the ranks of the payoff
matrices, we define the notion of the rank of an n-player continuous game and
use this to provide bounds on the cardinality of the support of equilibrium
strategies. We present a general characterization theorem that states that a
continuous game has finite rank if and only if it is separable. Using our rank
results, we present an efficient algorithm for computing approximate equilibria
of two-player separable games with fixed strategy spaces in time polynomial in
the rank of the game
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