151,111 research outputs found
Binary versus non-binary information in real time series: empirical results and maximum-entropy matrix models
The dynamics of complex systems, from financial markets to the brain, can be
monitored in terms of multiple time series of activity of the constituent
units, such as stocks or neurons respectively. While the main focus of time
series analysis is on the magnitude of temporal increments, a significant piece
of information is encoded into the binary projection (i.e. the sign) of such
increments. In this paper we provide further evidence of this by showing strong
nonlinear relations between binary and non-binary properties of financial time
series. These relations are a novel quantification of the fact that extreme
price increments occur more often when most stocks move in the same direction.
We then introduce an information-theoretic approach to the analysis of the
binary signature of single and multiple time series. Through the definition of
maximum-entropy ensembles of binary matrices and their mapping to spin models
in statistical physics, we quantify the information encoded into the simplest
binary properties of real time series and identify the most informative
property given a set of measurements. Our formalism is able to accurately
replicate, and mathematically characterize, the observed binary/non-binary
relations. We also obtain a phase diagram allowing us to identify, based only
on the instantaneous aggregate return of a set of multiple time series, a
regime where the so-called `market mode' has an optimal interpretation in terms
of collective (endogenous) effects, a regime where it is parsimoniously
explained by pure noise, and a regime where it can be regarded as a combination
of endogenous and exogenous factors. Our approach allows us to connect spin
models, simple stochastic processes, and ensembles of time series inferred from
partial information
The Complexity of Synthesizing Uniform Strategies
We investigate uniformity properties of strategies. These properties involve
sets of plays in order to express useful constraints on strategies that are not
\mu-calculus definable. Typically, we can state that a strategy is
observation-based. We propose a formal language to specify uniformity
properties, interpreted over two-player turn-based arenas equipped with a
binary relation between plays. This way, we capture e.g. games with winning
conditions expressible in epistemic temporal logic, whose underlying
equivalence relation between plays reflects the observational capabilities of
agents (for example, synchronous perfect recall). Our framework naturally
generalizes many other situations from the literature. We establish that the
problem of synthesizing strategies under uniformity constraints based on
regular binary relations between plays is non-elementary complete.Comment: In Proceedings SR 2013, arXiv:1303.007
Algebraic Properties of Qualitative Spatio-Temporal Calculi
Qualitative spatial and temporal reasoning is based on so-called qualitative
calculi. Algebraic properties of these calculi have several implications on
reasoning algorithms. But what exactly is a qualitative calculus? And to which
extent do the qualitative calculi proposed meet these demands? The literature
provides various answers to the first question but only few facts about the
second. In this paper we identify the minimal requirements to binary
spatio-temporal calculi and we discuss the relevance of the according axioms
for representation and reasoning. We also analyze existing qualitative calculi
and provide a classification involving different notions of a relation algebra.Comment: COSIT 2013 paper including supplementary materia
Algebraic foundations for qualitative calculi and networks
A qualitative representation is like an ordinary representation of a
relation algebra, but instead of requiring , as
we do for ordinary representations, we only require that , for each in the algebra. A constraint
network is qualitatively satisfiable if its nodes can be mapped to elements of
a qualitative representation, preserving the constraints. If a constraint
network is satisfiable then it is clearly qualitatively satisfiable, but the
converse can fail. However, for a wide range of relation algebras including the
point algebra, the Allen Interval Algebra, RCC8 and many others, a network is
satisfiable if and only if it is qualitatively satisfiable.
Unlike ordinary composition, the weak composition arising from qualitative
representations need not be associative, so we can generalise by considering
network satisfaction problems over non-associative algebras. We prove that
computationally, qualitative representations have many advantages over ordinary
representations: whereas many finite relation algebras have only infinite
representations, every finite qualitatively representable algebra has a finite
qualitative representation; the representability problem for (the atom
structures of) finite non-associative algebras is NP-complete; the network
satisfaction problem over a finite qualitatively representable algebra is
always in NP; the validity of equations over qualitative representations is
co-NP-complete. On the other hand we prove that there is no finite
axiomatisation of the class of qualitatively representable algebras.Comment: 22 page
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