9,614 research outputs found
On the max-algebraic core of a nonnegative matrix
The max-algebraic core of a nonnegative matrix is the intersection of column
spans of all max-algebraic matrix powers. Here we investigate the action of a
matrix on its core. Being closely related to ultimate periodicity of matrix
powers, this study leads us to new modifications and geometric
characterizations of robust, orbit periodic and weakly stable matrices.Comment: 27 page
On the Complexity of Finding a Sun in a Graph
The sun is the graph obtained from a cycle of length even and at least six by adding edges to make the even-indexed vertices pairwise adjacent. Suns play an important role in the study of strongly chordal graphs. A graph is chordal if it does not contain an induced cycle of length at least four. A graph is strongly chordal if it is chordal and every even cycle has a chord joining vertices whose distance on the cycle is odd. Farber proved that a graph is strongly chordal if and only if it is chordal and contains no induced suns. There are well known polynomial-time algorithms for recognizing a sun in a chordal graph. Recently, polynomial-time algorithms for finding a sun for a larger class of graphs, the so-called HHD-free graphs (graphs containing no house, hole, or domino), have been discovered. In this paper, we prove the problem of deciding whether an arbitrary graph contains a sun is NP-complete
Identifying States of a Financial Market
The understanding of complex systems has become a central issue because
complex systems exist in a wide range of scientific disciplines. Time series
are typical experimental results we have about complex systems. In the analysis
of such time series, stationary situations have been extensively studied and
correlations have been found to be a very powerful tool. Yet most natural
processes are non-stationary. In particular, in times of crisis, accident or
trouble, stationarity is lost. As examples we may think of financial markets,
biological systems, reactors or the weather. In non-stationary situations
analysis becomes very difficult and noise is a severe problem. Following a
natural urge to search for order in the system, we endeavor to define states
through which systems pass and in which they remain for short times. Success in
this respect would allow to get a better understanding of the system and might
even lead to methods for controlling the system in more efficient ways.
We here concentrate on financial markets because of the easy access we have
to good data and because of the strong non-stationary effects recently seen. We
analyze the S&P 500 stocks in the 19-year period 1992-2010. Here, we propose
such an above mentioned definition of state for a financial market and use it
to identify points of drastic change in the correlation structure. These points
are mapped to occurrences of financial crises. We find that a wide variety of
characteristic correlation structure patterns exist in the observation time
window, and that these characteristic correlation structure patterns can be
classified into several typical "market states". Using this classification we
recognize transitions between different market states. A similarity measure we
develop thus affords means of understanding changes in states and of
recognizing developments not previously seen.Comment: 9 pages, 8 figure
Evolutionary instability of Zero Determinant strategies demonstrates that winning isn't everything
Zero Determinant (ZD) strategies are a new class of probabilistic and
conditional strategies that are able to unilaterally set the expected payoff of
an opponent in iterated plays of the Prisoner's Dilemma irrespective of the
opponent's strategy, or else to set the ratio between a ZD player's and their
opponent's expected payoff. Here we show that while ZD strategies are weakly
dominant, they are not evolutionarily stable and will instead evolve into less
coercive strategies. We show that ZD strategies with an informational advantage
over other players that allows them to recognize other ZD strategies can be
evolutionarily stable (and able to exploit other players). However, such an
advantage is bound to be short-lived as opposing strategies evolve to
counteract the recognition.Comment: 14 pages, 4 figures. Change in title (again!) to comply with Nature
Communications requirements. To appear in Nature Communication
Does dark matter consist of baryons of new stable family quarks?
We investigate the possibility that the dark matter consists of clusters of
the heavy family quarks and leptons with zero Yukawa couplings to the lower
families. Such a family is predicted by the {\it approach unifying spin and
charges} as the fifth family. We make a rough estimation of properties of
baryons of this new family members, of their behaviour during the evolution of
the universe and when scattering on the ordinary matter and study possible
limitations on the family properties due to the cosmological and direct
experimental evidences.Comment: 28 pages, revtex, submitted to Phys. Rev. Let
X-simple image eigencones of tropical matrices
We investigate max-algebraic (tropical) one-sided systems
where is an eigenvector and lies in an interval . A matrix is
said to have -simple image eigencone associated with an eigenvalue
, if any eigenvector associated with and belonging to
the interval is the unique solution of the system in
. We characterize matrices with -simple image eigencone geometrically and
combinatorially, and for some special cases, derive criteria that can be
efficiently checked in practice.Comment: 25 page
Optimal Uniform Convergence Rates and Asymptotic Normality for Series Estimators Under Weak Dependence and Weak Conditions
We show that spline and wavelet series regression estimators for weakly
dependent regressors attain the optimal uniform (i.e. sup-norm) convergence
rate of Stone (1982), where is the number of
regressors and is the smoothness of the regression function. The optimal
rate is achieved even for heavy-tailed martingale difference errors with finite
th absolute moment for . We also establish the asymptotic
normality of t statistics for possibly nonlinear, irregular functionals of the
conditional mean function under weak conditions. The results are proved by
deriving a new exponential inequality for sums of weakly dependent random
matrices, which is of independent interest.Comment: forthcoming in Journal of Econometric
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