17,091 research outputs found
Revolutionaries and spies on random graphs
Pursuit-evasion games, such as the game of Revolutionaries and Spies, are a
simplified model for network security. In the game we consider in this paper, a
team of revolutionaries tries to hold an unguarded meeting consisting of
revolutionaries. A team of spies wants to prevent this forever. For
given and , the minimum number of spies required to win on a graph
is the spy number . We present asymptotic results for the game
played on random graphs for a large range of , and
. The behaviour of the spy number is analyzed completely for dense
graphs (that is, graphs with average degree at least n^{1/2+\eps} for some
\eps > 0). For sparser graphs, some bounds are provided
The determinant of the Dirichlet-to-Neumann map for surfaces with boundary
For any orientable compact surface with boundary, we compute the regularized
determinant of the Dirichlet-to-Neumann (DN) map in terms of particular values
of dynamical zeta functions by using natural uniformizations, one due to
Mazzeo-Taylor, the other to Osgood-Phillips-Sarnak. We also relate in any
dimension the DN map for the Yamabe operator to the scattering operator for a
conformally compact related problem by using uniformization.Comment: 16 page
Some aspects of dispersive horizons: lessons from surface waves
Hydrodynamic surface waves propagating on a moving background flow experience
an effective curved space-time. We discuss experiments with gravity waves and
capillary-gravity waves in which we study hydrodynamic black/white-hole
horizons and the possibility of penetrating across them. Such possibility of
penetration is due to the interaction with an additional "blue" horizon, which
results from the inclusion of surface tension in the low-frequency gravity-wave
theory. This interaction leads to a dispersive cusp beyond which both horizons
completely disappear. We speculate the appearance of high-frequency
"superluminal" corrections to be a universal characteristic of analogue gravity
systems, and discuss their relevance for the trans-Planckian problem. We also
discuss the role of Airy interference in hybridising the incoming waves with
the flowing background (the effective spacetime) and blurring the position of
the black/white-hole horizon.Comment: 29 pages. Lecture Notes for the IX SIGRAV School on "Analogue
Gravity", Como (Italy), May 201
Nonabelian cohomology jump loci from an analytic viewpoint
For a topological space, we investigate its cohomology support loci, sitting
inside varieties of (nonabelian) representations of the fundamental group. To
do this, for a CDG (commutative differential graded) algebra, we define its
cohomology jump loci, sitting inside varieties of (algebraic) flat connections.
We prove that the analytic germs at the origin 1 of representation varieties
are determined by the Sullivan 1-minimal model of the space. Under mild
finiteness assumptions, we show that, up to a degree , the two types of jump
loci have the same analytic germs at the origins, when the space and the
algebra have the same -minimal model. We apply this general approach to
formal spaces (for which we establish the degeneration of the Farber-Novikov
spectral sequence), quasi-projective manifolds, and finitely generated
nilpotent groups. When the CDG algebra has positive weights, we elucidate some
of the structure of (rank one complex) topological and algebraic jump loci: up
to degree , all their irreducible components passing through the origin are
connected affine subtori, respectively rational linear subspaces. Furthermore,
the global exponential map sends all algebraic cohomology jump loci, up to
degree , into their topological counterpart.Comment: New Corollary 1.7 added and Theorem D. strengthened. Final version,
to appear in Communications in Contemporary Mathematic
Expectation-driven interaction: a model based on Luhmann's contingency approach
We introduce an agent-based model of interaction, drawing on the contingency
approach from Luhmann's theory of social systems. The agent interactions are
defined by the exchange of distinct messages. Message selection is based on the
history of the interaction and developed within the confines of the problem of
double contingency. We examine interaction strategies in the light of the
message-exchange description using analytical and computational methods.Comment: 37 pages, 16 Figures, to appear in Journal of Artificial Societies
and Social Simulation
Anomalous scaling and Lee-Yang zeroes in Self-Organized Criticality
We show that the generating functions of avalanche observables in SOC models
exhibits a Lee-Yang phenomenon. This establishes a new link between the
classical theory of critical phenomena and SOC. A scaling theory of the
Lee-Yang zeroes is proposed including finite sampling effects.Comment: 33 pages, 19 figures, submitte
Could short selling make financial markets tumble?
It is suggested to consider long term trends of financial markets as a growth
phenomenon. The question that is asked is what conditions are needed for a long
term sustainable growth or contraction in a financial market? The paper discuss
the role of traditional market players of long only mutual funds versus hedge
funds which take both short and long positions. It will be argued that
financial markets since their very origin and only till very recently, have
been in a state of ``broken symmetry'' which favored long term growth instead
of contraction. The reason for this ``broken symmetry'' into a long term ``bull
phase'' is the historical almost complete dominance by long only players in
financial markets. Dangers connected to short trading are illustrated by the
appearence of long term bearish trends seen in analytical results and by
simulation results of an agent based market model. Recent short trade data of
the Nasdaq Composite index show an increase in the short activity prior to or
at the same time as dips in the market, and reveal an steadily increase in the
short trading activity, reaching levels never seen before.Comment: Revtex, 7 pages, 7 figure
Hyperoctahedral Chen calculus for effective Hamiltonians
The algebraic structure of iterated integrals has been encoded by Chen.
Formally, it identifies with the shuffle and Lie calculus of Lyndon, Ree and
Sch\"utzenberger. It is mostly incorporated in the modern theory of free Lie
algebras. Here, we tackle the problem of unraveling the algebraic structure of
computations of effective Hamiltonians. This is an important subject in view of
applications to chemistry, solid state physics, quantum field theory or
engineering. We show, among others, that the correct framework for these
computations is provided by the hyperoctahedral group algebras. We define
several structures on these algebras and give various applications. For
example, we show that the adiabatic evolution operator (in the time-dependent
interaction representation of an effective Hamiltonian) can be written
naturally as a Picard-type series and has a natural exponential expansion.Comment: Minor corrections. Some misleading notations and typos in the first
version have been fixe
Conformal harmonic forms, Branson-Gover operators and Dirichlet problem at infinity
For odd dimensional Poincar\'e-Einstein manifolds , we study the
set of harmonic -forms (for k<\ndemi) which are (with m\in\nn) on
the conformal compactification of . This is infinite dimensional
for small but it becomes finite dimensional if is large enough, and in
one-to-one correspondence with the direct sum of the relative cohomology
H^k(\bar{X},\pl\bar{X}) and the kernel of the Branson-Gover \cite{BG}
differential operators on the conformal infinity
(\pl\bar{X},[h_0]). In a second time we relate the set of
forms in the kernel of to the
conformal harmonics on the boundary in the sense of \cite{BG}, providing some
sort of long exact sequence adapted to this setting. This study also provides
another construction of Branson-Gover differential operators, including a
parallel construction of the generalization of curvature for forms.Comment: 35 page
Efficient resolution of the Colebrook equation
A robust, fast and accurate method for solving the Colebrook-like equations
is presented. The algorithm is efficient for the whole range of parameters
involved in the Colebrook equation. The computations are not more demanding
than simplified approximations, but they are much more accurate. The algorithm
is also faster and more robust than the Colebrook solution expressed in term of
the Lambert W-function. Matlab and FORTRAN codes are provided
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