2,449 research outputs found
On large deviation properties of Erdos-Renyi random graphs
We show that large deviation properties of Erd\"os-R\'enyi random graphs can
be derived from the free energy of the -state Potts model of statistical
mechanics. More precisely the Legendre transform of the Potts free energy with
respect to is related to the component generating function of the graph
ensemble. This generalizes the well-known mapping between typical properties of
random graphs and the limit of the Potts free energy. For
exponentially rare graphs we explicitly calculate the number of components, the
size of the giant component, the degree distributions inside and outside the
giant component, and the distribution of small component sizes. We also perform
numerical simulations which are in very good agreement with our analytical
work. Finally we demonstrate how the same results can be derived by studying
the evolution of random graphs under the insertion of new vertices and edges,
without recourse to the thermodynamics of the Potts model.Comment: 38 pages, 9 figures, Latex2e, corrected and extended version
including numerical simulation result
Blackjack in Holland Casino's: Basic, optimal and winning strategies
This paper considers the cardgame Blackjack according to the rules of Holland Casino's in the Netherlands. Expected gains of strategies are derived with simulation and also with analytic tools. New effiency concepts based on the gains of the basic and the optimal strategy are introduced. A general method for approximating expected gains for strategies based on card counting systems is developed. In particular it is shown how Thorp's Ten Count system and the High Low system should be used in order to get positive expected gains. This implies that in Holland Casino's it is possible to beat the dealer in practice.Gambling;Probability;60E05;Black Jack;62J05;Linear Regression;probability theory
Computing Probabilistic Bisimilarity Distances
Behavioural equivalences like probabilistic bisimilarity rely on the transition probabilities and, as a result, are sensitive to minuscule changes of those probabilities. Such behavioural equivalences are not robust, as first observed by Giacalone, Jou and Smolka. Probabilistic bisimilarity distances, a robust quantitative generalization of probabilistic bisimilarity, capture the similarity of the behaviour of states of a probabilistic model. The smaller the distance, the more alike the states behave. In particular, states are probabilistic bisimilar if and only if the distance between them is zero. In this dissertation, we focus on algorithms to compute probabilistic bisimilarity distances for two probabilistic models: labelled Markov chains and probabilistic automata.
In the late nineties, Desharnais, Gupta, Jagadeesan and Panangaden defined probabilistic bisimilarity distances on the states of a labelled Markov chain. This provided a quantitative generalization of probabilistic bisimilarity, which was introduced by Larsen and Skou a decade earlier. Several algorithms to approximate and compute these probabilistic bisimilarity distances have been put forward. In this dissertation, we correct and generalize some of these policy iteration algorithms. Moreover, we develop several new algorithms which have better performance in practice and can handle much larger systems.
Similarly, Deng, Chothia, Palamidessi and Pang presented probabilistic bisimilarity distances on the states of a probabilistic automaton. This provided a robust quantitative generalization of probabilistic bisimilarity introduced by Segala and Lynch. Although the complexity of computing probabilistic bisimilarity distances for probabilistic automata has already been studied and shown to be in NP coNP and PPAD, we are not aware of any practical algorithms to compute those distances. In this dissertation, we provide several key results that may prove to be useful for the development of algorithms to compute probabilistic bisimilarity distances for probabilistic automata. In particular, we present a polynomial time algorithm that decides distance one. Furthermore, we give an alternative characterization of the probabilistic bisimilarity distances as a basis for a policy iteration algorithm
Global supply chains of high value low volume products
Imperial Users onl
Reclaiming the energy of a schedule: models and algorithms
We consider a task graph to be executed on a set of processors. We assume
that the mapping is given, say by an ordered list of tasks to execute on each
processor, and we aim at optimizing the energy consumption while enforcing a
prescribed bound on the execution time. While it is not possible to change the
allocation of a task, it is possible to change its speed. Rather than using a
local approach such as backfilling, we consider the problem as a whole and
study the impact of several speed variation models on its complexity. For
continuous speeds, we give a closed-form formula for trees and series-parallel
graphs, and we cast the problem into a geometric programming problem for
general directed acyclic graphs. We show that the classical dynamic voltage and
frequency scaling (DVFS) model with discrete modes leads to a NP-complete
problem, even if the modes are regularly distributed (an important particular
case in practice, which we analyze as the incremental model). On the contrary,
the VDD-hopping model leads to a polynomial solution. Finally, we provide an
approximation algorithm for the incremental model, which we extend for the
general DVFS model.Comment: A two-page extended abstract of this work appeared as a short
presentation in SPAA'2011, while the long version has been accepted for
publication in "Concurrency and Computation: Practice and Experience
Blackjack in Holland Casino's:Basic, optimal and winning strategies
This paper considers the cardgame Blackjack according to the rules of Holland Casino's in the Netherlands. Expected gains of strategies are derived with simulation and also with analytic tools. New effiency concepts based on the gains of the basic and the optimal strategy are introduced. A general method for approximating expected gains for strategies based on card counting systems is developed. In particular it is shown how Thorp's Ten Count system and the High Low system should be used in order to get positive expected gains. This implies that in Holland Casino's it is possible to beat the dealer in practice.
Hot Streaks in Artistic, Cultural, and Scientific Careers
The hot streak, loosely defined as winning begets more winnings, highlights a
specific period during which an individual's performance is substantially
higher than her typical performance. While widely debated in sports, gambling,
and financial markets over the past several decades, little is known if hot
streaks apply to individual careers. Here, building on rich literature on
lifecycle of creativity, we collected large-scale career histories of
individual artists, movie directors and scientists, tracing the artworks,
movies, and scientific publications they produced. We find that, across all
three domains, hit works within a career show a high degree of temporal
regularity, each career being characterized by bursts of high-impact works
occurring in sequence. We demonstrate that these observations can be explained
by a simple hot-streak model we developed, allowing us to probe quantitatively
the hot streak phenomenon governing individual careers, which we find to be
remarkably universal across diverse domains we analyzed: The hot streaks are
ubiquitous yet unique across different careers. While the vast majority of
individuals have at least one hot streak, hot streaks are most likely to occur
only once. The hot streak emerges randomly within an individual's sequence of
works, is temporally localized, and is unassociated with any detectable change
in productivity. We show that, since works produced during hot streaks garner
significantly more impact, the uncovered hot streaks fundamentally drives the
collective impact of an individual, ignoring which leads us to systematically
over- or under-estimate the future impact of a career. These results not only
deepen our quantitative understanding of patterns governing individual
ingenuity and success, they may also have implications for decisions and
policies involving predicting and nurturing individuals with lasting impact
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