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Combinatorial optimization and metaheuristics
Today, combinatorial optimization is one of the youngest and most active areas of discrete mathematics. It is a branch of optimization in applied mathematics and computer science, related to operational research, algorithm theory and computational complexity theory. It sits at the intersection of several fields, including artificial intelligence, mathematics and software engineering. Its increasing interest arises for the fact that a large number of scientific and industrial problems can be formulated as abstract combinatorial optimization problems, through graphs and/or (integer) linear programs. Some of these problems have polynomial-time (“efficient”) algorithms, while most of them are NP-hard, i.e. it is not proved that they can be solved in polynomial-time. Mainly, it means that it is not possible to guarantee that an exact solution to the problem can be found and one has to settle for an approximate solution with known performance guarantees. Indeed, the goal of approximate methods is to find “quickly” (reasonable run-times), with “high” probability, provable “good” solutions (low error from the real optimal solution). In the last 20 years, a new kind of algorithm commonly called metaheuristics have emerged in this class, which basically try to combine heuristics in high level frameworks aimed at efficiently and effectively exploring the search space. This report briefly outlines the components, concepts, advantages and disadvantages of different metaheuristic approaches from a conceptual point of view, in order to analyze their similarities and differences. The two very significant forces of intensification and diversification, that mainly determine the behavior of a metaheuristic, will be pointed out. The report concludes by exploring the importance of hybridization and integration methods
Game Theoretical Interactions of Moving Agents
Game theory has been one of the most successful quantitative concepts to
describe social interactions, their strategical aspects, and outcomes. Among
the payoff matrix quantifying the result of a social interaction, the
interaction conditions have been varied, such as the number of repeated
interactions, the number of interaction partners, the possibility to punish
defective behavior etc. While an extension to spatial interactions has been
considered early on such as in the "game of life", recent studies have focussed
on effects of the structure of social interaction networks.
However, the possibility of individuals to move and, thereby, evade areas
with a high level of defection, and to seek areas with a high level of
cooperation, has not been fully explored so far. This contribution presents a
model combining game theoretical interactions with success-driven motion in
space, and studies the consequences that this may have for the degree of
cooperation and the spatio-temporal dynamics in the population. It is
demonstrated that the combination of game theoretical interactions with motion
gives rise to many self-organized behavioral patterns on an aggregate level,
which can explain a variety of empirically observed social behaviors
Balancing noise and plasticity in eukaryotic gene expression
Coupling the control of expression stochasticity (noise) to the ability of
expression change (plasticity) can alter gene function and influence
adaptation. A number of factors, such as transcription re-initiation, strong
chromatin regulation or genome neighboring organization, underlie this
coupling. However, these factors do not necessarily combine in equivalent ways
and strengths in all genes. Can we identify then alternative architectures that
modulate in distinct ways the linkage of noise and plasticity? Here we first
show that strong chromatin regulation, commonly viewed as a source of coupling,
can lead to plasticity without noise. The nature of this regulation is relevant
too, with plastic but noiseless genes being subjected to general activators
whereas plastic and noisy genes experience more specific repression.
Contrarily, in genes exhibiting poor transcriptional control, it is
translational efficiency what separates noise from plasticity, a pattern
related to transcript length. This additionally implies that genome neighboring
organization -as modifier- appears only effective in highly plastic genes. In
this class, we confirm bidirectional promoters (bipromoters) as a configuration
capable to reduce coupling by abating noise but also reveal an important
trade-off, since bipromoters also decrease plasticity. This presents ultimately
a paradox between intergenic distances and modulation, with short intergenic
distances both associated and disassociated to noise at different plasticity
levels. Balancing the coupling among different types of expression variability
appears as a potential shaping force of genome regulation and organization.
This is reflected in the use of different control strategies at genes with
different sets of functional constraints
On the genericity properties in networked estimation: Topology design and sensor placement
In this paper, we consider networked estimation of linear, discrete-time
dynamical systems monitored by a network of agents. In order to minimize the
power requirement at the (possibly, battery-operated) agents, we require that
the agents can exchange information with their neighbors only \emph{once per
dynamical system time-step}; in contrast to consensus-based estimation where
the agents exchange information until they reach a consensus. It can be
verified that with this restriction on information exchange, measurement fusion
alone results in an unbounded estimation error at every such agent that does
not have an observable set of measurements in its neighborhood. To over come
this challenge, state-estimate fusion has been proposed to recover the system
observability. However, we show that adding state-estimate fusion may not
recover observability when the system matrix is structured-rank (-rank)
deficient.
In this context, we characterize the state-estimate fusion and measurement
fusion under both full -rank and -rank deficient system matrices.Comment: submitted for IEEE journal publicatio
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