4,443 research outputs found
Quantification of coarse-graining error in Langevin and overdamped Langevin dynamics
In molecular dynamics and sampling of high dimensional Gibbs measures
coarse-graining is an important technique to reduce the dimensionality of the
problem. We will study and quantify the coarse-graining error between the
coarse-grained dynamics and an effective dynamics. The effective dynamics is a
Markov process on the coarse-grained state space obtained by a closure
procedure from the coarse-grained coefficients. We obtain error estimates both
in relative entropy and Wasserstein distance, for both Langevin and overdamped
Langevin dynamics. The approach allows for vectorial coarse-graining maps.
Hereby, the quality of the chosen coarse-graining is measured by certain
functional inequalities encoding the scale separation of the Gibbs measure. The
method is based on error estimates between solutions of (kinetic) Fokker-Planck
equations in terms of large-deviation rate functionals
On decompositions of non-reversible processes
Markov chains are studied in a formulation involving forces and fluxes.
First, the iso-dissipation force recently introduced in the physics literature
is investigated; we show that its non-uniqueness is linked to different notions
of duality giving rise to dual forces. We then study Hamiltonians associated to
variational formulations of Markov processes, and develop different
decompositions for them
Model reduction of Brownian oscillators: quantification of errors and long-time behaviour
A procedure for model reduction of stochastic ordinary differential equations
with additive noise was recently introduced in [Colangeli-Duong-Muntean,
Journal of Physics A: Mathematical and Theoretical, 2022], based on the
Invariant Manifold method and on the Fluctuation-Dissipation relation. A
general question thus arises as to whether one can rigorously quantify the
error entailed by the use of the reduced dynamics in place of the original one.
In this work we provide explicit formulae and estimates of the error in terms
of the Wasserstein distance, both in the presence or in the absence of a sharp
time-scale separation between the variables to be retained or eliminated from
the description, as well as in the long-time behaviour.
Keywords: Model reduction, Wasserstein distance, error estimates, coupled
Brownian oscillators, invariant manifold, Fluctuation-Dissipation relation
Cost optimisation of hybrid institutional incentives for promoting cooperation in finite populations
In this paper, we rigorously study the problem of cost optimisation of hybrid
(mixed) institutional incentives, which are a plan of actions involving the use
of reward and punishment by an external decision-maker, for maximising the
level (or guaranteeing at least a certain level) of cooperative behaviour in a
well-mixed, finite population of self-regarding individuals who interact via
cooperation dilemmas (Donation Game or Public Goods Game). We show that a mixed
incentive scheme can offer a more cost-efficient approach for providing
incentives while ensuring the same level or standard of cooperation in the
long-run. We establish the asymptotic behaviour (namely neutral drift, strong
selection, and infinite-population limits). We prove the existence of a phase
transition, obtaining the critical threshold of the strength of selection at
which the monotonicity of the cost function changes and providing an algorithm
for finding the optimal value of the individual incentive cost. Our analytical
results are illustrated with numerical investigations. Overall, our analysis
provides novel theoretical insights into the design of cost-efficient
institutional incentive mechanisms for promoting the evolution of cooperation
in stochastic systems
Efficiently Clustering Very Large Attributed Graphs
Attributed graphs model real networks by enriching their nodes with
attributes accounting for properties. Several techniques have been proposed for
partitioning these graphs into clusters that are homogeneous with respect to
both semantic attributes and to the structure of the graph. However, time and
space complexities of state of the art algorithms limit their scalability to
medium-sized graphs. We propose SToC (for Semantic-Topological Clustering), a
fast and scalable algorithm for partitioning large attributed graphs. The
approach is robust, being compatible both with categorical and with
quantitative attributes, and it is tailorable, allowing the user to weight the
semantic and topological components. Further, the approach does not require the
user to guess in advance the number of clusters. SToC relies on well known
approximation techniques such as bottom-k sketches, traditional graph-theoretic
concepts, and a new perspective on the composition of heterogeneous distance
measures. Experimental results demonstrate its ability to efficiently compute
high-quality partitions of large scale attributed graphs.Comment: This work has been published in ASONAM 2017. This version includes an
appendix with validation of our attribute model and distance function,
omitted in the converence version for lack of space. Please refer to the
published versio
Rate of convergence in the Smoluchowski-Kramers approximation for mean-field stochastic differential equations
In this paper we study a second-order mean-field stochastic differential
systems describing the movement of a particle under the influence of a
time-dependent force, a friction, a mean-field interaction and a space and
time-dependent stochastic noise. Using techniques from Malliavin calculus, we
establish explicit rates of convergence in the zero-mass limit
(Smoluchowski-Kramers approximation) in the -distances and in the total
variation distance for the position process, the velocity process and a
re-scaled velocity process to their corresponding limiting processes
Accounting conservatism and banking expertise on board of directors
Previous studies show mixed evidence of the role of banking expertise on the board of directors on accounting conservatism. In this paper, we add to this growing literature by providing an innovative way to measure banking expertise based on life-time working history in banks of all individual directors on the board. We find that accounting conservatism is negatively affected by banking expertise on the board. Also, the results indicate that banking expertise on the board has a more pronounced impact on accounting conservatism when firms have high bankruptcy risk and when firms have high financial leverage. The evidence has some implications for boards of directors
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