10,889 research outputs found
Robust Moment Closure Method for the Chemical Master Equation
The Chemical Master Equation (CME) is used to stochastically model
biochemical reaction networks, under the Markovian assumption. The low-order
statistical moments induced by the CME are often the key quantities that one is
interested in. However, in most cases, the moments equation is not closed; in
the sense that the first moments depend on the higher order moments, for
any positive integer . In this paper, we develop a moment closure technique
in which the higher order moments are approximated by an affine function of the
lower order moments. We refer to such functions as the affine Moment Closure
Functions (MCF) and prove that they are optimal in the worst-case context, in
which no a priori information on the probability distribution is available.
Furthermore, we cast the problem of finding the optimal affine MCF as a linear
program, which is tractable. We utilize the affine MCFs to derive a finite
dimensional linear system that approximates the low-order moments. We quantify
the approximation error in terms of the induced norm of some
linear system. Our results can be effectively used to approximate the low-order
moments and characterize the noise properties of the biochemical network under
study
On tests of general relativity with binary radio pulsars
The timing of radio pulsars in binary systems provides a superb testing
ground of general relativity. Here we propose a Bayesian approach to carry out
these tests, and a relevant efficient numerical implementation, that has
several conceptual and practical advantages with respect to traditional methods
based on least-square-fits that have been used so far: (i) it accounts for the
actual structure of the likelihood function - and it is not predicated on the
Laplace approximation which is implicitly built in least-square fits that can
potentially bias the inference - (ii) it provides the ratio of the evidences of
any two models under consideration as the statistical quantity to compare
different theories, and (iii) it allows us to put joint constraints from the
monitoring of multiple systems, that can be expressed in terms of ratio of
evidences or probability intervals of global (thus not system-dependent)
parameters of the theory, if any exists. Our proposed approach optimally
exploits the progress in timing of radio pulsars and the increase in the number
of observed systems. We demonstrate the power of this framework using simulated
data sets that are representative of current observations.Comment: Accepted for publication on MNRAS Letter
Boolean versus continuous dynamics on simple two-gene modules
We investigate the dynamical behavior of simple modules composed of two genes
with two or three regulating connections. Continuous dynamics for mRNA and
protein concentrations is compared to a Boolean model for gene activity. Using
a generalized method, we study within a single framework different continuous
models and different types of regulatory functions, and establish conditions
under which the system can display stable oscillations. These conditions
concern the time scales, the degree of cooperativity of the regulating
interactions, and the signs of the interactions. Not all models that show
oscillations under Boolean dynamics can have oscillations under continuous
dynamics, and vice versa.Comment: 8 pages, 10 figure
Gamma Ray Burst Prompt correlations
The mechanism responsible for the prompt emission of gamma-ray bursts (GRBs)
is still a debated issue. The prompt phase-related GRB correlations can allow
to discriminate among the most plausible theoretical models explaining this
emission. We present an overview of the observational two-parameter
correlations, their physical interpretations, their use as redshift estimators
and possibly as cosmological tools. The nowadays challenge is to make GRBs, the
farthest stellar-scaled objects observed (up to redshift ), standard
candles through well established and robust correlations. However, GRBs
spanning several orders of magnitude in their energetics are far from being
standard candles. We describe the advances in the prompt correlation research
in the past decades, with particular focus paid to the discoveries in the last
20 years
Solitons and nonsmooth diffeomorphisms in conformal nets
We show that any solitonic representation of a conformal (diffeomorphism
covariant) net on S^1 has positive energy and construct an uncountable family
of mutually inequivalent solitonic representations of any conformal net, using
nonsmooth diffeomorphisms. On the loop group nets, we show that these
representations induce representations of the subgroup of loops compactly
supported in S^1 \ {-1} which do not extend to the whole loop group.
In the case of the U(1)-current net, we extend the diffeomorphism covariance
to the Sobolev diffeomorphisms D^s(S^1), s > 2, and show that the
positive-energy vacuum representations of Diff_+(S^1) with integer central
charges extend to D^s(S^1). The solitonic representations constructed above for
the U(1)-current net and for Virasoro nets with integral central charge are
continuously covariant with respect to the stabilizer subgroup of Diff_+(S^1)
of -1 of the circle.Comment: 33 pages, 3 TikZ figure
An Interpretation of CCS into Ludics
Abstract Starting from works aimed at extending the Curry-Howard correspondence to process calculi through linear logic, we give another Curry-Howard counterpart for Milner's Calculus of Communicating Systems (CCS) by taking Ludics as the target system. Indeed interaction, Ludics' dynamic, allows to fully represent both the non-determinism and non-confluence of the calculus. We give an interpretation of CCS processes into carefully defined behaviours of Ludics using a new construction, called directed behaviour, that allows controlled interaction paths by using pruned designs. We characterize the execution of processes as interaction on behaviours, by implicitly representing the causal order and conflict relation of event structures. As a direct consequence, we are also able to interpret deadlocked processes, and identify deadlock-free ones
Entanglement R\'enyi Entropies from Ballistic Fluctuation Theory: the free fermionic case
The large-scale behaviour of entanglement entropy in finite-density states,
in and out of equilibrium, can be understood using the physical picture of
particle pairs. However, the full theoretical origin of this picture is not
fully established yet. In this work, we clarify this picture by investigating
entanglement entropy using its connection with the large-deviation theory for
thermodynamic and hydrodynamic fluctuations. We apply the universal framework
of Ballistic Fluctuation Theory (BFT), based the Euler hydrodynamics of the
model, to correlation functions of \emph{branch-point twist fields}, the
starting point for computing R\'enyi entanglement entropies within the replica
approach. Focusing on free fermionic systems in order to illustrate the ideas,
we show that both the equilibrium behavior and the dynamics of R\'enyi
entanglement entropies can be fully derived from the BFT. In particular, we
emphasise that long-range correlations develop after quantum quenches, and
accounting for these explain the structure of the entanglement growth. We
further show that this growth is related to fluctuations of charge transport,
generalising to quantum quenches the relation between charge fluctuations and
entanglement observed earlier. The general ideas we introduce suggest that the
large-scale behaviour of entanglement has its origin within hydrodynamic
fluctuations.Comment: 53 pages, 2 figure
Entanglement Rényi Entropies from Ballistic Fluctuation Theory: the free fermionic case
The large-scale behaviour of entanglement entropy in finite-density states, in and out of equilibrium, can be understood using the physical picture of particle pairs. However, the full theoretical origin of this picture is not fully established yet. In this work, we clarify this picture by investigating entanglement entropy using its connection with the large-deviation theory for thermodynamic and hydrodynamic fluctuations. We apply the universal framework of Ballistic Fluctuation Theory (BFT), based the Euler hydrodynamics of the model, to correlation functions of branch-point twist fields, the starting point for computing Rényi entanglement entropies within the replica approach. Focusing on free fermionic systems in order to illustrate the ideas, we show that both the equilibrium behavior and the dynamics of Rényi entanglement entropies can be fully derived from the BFT. In particular, we emphasise that long-range correlations develop after quantum quenches, and accounting for these explain the structure of the entanglement growth. We further show that this growth is related to fluctuations of charge transport, generalising to quantum quenches the relation between charge fluctuations and entanglement observed earlier. The general ideas we introduce suggest that the large-scale behaviour of entanglement has its origin within hydrodynamic fluctuations.</p
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