2,091 research outputs found
DNA viewed as an out-of-equilibrium structure
The complexity of the primary structure of human DNA is explored using
methods from nonequilibrium statistical mechanics, dynamical systems theory and
information theory. The use of chi-square tests shows that DNA cannot be
described as a low order Markov chain of order up to . Although detailed
balance seems to hold at the level of purine-pyrimidine notation it fails when
all four basepairs are considered, suggesting spatial asymmetry and
irreversibility. Furthermore, the block entropy does not increase linearly with
the block size, reflecting the long range nature of the correlations in the
human genomic sequences. To probe locally the spatial structure of the chain we
study the exit distances from a specific symbol, the distribution of recurrence
distances and the Hurst exponent, all of which show power law tails and long
range characteristics. These results suggest that human DNA can be viewed as a
non-equilibrium structure maintained in its state through interactions with a
constantly changing environment. Based solely on the exit distance distribution
accounting for the nonequilibrium statistics and using the Monte Carlo
rejection sampling method we construct a model DNA sequence. This method allows
to keep all long range and short range statistical characteristics of the
original sequence. The model sequence presents the same characteristic
exponents as the natural DNA but fails to capture point-to-point details
Supersymmetric probability distributions
We use anticommuting variables to study probability distributions of random
variables, that are solutions of Langevin's equation. We show that the
probability density always enjoys "worldpoint supersymmetry". The partition
function, however, may not. We find that the domain of integration can acquire
a boundary, that implies that the auxiliary field has a non-zero expectation
value, signalling spontaneous supersymmetry breaking. This is due to the
presence of "fermionic" zeromodes, whose contribution cannot be cancelled by a
surface term. This we prove by an explicit calculation of the regularized
partition function, as well as by computing the moments of the auxiliary field
and checking whether they satisfy the identities implied by Wick's theorem.
Nevertheless, supersymmetry manifests itself in the identities that are
satisfied by the moments of the scalar, whose expressions we can calculate,for
all values of the coupling constant. We also provide some quantitative
estimates concerning the visibility of supersymmetry breaking effects in the
identities for the moments and remark that the shape of the distribution of the
auxiliary field can influence quite strongly how easy it would be to mask them,
since the expectation value of the auxiliary field doesn't coincide with its
typical value.Comment: LaTeX2e: 24 pages, 7 figure
Derrick's theorem beyond a potential
Scalar field theories with derivative interactions are known to possess
solitonic excitations, but such solitons are generally unsatisfactory because
the effective theory fails precisely where nonlinearities responsible for the
solitons are important. A new class of theories possessing (internal) galilean
invariance can in principle bypass this difficulty. Here, we show that these
galileon theories do not possess stable solitonic solutions. As a by-product,
we show that no stable solitons exist for a different class of derivatively
coupled theories, describing for instance the infrared dynamics of superfluids,
fluids, solids and some k-essence models.Comment: 4 page
Superluminality in DGP
We reconsider the issue of superluminal propagation in the DGP model of
infrared modified gravity. Superluminality was argued to exist in certain
otherwise physical backgrounds by using a particular, physically relevant
scaling limit of the theory. In this paper, we exhibit explicit
five-dimensional solutions of the full theory that are stable against small
fluctuations and that indeed support superluminal excitations. The scaling
limit is neither needed nor invoked in deriving the solutions or in the
analysis of its small fluctuations. To be certain that the superluminality
found here is physical, we analyze the retarded Green's function of the scalar
excitations, finding that it is causal and stable, but has support on a widened
light-cone. We propose to use absence of superluminal propagation as a method
to constrain the parameters of the DGP model. As a first application of the
method, we find that whenever the 4D energy density is a pure cosmological
constant and a hierarchy of scales exists between the 4D and 5D Planck masses,
superluminal propagation unavoidably occurs.Comment: 23 pages. Minor corrections. Version to appear in JHE
Model error and sequential data assimilation. A deterministic formulation
Data assimilation schemes are confronted with the presence of model errors
arising from the imperfect description of atmospheric dynamics. These errors
are usually modeled on the basis of simple assumptions such as bias, white
noise, first order Markov process. In the present work, a formulation of the
sequential extended Kalman filter is proposed, based on recent findings on the
universal deterministic behavior of model errors in deep contrast with previous
approaches (Nicolis, 2004). This new scheme is applied in the context of a
spatially distributed system proposed by Lorenz (1996). It is found that (i)
for short times, the estimation error is accurately approximated by an
evolution law in which the variance of the model error (assumed to be a
deterministic process) evolves according to a quadratic law, in agreement with
the theory. Moreover, the correlation with the initial condition error appears
to play a secondary role in the short time dynamics of the estimation error
covariance. (ii) The deterministic description of the model error evolution,
incorporated into the classical extended Kalman filter equations, reveals that
substantial improvements of the filter accuracy can be gained as compared with
the classical white noise assumption. The universal, short time, quadratic law
for the evolution of the model error covariance matrix seems very promising for
modeling estimation error dynamics in sequential data assimilation
Energy's and amplitudes' positivity
In QFT, the null energy condition (NEC) for a classical field configuration
is usually associated with that configuration's stability against small
perturbations, and with the sub-luminality of these. Here, we exhibit an
effective field theory that allows for stable NEC-violating solutions with
exactly luminal excitations only. The model is the recently introduced
`galileon', or more precisely its conformally invariant version. We show that
the theory's low-energy S-matrix obeys standard positivity as implied by
dispersion relations. However we also show that if the relevant NEC-violating
solution is inside the effective theory, then other (generic) solutions allow
for superluminal signal propagation. While the usual association between
sub-luminality and positivity is not obeyed by our example, that between NEC
and sub-luminality is, albeit in a less direct way than usual.Comment: 21 pages. v2: Typos in eq. (2.41) and (2.41) corrected; discussion of
section 2.3 modified accordingly. Other sections and conclusions unchanged.
Matches the Erratum published in JHE
Reactive dynamics on fractal sets: anomalous fluctuations and memory effects
We study the effect of fractal initial conditions in closed reactive systems
in the cases of both mobile and immobile reactants. For the reaction , in the absence of diffusion, the mean number of particles is shown to
decay exponentially to a steady state which depends on the details of the
initial conditions. The nature of this dependence is demonstrated both
analytically and numerically. In contrast, when diffusion is incorporated, it
is shown that the mean number of particles decays asymptotically as
, the memory of the initial conditions being now carried by the
dynamical power law exponent. The latter is fully determined by the fractal
dimension of the initial conditions.Comment: 7 pages, 2 figures, uses epl.cl
More on gapped Goldstones at finite density: More gapped Goldstones
It was recently argued that certain relativistic theories at finite density
can exhibit an unconventional spectrum of Goldstone excitations, with gapped
Goldstones whose gap is exactly calculable in terms of the symmetry algebra. We
confirm this result as well as previous ones concerning gapless Goldstones for
non-relativistic systems via a coset construction of the low-energy effective
field theory. Moreover, our analysis unveils additional gapped Goldstones,
naturally as light as the others, but this time with a model-dependent gap.
Their exact number cannot be inferred solely from the symmetry breaking pattern
either, but rather depends on the details of the symmetry breaking mechanism--a
statement that we explicitly verify with a number of examples. Along the way we
provide what we believe to be a particularly transparent interpretation of the
so-called inverse-Higgs constraints for spontaneously broken spacetime
symmetries.Comment: 50 pages. v2: Fixed several typos in equations. Minor modifications
to the counting rule. Acknowledgements and references added. Matches JHEP
versio
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