123 research outputs found
On Convergence Properties of Shannon Entropy
Convergence properties of Shannon Entropy are studied. In the differential
setting, it is shown that weak convergence of probability measures, or
convergence in distribution, is not enough for convergence of the associated
differential entropies. A general result for the desired differential entropy
convergence is provided, taking into account both compactly and uncompactly
supported densities. Convergence of differential entropy is also characterized
in terms of the Kullback-Liebler discriminant for densities with fairly general
supports, and it is shown that convergence in variation of probability measures
guarantees such convergence under an appropriate boundedness condition on the
densities involved. Results for the discrete setting are also provided,
allowing for infinitely supported probability measures, by taking advantage of
the equivalence between weak convergence and convergence in variation in this
setting.Comment: Submitted to IEEE Transactions on Information Theor
High Light Induced Disassembly of Photosystem II Supercomplexes in Arabidopsis Requires STN7-Dependent Phosphorylation of CP29
Photosynthetic oxidation of water and production of oxygen by photosystem II (PSII) in thylakoid membranes of plant chloroplasts is highly affected by changes in light intensities. To minimize damage imposed by excessive sunlight and sustain the photosynthetic activity PSII, organized in supercomplexes with its light harvesting antenna, undergoes conformational changes, disassembly and repair via not clearly understood mechanisms. We characterized the phosphoproteome of the thylakoid membranes from Arabidopsis thaliana wild type, stn7, stn8 and stn7stn8 mutant plants exposed to high light. The high light treatment of the wild type and stn8 caused specific increase in phosphorylation of Lhcb4.1 and Lhcb4.2 isoforms of the PSII linker protein CP29 at five different threonine residues. Phosphorylation of CP29 at four of these residues was not found in stn7 and stn7stn8 plants lacking the STN7 protein kinase. Blue native gel electrophoresis followed by immunological and mass spectrometric analyses of the membrane protein complexes revealed that the high light treatment of the wild type caused redistribution of CP29 from PSII supercomplexes to PSII dimers and monomers. A similar high-light-induced disassembly of the PSII supercomplexes occurred in stn8, but not in stn7 and stn7stn8. Transfer of the high-light-treated wild type plants to normal light relocated CP29 back to PSII supercomplexes. We postulate that disassembly of PSII supercomplexes in plants exposed to high light involves STN7-kinase-dependent phosphorylation of the linker protein CP29. Disruption of this adaptive mechanism can explain dramatically retarded growth of the stn7 and stn7stn8 mutants under fluctuating normal/high light conditions, as previously reported
Complete characterization of convergence to equilibrium for an inelastic Kac model
Pulvirenti and Toscani introduced an equation which extends the Kac
caricature of a Maxwellian gas to inelastic particles. We show that the
probability distribution, solution of the relative Cauchy problem, converges
weakly to a probability distribution if and only if the symmetrized initial
distribution belongs to the standard domain of attraction of a symmetric stable
law, whose index is determined by the so-called degree of
inelasticity, , of the particles: . This result is
then used: (1) To state that the class of all stationary solutions coincides
with that of all symmetric stable laws with index . (2) To determine
the solution of a well-known stochastic functional equation in the absence of
extra-conditions usually adopted
Probabilistic study of the speed of approach to equilibrium for an inelastic Kac model
This paper deals with a one--dimensional model for granular materials, which
boils down to an inelastic version of the Kac kinetic equation, with
inelasticity parameter . In particular, the paper provides bounds for
certain distances -- such as specific weighted --distances and the
Kolmogorov distance -- between the solution of that equation and the limit. It
is assumed that the even part of the initial datum (which determines the
asymptotic properties of the solution) belongs to the domain of normal
attraction of a symmetric stable distribution with characteristic exponent
\a=2/(1+p). With such initial data, it turns out that the limit exists and is
just the aforementioned stable distribution. A necessary condition for the
relaxation to equilibrium is also proved. Some bounds are obtained without
introducing any extra--condition. Sharper bounds, of an exponential type, are
exhibited in the presence of additional assumptions concerning either the
behaviour, near to the origin, of the initial characteristic function, or the
behaviour, at infinity, of the initial probability distribution function
Changes in Community Mobility in Older Men and Women. A 13-Year Prospective Study
Community mobility, defined as “moving [ones] self in the community and using public or private transportation”, has a unique ability to promote older peoples’ wellbeing by enabling independence and access to activity arenas for interaction with others. Early predictors of decreased community mobility among older men and women are useful in developing health promoting strategies. However, long-term prediction is rare, especially when it comes to including both public and private transportation. The present study describes factors associated with community mobility and decreased community mobility over time among older men and women. In total, 119 men and 147 women responded to a questionnaire in 1994 and 2007. Respondents were between 82 and 96 years old at follow-up. After 13 years, 40% of men and 43% of women had decreased community mobility, but 47% of men and 45% of women still experienced some independent community mobility. Cross-sectional independent community mobility among men was associated with higher ratings of subjective health, reporting no depression and more involvement in sport activities. Among women, cross-sectional independent community mobility was associated with better subjective health and doing more instrumental activities of daily living outside the home. Lower subjective health predicted decreased community mobility for both men and women, whereas self-reported health conditions did not. Consequently, general policies and individual interventions aiming to improve community mobility should consider older persons’ subjective health
Differential Phosphorylation of Ribosomal Proteins in Arabidopsis thaliana Plants during Day and Night
Protein synthesis in plants is characterized by increase in the translation rates for numerous proteins and central metabolic enzymes during the day phase of the photoperiod. The detailed molecular mechanisms of this diurnal regulation are unknown, while eukaryotic protein translation is mainly controlled at the level of ribosomal initiation complexes, which also involves multiple events of protein phosphorylation. We characterized the extent of protein phosphorylation in cytosolic ribosomes isolated from leaves of the model plant Arabidopsis thaliana harvested during day or night. Proteomic analyses of preparations corresponding to both phases of the photoperiod detected phosphorylation at eight serine residues in the C-termini of six ribosomal proteins: S2-3, S6-1, S6-2, P0-2, P1 and L29-1. This included previously unknown phosphorylation of the 40S ribosomal protein S6 at Ser-231. Relative quantification of the phosphorylated peptides using stable isotope labeling and mass spectrometry revealed a 2.2 times increase in the day/night phosphorylation ratio at this site. Phosphorylation of the S6-1 and S6-2 variants of the same protein at Ser-240 increased by the factors of 4.2 and 1.8, respectively. The 1.6 increase in phosphorylation during the day was also found at Ser-58 of the 60S ribosomal protein L29-1. It is suggested that differential phosphorylation of the ribosomal proteins S6-1, S6-2 and L29-1 may contribute to modulation of the diurnal protein synthesis in plants
Uniform Boundary Harnack Principle for Rotationally Symmetric Levy processes in General Open Sets
In this paper we prove the uniform boundary Harnack principle in general open
sets for harmonic functions with respect to a large class of rotationally
symmetric purely discontinuous L\'evy processes.Comment: 21 Page
Large-deviation principles, stochastic effective actions, path entropies, and the structure and meaning of thermodynamic descriptions
The meaning of thermodynamic descriptions is found in large-deviations
scaling of the fluctuations probabilities. The primary large-deviations rate
function is the entropy, which is the basis for both fluctuation theorems and
for characterizing the thermodynamic interactions of systems. Freidlin-Wentzell
theory provides a general formulation of large-deviations scaling for
non-equilibrium stochastic processes, through a representation in terms of a
Hamiltonian dynamical system. A number of related methods now exist to
construct the Freidlin-Wentzell Hamiltonian for many kinds of stochastic
processes; one method due to Doi and Peliti, appropriate to integer counting
statistics, is widely used in reaction-diffusion theory.
Using these tools together with a path-entropy method due to Jaynes, we show
how to construct entropy functions that both express large-deviations scaling
of fluctuations, and describe system-environment interactions, for discrete
stochastic processes either at or away from equilibrium. A collection of
variational methods familiar within quantum field theory, but less commonly
applied to the Doi-Peliti construction, is used to define a "stochastic
effective action", which is the large-deviations rate function for arbitrary
non-equilibrium paths.
We show how common principles of entropy maximization, applied to different
ensembles of states or of histories, lead to different entropy functions and
different sets of thermodynamic state variables. Yet the relations of among all
these levels of description may be constructed explicitly and understood in
terms of information conditions. The example systems considered introduce
methods that may be used to systematically construct descriptions with all the
features familiar from equilibrium thermodynamics, for a much wider range of
systems describable by stochastic processes
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