On the Hausdorff dimension of invariant measures of weakly contracting on average measurable IFS

We consider measures which are invariant under a measurable iterated function system with positive, place-dependent probabilities in a separable metric space. We provide an upper bound of the Hausdorff dimension of such a measure if it is ergodic. We also prove that it is ergodic iff the related skew product is.Comment: 16 pages; to appear in Journal of Stat. Phy

Statistical Consequences of Devroye Inequality for Processes. Applications to a Class of Non-Uniformly Hyperbolic Dynamical Systems

In this paper, we apply Devroye inequality to study various statistical estimators and fluctuations of observables for processes. Most of these observables are suggested by dynamical systems. These applications concern the co-variance function, the integrated periodogram, the correlation dimension, the kernel density estimator, the speed of convergence of empirical measure, the shadowing property and the almost-sure central limit theorem. We proved in \cite{CCS} that Devroye inequality holds for a class of non-uniformly hyperbolic dynamical systems introduced in \cite{young}. In the second appendix we prove that, if the decay of correlations holds with a common rate for all pairs of functions, then it holds uniformly in the function spaces. In the last appendix we prove that for the subclass of one-dimensional systems studied in \cite{young} the density of the absolutely continuous invariant measure belongs to a Besov space.Comment: 33 pages; companion of the paper math.DS/0412166; corrected version; to appear in Nonlinearit

Roles for common MLL/COMPASS subunits and the 19S proteasome in regulating CIITA pIV and MHC class II gene expression and promoter methylation

<p>Abstract</p> <p>Background</p> <p>Studies indicate that the 19S proteasome contributes to chromatin reorganization, independent of the role the proteasome plays in protein degradation. We have previously shown that components of the 19S proteasome are crucial for regulating inducible histone activation events in mammalian cells. The 19S ATPase Sug1 binds to histone-remodeling enzymes, and in the absence of Sug1, a subset of activating epigenetic modifications including histone H3 acetylation, H3 lysine 4 trimethylation and H3 arginine 17 dimethylation are inhibited at cytokine-inducible major histocompatibilty complex (MHC)-II and class II transactivator (CIITA) promoters, implicating Sug1 in events required to initiate mammalian transcription.</p> <p>Results</p> <p>Our previous studies indicate that H3 lysine 4 trimethylation at cytokine-inducible MHC-II and CIITA promoters is dependent on proteolytic-independent functions of 19S ATPases. In this report, we show that multiple common subunits of the mixed lineage leukemia (MLL)/complex of proteins associated with Set I (COMPASS) complexes bind to the inducible MHC-II and CIITA promoters; that overexpressing a single common MLL/COMPASS subunit significantly enhances promoter activity and MHC-II <it>HLA-DRA </it>expression; and that these common subunits are important for H3 lysine 4 trimethylation at MHC-II and CIITA promoters. In addition, we show that H3 lysine 27 trimethylation, which is inversely correlated with H3 lysine 4 trimethylation, is significantly elevated in the presence of diminished 19S ATPase Sug1.</p> <p>Conclusion</p> <p>Taken together, these experiments suggest that the 19S proteasome plays a crucial role in the initial reorganization of events enabling the relaxation of the repressive chromatin structure surrounding inducible promoters.</p

Continuity of the Maximum-Entropy Inference

We study the inverse problem of inferring the state of a finite-level quantum system from expected values of a fixed set of observables, by maximizing a continuous ranking function. We have proved earlier that the maximum-entropy inference can be a discontinuous map from the convex set of expected values to the convex set of states because the image contains states of reduced support, while this map restricts to a smooth parametrization of a Gibbsian family of fully supported states. Here we prove for arbitrary ranking functions that the inference is continuous up to boundary points. This follows from a continuity condition in terms of the openness of the restricted linear map from states to their expected values. The openness condition shows also that ranking functions with a discontinuous inference are typical. Moreover it shows that the inference is continuous in the restriction to any polytope which implies that a discontinuity belongs to the quantum domain of non-commutative observables and that a geodesic closure of a Gibbsian family equals the set of maximum-entropy states. We discuss eight descriptions of the set of maximum-entropy states with proofs of accuracy and an analysis of deviations.Comment: 34 pages, 1 figur

The Dirac Equation Is Separable On The Dyon Black Hole Metric

Using the tetrad formalism, we carry out the separation of variables for the massive complex Dirac equation in the gravitational and electromagnetic field of a four-parameter (mass, angular momentum, electric and magnetic charges) black hole.Comment: 13 page

The [CII] 158 um Line Deficit in Ultraluminous Infrared Galaxies Revisited

We present a study of the [CII] 157.74 um fine-structure line in a sample of 15 ultraluminous infrared (IR) galaxies (L_IR>10^12 Lsun; ULIRGs) using the Long Wavelength Spectrometer (LWS) on the Infrared Space Observatory (ISO). We confirm the observed order of magnitude deficit (compared to normal and starburst galaxies) in the strength of the [CII] line relative to the far-IR dust continuum emission found in our initial report (Luhman et al. 1998), but here with a sample that is twice as large. This result suggests that the deficit is a general phenomenon affecting 4/5 ULIRGs. We present an analysis using observations of generally acknowledged photodissociation region (PDR) tracers ([CII], [OI] 63 and 145 um, and FIR continuum emission), which suggests that a high UV flux G_o incident on a moderate density n PDR could explain the deficit. However, comparisons with other ULIRG observations, including CO (1-0), [CI] (1-0), and 6.2 um polycyclic aromatic hydrocarbon (PAH) emission, suggest that high G_o/n PDRs alone cannot produce a self-consistent solution that is compatible with all of the observations. We propose that non-PDR contributions to the FIR continuum can explain the apparent [CII] deficiency. Here, unusually high G_o and/or n physical conditions in ULIRGs as compared to those in normal and starburst galaxies are not required to explain the [CII] deficit. Dust-bounded photoionization regions, which generate much of the FIR emission but do not contribute significant [CII] emission, offer one possible physical origin for this additional non-PDR component. Such environments may also contribute to the observed suppression of FIR fine-structure emission from ionized gas and PAHs, as well as the warmer FIR colors found in ULIRGs. The implications for observations at higher redshifts are also revisited.Comment: to be published in The Astrophysical Journal, 58 page

Long COVID in children and young after infection or reinfection with the Omicron variant: a prospective observational study

To describe the prevalence of long COVID in children infected for the first time (n = 332) or reinfected (n = 243) with Omicron compared with test-negative children (n = 311). Overall, 12%-16% of those infected with Omicron met the research definition of long COVID at 3 and 6 months after infection, with no evidence of difference between cases of first positive and reinfected (Pχ2 = 0.17)

Multidisciplinary Design Optimization of an Extreme Aspect Ration HALE UAV

Development of High Altitude Long Endurance (HALE) aircraft systems is part of a vision for a low cost communications/surveillance capability. Applications of a multi payload aircraft operating for extended periods at stratospheric altitudes span military and civil genres and support battlefield operations, communications, atmospheric or agricultural monitoring, surveillance, and other disciplines that may currently require satellite-based infrastructure. The central goal of this research was the development of a multidisciplinary tool for analysis, design, and optimization of HALE UAVs, facilitating the study of a novel configuration concept. Applying design ideas stemming from a unique WWII-era project, a pinned wing HALE aircraft would employ self-supporting wing segments assembled into one overall flying wing. When wrapped in an optimization routine, the integrated design environment shows potential for a 17.3% reduction in weight when wing thickness to chord ratio, aspect ratio, wing loading, and power to weight ratio are included as optimizer-controlled design variables. Investigation of applying the sustained day/night mission requirement and improved technology factors to the design shows that there are potential benefits associated with a segmented or pinned wing. As expected, wing structural weight is reduced, but benefits diminish as higher numbers of wing segments are considered. For an aircraft consisting of six wing segments, a maximum of 14.2% reduction in gross weight over an advanced technology optimal baseline is predicted

A Generalization of Quantum Stein's Lemma

We present a generalization of quantum Stein's Lemma to the situation in which the alternative hypothesis is formed by a family of states, which can moreover be non-i.i.d.. We consider sets of states which satisfy a few natural properties, the most important being the closedness under permutations of the copies. We then determine the error rate function in a very similar fashion to quantum Stein's Lemma, in terms of the quantum relative entropy. Our result has two applications to entanglement theory. First it gives an operational meaning to an entanglement measure known as regularized relative entropy of entanglement. Second, it shows that this measure is faithful, being strictly positive on every entangled state. This implies, in particular, that whenever a multipartite state can be asymptotically converted into another entangled state by local operations and classical communication, the rate of conversion must be non-zero. Therefore, the operational definition of multipartite entanglement is equivalent to its mathematical definition.Comment: 30 pages. (see posting by M. Piani arXiv:0904.2705 for a different proof of the strict positiveness of the regularized relative entropy of entanglement on every entangled state). published version