Limited Range Fractality of Randomly Adsorbed Rods

Multiple resolution analysis of two dimensional structures composed of randomly adsorbed penetrable rods, for densities below the percolation threshold, has been carried out using box-counting functions. It is found that at relevant resolutions, for box-sizes, $r$, between cutoffs given by the average rod length and the average inter-rod distance $r_1$, these systems exhibit apparent fractal behavior. It is shown that unlike the case of randomly distributed isotropic objects, the upper cutoff $r_1$ is not only a function of the coverage but also depends on the excluded volume, averaged over the orientational distribution. Moreover, the apparent fractal dimension also depends on the orientational distributions of the rods and decreases as it becomes more anisotropic. For box sizes smaller than the box counting function is determined by the internal structure of the rods, whether simple or itself fractal. Two examples are considered - one of regular rods of one dimensional structure and rods which are trimmed into a Cantor set structure which are fractals themselves. The models examined are relevant to adsorption of linear molecules and fibers, liquid crystals, stress induced fractures and edge imperfections in metal catalysts. We thus obtain a distinction between two ranges of length scales: $r$ where the internal structure of the adsorbed objects is probed, and $< r < r_1$ where their distribution is probed, both of which may exhibit fractal behavior. This distinction is relevant to the large class of systems which exhibit aggregation of a finite density of fractal-like clusters, which includes surface growth in molecular beam epitaxy and diffusion-limited-cluster-cluster-aggregation models.Comment: 10 pages, 7 figures. More info available at http://www.fh.huji.ac.il/~dani/ or http://www.fiz.huji.ac.il/staff/acc/faculty/biham or http://chem.ch.huji.ac.il/employee/avnir/iavnir.htm . Accepted for publication in J. Chem. Phy

CPT Violation Implies Violation of Lorentz Invariance

An interacting theory that violates CPT invariance necessarily violates Lorentz invariance. On the other hand, CPT invariance is not sufficient for out-of-cone Lorentz invariance. Theories that violate CPT by having different particle and antiparticle masses must be nonlocal.Comment: Minor changes in the published versio

Quantum field theory with a fundamental length: A general mathematical framework

We review and develop a mathematical framework for nonlocal quantum field theory (QFT) with a fundamental length. As an instructive example, we reexamine the normal ordered Gaussian function of a free field and find the primitive analyticity domain of its n-point vacuum expectation values. This domain is smaller than the usual future tube of local QFT, but we prove that in difference variables, it has the same structure of a tube whose base is the (n-1)-fold product of a Lorentz invariant region. It follows that this model satisfies Wightman-type axioms with an exponential high-energy bound which does not depend on n, contrary to the claims in the literature. In our setting, the Wightman generalized functions are defined on test functions analytic in the complex l-neighborhood of the real space, where l is an n-independent constant playing the role of a fundamental length, and the causality condition is formulated with the use of an analogous function space associated with the light cone. In contrast to the scheme proposed by Bruning and Nagamachi [J. Math. Phys. 45 (2004) 2199] in terms of ultra-hyperfunctions, the presented theory obviously becomes local as l tends to zero.Comment: 25 pages, v2: updated to match J. Math. Phys. versio

Verification of CPT-invariance of QED bound states for the production of muonium or antimuonium in scattering of electrons or positrons by nuclei

A possibility of a verification of CPT-invariance of QED for bound states by example of muonium or antimuonium produced in reactions of scattering of electrons or positrons by nuclei is considered. The number of events of the muonium production is estimated for contemporary accelerators. The method of the detection of muonium by measuring of oscillations of the decay curve caused by the interference between the ground and excited state of muonium is suggested. The admixture of the excited muonium to the final state is calculated.Comment: 7 pages, 3 figures, Latex, published in JETP 74, 196 (2001), corrected mistypes in eqs. (2.2), (2.4), (2.7

Gender and Inclusion Toolbox: Participatory Research in Climate Change and Agriculture

This manual is a resource and toolbox for NGO practitioners and programme designers interested in diagnostic and action research for gender sensitive and socially inclusive climate change programmes in the rural development context. It is meant to be an easy to use manual, increasing the research capacity, skills and knowledge of its users. Integrating gender and social differentiation frameworks should ideally begin from the start of the programme cycle and be coordinated throughout research, design, implementation, and monitoring and evaluation phases. The data gathered using this toolbox supports this programme work. While the manual emphasizes participatory and qualitative approaches, many of the activities and tools can produce quantitative data. Each chapter features a bundle of research tools intended to be used sequentially. However, we know that each organization has its diverse needs. The chapters are in modular format so that teams can assemble their own research toolbox specific to their needs

Extrapolation of K to \pi\pi decay amplitude

We examine the uncertainties involved in the off-mass-shell extrapolation of the $K\rightarrow \pi\pi$ decay amplitude with emphasis on those aspects that have so far been overlooked or ignored. Among them are initial-state interactions, choice of the extrapolated kaon field, and the relation between the asymptotic behavior and the zeros of the decay amplitude. In the inelastic region the phase of the decay amplitude cannot be determined by strong interaction alone and even its asymptotic value cannot be deduced from experiment. More a fundamental issue is intrinsic nonuniqueness of off-shell values of hadronic matrix elements in general. Though we are hampered with complexity of intermediate-energy meson interactions, we attempt to obtain a quantitative idea of the uncertainties due to the inelastic region and find that they can be much larger than more optimistic views portray.Comment: 16 pages with 5 eps figures in REVTE

The G protein-gated potassium current I(K,ACh) is constitutively active in patients with chronic atrial fibrillation

Background— The molecular mechanism of increased background inward rectifier current (IK1) in atrial fibrillation (AF) is not fully understood. We tested whether constitutively active acetylcholine (ACh)-activated IK,ACh contributes to enhanced basal conductance in chronic AF (cAF). Methods and Results— Whole-cell and single-channel currents were measured with standard voltage-clamp techniques in atrial myocytes from patients with sinus rhythm (SR) and cAF. The selective IK,ACh blocker tertiapin was used for inhibition of IK,ACh. Whole-cell basal current was larger in cAF than in SR, whereas carbachol (CCh)-activated IK,ACh was lower in cAF than in SR. Tertiapin (0.1 to 100 nmol/L) reduced IK,ACh in a concentration-dependent manner with greater potency in cAF than in SR (−logIC50: 9.1 versus 8.2; P<0.05). Basal current contained a tertiapin-sensitive component that was larger in cAF than in SR (tertiapin [10 nmol/L]-sensitive current at −100 mV: cAF, −6.7±1.2 pA/pF, n=16/5 [myocytes/patients] versus SR, −1.7±0.5 pA/pF, n=24/8), suggesting contribution of constitutively active IK,ACh to basal current. In single-channel recordings, constitutively active IK,ACh was prominent in cAF but not in SR (channel open probability: cAF, 5.4±0.7%, n=19/9 versus SR, 0.1±0.05%, n=16/9; P<0.05). Moreover, IK1 channel open probability was higher in cAF than in SR (13.4±0.4%, n=19/9 versus 11.4±0.7%, n=16/9; P<0.05) without changes in other channel characteristics. Conclusions— Our results demonstrate that larger basal inward rectifier K+ current in cAF consists of increased IK1 activity and constitutively active IK,ACh. Blockade of IK,ACh may represent a new therapeutic target in AF

Quantifying structure in networks

We investigate exponential families of random graph distributions as a framework for systematic quantification of structure in networks. In this paper we restrict ourselves to undirected unlabeled graphs. For these graphs, the counts of subgraphs with no more than k links are a sufficient statistics for the exponential families of graphs with interactions between at most k links. In this framework we investigate the dependencies between several observables commonly used to quantify structure in networks, such as the degree distribution, cluster and assortativity coefficients.Comment: 17 pages, 3 figure

Representation of Markov chains by random maps: existence and regularity conditions

We systematically investigate the problem of representing Markov chains by families of random maps, and which regularity of these maps can be achieved depending on the properties of the probability measures. Our key idea is to use techniques from optimal transport to select optimal such maps. Optimal transport theory also tells us how convexity properties of the supports of the measures translate into regularity properties of the maps via Legendre transforms. Thus, from this scheme, we cannot only deduce the representation by measurable random maps, but we can also obtain conditions for the representation by continuous random maps. Finally, we present conditions for the representation of Markov chain by random diffeomorphisms.Comment: 22 pages, several changes from the previous version including extended discussion of many detail