458 research outputs found
Mandelbrot's 1/f fractional renewal models of 1963-67: The non-ergodic missing link between change points and long range dependence
The problem of 1/f noise has been with us for about a century. Because it is
so often framed in Fourier spectral language, the most famous solutions have
tended to be the stationary long range dependent (LRD) models such as
Mandelbrot's fractional Gaussian noise. In view of the increasing importance to
physics of non-ergodic fractional renewal models, I present preliminary results
of my research into the history of Mandelbrot's very little known work in that
area from 1963-67. I speculate about how the lack of awareness of this work in
the physics and statistics communities may have affected the development of
complexity science, and I discuss the differences between the Hurst effect, 1/f
noise and LRD, concepts which are often treated as equivalent.Comment: 11 pages. Corrected and improved version of a manuscript submitted to
ITISE 2016 meeting in Granada, Spai
Anomalous spatial diffusion and multifractality in optical lattices
Transport of cold atoms in shallow optical lattices is characterized by slow,
nonstationary momentum relaxation. We here develop a projector operator method
able to derive in this case a generalized Smoluchowski equation for the
position variable. We show that this explicitly non-Markovian equation can be
written as a systematic expansion involving higher-order derivatives. We use
the latter to compute arbitrary moments of the spatial distribution and analyze
their multifractal properties.Comment: 5 pages, 3 figure
Superaging correlation function and ergodicity breaking for Brownian motion in logarithmic potentials
We consider an overdamped Brownian particle moving in a confining
asymptotically logarithmic potential, which supports a normalized Boltzmann
equilibrium density. We derive analytical expressions for the two-time
correlation function and the fluctuations of the time-averaged position of the
particle for large but finite times. We characterize the occurrence of aging
and nonergodic behavior as a function of the depth of the potential, and
support our predictions with extensive Langevin simulations. While the
Boltzmann measure is used to obtain stationary correlation functions, we show
how the non-normalizable infinite covariant density is related to the
super-aging behavior.Comment: 16 pages, 6 figure
The E8 geometry from a Clifford perspective
This paper considers the geometry of from a Clifford point of view in three complementary ways. Firstly, in earlier work, I had shown how to construct the four-dimensional exceptional root systems from the 3D root systems using Clifford techniques, by constructing them in the 4D even subalgebra of the 3D Clifford algebra; for instance the icosahedral root system gives rise to the largest (and therefore exceptional) non-crystallographic root system . Arnold's trinities and the McKay correspondence then hint that there might be an indirect connection between the icosahedron and . Secondly, in a related construction, I have now made this connection explicit for the first time: in the 8D Clifford algebra of 3D space the elements of the icosahedral group are doubly covered by 8-component objects, which endowed with a `reduced inner product' are exactly the root system. It was previously known that splits into -invariant subspaces, and we discuss the folding construction relating the two pictures. This folding is a partial version of the one used for the construction of the Coxeter plane, so thirdly we discuss the geometry of the Coxeter plane in a Clifford algebra framework. We advocate the complete factorisation of the Coxeter versor in the Clifford algebra into exponentials of bivectors describing rotations in orthogonal planes with the rotation angle giving the correct exponents, which gives much more geometric insight than the usual approach of complexification and search for complex eigenvalues. In particular, we explicitly find these factorisations for the 2D, 3D and 4D root systems, as well as , whose Coxeter versor factorises as . This explicitly describes 30-fold rotations in 4 orthogonal planes with the correct exponents arising completely algebraically from the factorisation
NIRVP: A robust structural proxy for sun-induced chlorophyll fluorescence and photosynthesis across scales
Gender Identity and Womens' Supply of Labor and Non-Market Work: Panel Data Evidence for Germany
The p75 receptor mediates axon growth inhibition through an association with PIR-B
The Nogo receptor and paired immunoglobulin-like receptor B (PIR-B) are receptors for three myelin-derived axon-growth inhibitors, including myelin-associated glycoprotein (MAG). In this study, we report that the p75 receptor is required for the signal transduction of PIR-B, which interacted with p75 upon ligand binding. In addition, p75 was required for activation of Src homology 2-containing protein tyrosine phosphatase (SHP), which is induced by MAG binding to PIR-B. Mice carrying a mutation in the p75 gene showed promotion of axonal regeneration after optic nerve injury. Thus, our results indicate that p75 has a critical role in axon growth inhibition in specific neuronal tracts
Using Web Search Query Data to Monitor Dengue Epidemics: A New Model for Neglected Tropical Disease Surveillance
A variety of obstacles, including bureaucracy and lack of resources, delay detection and reporting of dengue and exist in many countries where the disease is a major public health threat. Surveillance efforts have turned to modern data sources such as Internet usage data. People often seek health-related information online and it has been found that the frequency of, for example, influenza-related web searches as a whole rises as the number of people sick with influenza rises. Tools have been developed to help track influenza epidemics by finding patterns in certain web search activity. However, few have evaluated whether this approach would also be effective for other diseases, especially those that affect many people, that have severe consequences, or for which there is no vaccine. In this study, we found that aggregated, anonymized Google search query data were also capable of tracking dengue activity in Bolivia, Brazil, India, Indonesia and Singapore. Whereas traditional dengue data from official sources are often not available until after a long delay, web search query data is available for analysis within a day. Therefore, because it could potentially provide earlier warnings, these data represent a valuable complement to traditional dengue surveillance
On the continuing relevance of Mandelbrot’s non-ergodic fractional renewal models of 1963 to 1967
The problem of “1∕ƒ” noise has been with us for about a century. Because it is so often framed in Fourier spectral language, the most famous solutions have tended to be the stationary long range dependent (LRD) models such as Mandelbrot’s fractional Gaussian noise. In view of the increasing importance to physics of non-ergodic fractional renewal models, and their links to the CTRW, I present preliminary results of my research into the history of Mandelbrot’s very little known work in that area from 1963 to 1967. I speculate about how the lack of awareness of this work in the physics and statistics communities may have affected the development of complexity science, and I discuss the differences between the Hurst effect, “1∕ƒ” noise and LRD, concepts which are often treated as equivalent
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