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

Efficient Bayesian inference for natural time series using ARFIMA processes

Many geophysical quantities, such as atmospheric temperature, water levels in rivers, and wind speeds, have shown evidence of long memory (LM). LM implies that these quantities experience non-trivial temporal memory, which potentially not only enhances their predictability, but also hampers the detection of externally forced trends. Thus, it is important to reliably identify whether or not a system exhibits LM. In this paper we present a modern and systematic approach to the inference of LM. We use the flexible autoregressive fractional integrated moving average (ARFIMA) model, which is widely used in time series analysis, and of increasing interest in climate science. Unlike most previous work on the inference of LM, which is frequentist in nature, we provide a systematic treatment of Bayesian inference. In particular, we provide a new approximate likelihood for efficient parameter inference, and show how nuisance parameters (e.g., short-memory effects) can be integrated over in order to focus on long-memory parameters and hypothesis testing more directly. We illustrate our new methodology on the Nile water level data and the central England temperature (CET) time series, with favorable comparison to the standard estimators. For CET we also extend our method to seasonal long memory

Granzyme A Required for Regulatory T-Cell Mediated Prevention of Gastrointestinal Graft-versus-Host Disease

In our previous work we could identify defects in human regulatory T cells (Tregs) likely favoring the development of graft-versus-host disease (GvHD) following allogeneic stem cell transplantation (SCT). Treg transcriptome analyses comparing GvHD and immune tolerant patients uncovered regulated gene transcripts highly relevant for Treg cell function. Moreover, granzyme A (GZMA) also showed a significant lower expression at the protein level in Tregs of GvHD patients. GZMA induces cytolysis in a perforin-dependent, FAS- FASL independent manner and represents a cell-contact dependent mechanism for Tregs to control immune responses. We therefore analyzed the functional role of GZMA in a murine standard model for GvHD. For this purpose, adoptively transferred CD4+CD25+ Tregs from gzmA-/- mice were analyzed in comparison to their wild type counterparts for their capability to prevent murine GvHD. GzmA-/- Tregs home efficiently to secondary lymphoid organs and do not show phenotypic alterations with respect to activation and migration properties to inflammatory sites. Whereas gzmA-/- Tregs are highly suppressive in vitro, Tregs require GZMA to rescue hosts from murine GvHD, especially regarding gastrointestinal target organ damage. We herewith identify GZMA as critical effector molecule of human Treg function for gastrointestinal immune response in an experimental GvHD model

Epidermal ADAM17 maintains the skin barrier by regulating EGFR ligand-dependent terminal keratinocyte differentiation

ADAM17 (a disintegrin and metalloproteinase 17) is ubiquitously expressed and cleaves membrane proteins, such as epidermal growth factor receptor (EGFR) ligands, l-selectin, and TNF, from the cell surface, thus regulating responses to tissue injury and inflammation. However, little is currently known about its role in skin homeostasis. We show that mice lacking ADAM17 in keratinocytes (A17(ΔKC)) have a normal epidermal barrier and skin architecture at birth but develop pronounced defects in epidermal barrier integrity soon after birth and develop chronic dermatitis as adults. The dysregulated expression of epidermal differentiation proteins becomes evident 2 d after birth, followed by reduced transglutaminase (TGM) activity, transepidermal water loss, up-regulation of the proinflammatory cytokine IL-36α, and inflammatory immune cell infiltration. Activation of the EGFR was strongly reduced in A17(ΔKC) skin, and topical treatment of A17(ΔKC) mice with recombinant TGF-α significantly improved TGM activity and decreased skin inflammation. Finally, we show that mice lacking the EGFR in keratinocytes (Egfr(ΔKC)) closely resembled A17(ΔKC) mice. Collectively, these results identify a previously unappreciated critical role of the ADAM17–EGFR signaling axis in maintaining the homeostasis of the postnatal epidermal barrier and suggest that this pathway could represent a good target for treatment of epidermal barrier defects

What is the correct cost functional for variational data assimilation?

Variational approaches to data assimilation, and weakly constrained four dimensional variation (WC-4DVar) in particular, are important in the geosciences but also in other communities (often under different names). The cost functions and the resulting optimal trajectories may have a probabilistic interpretation, for instance by linking data assimilation with maximum aposteriori (MAP) estimation. This is possible in particular if the unknown trajectory is modelled as the solution of a stochastic differential equation (SDE), as is increasingly the case in weather forecasting and climate modelling. In this situation, the MAP estimator (or “most probable path” of the SDE) is obtained by minimising the Onsager–Machlup functional. Although this fact is well known, there seems to be some confusion in the literature, with the energy (or “least squares”) functional sometimes been claimed to yield the most probable path. The first aim of this paper is to address this confusion and show that the energy functional does not, in general, provide the most probable path. The second aim is to discuss the implications in practice. Although the mentioned results pertain to stochastic models in continuous time, they do have consequences in practice where SDE’s are approximated by discrete time schemes. It turns out that using an approximation to the SDE and calculating its most probable path does not necessarily yield a good approximation to the most probable path of the SDE proper. This suggest that even in discrete time, a version of the Onsager–Machlup functional should be used, rather than the energy functional, at least if the solution is to be interpreted as a MAP estimator

Isospin Dependence in the Odd-Even Staggering of Nuclear Binding Energies

The FRS-ESR facility at GSI provides unique conditions for precision measurements of large areas on the nuclear mass surface in a single experiment. Values for masses of 604 neutron-deficient nuclides (30<=Z<=92) were obtained with a typical uncertainty of 30 microunits. The masses of 114 nuclides were determined for the first time. The odd-even staggering (OES) of nuclear masses was systematically investigated for isotopic chains between the proton shell closures at Z=50 and Z=82. The results were compared with predictions of modern nuclear models. The comparison revealed that the measured trend of OES is not reproduced by the theories fitted to masses only. The spectral pairing gaps extracted from models adjusted to both masses, and density related observables of nuclei agree better with the experimental data.Comment: Physics Review Letters 95 (2005) 042501 http://link.aps.org/abstract/PRL/v95/e04250

Spatio-temporal evolution of global surface temperature distributions

Climate is known for being characterised by strong non-linearity and chaotic behaviour. Nevertheless, few studies in climate science adopt statistical methods specifically designed for non-stationary or non-linear systems. Here we show how the use of statistical methods from Information Theory can describe the non-stationary behaviour of climate fields, unveiling spatial and temporal patterns that may otherwise be difficult to recognize. We study the maximum temperature at two meters above ground using the NCEP CDAS1 daily reanalysis data, with a spatial resolution of 2.5 by 2.5 degree and covering the time period from 1 January 1948 to 30 November 2018. The spatial and temporal evolution of the temperature time series are retrieved using the Fisher Information Measure, which quantifies the information in a signal, and the Shannon Entropy Power, which is a measure of its uncertainty -- or unpredictability. The results describe the temporal behaviour of the analysed variable. Our findings suggest that tropical and temperate zones are now characterized by higher levels of entropy. Finally, Fisher-Shannon Complexity is introduced and applied to study the evolution of the daily maximum surface temperature distributions.Comment: 7 pages, 4 figure