Inverse spectral problems for Dirac operators with summable matrix-valued potentials

We consider the direct and inverse spectral problems for Dirac operators on $(0,1)$ with matrix-valued potentials whose entries belong to $L_p(0,1)$, $p\in[1,\infty)$. We give a complete description of the spectral data (eigenvalues and suitably introduced norming matrices) for the operators under consideration and suggest a method for reconstructing the potential from the corresponding spectral data.Comment: 32 page

A Universal Model of Global Civil Unrest

Civil unrest is a powerful form of collective human dynamics, which has led to major transitions of societies in modern history. The study of collective human dynamics, including collective aggression, has been the focus of much discussion in the context of modeling and identification of universal patterns of behavior. In contrast, the possibility that civil unrest activities, across countries and over long time periods, are governed by universal mechanisms has not been explored. Here, we analyze records of civil unrest of 170 countries during the period 1919-2008. We demonstrate that the distributions of the number of unrest events per year are robustly reproduced by a nonlinear, spatially extended dynamical model, which reflects the spread of civil disorder between geographic regions connected through social and communication networks. The results also expose the similarity between global social instability and the dynamics of natural hazards and epidemics.Comment: 8 pages, 3 figure

Analytic approach to stochastic cellular automata: exponential and inverse power distributions out of Random Domino Automaton

Inspired by extremely simplified view of the earthquakes we propose the stochastic domino cellular automaton model exhibiting avalanches. From elementary combinatorial arguments we derive a set of nonlinear equations describing the automaton. Exact relations between the average parameters of the model are presented. Depending on imposed triggering, the model reproduces both exponential and inverse power statistics of clusters.Comment: improved, new material added; 9 pages, 3 figures, 2 table

Morphology and tectonics of the Mid-Atlantic Ridge, 7°–12°S

We present swath bathymetric, gravity, and magnetic data from the Mid-Atlantic Ridge between the Ascension and the Bode Verde fracture zones, where significant ridge–hot spot interaction has been inferred. The ridge axis in this region may be divided into four segments. The central two segments exhibit rifted axial highs, while the northernmost and southernmost segments have deep rift valleys typical of slow-spreading mid-ocean ridges. Bathymetric and magnetic data indicate that both central segments have experienced ridge jumps since ~1 Ma. Mantle Bouguer anomalies (MBAs) derived from shipboard free air gravity and swath bathymetric data show deep subcircular lows centered on the new ridge axes, suggesting that mantle flow has been established beneath the new spreading centers for at least ~1 Myr. Inversion of gravity data indicates that crustal thicknesses vary by ~4 km along axis, with the thickest crust occurring beneath a large axial volcanic edifice. Once the effects of lithospheric aging have been removed, a model in which gravity variations are attributed entirely to crustal thickness variations is more consistent with data from an axis-parallel seismic line than a model that includes additional along-axis variations in mantle temperature. Both geophysical and geochemical data from the region may be explained by the melting of small (<200 km) mantle chemical heterogeneities rather than elevated temperatures. Therefore, there may be no Ascension/Circe plume

Boundary relations and generalized resolvents of symmetric operators

The Kre\u{\i}n-Naimark formula provides a parametrization of all selfadjoint exit space extensions of a, not necessarily densely defined, symmetric operator, in terms of maximal dissipative (in \dC_+) holomorphic linear relations on the parameter space (the so-called Nevanlinna families). The new notion of a boundary relation makes it possible to interpret these parameter families as Weyl families of boundary relations and to establish a simple coupling method to construct the generalized resolvents from the given parameter family. The general version of the coupling method is introduced and the role of boundary relations and their Weyl families for the Kre\u{\i}n-Naimark formula is investigated and explained.Comment: 47 page

A review of wildland fire spread modelling, 1990-present 3: Mathematical analogues and simulation models

In recent years, advances in computational power and spatial data analysis (GIS, remote sensing, etc) have led to an increase in attempts to model the spread and behvaiour of wildland fires across the landscape. This series of review papers endeavours to critically and comprehensively review all types of surface fire spread models developed since 1990. This paper reviews models of a simulation or mathematical analogue nature. Most simulation models are implementations of existing empirical or quasi-empirical models and their primary function is to convert these generally one dimensional models to two dimensions and then propagate a fire perimeter across a modelled landscape. Mathematical analogue models are those that are based on some mathematical conceit (rather than a physical representation of fire spread) that coincidentally simulates the spread of fire. Other papers in the series review models of an physical or quasi-physical nature and empirical or quasi-empirical nature. Many models are extensions or refinements of models developed before 1990. Where this is the case, these models are also discussed but much less comprehensively.Comment: 20 pages + 9 pages references + 1 page figures. Submitted to the International Journal of Wildland Fir

Characterization of Sleep Stages by Correlations of Heartbeat Increments

We study correlation properties of the magnitude and the sign of the increments in the time intervals between successive heartbeats during light sleep, deep sleep, and REM sleep using the detrended fluctuation analysis method. We find short-range anticorrelations in the sign time series, which are strong during deep sleep, weaker during light sleep and even weaker during REM sleep. In contrast, we find long-range positive correlations in the magnitude time series, which are strong during REM sleep and weaker during light sleep. We observe uncorrelated behavior for the magnitude during deep sleep. Since the magnitude series relates to the nonlinear properties of the original time series, while the signs series relates to the linear properties, our findings suggest that the nonlinear properties of the heartbeat dynamics are more pronounced during REM sleep. Thus, the sign and the magnitude series provide information which is useful in distinguishing between the sleep stages.Comment: 7 pages, 4 figures, revte

On the similarity of Sturm-Liouville operators with non-Hermitian boundary conditions to self-adjoint and normal operators

We consider one-dimensional Schroedinger-type operators in a bounded interval with non-self-adjoint Robin-type boundary conditions. It is well known that such operators are generically conjugate to normal operators via a similarity transformation. Motivated by recent interests in quasi-Hermitian Hamiltonians in quantum mechanics, we study properties of the transformations in detail. We show that they can be expressed as the sum of the identity and an integral Hilbert-Schmidt operator. In the case of parity and time reversal boundary conditions, we establish closed integral-type formulae for the similarity transformations, derive the similar self-adjoint operator and also find the associated "charge conjugation" operator, which plays the role of fundamental symmetry in a Krein-space reformulation of the problem.Comment: 27 page

Critical animal and media studies: Expanding the understanding of oppression in communication research

Critical and communication studies have traditionally neglected the oppression conducted by humans towards other animals. However, our (mis)treatment of other animals is the result of public consent supported by a morally speciesist-anthropocentric system of values. Speciesism or anthroparchy, as much as any other mainstream ideologies, feeds the media and at the same time is perpetuated by them. The goal of this article is to remedy this neglect by introducing the subdiscipline of Critical Animal and Media Studies. Critical Animal and Media Studies takes inspiration both from critical animal studies – which is so far the most consolidated critical field of research in the social sciences addressing our exploitation of other animals – and from the normative-moral stance rooted in the cornerstones of traditional critical media studies. The authors argue that the Critical Animal and Media Studies approach is an unavoidable step forward for critical media and communication studies to engage with the expanded circle of concerns of contemporary ethical thinking

Time trends and persistence in European temperature anomalies.

This paper looks at the level of persistence in the temperature anomalies series of 114 European cities. Once this level of persistence has been identified, the time trend coefficients are estimated and the results indicate that most of the series examined display positive trends, supporting thus climate warming. Moreover, the results obtained confirm the hypothesis that long-memory behaviour cannot be neglected in the study of temperature time series, changing, therefore, the estimated effect of global warming.pre-print825 K