The Vector Valued Quartile Operator

Certain vector-valued inequalities are shown to hold for a Walsh analog of the bilinear Hilbert transform. These extensions are phrased in terms of a recent notion of quartile type of a UMD (Unconditional Martingale Differences) Banach space X. Every known UMD Banach space has finite quartile type, and it was recently shown that the Walsh analog of Carleson's Theorem holds under a closely related assumption of finite tile type. For a Walsh model of the bilinear Hilbert transform however, the quartile type should be sufficiently close to that of a Hilbert space for our results to hold. A full set of inequalities is quantified in terms of quartile type.Comment: 32 pages, 5 figures, incorporates referee's report, to appear in Collect. Mat

Information-Preserving Markov Aggregation

We present a sufficient condition for a non-injective function of a Markov chain to be a second-order Markov chain with the same entropy rate as the original chain. This permits an information-preserving state space reduction by merging states or, equivalently, lossless compression of a Markov source on a sample-by-sample basis. The cardinality of the reduced state space is bounded from below by the node degrees of the transition graph associated with the original Markov chain. We also present an algorithm listing all possible information-preserving state space reductions, for a given transition graph. We illustrate our results by applying the algorithm to a bi-gram letter model of an English text.Comment: 7 pages, 3 figures, 2 table

Development and Evolution of Neural Networks in an Artificial Chemistry

We present a model of decentralized growth for Artificial Neural Networks (ANNs) inspired by the development and the physiology of real nervous systems. In this model, each individual artificial neuron is an autonomous unit whose behavior is determined only by the genetic information it harbors and local concentrations of substrates modeled by a simple artificial chemistry. Gene expression is manifested as axon and dendrite growth, cell division and differentiation, substrate production and cell stimulation. We demonstrate the model's power with a hand-written genome that leads to the growth of a simple network which performs classical conditioning. To evolve more complex structures, we implemented a platform-independent, asynchronous, distributed Genetic Algorithm (GA) that allows users to participate in evolutionary experiments via the World Wide Web.Comment: 8 pages LaTeX, style file included, 8 embedded postscript figures. To be published in Proc. of 3rd German Workshop on Artificial Life (GWAL

Glacier changes in the Bavarian Alps from 1989/90 to 2006/07

The five glaciers in Bavaria which today cover a total area of less than one square kilometer were frequently monitored by geodetic methods from the mid of the 20th century. In this paper, the record is extended by new surveys in 1999 and 2006. The glaciers show a prolonged surface lowering, which is intensified compared to the 1980s and reaches maximum rates from 1999-2006. Moreover, the ice thickness of four glaciers was determined in 2006 and 2007 by geophysical field techniques and allows the calculation of ice volumes. First simple extrapolations of observed volume losses indicate that the two Berchtesgaden glaciers and Südlicher Schneeferner could disappear by 2016, while the ice of Nördlicher Schneeferner endures until 2027. Ice thicknesses and surface changes are visualized in five annexed maps.Die fünf bayerischen Gletscher, die heute insgesamt eine Fläche von weniger als einem Quadratkilometer bedecken, wurden seit der Mitte des 20. Jahrhunderts regelmäßig geodätisch aufgenommen. Diese Reihe wird hier um zwei Neuvermessungen in den Jahren 1999 und 2006 erweitert. Alle Gletscher zeigen in dem Zeitraum eine fortgesetzte Erniedrigung ihrer Oberfläche, die im Vergleich zu den 1980er Jahren verstärkt ist und in der Periode 1999-2006 Maximalwerte aufzeigt. Außerdem wurden in den Jahren 2006 und 2007 die Eisdicken von vier Gletschern durch geophysikalische Messungen bestimmt, was erstmalig die Ermittlung des verbleibenden Eisvolumens erlaubt. Erste einfache Extrapolationen der beobachteten Volumenverluste in die Zukunft deuten an, dass die beiden Gletscher in den Berchtesgadener Alpen sowie der Südliche Schneeferner bis zum Jahr 2016 verschwinden könnten, während der Nördliche Schneeferner noch bis 2027 überdauern würde. Eisdicken und Oberflächenänderungen werden anhand von fünf Karten im Anhang verdeutlicht

Height-resolved Scaling Properties of Tropospheric Water Vapour based on Airborne Lidar Observations

Two-dimensional vertical water vapour cross sections of the free troposphere between altitudes of 2 and 10 km, measured by nadir-viewing airborne differential-absorption lidar with high spatial resolution, were analyzed using structure functions up to the fifth order. We found scale invariance, i.e. a power-law dependency of structure function on length scale, for scales between 5 and 100 km, for the horizontal time series of water vapour mixing ratio. In contrast to one-dimensional in situ measurements, the two-dimensional water vapor lidar observations allow height-resolved analyses of power-law scaling exponents at a vertical resolution of 200 m. The data reveal significantly different scaling properties above and below an air-mass boundary. They stem from three very dissimilar aircraft campaigns: COPS/ETReC over middle and southern Europe in summer 2007, T-PARC around Japan mostly over sea in late summer 2008, and T-IPY around Spitsbergen over sea in winter 2008. After discarding flight segments with low lidar signals or large data gaps, and after averaging horizontally to a resolution of between 1 and 5 km to obtain a high signal to noise ratio, structure functions were computed for 20 flights at various heights, adding up to a length of more than 300,000 km. The power-law scaling exponents of the structure functions do not show significant latitudinal, seasonal or land/sea dependency, but they do differ between air masses influenced by moist convection and air masses aloft, not influenced. A classification of the horizontal water vapour time series into two groups according to whether the series occurred above or below the level of nearby convective cloud tops could be performed by detecting the cloud top height from the lidar backscatter signal in the corresponding flight segment. We found that the scaling exponents can be divided into two groups depending on the respective air mass: The smoothness of the time series, expressed by the first-order scaling exponent, varies from less than 0.5 in the low-level convectively influenced air masses to values greater than 0.5 and most frequently near 0.6 in the higher-level air above the convective cloud tops. The time series’ intermittency, expressed by the variation of the scaling exponent with increasing order, is larger in convectively influenced air masses. These differences in variability strongly suggest that convection provides a source of moisture variability on small scales. Our results show that the high horizontal and vertical resolution of lidar observations allows a characterisation of the scale dependency of the water vapour field at scales close to and smaller than the smallest resolved scales in modern weather and climate models. This provides both a reference for validation of high resolution models and a basis for the design of stochastic or pdf-based parameterisations of clouds and convection

A composite parameterization of unitary groups, density matrices and subspaces

Unitary transformations and density matrices are central objects in quantum physics and various tasks require to introduce them in a parameterized form. In the present article we present a parameterization of the unitary group $\mathcal{U}(d)$ of arbitrary dimension $d$ which is constructed in a composite way. We show explicitly how any element of $\mathcal{U}(d)$ can be composed of matrix exponential functions of generalized anti-symmetric $\sigma$-matrices and one-dimensional projectors. The specific form makes it considerably easy to identify and discard redundant parameters in several cases. In this way, redundancy-free density matrices of arbitrary rank $k$ can be formulated. Our construction can also be used to derive an orthonormal basis of any $k$-dimensional subspaces of $\mathbb{C}^d$ with the minimal number of parameters. As an example it will be shown that this feature leads to a significant reduction of parameters in the case of investigating distillability of quantum states via lower bounds of an entanglement measure (the $m$-concurrence).Comment: 13 pages, 1 figur

Painting of human chromosomes with probes generated from hybrid cell lines by PCR with Alu and L1 primers

Specific amplification of human sequences of up to several kb length has recently been accomplished in man-hamster and man-mouse somatic hybrid cell DNA by IRS-PCR (interspersed repetitive sequence — polymerase chain reaction). This approach is based on oligonucleotide primers that anneal specifically to human Alu- or L1-sequences and allows the amplification of any human sequences located between adequately spaced, inverted Alu- or L1-blocks. Here, we demonstrate that probe pools generated from two somatic hybrid cell lines by Alu- and L1-PCR can be used for chromosome painting in normal human lymphocyte metaphase spreads by chromosomal in situ suppression (CISS-) hybridization. The painted chromosomes and chromosome subregions directly represent the content of normal and deleted human chromosomes in the two somatic hybrid cell lines. The combination of IRS-PCR and CISS-hybridization will facilitate and improve the cytogenetic analysis of somatic hybrid cell panels, in particular, in cases where structurally aberrant human chromosomes or human chromosome segments involved in interspecies translocations cannot be unequivocally identified by classical banding techniques. Moreover, this new approach will help to generate probe pools for the specific delineation of human chromosome subregions for use in cytogenetic diagnostics and research without the necessity of cloning

Improving ocean-glider's payload with a new generation of spectrophotometric PH sensor

Ocean gliders have clearly become nowadays useful autonomous platforms addressed to measure a wide range of seawater parameters in a more sustainable and efficient way. This new ocean monitoring approach has implied the need to develop smaller, faster and more efficient sensors without reducing key features like accuracy, resolution, time-response, among others, in order to fit the glider operational capabilities. This work is aiming to present the latest development stages of a new spectrophotometric pH sensor, its integration process into a Wave Glider SV3 platform and the preliminary results derived from an offshore mission performed in subtropical waters between the Canary Islands and Cape Verde archipelagos.Peer Reviewe