How (Not) to Cut Your Cheese

It is well known that a line can intersect at most 2n−1 unit squares of the n × n chessboard. Here we consider the three-dimensional version: how many unit cubes of the 3-dimensional cube [0,n]3 can a hyperplane intersect

Resistance of a delta wing in a supersonic flow

The resistance of a delta wing at small angle of attack in supersonic conical flow with its leading edges within the Mach cone is calculated by a method that separates out the suction force

Diagonally Neighbour Transitive Codes and Frequency Permutation Arrays

Constant composition codes have been proposed as suitable coding schemes to solve the narrow band and impulse noise problems associated with powerline communication. In particular, a certain class of constant composition codes called frequency permutation arrays have been suggested as ideal, in some sense, for these purposes. In this paper we characterise a family of neighbour transitive codes in Hamming graphs in which frequency permutation arrays play a central rode. We also classify all the permutation codes generated by groups in this family

Quantum fingerprinting

Classical fingerprinting associates with each string a shorter string (its fingerprint), such that, with high probability, any two distinct strings can be distinguished by comparing their fingerprints alone. The fingerprints can be exponentially smaller than the original strings if the parties preparing the fingerprints share a random key, but not if they only have access to uncorrelated random sources. In this paper we show that fingerprints consisting of quantum information can be made exponentially smaller than the original strings without any correlations or entanglement between the parties: we give a scheme where the quantum fingerprints are exponentially shorter than the original strings and we give a test that distinguishes any two unknown quantum fingerprints with high probability. Our scheme implies an exponential quantum/classical gap for the equality problem in the simultaneous message passing model of communication complexity. We optimize several aspects of our scheme.Comment: 8 pages, LaTeX, one figur

CHEMICAL MODIFICATION OF CELLULOSE

Thermolytic degradation of cellulose is dependant on its initial DP, accessibility and on the method and temperature of the treatment. A limiting DP could be detected in the depolymerizing reaction. The deteriorating action of aggressive water could be demonstrated. Quantitative correlation was elaborated concerning the role of accessibility in the reaction between cellulose and reactive dyestuffs. The role of temperature was cleared up in the ceIlulose-caustic soda interaction. New bleaching process was elaborated with the use of singlet oxygen. Physical characteristics, amount of releasable formaldehyde and colouristic influence of resin finishing of cotton could be optimized

Incremental dimension reduction of tensors with random index

We present an incremental, scalable and efficient dimension reduction technique for tensors that is based on sparse random linear coding. Data is stored in a compactified representation with fixed size, which makes memory requirements low and predictable. Component encoding and decoding are performed on-line without computationally expensive re-analysis of the data set. The range of tensor indices can be extended dynamically without modifying the component representation. This idea originates from a mathematical model of semantic memory and a method known as random indexing in natural language processing. We generalize the random-indexing algorithm to tensors and present signal-to-noise-ratio simulations for representations of vectors and matrices. We present also a mathematical analysis of the approximate orthogonality of high-dimensional ternary vectors, which is a property that underpins this and other similar random-coding approaches to dimension reduction. To further demonstrate the properties of random indexing we present results of a synonym identification task. The method presented here has some similarities with random projection and Tucker decomposition, but it performs well at high dimensionality only (n>10^3). Random indexing is useful for a range of complex practical problems, e.g., in natural language processing, data mining, pattern recognition, event detection, graph searching and search engines. Prototype software is provided. It supports encoding and decoding of tensors of order >= 1 in a unified framework, i.e., vectors, matrices and higher order tensors.Comment: 36 pages, 9 figure

Determination of the Michel Parameters rho, xi, and delta in tau-Lepton Decays with tau --> rho nu Tags

Using the ARGUS detector at the $e^+ e^-$ storage ring DORIS II, we have measured the Michel parameters $\rho$, $\xi$, and $\xi\delta$ for $\tau^{\pm}\to l^{\pm} \nu\bar\nu$ decays in $\tau$-pair events produced at center of mass energies in the region of the $\Upsilon$ resonances. Using $\tau^\mp \to \rho^\mp \nu$ as spin analyzing tags, we find $\rho_{e}=0.68\pm 0.04 \pm 0.08$, $\xi_{e}= 1.12 \pm 0.20 \pm 0.09$, $\xi\delta_{e}= 0.57 \pm 0.14 \pm 0.07$, $\rho_{\mu}= 0.69 \pm 0.06 \pm 0.08$, $\xi_{\mu}= 1.25 \pm 0.27 \pm 0.14$ and $\xi\delta_{\mu}= 0.72 \pm 0.18 \pm 0.10$. In addition, we report the combined ARGUS results on $\rho$, $\xi$, and $\xi\delta$ using this work und previous measurements.Comment: 10 pages, well formatted postscript can be found at http://pktw06.phy.tu-dresden.de/iktp/pub/desy97-194.p

PDLIM5 links kidney anion exchanger 1 (kAE1) to ILK and is required for membrane targeting of kAE1.

Anion exchanger 1 (AE1) mediates Cl-/HCO3- exchange in erythrocytes and kidney intercalated cells where it functions to maintain normal bodily acid-base homeostasis. AE1's C-terminal tail (AE1C) contains multiple potential membrane targeting/retention determinants, including a predicted PDZ binding motif, which are critical for its normal membrane residency. Here we identify PDLIM5 as a direct binding partner for AE1 in human kidney, via PDLIM5's PDZ domain and the PDZ binding motif in AE1C. Kidney AE1 (kAE1), PDLIM5 and integrin-linked kinase (ILK) form a multiprotein complex in which PDLIM5 provides a bridge between ILK and AE1C. Depletion of PDLIM5 resulted in significant reduction in kAE1 at the cell membrane, whereas over-expression of kAE1 was accompanied by increased PDLIM5 levels, underscoring the functional importance of PDLIM5 for proper kAE1 membrane residency, as a crucial linker between kAE1 and actin cytoskeleton-associated proteins in polarized cells.This work was supported by the Wellcome Trust (grant ref: 088489/Z/09/Z and Strategic award 100140/Z/12/Z to the Cambridge Institute for Medical Research), and the British Heart Foundation (grant ref: SBAG/120). The Addenbrooke's Human Research Tissue Bank is supported by the NIHR Cambridge Biomedical Research Centre.This is the final version of the article. It first appeared from Nature Publishing Group via https://doi.org/10.1038/srep3970