Determinantal measures related to big q-Jacobi polynomials

We define a novel combinatorial object—the extended Gelfand—Tsetlin graph with cotransition probabilities depending on a parameter q. The boundary of this graph admits an explicit description. We introduce a family of probability measures on the boundary and describe their correlation functions. These measures are a q-analogue of the spectral measures studied earlier in the context of the problem of harmonic analysis on the infinite-dimensional unitary group

Natron glass production and supply in the late antique and early medieval Near East: The effect of the Byzantine-Islamic transition

Palestine and Egypt supplied the Mediterranean and Europe with virtually all of its glass for most of the first millennium CE. While the Muslim conquest in the 7th century saw major political and economic adjustment, immediate changes to material culture appear to have been minimal. This paper examines the impact of the Byzantine-Islamic transition on the natron glass industry of Palestine from the 7th to 12th century. A series of 133 well-contextualised glass vessels from selected excavations in modern day Israel have been analysed for major, minor and trace elements using LA-ICP-MS. These glasses are assigned to previously established primary production groups, allowing the elucidation of the chronology of key changes in glass production in the region. Results indicate a relatively abrupt compositional change in the late 7th - early 8th centuries, covering the reforming reigns of al-Malik and al-Walid, which marks the end of “Byzantine” glass production and the establishment of the furnaces at Bet Eli'ezer. At about this time there was an influx of glass of an Egyptian composition. Production of Bet Eli'ezer type glass appears to have been limited to a short time span, less than 50 years, after which natron glass production in Palestine ceased. Plant ash glass is first encountered in the late 8th-early 9th century, probably as a result of reduced local natron glass production creating the conditions in which plant ash glass technology was adopted. Egypt continued to produce natron glass for up to a century after its demise in Palestine. It is reasoned that the change and then collapse in natron glass production in Palestine may well have been as a consequence of a reduction in the quantities of available natron. This affected Palestine first, and Egypt up to 100 years later, which suggests that the factors causing the reduction in natron supply originated at the source and were long term and gradual, not short term events

Simulation of static and random errors on Grover's search algorithm implemented in a Ising nuclear spin chain quantum computer with few qubits

We consider Grover's search algorithm on a model quantum computer implemented on a chain of four or five nuclear spins with first and second neighbour Ising interactions. Noise is introduced into the system in terms of random fluctuations of the external fields. By averaging over many repetitions of the algorithm, the output state becomes effectively a mixed state. We study its overlap with the nominal output state of the algorithm, which is called fidelity. We find either an exponential or a Gaussian decay for the fidelity as a function of the strength of the noise, depending on the type of noise (static or random) and whether error supression is applied (the 2pi k-method) or not.Comment: 18 pages, 8 figures, extensive revision with new figure

The multilevel trigger system of the DIRAC experiment

The multilevel trigger system of the DIRAC experiment at CERN is presented. It includes a fast first level trigger as well as various trigger processors to select events with a pair of pions having a low relative momentum typical of the physical process under study. One of these processors employs the drift chamber data, another one is based on a neural network algorithm and the others use various hit-map detector correlations. Two versions of the trigger system used at different stages of the experiment are described. The complete system reduces the event rate by a factor of 1000, with efficiency $\geq$95% of detecting the events in the relative momentum range of interest.Comment: 21 pages, 11 figure

Functionalization of PET track-etched membranes by UV-induced graft (co)polymerization for detection of heavy metal ions in water

Nowadays, water quality monitoring is an essential task since environmental contamination and human exposure to heavy metals increased. Sensors that are able to detect ever lower concentrations of heavy metal ions with greater accuracy and speed are needed to effectively monitor water quality and prevent poisoning. This article shows studies of the modification of flexible track-etched membranes as the basis for the sensor with various polymers and their influence on the accuracy of detection of copper, cadmium, and lead ions in water. We report the UV-induced graft (co)polymerization of acrylic acid (AA) and 4-vinylpyridine (4-VPy) on poly(ethylene terephthalate) track-etched membrane (PET TeMs) and use them after platinum layer sputtering in square wave anodic stripping voltammetry (SW-ASV) for detection of Cu2+, Cd2+, and Pb2+. Optimal conditions leading to functionalization of the surface and retention of the pore structure were found. Modified membranes were characterized by SEM, FTIR, X-ray photoelectron spectroscopy (XPS) and colorimetric analysis. The dependence of the modification method on the sensitivity of the sensor was shown. Membrane modified with polyacrylic acid (PET TeMs-g-PAA), poly(4-vinylpyridine) (PET TeMs-g-P4VPy), and their copolymer (PET TeMs-g-P4VPy/PAA) with average grafting yield of 3% have been found to be sensitive to μg/L concentration of copper, lead, and cadmium ions. Limits of detection (LOD) for sensors based on PET TeMs-g-PAA are 2.22, 1.05, and 2.53 μg/L for Cu2+, Pb2+, and Cd2+, respectively. LODs for sensors based on PET TeMs-g-P4VPy are 5.23 μg/L (Cu2+), 1.78 μg/L (Pb2+), and 3.64 μg/L (Cd2+) μg/L. PET TeMs-g-P4VPy/PAA electrodes are found to be sensitive with LODs of 0.74 μg/L(Cu2+), 1.13 μg/L (Pb2+), and 2.07 μg/L(Cd2+). Thus, it was shown that the modification of membranes by copolymers with carboxylic and amino groups leads to more accurate detection of heavy metal ions, associated with the formation of more stable complexes. © 2019 by the authors.Ministry of Education and Science of the Republic of KazakhstanMinistry of Education and Science of the Republic of KazakhstanFunding: The research was funded by the Ministry of Energy of the Republic of Kazakhstan (technological program, #74 on 02.04.2018).Acknowledgments: The research was funded by the Ministry of Energy of the Republic of Kazakhstan (technological program, #74 on 02.04.2018)

Generic spectral properties of right triangle billiards

This article presents a new method to calculate eigenvalues of right triangle billiards. Its efficiency is comparable to the boundary integral method and more recently developed variants. Its simplicity and explicitness however allow new insight into the statistical properties of the spectra. We analyse numerically the correlations in level sequences at high level numbers (>10^5) for several examples of right triangle billiards. We find that the strength of the correlations is closely related to the genus of the invariant surface of the classical billiard flow. Surprisingly, the genus plays and important role on the quantum level also. Based on this observation a mechanism is discussed, which may explain the particular quantum-classical correspondence in right triangle billiards. Though this class of systems is rather small, it contains examples for integrable, pseudo integrable, and non integrable (ergodic, mixing) dynamics, so that the results might be relevant in a more general context.Comment: 18 pages, 8 eps-figures, revised: stylistic changes, improved presentatio

Molecular pathways: Sterols and receptor signaling in cancer

Accelerated cholesterol and lipid metabolism are the hallmarks of cancer and contribute to malignant transformation due to the obligatory requirement for cholesterol for the function of eukaryotic membranes. To build new membranes and maintain active signaling, cancer cells depend on high intensity of endogenous cholesterol biosynthesis and uptake of lipid particles. This metabolic dependency of cancer cells on cholesterol and other lipids is tightly regulated by the cholesterol homeostasis network, including (i) sterol response element-binding proteins (SREBP), master transcriptional regulators of cholesterol and fatty acid pathway genes; (ii) nuclear sterol receptors (liver X receptors, LXR), which coordinate growth with the availability of cholesterol; and (iii) lipid particle receptors, such as low-density lipid particle (LDL) receptor, providing exogenous sterol and lipids to cancer cells. In addition, activity of oncogenic receptors, such as MUC1 or EGFR, accelerates sterol uptake and biosynthesis. Therefore, a general strategy of reducing the cholesterol pool in cancer cells is challenged by the highly efficient feedback loops compensating for a blockade at a single point in the cholesterol homeostatic network. Besides the well-established structural role of cholesterol in membranes, recent studies have uncovered potent biologic activities of certain cholesterol metabolic precursors and its oxidized derivatives, oxysterols. The former, meiosis-activating sterols, exert effects on trafficking and signaling of oncogenic EGF receptor (EGFR). Cholesterol epoxides, the highly active products of cholesterol oxidation, are being neutralized by the distal sterol pathway enzymes, emopamyl-binding protein (EBP) and dehydrocholesterol-7 reductase (DHCR7). These recently discovered "moonlighting" activities of the cholesterol pathway genes and metabolites expand our understanding of the uniquely conserved roles these sterol molecules play in the regulation of cellular proliferation and in cancer. Clin Cancer Res; 20(1); 28-34. © 2013 AACR

Counting homomorphisms onto finite solvable groups

We present a method for computing the number of epimorphisms from a finitely-presented group G to a finite solvable group \Gamma, which generalizes a formula of G\"aschutz. Key to this approach are the degree 1 and 2 cohomology groups of G, with certain twisted coefficients. As an application, we count low-index subgroups of G. We also investigate the finite solvable quotients of the Baumslag-Solitar groups, the Baumslag parafree groups, and the Artin braid groups.Comment: 30 pages; accepted for publication in the Journal of Algebr

Signatures of the correlation hole in total and partial cross sections

In a complex scattering system with few open channels, say a quantum dot with leads, the correlation properties of the poles of the scattering matrix are most directly related to the internal dynamics of the system. We may ask how to extract these properties from an analysis of cross sections. In general this is very difficult, if we leave the domain of isolated resonances. We propose to consider the cross correlation function of two different elastic or total cross sections. For these we can show numerically and to some extent also analytically a significant dependence on the correlations between the scattering poles. The difference between uncorrelated and strongly correlated poles is clearly visible, even for strongly overlapping resonances.Comment: 25 pages, 13 Postscript figures, typos corrected and references adde

Generalized Entanglement as a Natural Framework for Exploring Quantum Chaos

We demonstrate that generalized entanglement [Barnum {\em et al.}, Phys. Rev. A {\bf 68}, 032308 (2003)] provides a natural and reliable indicator of quantum chaotic behavior. Since generalized entanglement depends directly on a choice of preferred observables, exploring how generalized entanglement increases under dynamical evolution is possible without invoking an auxiliary coupled system or decomposing the system into arbitrary subsystems. We find that, in the chaotic regime, the long-time saturation value of generalized entanglement agrees with random matrix theory predictions. For our system, we provide physical intuition into generalized entanglement within a single system by invoking the notion of extent of a state. The latter, in turn, is related to other signatures of quantum chaos.Comment: clarified and expanded version accepted by Europhys. Let