A Sampling Theorem with Nonuniform Complex Nodes

AbstractUsing contour integration and a multiplier technique, we establish a sampling theorem with nonuniform complex nodes (tn)n∈Zwhich applies to entire functions of exponential type including band-limitedL2-functions. The sequence (tn)n∈Zmust satisfy supn∈Z|R(tn)−n|<∞ and supn∈Z|I(tn)|<∞. The sampled function may grow faster than any polynomial on the real line

A stochastic model for heart rate fluctuations

Normal human heart rate shows complex fluctuations in time, which is natural, since heart rate is controlled by a large number of different feedback control loops. These unpredictable fluctuations have been shown to display fractal dynamics, long-term correlations, and 1/f noise. These characterizations are statistical and they have been widely studied and used, but much less is known about the detailed time evolution (dynamics) of the heart rate control mechanism. Here we show that a simple one-dimensional Langevin-type stochastic difference equation can accurately model the heart rate fluctuations in a time scale from minutes to hours. The model consists of a deterministic nonlinear part and a stochastic part typical to Gaussian noise, and both parts can be directly determined from the measured heart rate data. Studies of 27 healthy subjects reveal that in most cases the deterministic part has a form typically seen in bistable systems: there are two stable fixed points and one unstable one.Comment: 8 pages in PDF, Revtex style. Added more dat

Rearrangement-free hydroxylation of methylcubanes by a cytochrome P450: the case for dynamical coupling of C-H abstraction and rebound

The highly strained cubylmethyl radical undergoes one of the fastest radical rearrangements known (reported k = 2.9 × 1010 s-1 at 25 °C) through scission of two bonds of the cube. The rearrangement has previously been used as a mechanistic probe to detect radical-based pathways in enzyme-catalyzed C-H oxidations. This paper reports the discovery of highly selective cytochrome P450-catalyzed methylcubane oxidations which notionally proceed via cubylmethyl radical intermediates yet are remarkably free of rearrangement. The bacterial cytochrome P450 CYP101B1 from Novosphingobium aromaticivorans DSM 12444 is found to hydroxylate the methyl group of a range of methylcubane substrates containing a regio-directing carbonyl functionality at C-4. Unlike other reported P450-catalyzed methylcubane oxidations, the designed methylcubanes are hydroxylated with high efficiency and selectivity, giving cubylmethanols in yields of up to 93%. The lack of cubane core ring-opening implies that the cubylmethyl radicals formed during these CYP101B1-catalyzed hydroxylations must have very short lifetimes, of just a few picoseconds, which are too short for them to manifest the side reactivity characteristic of a fully equilibrated P450 intermediate. We propose that the apparent ultrafast radical rebound can be explained by a mechanism in which C-H abstraction and C-O bond formation are merged into a dynamically coupled process, effectively bypassing a discrete radical intermediate. Related dynamical phenomena can be proposed to predict how P450s may achieve various other modes of reactivity by controlling the formation and fate of radical intermediates. In principle, dynamical ideas and two-state reactivity are each individually able to explain apparent ultrashort radical lifetimes in P450 catalysis, but they are best considered together.Md. Raihan Sarkar, Sevan D. Houston, G. Paul Savage, Craig M. Williams, Elizabeth H. Krenske, Stephen G. Bell and James J. De Vos

Anomalous roughening of wood fractured surfaces

Scaling properties of wood fractured surfaces are obtained from samples of three different sizes. Two different woods are studied: Norway spruce and Maritime pine. Fracture surfaces are shown to display an anomalous dynamic scaling of the crack roughness. This anomalous scaling behavior involves the existence of two different and independent roughness exponents. We determine the local roughness exponents ${\zeta}_{loc}$ to be 0.87 for spruce and 0.88 for pine. These results are consistent with the conjecture of a universal local roughness exponent. The global roughness exponent is different for both woods, $\zeta$ = 1.60 for spruce and $\zeta$ = 1.35 for pine. We argue that the global roughness exponent $\zeta$ is a good index for material characterization.Comment: 7 two columns pages plus 8 ps figures, uses psfig. To appear in Physical Review

Exploring the Factors which Result in Cytochrome P450 Catalyzed Desaturation Versus Hydroxylation

Published 14 December 2022The cytochrome P450 family of monooxygenase enzymes have essential biological roles involving the selective oxidation of carbon-hydrogen bonds. They can also catalyze other important metabolic reactions including desaturation to form alkenes. Currently the factors that control the partition between P450 hydroxylation and desaturation pathways are poorly defined. The CYP199A4 enzyme from the bacterium Rhodopseudomonas palustris HaA2 catalyzes the oxidation of 4-ethyl- and 4-isopropyl- benzoic acids with hydroxylation and desaturation occurring in significant quantities. Here we demonstrate that 4-cyclopropylbenzoic acid is regioselectively hydroxylated by CYP199A4 at the benzylic carbon. In contrast, the oxidation of 4- n -propylbenzoic acid by CYP199A4 results in three major metabolites: an alkene from desaturation and two hydroxylation products at the benzylic (Cα) and Cβ carbons in similar quantities. Extending the length of the alkyl substituent resulted in 4- n -butylbenzoic acid being oxidized at the benzylic position (45%) and desaturated (55%). In contrast, 4-isobutylbenzoic generated very little alkene (5%) but was hydroxylated at the benzylic position (54%) and at the tertiary Cβ position (41%). The oxidation of 4- n -propylbenzoic acid by the F298V mutant of CYP199A4 occurred with no hydroxylation at Cβ and a significant increase in metabolites arising from desaturation (73%). The X-ray crystal structures of CYP199A4 with each substrate revealed that they bind in the active site with the alkyl substituent positioned over the heme. However, the longer alkylbenzoic acids were bound in a different conformation as was 4- n -propylbenzoic acid in the F298V mutant. Overall, the changes in metabolite distribution could be ascribed to bond strength differences and the position of the alkyl group relative to the heme.Tom Coleman, Daniel Z. Doherty, Ting Zhang, Matthew N. Podgorski, Ruihong Qiao, Joel H. Z. Lee, John B. Bruning, James J. De Voss, Weihong Zhou, and Stephen G. Bel

Global QCD Analysis and the CTEQ Parton Distributions

The CTEQ program for the determination of parton distributions through a global QCD analysis of data for various hard scattering processes is fully described. A new set of distributions, CTEQ3, incorporating several new types of data is reported and compared to the two previous sets of CTEQ distributions. Comparison with current data is discussed in some detail. The remaining uncertainties in the parton distributions and methods to further reduce them are assessed. Comparisons with the results of other global analyses are also presented.Comment: (Change in Latex style only: 2up style removed since many don't have it.) 35 pages, 23 figures separately submitted as uuencoded compressed ps-file; Michigan State Report # MSU-HEP/41024 and CTEQ 40

Photoproduction of D∗±D^{*\pm} mesons associated with a leading neutron

The photoproduction of $D^{*\pm} (2010)$ mesons associated with a leading neutron has been observed with the ZEUS detector in $ep$ collisions at HERA using an integrated luminosity of 80 pb$^{-1}$. The neutron carries a large fraction, {$x_L>0.2$}, of the incoming proton beam energy and is detected at very small production angles, {$\theta_n<0.8$ mrad}, an indication of peripheral scattering. The $D^*$ meson is centrally produced with pseudorapidity {$|\eta| 1.9$ GeV}, which is large compared to the average transverse momentum of the neutron of 0.22 GeV. The ratio of neutron-tagged to inclusive $D^*$ production is $8.85\pm 0.93({\rm stat.})^{+0.48}_{-0.61}({\rm syst.})\%$ in the photon-proton center-of-mass energy range {$130 <W<280$ GeV}. The data suggest that the presence of a hard scale enhances the fraction of events with a leading neutron in the final state.Comment: 28 pages, 4 figures, 2 table

Measurement of the open-charm contribution to the diffractive proton structure function

Production of D*+/-(2010) mesons in diffractive deep inelastic scattering has been measured with the ZEUS detector at HERA using an integrated luminosity of 82 pb^{-1}. Diffractive events were identified by the presence of a large rapidity gap in the final state. Differential cross sections have been measured in the kinematic region 1.5 < Q^2 < 200 GeV^2, 0.02 < y < 0.7, x_{IP} < 0.035, beta 1.5 GeV and |\eta(D*+/-)| < 1.5. The measured cross sections are compared to theoretical predictions. The results are presented in terms of the open-charm contribution to the diffractive proton structure function. The data demonstrate a strong sensitivity to the diffractive parton densities.Comment: 35 pages, 11 figures, 6 table

Search for contact interactions, large extra dimensions and finite quark radius in ep collisions at HERA

A search for physics beyond the Standard Model has been performed with high-Q^2 neutral current deep inelastic scattering events recorded with the ZEUS detector at HERA. Two data sets, e^+ p \to e^+ X and e^- p \to e^- X, with respective integrated luminosities of 112 pb^-1 and 16 pb^-1, were analyzed. The data reach Q^2 values as high as 40000 GeV^2. No significant deviations from Standard Model predictions were observed. Limits were derived on the effective mass scale in eeqq contact interactions, the ratio of leptoquark mass to the Yukawa coupling for heavy leptoquark models and the mass scale parameter in models with large extra dimensions. The limit on the quark charge radius, in the classical form factor approximation, is 0.85 10^-16 cm.Comment: 28 pages, 4 figures, accepted for publication in Physics Letters