Prediction and Generation of Binary Markov Processes: Can a Finite-State Fox Catch a Markov Mouse?

Understanding the generative mechanism of a natural system is a vital component of the scientific method. Here, we investigate one of the fundamental steps toward this goal by presenting the minimal generator of an arbitrary binary Markov process. This is a class of processes whose predictive model is well known. Surprisingly, the generative model requires three distinct topologies for different regions of parameter space. We show that a previously proposed generator for a particular set of binary Markov processes is, in fact, not minimal. Our results shed the first quantitative light on the relative (minimal) costs of prediction and generation. We find, for instance, that the difference between prediction and generation is maximized when the process is approximately independently, identically distributed.Comment: 12 pages, 12 figures; http://csc.ucdavis.edu/~cmg/compmech/pubs/gmc.ht

The Role of Regulated mRNA Stability in Establishing Bicoid Morphogen Gradient in Drosophila Embryonic Development

The Bicoid morphogen is amongst the earliest triggers of differential spatial pattern of gene expression and subsequent cell fate determination in the embryonic development of Drosophila. This maternally deposited morphogen is thought to diffuse in the embryo, establishing a concentration gradient which is sensed by downstream genes. In most model based analyses of this process, the translation of the bicoid mRNA is thought to take place at a fixed rate from the anterior pole of the embryo and a supply of the resulting protein at a constant rate is assumed. Is this process of morphogen generation a passive one as assumed in the modelling literature so far, or would available data support an alternate hypothesis that the stability of the mRNA is regulated by active processes? We introduce a model in which the stability of the maternal mRNA is regulated by being held constant for a length of time, followed by rapid degradation. With this more realistic model of the source, we have analysed three computational models of spatial morphogen propagation along the anterior-posterior axis: (a) passive diffusion modelled as a deterministic differential equation, (b) diffusion enhanced by a cytoplasmic flow term; and (c) diffusion modelled by stochastic simulation of the corresponding chemical reactions. Parameter estimation on these models by matching to publicly available data on spatio-temporal Bicoid profiles suggests strong support for regulated stability over either a constant supply rate or one where the maternal mRNA is permitted to degrade in a passive manner

Measurement of the diffractive structure function in deep inelastic scattering at HERA

This paper presents an analysis of the inclusive properties of diffractive deep inelastic scattering events produced in $ep$ interactions at HERA. The events are characterised by a rapidity gap between the outgoing proton system and the remaining hadronic system. Inclusive distributions are presented and compared with Monte Carlo models for diffractive processes. The data are consistent with models where the pomeron structure function has a hard and a soft contribution. The diffractive structure function is measured as a function of \xpom, the momentum fraction lost by the proton, of $\beta$, the momentum fraction of the struck quark with respect to \xpom, and of $Q^2$. The \xpom dependence is consistent with the form \xpoma where $a~=~1.30~\pm~0.08~(stat)~^{+~0.08}_{-~0.14}~(sys)$ in all bins of $\beta$ and $Q^2$. In the measured $Q^2$ range, the diffractive structure function approximately scales with $Q^2$ at fixed $\beta$. In an Ingelman-Schlein type model, where commonly used pomeron flux factor normalisations are assumed, it is found that the quarks within the pomeron do not saturate the momentum sum rule.Comment: 36 pages, latex, 11 figures appended as uuencoded fil

Measurement of the cross-section ratio sigma_{psi(2S)}/sigma_{J/psi(1S)} in deep inelastic exclusive ep scattering at HERA

The exclusive deep inelastic electroproduction of $\psi(2S)$ and $J/\psi(1S)$ at an $ep$ centre-of-mass energy of 317 GeV has been studied with the ZEUS detector at HERA in the kinematic range $2 < Q^2 < 80$ GeV$^2$, $30 < W < 210$ GeV and $|t| < 1$ GeV$^2$, where $Q^2$ is the photon virtuality, $W$ is the photon-proton centre-of-mass energy and $t$ is the squared four-momentum transfer at the proton vertex. The data for $2 < Q^2 < 5$ GeV$^2$ were taken in the HERA I running period and correspond to an integrated luminosity of 114 pb$^{-1}$. The data for $5 < Q^2 < 80$ GeV$^2$ are from both HERA I and HERA II periods and correspond to an integrated luminosity of 468 pb$^{-1}$. The decay modes analysed were $\mu^+\mu^-$ and $J/\psi(1S) \,\pi^+\pi^-$ for the $\psi(2S)$ and $\mu^+\mu^-$ for the $J/\psi(1S)$. The cross-section ratio $\sigma_{\psi(2S)}/\sigma_{J/\psi(1S)}$ has been measured as a function of $Q^2, W$ and $t$. The results are compared to predictions of QCD-inspired models of exclusive vector-meson production.Comment: 24 pages, 8 figure

An NLO QCD analysis of inclusive cross-section and jet-production data from the ZEUS experiment

The ZEUS inclusive differential cross-section data from HERA, for charged and neutral current processes taken with e+ and e- beams, together with differential cross-section data on inclusive jet production in e+ p scattering and dijet production in \gamma p scattering, have been used in a new NLO QCD analysis to extract the parton distribution functions of the proton. The input of jet data constrains the gluon and allows an accurate extraction of \alpha_s(M_Z) at NLO; \alpha_s(M_Z) = 0.1183 \pm 0.0028(exp.) \pm 0.0008(model) An additional uncertainty from the choice of scales is estimated as \pm 0.005. This is the first extraction of \alpha_s(M_Z) from HERA data alone.Comment: 37 pages, 14 figures, to be submitted to EPJC. PDFs available at http://durpdg.dur.ac.uk/hepdata in LHAPDFv

Limits on the effective quark radius from inclusive epep scattering at HERA

The high-precision HERA data allows searches up to TeV scales for Beyond the Standard Model contributions to electron-quark scattering. Combined measurements of the inclusive deep inelastic cross sections in neutral and charged current $ep$ scattering corresponding to a luminosity of around 1 fb$^{-1}$ have been used in this analysis. A new approach to the beyond the Standard Model analysis of the inclusive $ep$ data is presented; simultaneous fits of parton distribution functions together with contributions of "new physics" processes were performed. Results are presented considering a finite radius of quarks within the quark form-factor model. The resulting 95% C.L. upper limit on the effective quark radius is $0.43\cdot 10^{-16}$ cm.Comment: 10 pages, 4 figures, accepted by Phys. Lett.

High-E_T dijet photoproduction at HERA

The cross section for high-E_T dijet production in photoproduction has been measured with the ZEUS detector at HERA using an integrated luminosity of 81.8 pb-1. The events were required to have a virtuality of the incoming photon, Q^2, of less than 1 GeV^2 and a photon-proton centre-of-mass energy in the range 142 < W < 293 GeV. Events were selected if at least two jets satisfied the transverse-energy requirements of E_T(jet1) > 20 GeV and E_T(jet2) > 15 GeV and pseudorapidity requirements of -1 < eta(jet1,2) < 3, with at least one of the jets satisfying -1 < eta(jet) < 2.5. The measurements show sensitivity to the parton distributions in the photon and proton and effects beyond next-to-leading order in QCD. Hence these data can be used to constrain further the parton densities in the proton and photon.Comment: 36 pages, 13 figures, 20 tables, including minor revisions from referees. Accepted by Phys. Rev.

Measurement of event shapes in deep inelastic scattering at HERA

Inclusive event-shape variables have been measured in the current region of the Breit frame for neutral current deep inelastic ep scattering using an integrated luminosity of 45.0 pb^-1 collected with the ZEUS detector at HERA. The variables studied included thrust, jet broadening and invariant jet mass. The kinematic range covered was 10 < Q^2 < 20,480 GeV^2 and 6.10^-4 < x < 0.6, where Q^2 is the virtuality of the exchanged boson and x is the Bjorken variable. The Q dependence of the shape variables has been used in conjunction with NLO perturbative calculations and the Dokshitzer-Webber non-perturbative corrections (`power corrections') to investigate the validity of this approach.Comment: 7+25 pages, 6 figure