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

Minimum memory for generating rare events

We classify the rare events of structured, memoryful stochastic processes and use this to analyze sequential and parallel generators for these events. Given a stochastic process, we introduce a method to construct a process whose typical realizations are a given process' rare events. This leads to an expression for the minimum memory required to generate rare events. We then show that the recently discovered classical-quantum ambiguity of simplicity also occurs when comparing the structure of process fluctuations

Palaeo-environmental evolution of Central Asia during the Cenozoic: new insights from the continental sedimentary archive of the Valley of Lakes (Mongolia)

The Valley of Lakes basin (Mongolia) contains a unique continental sedimentary archive, suitable for constraining the influence of tectonics and climate change on the aridification of Central Asia in the Cenozoic. We identify the sedimentary provenance, the (post)depositional environment and the palaeo-climate based on sedimentological, petrographical, mineralogical, and (isotope) geochemical signatures recorded in authigenic and detrital silicates as well as soil carbonates in a sedimentary succession spanning from ~34 to 21 Ma. The depositional setting was characterized by an ephemeral braided river system draining prograding alluvial fans, with episodes of lake, playa or open-steppe sedimentation. Metamorphics from the northern adjacent Neoarchean to late Proterozoic hinterlands provided a continuous influx of silicate detritus to the basin, as indicated by K-Ar ages of detrital muscovite (~798-728 Ma) and discrimination function analysis. The authigenic clay fraction is dominated by illite-smectite and “hairy” illite (K-Ar ages of ~34-25 Ma), which formed during coupled petrogenesis and precipitation from hydrothermal fluids originating from major basalt flow events (~32-29 and ~29-25 Ma). Changes in hydroclimate are recorded in [delta]18O and [delta]13C profiles of soil carbonates and in silicate mineral weathering patterns, indicating that comparatively humid to semi-arid conditions prevailed in the late(st) Eocene, changing into arid conditions in the Oligocene and back to humid to semi-arid conditions in the early Miocene. Aridification steps are indicated at ~34-33, ~31, ~28 and ~23 Ma and coincide with some episodes of high-latitude ice-sheet expansion inferred from marine deep-sea sedimentary records. This suggests that long-term variations in the ocean-atmosphere circulation patterns due to pCO2 fall, reconfiguration of ocean gateways and ice-sheet expansion in Antarctica could have impacted the hydroclimate and weathering regime in the basin. We conclude that the aridification in Central Asia was triggered by reduced moisture influx by westerly winds driven by Cenozoic climate forcing and the exhumation of the Tian Shan and Altai Mountains and modulated by global climate events

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

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.