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The evolution and lifetime of protoplanetary disks (PPDs) play a central role in the formation and architecture of planetary systems. Astronomical observations suggest that PPDs evolve in two timescales, accreting onto the star for up to several million years (Myr) followed by gas dissipation within <1 Myr. Because solar nebula magnetic fields are sustained by the gas of the protoplanetary disk, we can use paleomagnetic measurements to infer the lifetime of the solar nebula. Here, we use paleomagnetic measurements of meteorites to constrain this lifetime and investigate whether the solar nebula had a two-timescale evolution. We report on paleomagnetic measurements of bulk subsamples of two CO carbonaceous chondrites: Allan Hills A77307 and Dominion Range 08006. If magnetite in these meteorites can acquire a crystallization remanent magnetization that recorded the ambient field during aqueous alteration, our measurements suggest that the local magnetic field strength at the CO parent body location was <0.9 \muT at some time between 2.7 and 5.1 Myr after the formation of calcium-aluminum-rich inclusions. Coupled with previous paleomagnetic studies, we conclude that the dissipation of the solar nebula in the 3-7 AU region occurred <1.5 Myr after the dissipation of the nebula in the 1-3 AU region, suggesting that protoplanetary disks go through a two-timescale evolution in their lifetime, consistent with dissipation by photoevaporation and/or magnetohydrodynamic winds. We also discuss future directions necessary to obtain robust records of solar nebula fields using bulk chondrites, including obtaining ages from meteorites and experimental work to determine how magnetite acquires magnetization during chondrite parent body alteration., Comment: 30 pages, 7 figures, 4 tables

The problem of extracting as much information as possible from a sequence of observations of a stationary stochastic process $X_0,X_1,...X_n$ has been considered by many authors from different points of view. It has long been known through the work of D. Bailey that no universal estimator for $\textbf{P}(X_{n+1}|X_0,X_1,...X_n)$ can be found which converges to the true estimator almost surely. Despite this result, for restricted classes of processes, or for sequences of estimators along stopping times, universal estimators can be found. We present here a survey of some of the recent work that has been done along these lines.

Let $\{X_n\}$ be a stationary and ergodic time series taking values from a finite or countably infinite set ${\cal X}$. Assume that the distribution of the process is otherwise unknown. We propose a sequence of stopping times $\lambda_n$ along which we will be able to estimate the conditional probability $P(X_{\lambda_n+1}=x|X_0,...,X_{\lambda_n})$ from data segment $(X_0,...,X_{\lambda_n})$ in a pointwise consistent way for a restricted class of stationary and ergodic finite or countably infinite alphabet time series which includes among others all stationary and ergodic finitarily Markovian processes. If the stationary and ergodic process turns out to be finitarily Markovian (among others, all stationary and ergodic Markov chains are included in this class) then $ \lim_{n\to \infty} {n\over \lambda_n}>0$ almost surely. If the stationary and ergodic process turns out to possess finite entropy rate then $\lambda_n$ is upperbounded by a polynomial, eventually almost surely.

We describe estimators $\chi_n(X_0,X_1,...,X_n)$, which when applied to an unknown stationary process taking values from a countable alphabet ${\cal X}$, converge almost surely to $k$ in case the process is a $k$-th order Markov chain and to infinity otherwise.

Let $\{X_n\}_{n=0}^{\infty}$ be a stationary real-valued time series with unknown distribution. Our goal is to estimate the conditional expectation of $X_{n+1}$ based on the observations $X_i$, $0\le i\le n$ in a strongly consistent way. Bailey and Ryabko proved that this is not possible even for ergodic binary time series if one estimates at all values of $n$. We propose a very simple algorithm which will make prediction infinitely often at carefully selected stopping times chosen by our rule. We show that under certain conditions our procedure is strongly (pointwise) consistent, and $L_2$ consistent without any condition. An upper bound on the growth of the stopping times is also presented in this paper.

This article reviews a generous sampling of both classical and more recent results on the interplay between measurable and topological dynamics. In the first part we have surveyed the strong analogies between ergodic theory and topological dynamics as shown in the treatment of recurrence phenomena, equicontinuity and weak mixing, distality and entropy. The prototypical result of the second part is the statement that any abstract measure probability preserving system can be represented as a continuous transformation of a compact space, and thus in some sense ergodic theory embeds into topological dynamics. The work also contains several new results. In particular (1) we prove, for a Polish dynamical system, the equivalence of the existence of a Borel cross-section with the coincidence of recurrence and periodicity; and (2) for compact dynamical systems we provide a converse to the local variational principle., Comment: This article is going to appear in the volume: Handbook of Dynamical systems, Vol. 1B, Hasselblatt and Katok, eds., Elsevier, Amsterdam

This paper continues the work Glasner-Tsirelson-Weiss, ArXiv math.DS/0311450. For a Polish group G the notions of G-continuous functions and whirly actions are further exploited to show that: (i) A G-action is whirly iff it admits no nontrivial spatial (= pointwise) factors. (ii) Every action of a Polish Levy group is whirly. (iii) There exists a Polish monothetic group which is not Levy but admits a whirly action. (iv) In the Polish group Aut(X,\mu), for the generic automorphism T, the action of the Polish group \Lambda(T) = closure {T^n: n \in Z} \subset Aut(X,\mu) on the Lebesgue space (X,\mu) is whirly. (v) The Polish additive group underlying a separable Hilbert space admits both spatial and whirly faithful actions. (vi) When G is a non-archimedean Polish group then every G-action is spatial., Comment: 17 pages

Classical ergodic theory deals with measure (or measure class) preserving actions of locally compact groups on Lebesgue spaces. An important tool in this setting is a theorem of Mackey which provides spatial models for Boolean G-actions. We show that in full generality this theorem does not hold for actions of Polish groups. In particular there is no Borel model for the Polish automorphism group of a Gaussian measure. In fact, we show that this group as well as many other Polish groups do not admit any nontrivial Borel measure preserving actions., Comment: v2 (final), 18 pages. Added: remarks 1.4, 1.5, 1.9, 3.6 (supplemented); Appendix B; some historical background; refs 1, 5, 12, 18, 20-25, 29, 32

Seeking the signs of life on Mars is often considered the "first among equal" objectives for any potential Mars Sample Return (MSR) campaign. Among the geological settings considered to have the greatest potential for recording evidence of ancient life or its pre-biotic chemistry on Mars are lacustrine (and marine, if ever present) sedimentary depositional environments. This potential, and the possibility of returning samples that could meaningfully address this objective, have been greatly enhanced by investigations of an ancient redox stratified lake system in Gale crater by the Curiosity rover.

Highly promising locales for biosignature prospecting on Mars are ancient hydrothermal deposits, formed by the interaction of surface water with heat from volcanism or impacts. On Earth, they occur throughout the geological record (to at least approx. 3.5 Ga), preserving robust mineralogical, textural and compositional evidence of thermophilic microbial activity. Hydrothermal systems were likely present early in Mars' history, including at two of the three finalist candidate landing sites for M2020, Columbia Hills and NE Syrtis Major. Hydrothermal environments on Earth's surface are varied, constituting subaerial hot spring aprons, mounds and fumaroles; shallow to deep-sea hydrothermal vents (black and white smokers); and vent mounds and hot-spring discharges in lacustrine and fluvial settings. Biological information can be preserved by rapid, spring-sourced mineral precipitation, but also could be altered or destroyed by postdepositional events. Thus, field observations need to be followed by detailed laboratory analysis to verify potential biosignatures. See Attachment

The red planet is a magnetic planet. Mars' iron-rich surface is strongly magnetized, likely dating back to the Noachian epoch when the surface may have been habitable. Paleomagnetic measurements of returned samples could transform our understanding of the Martian dynamo and its connection to climatic and planetary thermal evolution and provide powerful constraints on the preservation state of biosignatures in the samples.

The 2011 Visions & Voyages Planeary Science Decadal Survey identified making significant progress toward the return of samples from Mars as the highest priority goal for flagship missions in next decade. Numerous scientific objectives have been identified that could be advanced through the potential return and analysis of martian rock, regolith, and atmospheric samples. The analysis of returned martian samples would be particularly valuable in in-creasing our understanding of Early Mars. There are many outstanding gaps in our knowledge about Early Mars in areas such as potential astrobiology, geochronology, planetary evolution (including the age, context, and processes of accretion, differentiation, magmatic, and magnetic history), the history of water at the martian surface, and the origin and evolution of the martian atmosphere. Here we will discuss scientific objectives that could be significantly advanced by Mars sample return.

The Mars 2020 rover will collect carefully selected samples of rock and regolith as it explores a potentially habitable ancient environment on Mars. Using the drill, rock cores and regolith will be collected directly into ultraclean sample tubes that are hermetically sealed and, later, deposited on the surface of Mars for potential return to Earth by a subsequent mission. Thorough characterization of any contamination of the samples at the time of their analysis will be essential for achieving the objectives of Mars returned sample science (RSS). We refer to this characterization as contamination knowledge (CK), which is distinct from contamination control (CC). CC is the set of activities that limits the input of contaminating species into a sample, and is specified by requirement thresholds. CK consists of identifying and characterizing both potential and realized contamination to better inform scientific investigations of the returned samples. Based on lessons learned by other sample return missions with contamination-sensitive scientific objectives, CC needs to be "owned" by engineering, but CK needs to be "owned" by science. Contamination present at the time of sample analysis will reflect the sum of contributions from all contamination vectors up to that point in time. For this reason, understanding the integrated history of contamination may be crucial for deciphering potentially confusing contaminant-sensitive observations. Thus, CK collected during the Mars sample return (MSR) campaign must cover the time period from the initiation of hardware construction through analysis of returned samples in labs on Earth. Because of the disciplinary breadth of the scientific objectives of MSR, CK must include a broad spectrum of contaminants covering inorganic (i.e., major, minor, and trace elements), organic, and biological molecules and materials.

Integration of Apollo 17 field observations and photographs, sample investigations, Lunar Reconnaissance Orbiter Camera images, Chandrayaan-1 Moon Mineralogy Mapper (M(sup 3)) spectra, and Miniature Radio Frequency (Mini-RF) S-band radar images provides new insights into the geology of the valley of Taurus-Littrow on the Moon. Connecting the various remote observations to sample data enables a set of new conclusions to be drawn regarding the geological evolution of the valley. Structural considerations and published and recalculated Ar-40/Ar-39 analyses of samples from the North Massif and the Sculptured Hills indicate that the Crisium basin formed about 3.93 Ga; the Serenitatis basin about 3.82 Ga; and the Imbrium basin no earlier than 3.82 Ga and no later than the average of 3.72 Ga for 33 age dates from samples of the valley's mare basalts. Strong evidence continues to support the conclusion of others (Lucchitta, 1972; Spudis et al., 2011; Fassett et al., 2012) that the Sculptured Hills physiographic unit consists of Imbrium ejecta. Interpretation of M(sup 3) spectral data and Apollo 17 samples indicate that rock units of the Sculptured Hills consist of a largely coherent, Mg-suite pluton. LROC NAC stereo images and Mini-RF data indicate the presence of several exposed pyroclastic fissures across the Sculptured Hills. Rim boulders at Camelot Crater constitute nearly in situ wall rocks of that crater rather than ejecta and provide an opportunity for investigations of remanent magnetic field orientation at the time of the eruption of late mare basalt lavas in the valley. Paleomagnetic field orientation information also may be obtained relative to melt-breccia contacts in North Massif boulders that suggest original horizontal orientations. LROC images indicate the existence of two temporally separate light mantle avalanche deposits. The origin, potential flow mechanisms, and geology of the youngest avalanche from the South Massif have been clarified. The existence of two distinct light mantle avalanches raises doubt about the association of either light mantle avalanche with secondary impacts related to the Tycho impact event. Alternatively, the Lee-Lincoln thrust fault appears to have triggered the second light mantle avalanche between 70 and 110 Ma. A simple structural analysis shows that this thrust fault dips 20-25 degrees to the southwest where it crosses the North Massif and to the west where it crosses the valley floor. Mini-RF data reveal a line of reduced reflections roughly perpendicular to contours on the North Massif about 3 km to the east of the Lee-Lincoln fault. Although this line is possibly an older ancillary fault, LROC NAC stereo images indicate that it may be best explained as a pyroclastic fissure. A debris flow of dark, apparent pyroclastic ash lies below the southeast end of the potential fissure. Finally, young lunar impact glass sample 70019 has been precisely located within LROC NAC images and oriented for the first time using 60 mm (f.l.) sample documentation photographs. Sample 70019 can now be employed in lunar paleomagnetic field orientation studies.