Inférence topologique

Les données provenant de l'échantillonnage fin d'un processus continu (champ aléatoire) peuvent être représentées sous forme d'images. Un test statistique permettant de détecter une différence entre deux images peut être vu comme un ensemble de tests où chaque pixel est comparé au pixel correspondant de l'autre image. On utilise alors une méthode de contrôle de l'erreur de type I au niveau de l'ensemble de tests, comme la correction de Bonferroni ou le contrôle du taux de faux-positifs (FDR). Des méthodes d'analyse de données ont été développées en imagerie médicale, principalement par Keith Worsley, utilisant la géométrie des champs aléatoires afin de construire un test statistique global sur une image entière. Il s'agit d'utiliser l'espérance de la caractéristique d'Euler de l'ensemble d'excursion du champ aléatoire sous-jacent à l'échantillon au-delà d'un seuil donné, pour déterminer la probabilité que le champ aléatoire dépasse ce même seuil sous l'hypothèse nulle (inférence topologique). Nous exposons quelques notions portant sur les champs aléatoires, en particulier l'isotropie (la fonction de covariance entre deux points du champ dépend seulement de la distance qui les sépare). Nous discutons de deux méthodes pour l'analyse des champs anisotropes. La première consiste à déformer le champ puis à utiliser les volumes intrinsèques et les compacités de la caractéristique d'Euler. La seconde utilise plutôt les courbures de Lipschitz-Killing. Nous faisons ensuite une étude de niveau et de puissance de l'inférence topologique en comparaison avec la correction de Bonferroni. Finalement, nous utilisons l'inférence topologique pour décrire l'évolution du changement climatique sur le territoire du Québec entre 1991 et 2100, en utilisant des données de température simulées et publiées par l'Équipe Simulations climatiques d'Ouranos selon le modèle régional canadien du climat.

On the Meridional Structure of Annular Modes

Using a simple stochastic model, the authors illustrate that the occurrence of a meridional dipole in the first empirical orthogonal function (EOF) of a time-dependent zonal jet is a simple consequence of the north–south excursion of the jet center, and this geometrical fact can be understood without appealing to fluid dynamical principles. From this it follows that one ought not, perhaps, be surprised at the fact that such dipoles, commonly referred to as the Arctic Oscillation (AO) or the Northern Annular Mode (NAM), have robustly been identified in many observational studies and appear to be ubiquitous in atmospheric models across a wide range of complexity.

The Upper Valanginian (Early Cretaceous) positive carbon-isotope event recorded in terrestrial plants

Our understanding of the ancient ocean-atmosphere system has focused on oceanic proxies. However, the study of terrestrial proxies is equally necessary to constrain our understanding of ancient climates and linkages between the terrestrial and oceanic carbon reservoirs. We have analyzed carbon-isotope ratios from fossil plant material through the Valanginian and Lower Hauterivian from a shallow-marine, ammonite-constrained succession in the Crimean Peninsula of the southern Ukraine in order to determine if the Upper Valanginian positive carbon-isotope excursion is expressed in the atmosphere. delta(13)C(plant) values fluctuate around -23% to -22% for the Valanginian-Hauterivian, except during the Upper Valanginian where delta(13)C(plant) values record a positive excursion to similar to-18%. Based upon ammonite biostratigraphy from Crimea, and in conjunction with a composite Tethyan marine delta(13)C(carb) curve, several conclusions can be drawn: (1) the delta(13)C(plant) record indicates that the atmospheric carbon reservoir was affected; (2) the defined ammonite correlations between Europe and Crimea are synchronous; and (3) a change in photosynthetic carbon-isotope fractionation, caused by a decrease in atmospheric PCO2, occurred during the Upper Valanginian Positive delta(13)C excursion. Our new data, combined with other paleoenvironmental and paleoclimatic information, indicate that the Upper Valanginian was a cool period (icehouse) and highlights that the Cretaceous period was interrupted by periods of cooling and was not an equable climate as previously thought. (C) 2005 Elsevier B.V. All rights reserved.

Smoothness of scale functions for spectrally negative Lévy processes

Scale functions play a central role in the fluctuation theory of spectrally negative Lévy processes and often appear in the context of martingale relations. These relations are often require excursion theory rather than Itô calculus. The reason for the latter is that standard Itô calculus is only applicable to functions with a sufficient degree of smoothness and knowledge of the precise degree of smoothness of scale functions is seemingly incomplete. The aim of this article is to offer new results concerning properties of scale functions in relation to the smoothness of the underlying Lévy measure. We place particular emphasis on spectrally negative Lévy processes with a Gaussian component and processes of bounded variation. An additional motivation is the very intimate relation of scale functions to renewal functions of subordinators. The results obtained for scale functions have direct implications offering new results concerning the smoothness of such renewal functions for which there seems to be very little existing literature on this topic.

Middle and Late Cenomanian anoxia in shallow and deeper shelf environments of western Morocco

The response of shallow-water sequences to oceanic anoxic event 2 and mid-Cenomanian events 1a and 1b was investigated along the west African margin of Morocco north of Agadir (Azazoul) and correlated with the deep-water sequence of the Tarfaya Basin (Mohammed Beach) based on biostratigraphy, mineralogy, phosphorus and stable isotopes. In the deeper Mohammed Beach section results show double peaks in δ13Corg for mid-Cenomanian events 1a and 1b (Rotalipora reicheli biozone, lower CC10a biozone), the characteristic oceanic anoxic event 2 δ13C excursion (Rotalipora cushmani extinction, top of CC10a biozone) and laminated (anoxic) black shale. In the shallow environment north of Agadir, a fluctuating sea-level associated with dysoxic, brackish and mesotrophic conditions prevailed during the middle to late Cenomanian, as indicated by oyster biostromes, nannofossils, planktonic and benthonic foraminiferal assemblages. Anoxic conditions characteristic of oceanic anoxic event 2 (for example, laminated black shales) did not reach into shallow-water environments until the maximum transgression of the early Turonian. Climate conditions decoupled along the western margin of Morocco between mid-Cenomanian event 1b and the Cenomanian–Turonian boundary, as also observed in eastern Tethys. North of Agadir alternating humid and dry seasonal conditions prevailed, whereas in the Tarfaya Basin the climate was dry and seasonal. This climatic decoupling can be attributed to variations in the Intertropical Convergence Zone and in the intensity of the north-east trade winds in tropical areas.

The expression of the end-Cenomanian oceanic anoxic event (OAE 2) in the Helvetic Alps

Upper Cenomanian pelagic sediments from the northern Alpine Helvetic fold-and-thrust belt (northern Tethyan margin) coeval with Oceanic Anoxic Event (OAE) 2 are characterized by the temporal persistence of micrite sedimentation and lack of organic carbon-rich layers. We studied an expanded section in the Chrummflueschlucht (east of Euthal, Switzerland), which encompasses the OAE 2 time interval. In order to identify the paleoceanographic and paleoenvironmental conditions during OAE 2 in this part of the northern Tethyan margin, and more specifically to trace eventual changes in nutrient levels and oxic conditions, we investigated the biostratigraphy (planktonic foraminifera), the bulk-rock mineralogy, and measured stable carbon- and oxygen-isotopes, total phosphorus (P) and redox-sensitive trace-element (RSTE) contents. We were able to determine – with some remaining uncertainties – the different planktonic foraminiferal biozones characteristic of the Cenomanian–Turonian boundary interval (Rotalipora cushmani, Whiteinella archaeocretacea and Helvetoglobotruncana helvetica zones). In the lower part of the section (R. cushmani total range zone), the bulk-rock δ13C record shows a long-term increase. Within sediments attributed to the W. archaeocretacea partial range zone, δ13C values reach a maximum of 3.3‰ (peak “a”). In the following the values decrease and increase again to arrive at a plateau with high δ13C values of around 3.1‰, which ends with a peak of 3.3‰ (peak “c”). At the top of the section, in sediments belonging to the H. helvetica total range zone, δ13C values decrease to post-OAE values of around 2.2‰. The last occurrence of R. cushmani is observed just above the positive δ13C shift characterizing OAE 2. P contents display small variations along the section with a long-term decreasing trend towards the top. Before the OAE 2 interval, P values show higher values and relatively good covariation with detrital input, indicating higher nutrient input before OAE 2. In sediments corresponding to the onset of the δ13C positive excursion, P content is marked by a sharp peak probably linked to a slowdown in sedimentation rates and/or the presence of a small hiatus, as is shown by the presence of glauconite and phosphatic grains. In the interval corresponding to OAE 2, P values remain low and increase slightly at the end of the positive shift in the δ13C record (in the H. helvetica total range zone). The average contents of RSTE (U, V, As, Co, Mo and Mn) remain low throughout the section and appreciable RSTE enrichments have not been observed for the sedimentary interval corresponding to OAE 2. No correlation is observed with stratigraphic trends in RSTE contents in organic-rich deeper-water sections. The presence of double-keeled planktonic foraminifera species during most of the Cenomanian/Turonian boundary event is another evidence of relatively well-oxygenated conditions in this part of the northern Tethyan outer shelf. Our results show that the Chrummflueschlucht section corresponds to one of the most complete section for the Cenomanian–Turonian boundary interval known from the Helvetic realm even if a small hiatus may be present at the onset of the δ13C record (peak “a”). The evolution of P contents suggests an increase in input of this nutritive element at the onset of OAE2. However, the trends in RSTE contents and the planktonic foraminifera assemblages show that the Helvetic realm has not been affected by strongly depleted oxygen conditions during OAE 2.

Solar wind control of magnetospheric energy content: substorm quenching and multiple onsets

In this paper we report coordinated multispacecraft and ground-based observations of a double substorm onset close to Scandinavia on November 17, 1996. The Wind and the Geotail spacecraft, which were located in the solar wind and the subsolar magnetosheath, respectively, recorded two periods of southward directed interplanetary magnetic field (IMF). These periods were separated by a short northward IMF excursion associated with a solar wind pressure pulse, which compressed the magnetosphere to such a degree that Geotail for a short period was located outside the bow shock. The first period of southward IMF initiated a substorm growth. phase, which was clearly detected by an array of ground-based instrumentation and by Interball in the northern tail lobe. A first substorm onset occurred in close relation to the solar wind pressure pulse impinging on the magnetopause and almost simultaneously with the northward turning of the IMF. However, this substorm did not fully develop. In clear association with the expansion of the magnetosphere at the end of the pressure pulse, the auroral expansion was stopped, and the northern sky cleared. We will present evidence that the change in the solar wind dynamic pressure actively quenched the energy available for any further substorm expansion. Directly after this period, the magnetometer network detected signatures of a renewed substorm growth phase, which was initiated by the second southward turning of the IMF and which finally lead to a second, and this time complete, substorm intensification. We have used our multipoint observations in order to understand the solar wind control of the substorm onset and substorm quenching. The relative timings between the observations on the various satellites and on the ground were used to infer a possible causal relationship between the solar wind pressure variations and consequent substorm development. Furthermore, using a relatively simple algorithm to model the tail lobe field and the total tail flux, we show that there indeed exists a close relationship between the relaxation of a solar wind pressure pulse, the reduction of the tail lobe field, and the quenching of the initial substorm.

On the cause of a magnetospheric flux transfer event

We present a detailed investigation of a magnetospheric flux transfer event (FTE) seen by the Active Magnetospheric Tracer Explorer (AMPTE) UKS and IRM satellites around 1046 UT on October 28, 1984. This event has been discussed many times previously in the literature and has been cited as support for a variety of theories of FTE formation. We make use of a model developed to reproduce ion precipitations seen in the cusp ionosphere. The analysis confirms that the FTE is well explained as a brief excursion into an open low-latitude boundary layer (LLBL), as predicted by two theories of magnetospheric FTEs: namely, that they are bulges in the open LLBL due to reconnection rate enhancements or that they are indentations of the magnetopause by magnetosheath pressure increases (but in the presence of ongoing steady reconnection). The indentation of the inner edge of the open LLBL that these two models seek to explain is found to be shallow for this event. The ion model reproduces the continuous evolution of the ion distribution function between the sheath-like population at the event center and the surrounding magnetospheric populations; it also provides an explanation of the high-pressure core of the event as comprising field lines that were reconnected considerably earlier than those that are draped over it to give the event boundary layer. The magnetopause transition parameter is used to isolate a field rotation on the boundaries of the core, which is subjected to the tangential stress balance test. The test identifies this to be a convecting structure, which is neither a rotational discontinuity (RD) nor a contact discontinuity, but could possibly be a slow shock. In addition, evidence for ion reflection off a weak RD on the magnetospheric side of this structure is found. The event structure is consistent in many ways with features predicted for the open LLBL by analytic MHD theories and by MHD and hybrid simulations. The de Hoffman-Teller velocity of the structure is significantly different from that of the magnetosheath flow, indicating that it is not an indentation caused by a high-pressure pulse in the sheath but is consistent with the motion of newly opened field lines (different from the sheath flow because of the magnetic tension force) deduced from the best fit to the ion data. However, we cannot here rule out the possibility that the sheath flow pattern has changed in the long interval between the two satellites observing the FTE and subsequently emerging into the magnetosheath; thus this test is not conclusive in this particular case. Analysis of the fitted elapsed time since reconnection shows that the core of the event was reconnected in one pulse and the event boundary layer was reconnected in a subsequent pulse. Between these two pulses is a period of very low (but nonzero) reconnection rate, which lasts about 14 mins. Thus the analysis supports, but does not definitively verify, the concept that the FTE is a partial passage into an open LLBL caused by a traveling bulge in that layer produced by a pulse in reconnection rate.

Interplanetary magnetic field control of dayside auroral activity and the transfer of momentum across the dayside magnetopause

The orientation of the Interplanetary Magnetic Field (IMF) during transient bursts of ionospheric flow and auroral activity in the dayside auroral ionosphere is studied, using data from the EISCAT radar, meridian-scanning photometers, and an all-sky TV camera, in conjunction with simultaneous observations of the interplanetary medium by the IMP-8 satellite. It is found that the ionospheric flow and auroral burst events occur regularly (mean repetition period equal to 8.3 ± 0.6 min) during an initial period of about 45 min when the IMF is continuously and strongly southward in GSM coordinates, consistent with previous observations of the occurrence of transient dayside auroral activity. However, in the subsequent 1.5 h, the IMF was predominantly northward, and only made brief excursions to a southward orientation. During this period, the mean interval between events increased to 19.2 ± 1.7 min. If it is assumed that changes in the North-South component of the IMF are aligned with the IMF vector in the ecliptic plane, the delays can be estimated between such a change impinging upon IMP-8 and the response in the cleft ionosphere within the radar field-of-view. It is found that, to within the accuracy of this computed lag, each transient ionospheric event during the period of predominantly northward IMF can be associated with a brief, isolated southward excursion of the IMF, as observed by IMP-8. From this limited period of data, we therefore suggest that transient momentum exchange between the magnetosheath and the ionosphere occurs quasi-periodically when the IMF is continuously southward, with a mean period which is strikingly similar to that for Flux Transfer Events (FTEs) at the magnetopause. During periods of otherwise northward IMF, individual momentum transfer events can be triggered by brief swings to southward IMF. Hence under the latter conditions the periodicity of the events can reflect a periodicity in the IMF, but that period will always be larger than the minimum value which occurs when the IMF is strongly and continuously southward.

Palaeoenvironmental changes during the Valanginian: new insights from variations in phosphorus contents and bulk- and clay mineralogies in the western Tethys

Paleoenvironmental and paleoclimatic changes during the Valanginian carbon isotopic excursion (CIE) have been investigated in the western Tethys. For this purpose, bulk-rock and clay mineralogies, as well as phosphorus (P) contents were evaluated in a selection of five sections located in the Vocontian Basin (Angles, SE France; Alvier, E Switzerland; Malleval, E France), and the Lombardian Basin (Capriolo, N Italy; Breggia, S Switzerland). Within the CIE interval, bulk-rock and clay mineralogies are inferred to reflect mostly climate change. The onset of the CIE (Busnardoites campylotoxus ammonite Zone) is characterized by higher detrital index (DI: sum of the detrital minerals divided by calcite contents) values and the presence of kaolinite in their clay-mineral assemblages. In the late Valanginian (from the Saynoceras verrucosum Zone up to the end of the Valanginian), the samples show relatively variable DI and lower values or the absence of kaolinite. The variation in the mineralogical composition is interpreted as reflecting a change from a climate characterized by optimal weathering conditions associated with an increase in terrigenous input on the southern European margin during the CIE towards an overall unstable climate associated with drier conditions in the late Valanginian. This is contrasted by a dissymmetry (proximal vs distal) along the studied transect, the northern Tethyan margin being more sensitive to changes in continental input compared to the distal environments. P accumulation rates (PAR) present similar features. In the Vocontian basin, P content variations are associated with changes in terrigenous influx, whereas in the Lombardian basin (i.e. Capriolo and Breggia), PAR values are less well correlated. This is mainly because the deeper part of the Tethys was less sensitive to changes in continental inputs. The onset of the CIE (top of the B. campylotoxus Zone) records a general increase in PAR suggesting an increase in marine nutrient levels. This is linked to higher continental weathering rates and the enhanced influx of nutrients into the ocean. In the period corresponding to the shift itself, P contents show a dissymmetry between the Vocontian and Lombardian basins (proximal vs distal). For the sections of Malleval, Alvier and Angles, a decrease in P concentrations associated to a decrease in detrital input is observed. In Capriolo and Breggia, PAR show maximum values during the plateau, indicating a more complex interaction between different P sources. The time interval including the top of S. verrucosum Zone up to the end of the Valanginian is characterized by variable PAR values, suggesting variable nutrient influxes. These changes are in agreement with an evolution towards seasonally contrasted conditions in the late Valanginian.

The expression of the Cenomanian-Turonian oceanic anoxic event in Tibet

The Gongzha section of Tibet, China is located at the northern margin of the Indian Plate (SE Tethys) and is characterized by hemipelagic grey marls and marly limestones, light grey limestones and silty limestones, but no organic-rich sediments. High-resolution biostratigraphy reveals an expanded Cenomanian–Turonian (CT) boundary interval and the δ13C record includes the main features of the classical positive carbon-isotope excursion that characterizes the CT oceanic anoxic event. The biotic response inferred from the foraminifera suggests that oxic to dysoxic conditions prevailed, except for a short interval marked by peak abundance of Heterohelix that indicates a significantly dysoxic environment during the δ13C “b” peak excursion. The overall decreasing trend in redox-sensitive trace elements (RSTE) during the maximum δ13C excursion confirms the absence of significant longer-lasting anoxia in the Gongzha section. Enrichments in RSTE are linked to phases of increased detrital input. Chemical weathering indices suggest that the upper Cenomanian sediments accumulated under an increasingly hot and humid climate that culminated near the CT boundary. In the early Turonian lower weathering indices suggest a warm, drier climatic regime with reduced continental runoff. Phosphorus mass-accumulation rates show a significant peak at the onset of the positive δ13C excursion, followed by a decrease up to the basal Turonian. This pattern is positively correlated with the long-term decrease in detrital index as also observed in numerous other CT boundary sections (e.g., Eastbourne, Pueblo, and Whadi El Ghaib, Sinaï). Long-term phosphorus accumulation in the Gongzha section is therefore associated with changes in detrital input. The overall decreased detrital input can be explained by the increasingly remote continental sources due to the major transgression at the end of Cenomanian, coupled with changes in continental weathering intensity linked to increasingly more arid climate conditions.

Late Barremian-Early Aptian palaeoenvironmental change: the Cassis-La Bedoule section (SE France)

The well-dated section of Cassis-La Bédoule in the South Provencal Basin (southern France) allows for a detailed reconstruction of palaeoenvironmental change during the latest Barremian and Early Aptian. For this study, phosphorus (P) and clay-mineral contents, stable-isotope ratios on carbonate (δ13Ccarb) and organic matter (δ13Corg), and redox-sensitive trace elements (RSTE: V, U, As, Co, and Mo) have been measured in this historical stratotype. The base of the section consists of rudist limestone, which is attributed to the Urgonian platform. The presence of low P and RSTE content, and content of up to 30% kaolinite indicate deposition under oligotrophic and oxic conditions, and the presence of warm, humid climatic conditions on the adjacent continent. The top of the Urgonian succession is marked by a hardground with encrusted brachiopods and bivalves, which is interpreted as a drowning surface. The section continues with a succession of limestone and marl containing the first occurrence of planktonic foraminifera. This interval includes several laminated, organic-rich layers recording RSTE enrichments and high Corg:Ptot ratios. The deposition of these organic-rich layers was associated with oxygen-depleted conditions and a large positive excursion in δ13Corg. During this interval, a negative peak in the δ13Ccarb record is observed, which dates as latest Barremian. This excursion is coeval with negative excursions elsewhere in Tethyan platform and basin settings and is explained by the increased input of light dissolved inorganic carbon by rivers and/or volcanic activity. In this interval, an increase in P content, owing to reworking of nearshore sediments during the transgression, is coupled with a decrease in kaolinite content, which tends to be deposited in more proximal areas. The overlying hemipelagic sediments of the Early Aptian Deshayesites oglanlensis and D. weissi zones indicate rather stable palaeoenvironmental conditions with low P content and stable δ13C records. A change towards marl-dominated beds occurs close to the end of the D. weissi zone. These beds display a long decrease in their δ13Ccarb and δ13Corg records, which lasted until the end of the Deshayesites deshayesi subzone (corresponding to C3 in Menegatti et al., 1998). This is followed by a positive shift during the Roloboceras hambrovi and Deshayesites grandis subzones, which corresponds in time to oceanic anoxic event (OAE) 1a interval. This positive shift is coeval with two increases in the P content. The marly interval equivalent to OAE 1a lacks organic-rich deposits and RSTE enrichments indicating that oxic conditions prevailed in this particular part of the Tethys ocean. The clay mineralogy is dominated by smectite, which is interpreted to reflect trapping of kaolinite on the surrounding platforms rather than indicating a drier climate.

Chemostratigraphy of the Tamengo Formation (Corumba Group, Brazil) A contribution to the calibration of the Ediacaran carbon-isotope curve

The Corumba Group cropping out in the southern Paraguay Belt in Brazil is one of the most complete Ediacaran sedimentary archives of palaeogeographic climatic biogeochemical and biotic evolution in southwestern Gondwana The unit hosts a rich fossil record including acritarchs vendotaenids (Vendo taenia Eoholynia) soft-bodied metazoans (Corumbella) and skeletal fossils (Cloudina Titanotheca) The Tamengo Formation made up mainly of limestones and marls provides a rich bio- and chemostratigraphic record Several outcrops formerly assigned to the Cuiaba Group are here included in the Tamengo Formation on the basis of lithological and chemostratigraphical criteria High-resolution carbon isotopic analyses are reported for the Tamengo Formation showing (from base to top) (1) a positive delta(13)C excursion to +4 parts per thousand PDB above post-glacial negative values (2) a negative excursion to -3 5 parts per thousand associated with a marked regression and subsequent transgression (3) a positive excursion to +5 5 parts per thousand and (4) a plateau characterized by delta(13)C around +3 parts per thousand A U-Pb SHRIMP zircon age of an ash bed Interbedded in the upper part of the delta(13)C positive plateau yielded 543 +/- 3 Ma which is considered as the depositional age (Babinski et al 2008a) The positive plateau in the upper Tamengo Formation and the preceding positive excursion are ubiquitous features in several successions worldwide including the Nama Group (Namibia) the Dengying Formation (South China) and the Nafun and Ara groups (Oman) This plateau is constrained between 542 and 551 Ma thus consistent with the age of the upper Tamengo Formation The negative excursion of the lower Tamengo Formation may be correlated to the Shuram-Wonoka negative anomaly although delta(13)C values do not fall beyond -3 5 parts per thousand in the Brazilian sections Sedimentary breccias occur just beneath this negative excursion in the lower Tamengo Formation One possible interpretation of the origin of these breccias is a glacioeustatic sea-level fall but a tectonic interpretation cannot be completely ruled out Published by Elsevier B V

Global perturbation of the marine Ca isotopic composition in the aftermath of the Marinoan global glaciation

Ca isotopic compositions of Marinoan post-glacial carbonate successions in Brazil and NW Canada were measured Both basal dolostones display delta(44/40)Ca values between 1 and 0 7 parts per thousand overlying limestones show a negative Ca isotope excursion to values around 0 1 parts per thousand and delta(44/40)Ca values rapidly increase up-section to near 2 0 parts per thousand In the Brazilian successions those high delta(44/40)Ca values rapidly decrease and stabilize to values between 0 6 and 0 9 parts per thousand These Ca isotope secular variation trends are unlike those of Sturtian post-glacial carbonate successions but similar to those of Marinoan post-glacial carbonate successions in Namibia suggesting that the perturbation of the marine Ca cycle was global This recommends Ca isotope stratigraphy as a tool to correlate Neoproterozoic post-glacial carbonate successions worldwide While the lowermost and uppermost strata have delta(44/40)Ca values typical of Phanerozoic carbonates the extremes 0 1 and 2 0 parts per thousand have not been thus far reported for other marine carbonates These extreme values suggest a short-lived non-actualistic perturbation in the marine Ca cycle Simple box modelling of the Marinoan post-glacial marine Ca cycle can reproduce the extreme values only by postulating a two-step process with Ca input initially exceeding Ca removal trough carbonate precipitation followed by precipitation overtaking a decreased Ca Input (C) 2010 Elsevier B V All rights reserved

On slowdown and speedup of transient random walks in random environment

We consider one-dimensional random walks in random environment which are transient to the right. Our main interest is in the study of the sub-ballistic regime, where at time n the particle is typically at a distance of order O(n (kappa) ) from the origin, kappa is an element of (0, 1). We investigate the probabilities of moderate deviations from this behaviour. Specifically, we are interested in quenched and annealed probabilities of slowdown (at time n, the particle is at a distance of order O (n (nu 0)) from the origin, nu(0) is an element of (0, kappa)), and speedup (at time n, the particle is at a distance of order n (nu 1) from the origin , nu(1) is an element of (kappa, 1)), for the current location of the particle and for the hitting times. Also, we study probabilities of backtracking: at time n, the particle is located around (-n (nu) ), thus making an unusual excursion to the left. For the slowdown, our results are valid in the ballistic case as well.