On the limiting law of the length of the longest common and increasing subsequences in random words

Let $X=(X_i)_{i\ge 1}$ and $Y=(Y_i)_{i\ge 1}$ be two sequences of independent and identically distributed (iid) random variables taking their values, uniformly, in a common totally ordered finite alphabet. Let LCI$_n$ be the length of the longest common and (weakly) increasing subsequence of $X_1\cdots X_n$ and $Y_1\cdots Y_n$. As $n$ grows without bound, and when properly centered and normalized, LCI$_n$ is shown to converge, in distribution, towards a Brownian functional that we identify.Comment: Some corrections from the published version are provided, some typos are also correcte

Asymptotics for random Young diagrams when the word length and alphabet size simultaneously grow to infinity

Given a random word of size $n$ whose letters are drawn independently from an ordered alphabet of size $m$, the fluctuations of the shape of the random RSK Young tableaux are investigated, when $n$ and $m$ converge together to infinity. If $m$ does not grow too fast and if the draws are uniform, then the limiting shape is the same as the limiting spectrum of the GUE. In the non-uniform case, a control of both highest probabilities will ensure the convergence of the first row of the tableau toward the Tracy--Widom distribution.Comment: Published in at http://dx.doi.org/10.3150/09-BEJ218 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Impact of dry weather discharges on annual pollution from a separate storm sewer in Toulouse, France

The city of Toulouse with its separate sewer system is ideal for studying stormwater. However, during dry weather, the storm sewer also discharges water into the environment, and it is the impact of these discharges on annual pollution from storm sewer that is the object of this study. Samples have been taken from the outlets of two storm drains located in heavily and moderately urbanized areas. Sampling has been undertaken during wet weather and during dry weather between January 2010 and February 2011. Three dry weather and two wet weather samples have been taken every three months and from each outlet. The overall pollution parameters have been analyzed (chemical oxygen demand, biological oxygen demand, total nitrogen, ammonium, nitrate, total phosphorus, suspended solid matter, volatile suspended matter, pH, conductivity, turbidity). Characterization has been completed by analysis of trace organic compounds: polycyclic aromatic hydrocarbons, total hydrocarbons, methyl tert-butyl ether, diethylhexylphthalate, nonylphenols, hormones (estradiol, ethinylestradiol). For certain parameters, the results obtained did not conform to legislative requirements concerning discharge into the natural environment. Correlations between these parameters have been studied, and identified between several of them using principal component analysis. The most important correlation observed was between conductivity and concentration in total phosphorus for one of the outlet. Results showed that dry weather had an impact on annual pollution load from separate storm sewer and that level of urbanization was also a factor. The effect of season has been studied but no significant impact was found

Investigating the plate motion of the Adriatic microplate by 3D thermomechanical modelling

Mantle dynamics in the Alpine-Mediterranean area provides a complex geodynamic picture and is still subject of ongoing debate. The Adriatic microplate represents the central part of the Mediterranean and is affected by various subduction zones, like the Hellenic slab, the Calabrian slab or the Apenninic slab. These different processes pose challenges in making qualitative assumptions about the unique impact factors influencing the plate motion. In this study, we conduct 3D thermomechanical forward simulations of the Alpine-Mediterranean area using the LaMEM (Kaus et al., 2016). Our simulations incorporate a viscoelastoplastic rheology and an internal free surface, enabling us to investigate both internal dynamics and surface response. The initial setup for the simulations is based on the kinematic reconstructions of Le Breton et al. (2021) at 35 Ma. Our objective is to determine the main driving forces behind the plate motion of the Adriatic microplate by examining the effects of different model parameters, such as the thermal structure, slab geometry, mantle viscosity, and brittle parameters of the crust. Although these forward simulations do not yet precisely reproduce the present-day tectonic setting, they provide valuable insights into the parameters that influence the plate dynamics. Based on our findings, we have identified two distinct stages of plate motion affecting Adria over the past 35 million years. The initial phase is dominated by the northwards moving African plate, which pushes Adria to the north. However, as the Hellenic slab advances from the east and the Calabrian and Apenninic slabs propagate from the west, the Adriatic microplate is decoupling from the African plate which induces an anticlockwise rotation of Adria. The extent and the thermal structure of the Ionian oceanic lithosphere are significant parameters that influence the retreat of the Hellenic and Calabrian slab and therefore the rotation of Adria. Simultaneously, the northwards motion of Adria during the rotation is caused by the retreat of the Western Alpine slab

3D geodynamic modelling of the present-day and long-term deformation of the Alps and Adria

Linking geophysical data with geological constraints to understand the dynamics of Alpine Mountain building was one of the main goals of the 4D-MB SPP project. Whereas seismic tomography inversions give a snapshot of how the seismic velocity structure may look like today, geological constraints give (incomplete) pieces of information of how it may have evolved over time. Linking such information with the physics of the lithosphere requires geodynamic numerical models and due to the geometric complexity of the region, 3D is a must. A problem with geodynamic models is that the driving forces are usually the density differences of subducting plates with the surrounding mantle (or far-field forces), whereas the (uncertain) rheology of mantle and crustal rocks plays a crucial role as well. As such, there are quite a few uncertainties in the input parameters, even if the geometry is well-constrained. During the first phase of the 4D-MB project, we focused on present-day models of the Alpine system. Whereas it is possible to invert for the rheology of the lithosphere in mountain belts using probabilistic Bayesian methods (Baumann and Kaus, 2015), this method requires a large number of forward simulations and thus remains infeasible in 3D. An alternative approach is to employ gradient-based inversion methods, in which the adjoint method is employed as a particularly efficient method to compute the gradient of the misfit of the model and data (usually GPS data) versus model parameters (Reuber et al., 2020; Reuber, 2021). Since the adjoint gradient method is computationally cheap (compared to a forward simulation), it can also be used to quickly determine the key model parameters of a particular simulation (Reuber et al., 2018b) or can be combined with gravity and seismic inversions (Reuber and Simons, 2020). We had initially applied this to a case where the starting forward model setup was already giving a reasonably good fit to the uplift data, in which case the method rapidly converged (Reuber et al., 2018a). It thus seemed straightforward to do the same for the Alps. Yet, several issues were encountered in the process: a) we need to consider a much wider region than just the Alps to avoid issues with the lateral boundaries; b) even with high-resolution P-wave tomographic models at hand, one still needs to interpret the seismic velocity anomalies to create an initial model setup, which is a highly non-unique step and results in various possible interpretations; c) coming up with an initial forward model that gives a reasonably good fit to the GPS data turned out to be a significant challenge. Despite running well over 350 forward simulations, we failed to obtain forward simulations that provided a well-enough fit of the velocity in Adria, and without a good starting model, gradient based geodynamic inversions do not converge to a meaningful solution (Reuber, 2020). More recently, we made another attempt in which seismic velocity was directly translated to density and viscosity anomalies using a simple, linear, scaling law, while also prescribing the far-field velocities at the model boundaries (such as that of the N. Anatolian plate). Results give a better fit in Adria (Fig. 1A), but also show that the details of the slab geometry underneath the Alps do not have much impact on the model results, while the model fit within the Alps remains unsatisfying (perhaps because of the small velocities there). Instead of just focusing at the present day structure of the Alps, it is also interesting to see how the system evolved over the last 20-30 million years, which was the focus of our project during the 2nd phase of 4D-MB. The idea was to start with a plate tectonic reconstruction (Le Breton et al., 2021) and let the model evolve forward in time. As for the present-day models, there are many uncertainties in the plate tectonic reconstructions, such as: What was the slab dip? What were the lengths of the slabs? Were they laterally broken or not? What was the thermal and rheological structure of the plates? Given the difficulties with the present-day models, and the increased computational demands of time-dependent simulations, it is unreasonable to expect model results that magically fit all available constraints. Yet, after performing many hundreds of forward simulations, we do get some consistent results and in some of the simulations Adria moves northward and rotates anticlockwise relative to Europe by about the correct amount. The Gibraltar slab arrives at the correct place (Fig. 1B), and the models clearly show that the northward motion of Africa has little impact on the dynamics of Adria, which is instead mostly driven by the interaction of the Hellenic and Calabrian slabs while being pulled northwards by the retreating Western Alpine slab. The size and thermal structure of the Ionian oceanic lithosphere is important as well. Figure 1: A) Example of present-day geodynamic models, B) Snapshot of a forward geodynamic simulation that started at 30 Ma. We also made various technical advances, which includes the Julia package GeophysicalModelGenerator.jl to create complicated 3D geodynamic model setups from geophysical/geological data, DataPicker.jl which provides a GUI for GMG, and LaMEM.jl which is the Julia interface to LaMEM and allows installing and running LaMEM in parallel (either directly from Julia or via Jupyter or Pluto notebooks). We also extended LaMEM to include a continuous integration, adjoint inversion (Reuber et al., 2020; Reuber, 2021) and sensitivity testing (Reuber et al., 2018b)

Les robots apparaissent dans l'espace de vie des humains

National audienceLes robots industriels feront bientôt figure de dinosaures devant les systèmes autonomes et " intelligents " en préparation. Certains, comme les systèmes d'assistance à la conduite, les métros automatiques ou encore les robots pour les blocs opératoires sont déjà familiers ; beaucoup d'autres sont dans les cartons, notamment dans le domaine des services et dans celui de l'assistance aux personnes âgées ou handicapées. Ces premières réalisations marquent le début d'une ère où les robots seront capables de partager l'espace de vie des humains et d'interagir avec eux d'une manière sûre et socialement acceptable

A Global Plate Model Including Lithospheric Deformation Along Major Rifts and Orogens Since the Triassic

Global deep‐time plate motion models have traditionally followed a classical rigid plate approach, even though plate deformation is known to be significant. Here we present a global Mesozoic–Cenozoic deforming plate motion model that captures the progressive extension of all continental margins since the initiation of rifting within Pangea at ~240 Ma. The model also includes major failed continental rifts and compressional deformation along collision zones. The outlines and timing of regional deformation episodes are reconstructed from a wealth of published regional tectonic models and associated geological and geophysical data. We reconstruct absolute plate motions in a mantle reference frame with a joint global inversion using hot spot tracks for the last 80 million years and minimizing global trench migration velocities and net lithospheric rotation. In our optimized model, net rotation is consistently below 0.2°/Myr, and trench migration scatter is substantially reduced. Distributed plate deformation reaches a Mesozoic peak of 30 × 106 km2 in the Late Jurassic (~160–155 Ma), driven by a vast network of rift systems. After a mid‐Cretaceous drop in deformation, it reaches a high of 48 x 106 km2 in the Late Eocene (~35 Ma), driven by the progressive growth of plate collisions and the formation of new rift systems. About a third of the continental crustal area has been deformed since 240 Ma, partitioned roughly into 65% extension and 35% compression. This community plate model provides a framework for building detailed regional deforming plate networks and form a constraint for models of basin evolution and the plate‐mantle system