Dimension improvement in Dhar's refutation of the Eden conjecture

We consider the Eden model on the d-dimensional hypercubical unoriented lattice , for large d. Initially, every lattice point is healthy, except the origin which is infected. Then, each infected lattice point contaminates any of its neighbours with rate 1. The Eden model is equivalent to first passage percolation, with exponential passage times on edges. The Eden conjecture states that the limit shape of the Eden model is a Euclidean ball. By putting the computations of Dhar [Dha88] a little further with modern computers and efficient implementation we obtain improved bounds for the speed of infection. This shows that the Eden conjecture does not hold in dimension superior to 22 (the lower known dimension was 35)

Active network management for electrical distribution systems: problem formulation, benchmark, and approximate solution

With the increasing share of renewable and distributed generation in electrical distribution systems, Active Network Management (ANM) becomes a valuable option for a distribution system operator to operate his system in a secure and cost-effective way without relying solely on network reinforcement. ANM strategies are short-term policies that control the power injected by generators and/or taken off by loads in order to avoid congestion or voltage issues. Advanced ANM strategies imply that the system operator has to solve large-scale optimal sequential decision-making problems under uncertainty. For example, decisions taken at a given moment constrain the future decisions that can be taken and uncertainty must be explicitly accounted for because neither demand nor generation can be accurately forecasted. We first formulate the ANM problem, which in addition to be sequential and uncertain, has a nonlinear nature stemming from the power flow equations and a discrete nature arising from the activation of power modulation signals. This ANM problem is then cast as a stochastic mixed-integer nonlinear program, as well as second-order cone and linear counterparts, for which we provide quantitative results using state of the art solvers and perform a sensitivity analysis over the size of the system, the amount of available flexibility, and the number of scenarios considered in the deterministic equivalent of the stochastic program. To foster further research on this problem, we make available at http://www.montefiore.ulg.ac.be/~anm/ three test beds based on distribution networks of 5, 33, and 77 buses. These test beds contain a simulator of the distribution system, with stochastic models for the generation and consumption devices, and callbacks to implement and test various ANM strategies

Beyond L1: Faster and Better Sparse Models with skglm

We propose a new fast algorithm to estimate any sparse generalized linear model with convex or non-convex separable penalties. Our algorithm is able to solve problems with millions of samples and features in seconds, by relying on coordinate descent, working sets and Anderson acceleration. It handles previously unaddressed models, and is extensively shown to improve state-of-art algorithms. We provide a flexible, scikit-learn compatible package, which easily handles customized datafits and penalties

The Curse of Unrolling: Rate of Differentiating Through Optimization

Computing the Jacobian of the solution of an optimization problem is a central problem in machine learning, with applications in hyperparameter optimization, meta-learning, optimization as a layer, and dataset distillation, to name a few. Unrolled differentiation is a popular heuristic that approximates the solution using an iterative solver and differentiates it through the computational path. This work provides a non-asymptotic convergence-rate analysis of this approach on quadratic objectives for gradient descent and the Chebyshev method. We show that to ensure convergence of the Jacobian, we can either 1) choose a large learning rate leading to a fast asymptotic convergence but accept that the algorithm may have an arbitrarily long burn-in phase or 2) choose a smaller learning rate leading to an immediate but slower convergence. We refer to this phenomenon as the curse of unrolling. Finally, we discuss open problems relative to this approach, such as deriving a practical update rule for the optimal unrolling strategy and making novel connections with the field of Sobolev orthogonal polynomials

Dos Enfoques para Mejorar la Navegación Pedestre por GPS

El presente artículo presenta la calibración de los diferentes modelos utilizados para la navegación pedestre. La información sobre distancias recorridas y elazimut detectado por sensores inerciales es combinada con observaciones de GPSutilizando filtrado de Kalman. Todos los modelos utilizan posiciones de GPS sincorrecciones diferenciales para calibrar los errores sistemáticos presentes en sensores inerciales.Han sido desarrollados diferentes prototipos que integran compases: c.agnéticosdigitales o giroscopios, acelerómetros tri- o bi-axiales, un altímetro y un receptorGPS de monofrecuencia.Los resultados demuestran que un sistema integrado, comparado al uso de unreceptor GPS solo, mejora la fiabilidad y precisión de la trayectoria. Una precisiónabsoluta de menos de 5 metros se logra y se mantiene incluso bajo el modo DecidReckoning (DR.) (cálculo estimado), por ejemplo cuando ninguna señal de satéliteestá disponible. Aprovechando la fuerte correlación entre épocas, no es necesarioel uso de correcciones de DGPS para calibrar los modelos de DR.Lo numerosos desafíos de este campo de investigación se desarrollan en estemomento en el Instituto de Geomática (IGEO-TOPO) del Swiss Federal Instituteof Technology (EPFL) en estrecha colaboración con el Swiss Center for Electronicsand Microtechnology (CSEM) como también con Leica Geosystems AG

Stochastic Timed Automata

A stochastic timed automaton is a purely stochastic process defined on a timed automaton, in which both delays and discrete choices are made randomly. We study the almost-sure model-checking problem for this model, that is, given a stochastic timed automaton A and a property $\Phi$, we want to decide whether A satisfies $\Phi$ with probability 1. In this paper, we identify several classes of automata and of properties for which this can be decided. The proof relies on the construction of a finite abstraction, called the thick graph, that we interpret as a finite Markov chain, and for which we can decide the almost-sure model-checking problem. Correctness of the abstraction holds when automata are almost-surely fair, which we show, is the case for two large classes of systems, single- clock automata and so-called weak-reactive automata. Techniques employed in this article gather tools from real-time verification and probabilistic verification, as well as topological games played on timed automata.Comment: 40 pages + appendi

A detailed source model for the M_w9.0 Tohoku-Oki earthquake reconciling geodesy, seismology, and tsunami records

The 11 March 2011 M_w9.0 Tohoku-Oki earthquake was recorded by an exceptionally large amount of diverse data offering a unique opportunity to investigate the details of this major megathrust rupture. Many studies have taken advantage of the very dense Japanese onland strong motion, broadband, and continuous GPS networks in this sense. But resolution tests and the variability in the proposed solutions have highlighted the difficulty to uniquely resolve the slip distribution from these networks, relatively distant from the source region, and with limited azimuthal coverage. In this context, we present a finite fault slip joint inversion including an extended amount of complementary data (teleseismic, strong motion, high-rate GPS, static GPS, seafloor geodesy, and tsunami records) in an attempt to reconcile them into a single better resolved model. The inversion reveals a patchy slip distribution with large slip (up to 64 m) mostly located updip of the hypocenter and near the trench. We observe that most slip is imaged in a region where almost no earthquake was recorded before the main shock and around which intense interplate seismicity is observed afterward. At a smaller scale, the largest slip pattern is imaged just updip of an important normal fault coseismically activated. This normal fault has been shown to be the mark of very low dynamic friction allowing extremely large slip to propagate up to the free surface. The spatial relationship between this normal fault and our slip distribution strengthens its key role in the rupture process of the Tohoku-Oki earthquake

Plant biodiversity assessment through soil eDNA reflects temporal and local diversity

1. Several studies have shown the potential of eDNA-based proxies for plant identification, but little is known about their spatial and temporal resolution. This limits its use for plant biodiversity assessments and monitoring of vegetation responses to environmental changes. Here we calibrate the temporal and spatial plant signals detected with soil eDNA surveys by comparing with a standard visual above-ground vegetation survey. 2. Our approach compares vegetation in an old-growth boreal forest in southern Norway, surveyed in 100 permanent 1-m2 plots seven times over a 30-year period, with a single soil eDNA metabarcoding-based survey from soil samples collected at the same 100 plots in the year of the last vegetation survey. 3. On average, 60% and 10% of the vascular plants and bryophytes recorded across all vegetation surveys were detected by soil eDNA. Taxa detected by soil eDNA were more representative for the local taxa pool than for the specific plot, and corresponded to those surveyed over the 30-year period although most closely matched the current taxa composition. Soil eDNA detected abundant taxa better than rare ones although both rare taxa and taxa unrecorded by the visual survey were detected. 4. Our study highlights the potential of soil eDNA assessments for monitoring of vegetation responses over broad spatial and temporal scales. The method's ability to detect abundant taxa makes it suitable for assessment of vegetation composition in a specific area and for broad-scale plant diversity assessments