The log-linear group-lasso estimator and its asymptotic properties

We define the group-lasso estimator for the natural parameters of the exponential families of distributions representing hierarchical log-linear models under multinomial sampling scheme. Such estimator arises as the solution of a convex penalized likelihood optimization problem based on the group-lasso penalty. We illustrate how it is possible to construct an estimator of the underlying log-linear model using the blocks of nonzero coefficients recovered by the group-lasso procedure. We investigate the asymptotic properties of the group-lasso estimator as a model selection method in a double-asymptotic framework, in which both the sample size and the model complexity grow simultaneously. We provide conditions guaranteeing that the group-lasso estimator is model selection consistent, in the sense that, with overwhelming probability as the sample size increases, it correctly identifies all the sets of nonzero interactions among the variables. Provided the sequences of true underlying models is sparse enough, recovery is possible even if the number of cells grows larger than the sample size. Finally, we derive some central limit type of results for the log-linear group-lasso estimator.Comment: Published in at http://dx.doi.org/10.3150/11-BEJ364 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Tunneling behavior of Ising and Potts models in the low-temperature regime

We consider the ferromagnetic $q$-state Potts model with zero external field in a finite volume and assume that the stochastic evolution of this system is described by a Glauber-type dynamics parametrized by the inverse temperature $\beta$. Our analysis concerns the low-temperature regime $\beta \to \infty$, in which this multi-spin system has $q$ stable equilibria, corresponding to the configurations where all spins are equal. Focusing on grid graphs with various boundary conditions, we study the tunneling phenomena of the $q$-state Potts model. More specifically, we describe the asymptotic behavior of the first hitting times between stable equilibria as $\beta \to \infty$ in probability, in expectation, and in distribution and obtain tight bounds on the mixing time as side-result. In the special case $q=2$, our results characterize the tunneling behavior of the Ising model on grid graphs.Comment: 13 figure

The mechanism of iron binding processes in erionite fibres

Fibrous erionite-Na from Rome (Oregon, USA) was K-exchanged and characterized from the structural point of view. In addition, the modifications experienced after contact with a Fe(II) source were investigated for evaluating if the large potassium ions, blocking off nearly all the erionite cavity openings, might prevent the Fe(II) binding process, which is currently assumed to be one of the reasons of the toxicity of erionite. The K-exchanged sample had a 95% reduction of the BET surface area indicating that it behaves as a mesoporous material. Exchanged K is segregated at K2 and at OW sites commonly occupied by H2O. The latter K cations provide a relevant contribution to the reduction of the surface area. Surprisingly, despite the collapse of its surface area the sample preserves the tendency to bind Fe(II). Therefore, yet in the case of a peculiar and potentially hostile structural environment the Fe(II) ion-exchange process has essentially the same kinetics observed in a typical erionite sample. This is a clear evidence of the very limited effect of the chemical composition of erionite on the Fe(II) binding process and reasonably it does not play a significant role in its toxicity

Delay performance in random-access grid networks

We examine the impact of torpid mixing and meta-stability issues on the delay performance in wireless random-access networks. Focusing on regular meshes as prototypical scenarios, we show that the mean delays in an $L\times L$ toric grid with normalized load $\rho$ are of the order $(\frac{1}{1-\rho})^L$. This superlinear delay scaling is to be contrasted with the usual linear growth of the order $\frac{1}{1-\rho}$ in conventional queueing networks. The intuitive explanation for the poor delay characteristics is that (i) high load requires a high activity factor, (ii) a high activity factor implies extremely slow transitions between dominant activity states, and (iii) slow transitions cause starvation and hence excessively long queues and delays. Our proof method combines both renewal and conductance arguments. A critical ingredient in quantifying the long transition times is the derivation of the communication height of the uniformized Markov chain associated with the activity process. We also discuss connections with Glauber dynamics, conductance and mixing times. Our proof framework can be applied to other topologies as well, and is also relevant for the hard-core model in statistical physics and the sampling from independent sets using single-site update Markov chains

Indoor real-time localisation for multiple autonomous vehicles fusing vision, odometry and IMU data

Due to the increasing usage of service and industrial autonomous vehicles, a precise localisation is an essential component required in many applications, e.g. indoor robot navigation. In open outdoor environments, differential GPS systems can provide precise positioning information. However, there are many applications in which GPS cannot be used, such as indoor environments. In this work, we aim to increase robot autonomy providing a localisation system based on passive markers, that fuses three kinds of data through extended Kalman filters. With the use of low cost devices, the optical data are combined with other robots’ sensor signals, i.e. odometry and inertial measurement units (IMU) data, in order to obtain accurate localisation at higher tracking frequencies. The entire system has been developed fully integrated with the Robotic Operating System (ROS) and has been validated with real robots

Effects of fuel composition on charge preparation, combustion and knock tendency in a high performance GDI engine. Part I: RANS analysis

The paper analyses the effects of fuel composition modelling in a turbocharged GDI engine for sport car applications. Particularly, a traditional single-component gasoline-surrogate fuel is compared to a seven-component fuel model available in the open literature. The multi-component fuel is represented using the Discrete-Continuous-Multi-Component modelling approach, and it is specifically designed in order to match the volatility of an actual RON95 European gasoline. The comparison is carried out following a detailed calibration with available experimental measurements for a full load maximum power engine speed operation of the engine, and differences are analyzed and critically discussed for each of the spray evolution, mixture stratification and combustion. In the present paper (Part I), a RANS approach is used to preliminarily investigate the behaviour of the fuel model on the average engine cycle. In the subsequent Part II of the same paper, the numerical framework is evolved into a more refined LES approach, in order to take into account cycle-to-cycle variations in mixture formation and knock tendency

Effects of fuel composition on charge preparation, combustion and knock tendency in a high performance GDI engine. Part II: Les analysis

As discussed in the Part I of this paper, a numerical activity is carried out in order to analyse the effects of fuel composition modelling in a turbocharged GDI engine for sport car applications. While Part I analyses the "ensemble averaged" macroscopic effects on spray evolution, mixture stratification, combustion and knock tendency, in Part II of this paper cycle-to-cycle variations are analysed and discussed using a multi-cycle LES numerical framework, again comparing results from a more traditional single-component fuel surrogate model to those of a multi-component one. A purposely developed numerical approach is applied to properly account for the effects of the Discrete-Continuous-Multi-Component fuel formulation on the charge preparation: just before the spark timing, each vaporized fuel fraction is lumped back into a single-component surrogate fuel to allow the combustion model (ECFM-3Z, in its LES formulation) to take place. At the beginning of a new injection process, the numerical framework for the injected spray is switched back to Multi-Component, thus allowing each fuel fraction to independently spread, vaporize and diffuse in the combustion chamber according to the cycle-specific characteristics. A detailed comparison between the two fuel formulations is carried out on both average and rms values of the most influencing fields just before the spark discharge