Bayesian optimization using sequential Monte Carlo

We consider the problem of optimizing a real-valued continuous function $f$ using a Bayesian approach, where the evaluations of $f$ are chosen sequentially by combining prior information about $f$, which is described by a random process model, and past evaluation results. The main difficulty with this approach is to be able to compute the posterior distributions of quantities of interest which are used to choose evaluation points. In this article, we decide to use a Sequential Monte Carlo (SMC) approach

A process very similar to multifractional Brownian motion

In Ayache and Taqqu (2005), the multifractional Brownian (mBm) motion is obtained by replacing the constant parameter $H$ of the fractional Brownian motion (fBm) by a smooth enough functional parameter $H(.)$ depending on the time $t$. Here, we consider the process $Z$ obtained by replacing in the wavelet expansion of the fBm the index $H$ by a function $H(.)$ depending on the dyadic point $k/2^j$. This process was introduced in Benassi et al (2000) to model fBm with piece-wise constant Hurst index and continuous paths. In this work, we investigate the case where the functional parameter satisfies an uniform H\"older condition of order \beta>\sup_{t\in \rit} H(t) and ones shows that, in this case, the process $Z$ is very similar to the mBm in the following senses: i) the difference between $Z$ and a mBm satisfies an uniform H\"older condition of order $d>\sup_{t\in \R} H(t)$; ii) as a by product, one deduces that at each point $t\in \R$ the pointwise H\"older exponent of $Z$ is $H(t)$ and that $Z$ is tangent to a fBm with Hurst parameter $H(t)$.Comment: 18 page

Pumice and lapillus scraps: New national environmental-friendly chance for the production of ceramic tiles

Italian pumice and volcanic lapillus scraps have been used in different percentages as alternative raw materials to foreign feldspars in porcelain stoneware mixtures. The aim of this work was to create naturally colored support to limit the use of artificial dyes while maintaining the technical properties of the reference product. For this purpose, the significant presence of chromophores (Fe and Ti in particular) in by-products from extraction of Italian volcanic pumice and lapillus was exploited. The work was carried out in collaboration with a company: the products were made on a laboratory scale and then they were glazed and fired within the industrial production cycle (48 min, 1210 ◦C). The resulting slip and the fired samples were characterized by measuring the efflux time, density, linear shrinkage, water absorption and tensile strength to evaluate the technological performance. In addition, thermogravimetric analysis (TG), differential thermal analysis (DTA), and optical and mechanical dilatometry were performed to study the thermal behavior of the formulations. The obtained products could be classified as porcelain stoneware and belong to the BIa group (WA 0.5%, B. S.>35 MPa) in accordance with UNI EN 14411 ISO 13006

On the asymmetric zero-range in the rarefaction fan

We consider the one-dimensional asymmetric zero-range process starting from a step decreasing profile. In the hydrodynamic limit this initial condition leads to the rarefaction fan of the associated hydrodynamic equation. Under this initial condition and for totally asymmetric jumps, we show that the weighted sum of joint probabilities for second class particles sharing the same site is convergent and we compute its limit. For partially asymmetric jumps we derive the Law of Large Numbers for the position of a second class particle under the initial configuration in which all the positive sites are empty, all the negative sites are occupied with infinitely many first class particles and with a single second class particle at the origin. Moreover, we prove that among the infinite characteristics emanating from the position of the second class particle, this particle chooses randomly one of them. The randomness is given in terms of the weak solution of the hydrodynamic equation through some sort of renormalization function. By coupling the zero-range with the exclusion process we derive some limiting laws for more general initial conditions.Comment: 22 pages, to appear in Journal of Statistical Physic