Typical Gibbs configurations for the 1d Random Field Ising Model with long range interaction

We study a one--dimensional Ising spin systems with ferromagnetic, long--range interaction decaying as n^{-2+\a}, \a \in [0,\frac 12], in the presence of external random fields. We assume that the random fields are given by a collection of symmetric, independent, identically distributed real random variables, gaussian or subgaussian with variance $\theta$. We show that for temperature and variance of the randomness small enough, with an overwhelming probability with respect to the random fields, the typical configurations, within volumes centered at the origin whose size grow faster than any power of $\th^{-1}$, % {\bf around the origin} are intervals of $+$ spins followed by intervals of $-$ spins whose typical length is \simeq \th^{-\frac{2}{(1-2\a)}} for 0\le \a<1/2 and $\simeq e^{\frac 1 {\th^{2}}}$ for \a=1/2

Partially observed Markov random fields are variable neighborhood random fields

The present paper has two goals. First to present a natural example of a new class of random fields which are the variable neighborhood random fields. The example we consider is a partially observed nearest neighbor binary Markov random field. The second goal is to establish sufficient conditions ensuring that the variable neighborhoods are almost surely finite. We discuss the relationship between the almost sure finiteness of the interaction neighborhoods and the presence/absence of phase transition of the underlying Markov random field. In the case where the underlying random field has no phase transition we show that the finiteness of neighborhoods depends on a specific relation between the noise level and the minimum values of the one-point specification of the Markov random field. The case in which there is phase transition is addressed in the frame of the ferromagnetic Ising model. We prove that the existence of infinite interaction neighborhoods depends on the phase.Comment: To appear in Journal of Statistical Physic

DNA barcoding as a molecular tool to track down mislabeling and food piracy

DNA barcoding is a molecular technology that allows the identification of any biological species by amplifying, sequencing and querying the information from genic and/or intergenic standardized target regions belonging to the extranuclear genomes. Although these sequences represent a small fraction of the total DNA of a cell, both chloroplast and mitochondrial barcodes chosen for identifying plant and animal species, respectively, have shown sufficient nucleotide diversity to assess the taxonomic identity of the vast majority of organisms used in agriculture. Consequently, cpDNA and mtDNA barcoding protocols are being used more and more in the food industry and food supply chains for food labeling, not only to support food safety but also to uncover food piracy in freshly commercialized and technologically processed products. Since the extranuclear genomes are present in many copies within each cell, this technology is being more easily exploited to recover information even in degraded samples or transformed materials deriving from crop varieties and livestock species. The strong standardization that characterizes protocols used worldwide for DNA barcoding makes this technology particularly suitable for routine analyses required by agencies to safeguard food safety and quality. Here we conduct a critical review of the potentials of DNA barcoding for food labeling along with the main findings in the area of food piracy, with particular reference to agrifood and livestock foodstuffs

Phase Transitions in Ferromagnetic Ising Models with spatially dependent magnetic fields

In this paper we study the nearest neighbor Ising model with ferromagnetic interactions in the presence of a space dependent magnetic field which vanishes as $|x|^{-\alpha}$, $\alpha >0$, as $|x|\to \infty$. We prove that in dimensions $d\ge 2$ for all $\beta$ large enough if $\alpha>1$ there is a phase transition while if $\alpha<1$ there is a unique DLR state.Comment: to appear in Communications in Mathematical Physic

Geometry of contours and Peierls estimates in d=1 Ising models

Following Fr\"ohlich and Spencer, we study one dimensional Ising spin systems with ferromagnetic, long range interactions which decay as $|x-y|^{-2+\alpha}$, $0\leq \alpha\leq 1/2$. We introduce a geometric description of the spin configurations in terms of triangles which play the role of contours and for which we establish Peierls bounds. This in particular yields a direct proof of the well known result by Dyson about phase transitions at low temperatures.Comment: 28 pages, 3 figure