Random-field random surfaces

We study how the typical gradient and typical height of a random surface are modified by the addition of quenched disorder in the form of a random independent external field. The results provide quantitative estimates, sharp up to multiplicative constants, in the following cases. It is shown that for real-valued disordered random surfaces of the $\nabla \phi$ type with a uniformly convex interaction potential: (i) The gradient of the surface delocalizes in dimensions $1\le d\le 2$ and localizes in dimensions $d\ge3$. (ii) The surface delocalizes in dimensions $1\le d\le 4$ and localizes in dimensions $d\ge 5$. It is further shown that for the integer-valued disordered Gaussian free field: (i) The gradient of the surface delocalizes in dimensions $d=1,2$ and localizes in dimensions $d\ge3$. (ii) The surface delocalizes in dimensions $d=1,2$. (iii) The surface localizes in dimensions $d\ge 3$ at weak disorder strength. The behavior in dimensions $d\ge 3$ at strong disorder is left open. The proofs rely on several tools: explicit identities satisfied by the expectation of the random surface, the Efron--Stein concentration inequality, a coupling argument for Langevin dynamics (originally due to Funaki and Spohn) and the Nash--Aronson estimate.Comment: Revised version streamlines some of the proofs, improves the introduction and extends the discussion and open questions section; 45 page

SMT Sampling via Model-Guided Approximation

We investigate the domain of satisfiable formulas in satisfiability modulo theories (SMT), in particular, automatic generation of a multitude of satisfying assignments to such formulas. Despite the long and successful history of SMT in model checking and formal verification, this aspect is relatively under-explored. Prior work exists for generating such assignments, or samples, for Boolean formulas and for quantifier-free first-order formulas involving bit-vectors, arrays, and uninterpreted functions (QF_AUFBV). We propose a new approach that is suitable for a theory T of integer arithmetic and to T with arrays and uninterpreted functions. The approach involves reducing the general sampling problem to a simpler instance of sampling from a set of independent intervals, which can be done efficiently. Such reduction is carried out by expanding a single model - a seed - using top-down propagation of constraints along the original first-order formula

Quantitative disorder effects in low-dimensional spin systems

The Imry-Ma phenomenon, predicted in 1975 by Imry and Ma and rigorously established in 1989 by Aizenman and Wehr, states that first-order phase transitions of low-dimensional spin systems are `rounded' by the addition of a quenched random field to the quantity undergoing the transition. The phenomenon applies to a wide class of spin systems in dimensions $d\le 2$ and to spin systems possessing a continuous symmetry in dimensions $d\le 4$. This work provides quantitative estimates for the Imry--Ma phenomenon: In a cubic domain of side length $L$, we study the effect of the boundary conditions on the spatial and thermal average of the quantity coupled to the random field. We show that the boundary effect diminishes at least as fast as an inverse power of $\log\log L$ for general two-dimensional spin systems and for four-dimensional spin systems with continuous symmetry, and at least as fast as an inverse power of $L$ for two- and three-dimensional spin systems with continuous symmetry. Specific models of interest for the obtained results include the two-dimensional random-field $q$-state Potts and Edwards-Anderson spin glass models, and the $d$-dimensional random-field spin $O(n)$ models ($n\ge 2$) in dimensions $d\le 4$.Comment: 48 pages, 2 figure

Retention of strontium in high- & low-pH cementitious matrices – OPC vs. model systems

International audienc

hfAIM: a reliable bioinformatics approach for in silico genome-wide identification of autophagy-associated Atg8-interacting motifs in various organisms

Most of the proteins that are specifically turned over by selective autophagy are recognized by the presence of short Atg8 interacting motifs (AIMs) that facilitate their association with the autophagy apparatus. Such AIMs can be identified by bioinformatics methods based on their defined degenerate consensus F/W/Y-X-X-L/I/V sequences in which X represents any amino acid. Achieving reliability and/or fidelity of the prediction of such AIMs on a genome-wide scale represents a major challenge. Here, we present a bioinformatics approach, high fidelity AIM (hfAIM), which uses additional sequence requirementsthe presence of acidic amino acids and the absence of positively charged amino acids in certain positionsto reliably identify AIMs in proteins. We demonstrate that the use of the hfAIM method allows for in silico high fidelity prediction of AIMs in AIM-containing proteins (ACPs) on a genome-wide scale in various organisms. Furthermore, by using hfAIM to identify putative AIMs in the Arabidopsis proteome, we illustrate a potential contribution of selective autophagy to various biological processes. More specifically, we identified 9 peroxisomal PEX proteins that contain hfAIM motifs, among which AtPEX1, AtPEX6 and AtPEX10 possess evolutionary-conserved AIMs. Bimolecular fluorescence complementation (BiFC) results verified that AtPEX6 and AtPEX10 indeed interact with Atg8 in planta. In addition, we show that mutations occurring within or nearby hfAIMs in PEX1, PEX6 and PEX10 caused defects in the growth and development of various organisms. Taken together, the above results suggest that the hfAIM tool can be used to effectively perform genome-wide in silico screens of proteins that are potentially regulated by selective autophagy. The hfAIM system is a web tool that can be accessed at link: http://bioinformatics.psb.ugent.be/hfAIM/