Sample path large deviations for Laplacian models in (1+1)(1+1)-dimensions

For Laplacian models in dimension $(1+1)$ we derive sample path large deviations for the profile height function, that is, we study scaling limits of Gaussian integrated random walks and Gaussian integrated random walk bridges perturbed by an attractive force towards the zero-level, called pinning. We study in particular the regime when the rate functions of the corresponding large deviation principles admit more than one minimiser, in our models either two, three, or five minimiser depending on the pinning strength and the boundary conditions. This study complements corresponding large deviation results for gradient systems with pinning for Gaussian random walk bridges in $(1+1)$-dimension (\cite{FS04}) and in $(1+d)$-dimension (\cite{BFO}), and recently in higher dimensions in \cite{BCF}. In particular it turns out that the Laplacian cases, i.e., integrated random walks, show richer and more complex structures of the minimiser of the rate functions which are linked to different phases.Comment: 37, 5 figure

Sample path large deviations for the Laplacian model with pinning interaction in (1 + 1)-dimension

We consider the (1+1) dimensional Laplacian model with pinning interaction. This is a probabilistic model for a polymer or an interface that is attracted to the zero line. Without the pinning interaction, the Laplacian model is a Gaussian field (Φi)iEΛN, where ΛN = {1, 2, ..., N - 1}. The covariance matrix of this field is given by the inverse of Φ -> 1/2 ENi=0(ΔΦi)2, where Δ is the discrete Laplacian. Furthermore the values at {-1, 0, N, N+1} are fixed boundary values. The pinning interaction is introduced by giving the field a reward each time it touches the zero line. Depending on the reward the model with pinning and the one without pinning show different behaviour. Caravenna and Deuschel [10] study the localisation behaviour of the polymer. The model is delocalised if the number of times a typical field touches the zero line is of order o(N). The authors of [10] show that for zero boundary conditions there is a critical reward such that for smaller rewards the model is delocalised whilst for larger rewards the model is localised. In this thesis we study the behaviour of the empirical profile of the field. We show that for non zero boundary conditions there is a critical reward such that for smaller rewards the empirical profile for the model with pinning and the one for the model without pinning behave in the same way whilst for larger rewards the empirical profile of the model with pinning interaction is attracted to the zero line

Interaction for Immersive Analytics

International audienceIn this chapter, we briefly review the development of natural user interfaces and discuss their role in providing human-computer interaction that is immersive in various ways. Then we examine some opportunities for how these technologies might be used to better support data analysis tasks. Specifically, we review and suggest some interaction design guidelines for immersive analytics. We also review some hardware setups for data visualization that are already archetypal. Finally, we look at some emerging system designs that suggest future directions

Amino Acid Distribution Rules Predict Protein Fold: Protein Grammar for Beta-Strand Sandwich-Like Structures

We present an alternative approach to protein 3D folding prediction based on determination of rules that specify distribution of “favorable” residues, that are mainly responsible for a given fold formation, and “unfavorable” residues, that are incompatible with that fold, in polypeptide sequences. The process of determining favorable and unfavorable residues is iterative. The starting assumptions are based on the general principles of protein structure formation as well as structural features peculiar to a protein fold under investigation. The initial assumptions are tested one-by-one for a set of all known proteins with a given structure. The assumption is accepted as a “rule of amino acid distribution” for the protein fold if it holds true for all, or near all, structures. If the assumption is not accepted as a rule, it can be modified to better fit the data and then tested again in the next step of the iterative search algorithm, or rejected. We determined the set of amino acid distribution rules for a large group of beta sandwich-like proteins characterized by a specific arrangement of strands in two beta sheets. It was shown that this set of rules is highly sensitive (~90%) and very specific (~99%) for identifying sequences of proteins with specified beta sandwich fold structure. The advantage of the proposed approach is that it does not require that query proteins have a high degree of homology to proteins with known structure. So long as the query protein satisfies residue distribution rules, it can be confidently assigned to its respective protein fold. Another advantage of our approach is that it allows for a better understanding of which residues play an essential role in protein fold formation. It may, therefore, facilitate rational protein engineering design

Finding of residues crucial for supersecondary structure formation

This work evaluates the hypothesis that proteins with an identical supersecondary structure (SSS) share a unique set of residues—SSS-determining residues—even though they may belong to different protein families and have very low sequence similarities. This hypothesis was tested on two groups of sandwich-like proteins (SPs). Proteins in each group have an identical SSS, but their sequence similarity is below the “twilight zone.” To find the SSS-determining residues specific to each group, a unique structure-based algorithm of multiple sequences alignment was developed. The units of alignment are individual strands and loops rather than whole sequences. The algorithm is based on the alignment of residues that form hydrogen bonds between corresponding strands. Structure-based alignment revealed that 30–35% of the positions in the sequences in each group of proteins are “conserved positions” occupied either by hydrophobic-only or hydrophilic-only residues. Moreover, each group of SPs is characterized by a unique set of SSS-determining residues found at the conserved positions. The set of SSS-determining residues has very high sensitivity and specificity for identifying proteins with a corresponding SSS: It is an “amino acid tag” that brands a sequence as having a particular SSS. Thus, the sets of SSS-determining residues can be used to classify proteins and to predict the SSS of a query amino acid sequence

Robustness in Fatigue Strength Estimation

Fatigue strength estimation is a costly manual material characterization process in which state-of-the-art approaches follow a standardized experiment and analysis procedure. In this paper, we examine a modular, Machine Learning-based approach for fatigue strength estimation that is likely to reduce the number of experiments and, thus, the overall experimental costs. Despite its high potential, deployment of a new approach in a real-life lab requires more than the theoretical definition and simulation. Therefore, we study the robustness of the approach against misspecification of the prior and discretization of the specified loads. We identify its applicability and its advantageous behavior over the state-of-the-art methods, potentially reducing the number of costly experiments