Triviality of the ground-state metastate in long-range Ising spin glasses in one dimension

We consider the one-dimensional model of a spin glass with independent Gaussian-distributed random interactions, that have mean zero and variance $1/|i-j|^{2\sigma}$, between the spins at sites $i$ and $j$ for all $i\neq j$. It is known that, for $\sigma>1$, there is no phase transition at any non-zero temperature in this model. We prove rigorously that, for $\sigma>3/2$, any Newman-Stein metastate for the ground states (i.e.\ the frequencies with which distinct ground states are observed in finite size samples in the limit of infinite size, for given disorder) is trivial and unique. In other words, for given disorder and asymptotically at large sizes, the same ground state, or its global spin flip, is obtained (almost) always. The proof consists of two parts: one is a theorem (based on one by Newman and Stein for short-range two-dimensional models), valid for all $\sigma>1$, that establishes triviality under a convergence hypothesis on something similar to the energies of domain walls, and the other (based on older results for the one-dimensional model) establishes that the hypothesis is true for $\sigma>3/2$. In addition, we derive heuristic scaling arguments and rigorous exponent inequalities which tend to support the validity of the hypothesis under broader conditions. The constructions of various metastates are extended to all values $\sigma>1/2$. Triviality of the metastate in bond-diluted power-law models for $\sigma>1$ is proved directly.Comment: 18 pages. v2: subsection on bond-diluted models added, few extra references. 19 pages. v3: published version; a few changes; 20 page

Data-driven prediction of usefulness of datasets vs. their citation counts.

<p>Manual checks comparing sets for which the two scores differed revealed inconsistent database records for two datasets; the blue arrows point to their corrected locations, which are more in line with the data-driven model. Regions A, B, and C: see text.</p

Relevance network of datasets in the human gene expression atlas; data-driven links from the model (left) and citation links (right).

<p>Left: each dataset was used as a query to retrieve earlier datasets; a link from an earlier dataset to a later one means the earlier dataset is relevant as a partial model of activity in the later dataset. Link width is proportional to the normalized relevance weight (combination weight ; only links with are shown, and datasets without links have been discarded). Right: links are direct (gray) and indirect (purple) citations. Node size is proportional to the estimated influence, <i>i.e.</i>, the total outgoing weight. Colors: tissue types (six meta tissue types <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0113053#pone.0113053-Lukk1" target="_blank">[12]</a>). The node layout was computed from the data-driven network (details in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0113053#s4" target="_blank"><i>Methods</i></a>).</p

Data-driven retrieval outperforms the state of the art of keyword search on the human gene expression atlas [12].

<p>Blue: Traditional precision-recall curve where progressively more datasets are retrieved from left to right. All experiments sharing one or more of the 96 biological categories of the atlas were considered relevant. In keyword retrieval, either the category names (“Keyword: 96 classes”) or the disease annotations (“Keyword: disease”) were used as keywords. All datasets having at least 10 samples were used as query datasets, and the curves are averages over all queries.</p

Additional file 3: of Relationships between drought, heat and air humidity responses revealed by transcriptome-metabolome co-analysis

Result lists of condition-specific gene expression and metabolomic mass levels estimated by linear modeling across the whole dataset. Tables show mean log2 gene expression values and log2metabolomic mass levels for each of the six environmental conditions: control, drought (D), heat with low relative air humidity (H_LrH), heat with high relative air humidity (H_HrH), drought stress combined with low air humidity heat stress (DH_LrH) and drought stress combined with high air humidity heat stress (DH_HrH). Values of all individual samples are available in the processed data file deposited at the ArrayExpress and MetaboLights databases, respectively (Availability of data and materials). (XLSX 2264 kb

Integrative and Personalized QSAR Analysis in Cancer by Kernelized Bayesian Matrix Factorization

With data from recent large-scale drug sensitivity measurement campaigns, it is now possible to build and test models predicting responses for more than one hundred anticancer drugs against several hundreds of human cancer cell lines. Traditional quantitative structure–activity relationship (QSAR) approaches focus on small molecules in searching for their structural properties predictive of the biological activity in a single cell line or a single tissue type. We extend this line of research in two directions: (1) an integrative QSAR approach predicting the responses to new drugs for a panel of multiple known cancer cell lines simultaneously and (2) a personalized QSAR approach predicting the responses to new drugs for new cancer cell lines. To solve the modeling task, we apply a novel kernelized Bayesian matrix factorization method. For maximum applicability and predictive performance, the method optionally utilizes genomic features of cell lines and target information on drugs in addition to chemical drug descriptors. In a case study with 116 anticancer drugs and 650 cell lines, we demonstrate the usefulness of the method in several relevant prediction scenarios, differing in the amount of available information, and analyze the importance of various types of drug features for the response prediction. Furthermore, after predicting the missing values of the data set, a complete global map of drug response is explored to assess treatment potential and treatment range of therapeutically interesting anticancer drugs