Determine the value of the variable in each equation.

Basic Algebra = 代数学入門

To respond to environmental changes, such as drought, plants must regulate numerous cellular processes. Working in the model plant Arabidopsis , Song et al. profiled the binding of 21 transcription factors to chromatin and mapped the complex gene regulatory networks involved in the response to the plant hormone abscisic acid. The work provides a framework for understanding and modulating plant responses to stress.

Science , this issue p. [598][1]

 [1]: http://www.sciencemag.org/content/354/6312/aag1550.full

/pdf/a-transcription-factor-hierarchy-defines-an-environmental-5ftfhxbk42.pdf

A transcription factor hierarchy defines an environmental stress response network

Computer systems commonly cache the values of variables to gain efficiency. In applications where the goal is to track attributes of a continuously moving or deforming physical system over time, caching relations between variables works better than caching individual values. The reason is that, as the system evolves, such relationships are more stable than the values of individual variables.Kinetic data structures (KDSs) are a novel formal framework for designing and analyzing sets of assertions to cache about the environment, so that these assertion sets are at once relatively stable and tailored to facilitate or trivialize the computation of the attribute of interest. Formally, a KDS is a mathematical proof animated through time, proving the validity of a certain computation for the attribute of interest. KDSs have rigorous associated measures of performance and their design shares many qualities with that of classical data structures.The KDS framework has led to many new and promising algorithms in applications where the efficient modeling of motion is essential. Among these are collision detection for moving rigid and deformable bodies, connectivity maintenace in ad-hoc networks, local environment tracking for mobile agents, and visibility/occlusion maintenance. This talk will survey the general ideas behind KDSs and illustrate their application to simple geometric problems that arise in virtual and physical environments.

Data structures for mobile data (invited talk) (abstract only)

an introduction to the theory of graph spectra is available in our book collection an online access to it is set as public so you can download it instantly. Our digital library hosts in multiple countries, allowing you to get the most less latency time to download any of our books like this one. Merely said, the an introduction to the theory of graph spectra is universally compatible with any devices to read.

An Introduction To The Theory Of Graph Spectra

While only recently developed, the ability to profile expression data in single cells (scRNA-Seq) has already led to several important studies and findings. However, this technology has also raised several new computational challenges. These include questions about the best methods for clustering scRNA-Seq data, how to identify unique group of cells in such experiments, and how to determine the state or function of specific cells based on their expression profile. To address these issues we develop and test a method based on neural networks (NN) for the analysis and retrieval of single cell RNA-Seq data. We tested various NN architectures, some of which incorporate prior biological knowledge, and used these to obtain a reduced dimension representation of the single cell expression data. We show that the NN method improves upon prior methods in both, the ability to correctly group cells in experiments not used in the training and the ability to correctly infer cell type or state by querying a database of tens of thousands of single cell profiles. Such database queries (which can be performed using our web server) will enable researchers to better characterize cells when analyzing heterogeneous scRNA-Seq samples.

/pdf/using-neural-networks-for-reducing-the-dimensions-of-single-1znr2x42sn.pdf

Using neural networks for reducing the dimensions of single-cell RNA-Seq data

Modeling dynamic regulatory networks is a major challenge since much of the protein-DNA interaction data available is static. The Dynamic Regulatory Events Miner (DREM) uses a Hidden Markov Model-based approach to integrate this static interaction data with time series gene expression leading to models that can determine when transcription factors (TFs) activate genes and what genes they regulate. DREM has been used successfully in diverse areas of biological research. However, several issues were not addressed by the original version. DREM 2.0 is a comprehensive software for reconstructing dynamic regulatory networks that supports interactive graphical or batch mode. With version 2.0 a set of new features that are unique in comparison with other softwares are introduced. First, we provide static interaction data for additional species. Second, DREM 2.0 now accepts continuous binding values and we added a new method to utilize TF expression levels when searching for dynamic models. Third, we added support for discriminative motif discovery, which is particularly powerful for species with limited experimental interaction data. Finally, we improved the visualization to support the new features. Combined, these changes improve the ability of DREM 2.0 to accurately recover dynamic regulatory networks and make it much easier to use it for analyzing such networks in several species with varying degrees of interaction information. DREM 2.0 provides a unique framework for constructing and visualizing dynamic regulatory networks. DREM 2.0 can be downloaded from: http://www.sb.cs.cmu.edu/drem
 .

/pdf/drem-2-0-improved-reconstruction-of-dynamic-regulatory-1l9hd832t9.pdf

DREM 2.0: Improved reconstruction of dynamic regulatory networks from time-series expression data

We investigate two types of graph layouts, track layouts and layered path decompositions, and the relations between their associated parameters track-number and layered pathwidth. We use these two types of layouts to characterize leveled planar graphs, which are the graphs with planar leveled drawings with no dummy vertices. It follows from the known NP-completeness of leveled planarity that track-number and layered pathwidth are also NP-complete, even for the smallest constant parameter values that make these parameters nontrivial. We prove that the graphs with bounded layered pathwidth include outerplanar graphs, Halin graphs, and squaregraphs, but that (despite having bounded track-number) series–parallel graphs do not have bounded layered pathwidth. Finally, we investigate the parameterized complexity of these layouts, showing that past methods used for book layouts do not work to parameterize the problem by treewidth or almost-tree number but that the problem is (non-uniformly) fixed-parameter tractable for tree-depth.

Track Layouts, Layered Path Decompositions, and Leveled Planarity

An old open problem in graph drawing asks for the size of a universal point set, a set of points that can be used as vertices for straight-line drawings of all n-vertex planar graphs. We connect this problem to the theory of permutation patterns, where another open problem concerns the size of superpatterns, permutations that contain all patterns of a given size. We generalize superpatterns to classes of permutations determined by forbidden patterns, and we construct superpatterns of size n^2/4 + Theta(n) for the 213-avoiding permutations, half the size of known superpatterns for unconstrained permutations. We use our superpatterns to construct universal point sets of size n^2/4 - Theta(n), smaller than the previous bound by a 9/16 factor. We prove that every proper subclass of the 213-avoiding permutations has superpatterns of size O(n log^O(1) n), which we use to prove that the planar graphs of bounded pathwidth have near-linear universal point sets.

Superpatterns and Universal Point Sets

Many well-known graph drawing techniques, including force directed drawings, spectral graph layouts, multidimensional scaling, and circle packings, have algebraic formulations. However, practical methods for producing such drawings ubiquitously use iterative numerical approximations rather than constructing and then solving algebraic expressions representing their exact solutions. To explain this phenomenon, we use Galois theory to show that many variants of these problems have solutions that cannot be expressed by nested radicals or nested roots of low-degree polynomials. Hence, such solutions cannot be computed exactly even in extended computational models that include such operations.

William E. Devanny

Papers

DREM 2.0: Improved reconstruction of dynamic regulatory networks from time-series expression data

Track Layouts, Layered Path Decompositions, and Leveled Planarity

Superpatterns and Universal Point Sets

Superpatterns and Universal Point Sets

The Galois Complexity of Graph Drawing: Why Numerical Solutions are Ubiquitous for Force-Directed, Spectral, and Circle Packing Drawings