Nonpositive Eigenvalues of the Adjacency Matrix and Lower Bounds for Laplacian Eigenvalues

Let $NPO(k)$ be the smallest number $n$ such that the adjacency matrix of any undirected graph with $n$ vertices or more has at least $k$ nonpositive eigenvalues. We show that $NPO(k)$ is well-defined and prove that the values of $NPO(k)$ for $k=1,2,3,4,5$ are $1,3,6,10,16$ respectively. In addition, we prove that for all $k \geq 5$, $R(k,k+1) \ge NPO(k) > T_k$, in which $R(k,k+1)$ is the Ramsey number for $k$ and $k+1$, and $T_k$ is the $k^{th}$ triangular number. This implies new lower bounds for eigenvalues of Laplacian matrices: the $k$-th largest eigenvalue is bounded from below by the $NPO(k)$-th largest degree, which generalizes some prior results.Comment: 23 pages, 12 figure

Variability in the analysis of a single neuroimaging dataset by many teams

Data analysis workflows in many scientific domains have become increasingly complex and flexible. To assess the impact of this flexibility on functional magnetic resonance imaging (fMRI) results, the same dataset was independently analyzed by 70 teams, testing nine ex-ante 1 hypotheses . The flexibility of analytic approaches is exemplified by the fact that no two teams chose identical workflows to analyze the data. This flexibility resulted in sizeable variation in hypothesis test results, even for teams whose statistical maps were highly correlated at intermediate stages of their analysis pipeline. Variation in reported results was related to several aspects of analysis methodology. Importantly, a meta-analytic approach that aggregated information across teams yielded significant consensus in activated regions across teams. Furthermore, prediction markets of researchers in the field revealed an overestimation of the likelihood of significant findings, even by researchers with direct knowledge of the dataset findings show that analytic flexibility can have substantial effects on scientific conclusions, and demonstrate factors possibly related to variability in fMRI. The results emphasize the importance of validating and sharing complex analysis workflows, and demonstrate the need for multiple analyses of the same data. Potential approaches to mitigate issues related to analytical variability are discusse

COX-2 expression mediated by calcium-TonEBP signaling axis under hyperosmotic conditions serves osmoprotective function in nucleus pulposus cells.

The nucleus pulposus (NP) of intervertebral discs experiences dynamic changes in tissue osmolarity because of diurnal loading of the spine. TonEBP/NFAT5 is a transcription factor that is critical in osmoregulation as well as survival of NP cells in the hyperosmotic milieu. The goal of this study was to investigate whether cyclooxygenase-2 (COX-2) expression is osmoresponsive and dependent on TonEBP, and whether it serves an osmoprotective role. NP cells up-regulated COX-2 expression in hyperosmotic media. The induction of COX-2 depended on elevation of intracellular calcium levels and p38 MAPK pathway, but independent of calcineurin signaling as well as MEK/ERK and JNK pathways. Under hyperosmotic conditions, both COX-2 mRNA stability and its proximal promoter activity were increased. The proximal COX-2 promoter (-1840/+123 bp) contained predicted binding sites for TonEBP, AP-1, NF-κB, and C/EBP-β. While COX-2 promoter activity was positively regulated by both AP-1 and NF-κB, AP-1 had no effect and NF-κB negatively regulated COX-2 protein levels under hyperosmotic conditions. On the other hand, TonEBP was necessary for both COX-2 promoter activity and protein up-regulation in response to hyperosmotic stimuli

Convolutional neural networks can decode eye movement data: A black box approach to predicting task from eye movements

Previous attempts to classify task from eye movement data have relied on model architectures designed to emulate theoretically defined cognitive processes and/or data that have been processed into aggregate (e.g., fixations, saccades) or statistical (e.g., fixation density) features. Black box convolutional neural networks (CNNs) are capable of identifying relevant features in raw and minimally processed data and images, but difficulty interpreting these model architectures has contributed to challenges in generalizing lab-trained CNNs to applied contexts. In the current study, a CNN classifier was used to classify task from two eye movement datasets (Exploratory and Confirmatory) in which participants searched, memorized, or rated indoor and outdoor scene images. The Exploratory dataset was used to tune the hyperparameters of the model, and the resulting model architecture was retrained, validated, and tested on the Confirmatory dataset. The data were formatted into timelines (i.e., x-coordinate, y-coordinate, pupil size) and minimally processed images. To further understand the informational value of each component of the eye movement data, the timeline and image datasets were broken down into subsets with one or more components systematically removed. Classification of the timeline data consistently outperformed the image data. The Memorize condition was most often confused with Search and Rate. Pupil size was the least uniquely informative component when compared with the x- and y-coordinates. The general pattern of results for the Exploratory dataset was replicated in the Confirmatory dataset. Overall, the present study provides a practical and reliable black box solution to classifying task from eye movement data

Graph isomorphism for (H1,H2)-free graphs : an almost complete dichotomy.

We almost completely resolve the computational complexity of Graph Isomorphism for classes of graphs characterized by two forbidden induced subgraphs H1 and H2. Schweitzer settled the complexity of this problem restricted to (H1;H2)-free graphs for all but a nite number of pairs (H1;H2), but without explicitly giving the number of open cases. Grohe and Schweitzer proved that Graph Isomorphism is polynomialtime solvable on graph classes of bounded clique-width. By combining known results with a number of new results, we reduce the number of open cases to seven. By exploiting the strong relationship between Graph Isomorphism and clique-width, we simultaneously reduce the number of open cases for boundedness of clique-width for (H1;H2)-free graphs to ve

Characterizing the Cool KOIs II. The M Dwarf KOI-254 and its Hot Jupiter

We report the confirmation and characterization of a transiting gas giant planet orbiting the M dwarf KOI-254 every 2.455239 days, which was originally discovered by the Kepler mission. We use radial velocity measurements, adaptive optics imaging and near infrared spectroscopy to confirm the planetary nature of the transit events. KOI-254b is the first hot Jupiter discovered around an M-type dwarf star. We also present a new model-independent method of using broadband photometry to estimate the mass and metallicity of an M dwarf without relying on a direct distance measurement. Included in this methodology is a new photometric metallicity calibration based on J-K colors. We use this technique to measure the physical properties of KOI-254 and its planet. We measure a planet mass of Mp = 0.505 Mjup, radius Rp = 0.96 Rjup and semimajor axis a = 0.03 AU, based on our measured stellar mass Mstar = 0.59 Msun and radius Rstar = 0.55 Rsun. We also find that the host star is metal-rich, which is consistent with the sample of M-type stars known to harbor giant planets.Comment: AJ accepted (in press

Relief of the Dma1-mediated checkpoint requires Dma1 autoubiquitination and dynamic localization

© 2018 Jones, Chen, et al. Chromosome segregation and cell division are coupled to prevent aneuploidy and cell death. In the fission yeast Schizosaccharomyces pombe, the septation initiation network (SIN) promotes cytokinesis, but upon mitotic checkpoint activation, the SIN is actively inhibited to prevent cytokinesis from occurring before chromosomes have safely segregated. SIN inhibition during the mitotic checkpoint is mediated by the E3 ubiquitin ligase Dma1. Dma1 binds to the CK1-phosphorylated SIN scaffold protein Sid4 at the spindle pole body (SPB), and ubiquitinates it. Sid4 ubiquitination antagonizes the SPB localization of the Polo-like kinase Plo1, the major SIN activator, so that SIN signaling is delayed. How this checkpoint is silenced once spindle defects are resolved has not been clear. Here we establish that Dma1 transiently leaves SPBs during anaphase B due to extensive autoubiquitination. The SIN is required for Dma1 to return to SPBs later in anaphase. Blocking Dma1 removal from SPBs by permanently tethering it to Sid4 prevents SIN activation and cytokinesis. Therefore, controlling Dma1’s SPB dynamics in anaphase is an essential step in S. pombe cell division and the silencing of the Dma1-dependent mitotic checkpoint