Alterations in the extracellular matrix occur during the cardiac hypertrophic process. Because integrins mediate cell-matrix adhesion and beta(1D)-integrin (beta1D) is expressed exclusively in cardiac and skeletal muscle, we hypothesized that beta1D and focal adhesion kinase (FAK), a proximal integrin-signaling molecule, are involved in cardiac growth. With the use of cultured ventricular myocytes and myocardial tissue, we found the following: 1) beta1D protein expression was upregulated perinatally; 2) alpha(1)-adrenergic stimulation of cardiac myocytes increased beta1D protein levels 350% and altered its cellular distribution; 3) adenovirally mediated overexpression of beta1D stimulated cellular reorganization, increased cell size by 250%, and induced molecular markers of the hypertrophic response; and 4) overexpression of free beta1D cytoplasmic domains inhibited alpha(1)-adrenergic cellular organization and atrial natriuretic factor (ANF) expression. Additionally, FAK was linked to the hypertrophic response as follows: 1) coimmunoprecipitation of beta1D and FAK was detected; 2) FAK overexpression induced ANF-luciferase; 3) rapid and sustained phosphorylation of FAK was induced by alpha(1)-adrenergic stimulation; and 4) blunting of the alpha(1)-adrenergically modulated hypertrophic response was caused by FAK mutants, which alter Grb2 or Src binding, as well as by FAK-related nonkinase, a dominant interfering FAK mutant. We conclude that beta1D and FAK are both components of the hypertrophic response pathway of cardiac myocytes.

We present space-efficient data stream algorithms for approximating the number of triangles in a graph up to a factor 1 +. While it can be shown that determining whether a graph is triangle-free is not possible in sub-linear space, a large body of work has focused on minimizing the space required in terms of the number of triangles T (or a lower bound on this quantity) and other parameters including the number of nodes n and the number of edges m. Two models are important in the literature: the arbitrary order model in which the stream consists of the edges of the graph in arbitrary order and the adjacency list order model in which all edges incident to the same node appear consecutively. We improve over the state of the art results in both models. For the adjacency list order model, we show thatÕ(−2 m/ √ T) space is sufficient in one pass and O(−2 m 3/2 /T) space is sufficient in two passes where theÕ(•) notation suppresses log factors. For the arbitrary order model, we show thatÕ(−2 m/ √ T) space suffices given two passes and that O(−2 m 3/2 /T) space suffices given three passes and oracle access to the degrees. Finally, we show how to efficiently implement the "wedge sampling" approach to triangle estimation in the arbitrary order model. To do this, we develop the first algorithm for p sampling such that multiple independent samples can be generated with O(polylog n) update time; this primitive is widely applicable and this result may be of independent interest.

We study the classic NP-Hard problem of nding the maximum k-set coverage in the data stream model: given a set system of m sets that are subsets of a universe {1, . . . , n}, nd the k sets that cover the most number of distinct elements. e problem can be approximated up to a factor 1 − 1/e in polynomial time. In the streaming-set model, the sets and their elements are revealed online. e main goal of our work is to design algorithms, with approximation guarantees as close as possible to 1 − 1/e, that use sublinear space o(mn). Our main results are:• Two (1 − 1/e − ) approximation algorithms: One uses O( −1 ) passes andÕ( −2 k) space whereas the other uses only a single pass butÕ( −2 m) space.Õ(·) suppresses polylog factors.

In this paper, we consider the problem of approximating the densest subgraph in the dynamic graph stream model. In this model of computation, the input graph is defined by an arbitrary sequence of edge insertions and deletions and the goal is to analyze properties of the resulting graph given memory that is sub-linear in the size of the stream. We present a single-pass algorithm that returns a (1 + ǫ) approximation of the maximum density with high probability; the algorithm uses O(ǫ −2 n polylog n) space, processes each stream update in polylog(n) time, and uses poly(n) post-processing time where n is the number of nodes. The space used by our algorithm matches the lower bound of Bahmani et al. (PVLDB 2012) up to a poly-logarithmic factor for constant ǫ. The best existing results for this problem were established recently by Bhattacharya et al. (STOC 2015). They presented a (2 + ǫ) approximation algorithm using similar space and another algorithm that both processed each update and maintained a (4 + ǫ) approximation of the current maximum density in polylog(n) time per-update.