Optimal Deterministic Sorting and Routing on Grids and Tori with Diagonals

We present deterministic sorting and routing algorithms for grids and tori with additional diagonal connections. For large loads ( ), where each processor has at most h data packets in the beginning and in the end, the sorting problem can be solved in optimal hn/6+o(n) and hn/12+o(n) steps for grids and tori with diagonals, respectively. For smaller loads, we present a new concentration technique that yields very fast algorithms for h<12 . For a load of 1, the previously most studied case, sorting only takes 1.2n+o(n) steps and routing only 1.1n+o(n) steps. For tori, we can present optimal algorithms for all loads . The above algorithms all use a constant-size memory for all processors and never copy or split packets, a property that the corresponding lower bounds make use of. If packets may be copied, 1—1 sorting can be done in only 2n/3+o(n) on a torus with diagonals. Generally gaining a speedup of 3 by only doubling the number of communication links compared with a grid without diagonals, our work suggests building grids and tori with diagonals. Received August 18, 1997; revised December 28, 1997.     

Value of ultrasound in differential diagnosis of pediatric hip joint effusion (Perthes disease, C. fugax, epiphysiolysis coapitis femoris

Migrating cells form dynamic and highly regulated adhesive interactions with their environment. In particular, integrin-mediated adhesions to the extracellular matrix (ECM) play a central role in cell migration. This review focuses on recent advances in understanding the adhesive mechanisms that regulate cell detachment at the rear of migrating fibroblasts and neutrophils. The contribution of several key adhesive regulators is discussed, including myosin mediated cell contractility, tyrosine phosphorylation, rho, calcium fluxes, and calpain. A challenge for future investigation will be to determine how adhesive events are spatially and temporally coordinated to promote productive directional cell movements.     

Compression-based fixed-parameter algorithms for feedback vertex set and edge bipartization

We show that the NP-complete Feedback Vertex Set problem, which asks for the smallest set of vertices to remove from a graph to destroy all cycles, is deterministically solvable in O(ck⋅m) time. Here, m denotes the number of graph edges, k denotes the size of the feedback vertex set searched for, and c is a constant. We extend this to an algorithm enumerating all solutions in O(dk⋅m) time for a (larger) constant d. As a further result, we present a fixed-parameter algorithm with runtime O(k²⋅m²) for the NP-complete Edge Bipartization problem, which asks for at most k edges to remove from a graph to make it bipartite.     

Graph separators: a parameterized view

Graph separation is a well-known tool to make (hard) graph problems accessible to a divide-and-conquer approach. We show how to use graph separator theorems in combination with (linear) problem kernels in order to develop fixed parameter algorithms for many well-known NP-hard (planar) graph problems. We coin the key notion of glueable select&verify graph problems and derive from that a prospective way to easily check whether a planar graph problem will allow for a fixed parameter algorithm of running time for constant c. One of the main contributions of the paper is to exactly compute the base c of the exponential term and its dependence on the various parameters specified by the employed separator theorem and the underlying graph problem. We discuss several strategies to improve on the involved constant c.     

A refined search tree technique for Dominating Set on planar graphs

We establish a refined search tree technique for the parameterized DOMINATING SET problem on planar graphs. Here, we are given an undirected graph and we ask for a set of at most k vertices such that every other vertex has at least one neighbor in this set. We describe algorithms with running times O(8^kn) and O(8^kk+n³), where n is the number of vertices in the graph, based on bounded search trees. We describe a set of polynomial time data-reduction rules for a more general “annotated” problem on black/white graphs that asks for a set of k vertices (black or white) that dominate all the black vertices. An intricate argument based on the Euler formula then establishes an efficient branching strategy for reduced inputs to this problem. In addition, we give a family examples showing that the bound of the branching theorem is optimal with respect to our reduction rules. Our final search tree algorithm is easy to implement; its analysis, however, is involved.     

Fixed-Parameter Algorithms for Cluster Vertex Deletion

We initiate the first systematic study of the NP-hard Cluster Vertex Deletion (CVD) problem (unweighted and weighted) in terms of fixed-parameter algorithmics. In the unweighted case, one searches for a minimum number of vertex deletions to transform a graph into a collection of disjoint cliques. The parameter is the number of vertex deletions. We present efficient fixed-parameter algorithms for CVD applying the fairly new iterative compression technique. Moreover, we study the variant of CVD where the maximum number of cliques to be generated is prespecified. Here, we exploit connections to fixed-parameter algorithms for (weighted) Vertex Cover.     

Combining mixed titania morphologies into a complex assembly thin film by iterative block-copolymer-based sol–gel templating

Sol–gel templating combined with iterative spin-coating steps are used to custom-tailor hierarchically structured titania thin films. Using poly(styrene-block-ethylene oxide) P(S-b-PEO) as the structure directing agent, a foam-like structure is combined with nanogranules. Both structural elements are merged into a complex assembly in thin film geometry. The resulting morphology is pictured by SEM and probed with GISAXS. The installed mesoporous titania sandwich structure exhibits holes with a size of 45 nm which makes it promising for applications in photovoltaics or photocatalysis. An optical characterization completes the structural investigation.     

Virtual Energy Information Network: a resilience perspective

Increasing demand in energy consumption, missed modernisations, and the increasing difficulties in predicting power production due to volatile renewable energy sources (e.g., based on wind or sun) impose major challenges to the power grid. Power supply and power demand are closely interconnected with the need to maintain the power grid in a stable state with a sufficient quality of power. This requires energy-relevant information to be exchanged through the so called Energy Information Network. Communication, however, is challenging within the Energy Information Network due to privacy, security, resiliency, and quality-of-service requirements. Particularly, the resilience of communication within the Energy Information Network needs to be considered to maintain the power grid in a stable and controlled state. This paper suggests a Virtualised Energy Information Network (VEIN), where the Energy Information Network is divided into multiple virtual networks that run over a common substrate network. Furthermore, this paper discusses benefits of this approach in terms of privacy, security, and resilience and points out open research questions.