On partitioning a graph into two connected subgraphs

Suppose a graph G is given with two vertex-disjoint sets of vertices Z₁ and Z₂. Can we partition the remaining vertices of G such that we obtain two connected vertex-disjoint subgraphs of G that contain Z₁ and Z₂, respectively? This problem is known as the 2-Disjoint Connected Subgraphs problem. It is already NP-complete for the class of n-vertex graphs G=(V,E) in which Z₁ and Z₂ each contain a connected set that dominates all vertices in V?(Z₁∪Z₂). We present an O^∗(1.2051ⁿ) time algorithm that solves it for this graph class. As a consequence, we can also solve this problem in O^∗(1.2051ⁿ) time for the classes of n-vertex P₆-free graphs and split graphs. This is an improvement upon a recent O^∗(1.5790ⁿ) time algorithm for these two classes. Our approach translates the problem to a generalized version of hypergraph 2-coloring and combines inclusion/exclusion with measure and conquer.     

On the number of Dejean words over alphabets of 5, 6, 7, 8, 9 and 10 letters

We give lower bounds on the growth rate of Dejean words, i.e. minimally repetitive words, over a k-letter alphabet, for 5≤k≤10. Put together with the known upper bounds, we estimate these growth rates with the precision of 0.005. As a consequence, we establish the exponential growth of the number of Dejean words over a k-letter alphabet, for 5≤k≤10.     

A characterization of span program size and improved lower bounds for monotone span programs

We give a characterization of span program size by a combinatorial-algebraic measure. The measure we consider is a generalization of a measure on covers which has been used to prove lower bounds on formula size and has also been studied with respect to communication complexity.?In the monotone case our new methods yield lower bounds for the monotone span program complexity of explicit Boolean functions in n variables over arbitrary fields, improving the previous lower bounds on monotone span program size. Our characterization of span program size implies that any matrix with superpolynomial separation between its rank and cover number can be used to obtain superpolynomial lower bounds on monotone span program size. We also identify a property of bipartite graphs that is suficient for constructing Boolean functions with large monotone span program complexity. Received: September 30, 2000.     

Generalised Stream X-Machines with Output Delimited Type

Some conditions relating to the automata involved in the W-testing method are discussed. It is also shown how to use the method for reduced automata instead of minimal automata. New design test conditions (weak output distinguishable, strong test-complete and output delimited type) are considered for the generalised stream X-machines (stream X-machines with basic functions replaced by relations and having as output strings of symbols rather than single symbols). It is proved that testing methods similar to those already developed for ordinary deterministic stream X-machines may be applied for generalised stream X-machines with output delimited types. A particular case of generalised stream X-machine with output delimited type is the X-machine with output delimiter, which produces outputs having a distinct right end character. Received October 2000 / Accepted in revised form January 2001     

Food vacuole proteome of the malarial parasite Plasmodium falciparum

The Plasmodium falciparum food vacuole (FV) is a lysosome-like organelle where erythrocyte hemoglobin digestion occurs. It is a favorite target in the development of antimalarials. We have used a tandem mass spectrometry approach to investigate the proteome of an FV-enriched fraction and identified 116 proteins. The electron microscopy analysis and the Western blot data showed that the major component of the fraction was the FV and, as expected, the majority of previously known FV markers were recovered. Of particular interest, several proteins involved in vesicle-mediated trafficking were identified, which are likely to play a key role in FV biogenesis and/or FV protein trafficking. Recovery of parasite surface proteins lends support to the cytostomal pathway of hemoglobin ingestion as a FV trafficking route. We have identified 32 proteins described as hypothetical in the databases. This insight into FV protein content provides new clues towards understanding the biological function of this organelle in P. falciparum.     

Oxidation of proteins: Basic principles and perspectives for blood proteomics

Protein oxidation mechanisms result in a wide array of modifications, from backbone cleavage or protein crosslinking to more subtle modifications such as side chain oxidations. Protein oxidation occurs as part of normal regulatory processes, as a defence mechanism against oxidative stress, or as a deleterious processes when antioxidant defences are overcome. Because blood is continually exposed to reactive oxygen and nitrogen species, blood proteomics should inherently adopt redox proteomic strategies. In this review, we recall the biochemical basis of protein oxidation, review the proteomic methodologies applied to analyse redox modifications, and highlight some physiological and in vitro responses to oxidative stress of various blood components.     

Satisfiability of co-nested formulas

As a notion dual to Knuth's nested formulas [4], we call a boolean formula in conjunctive normal formco-nested if its clauses can be linearly ordered (sayC={c _i ;i=1,2, ...,n})so that the graphG ^cl =(XC, {xc _i ;xc _i or ¬xc _i } {c _i c _i+1;i=1, 2, ...,n}) allows a noncrossing drawing in the plane so that the circlec ₁,c ₂, ...,c _n bounds the outerface. Our main result is that maximum satisfiability of co-nested formulas can be decided in linear time.Both authors acknowledge a partial support of Ec Cooperative Action IC-1000 (project ALTEC:Algorithms for Future Technologies).     

Three-dimensional micro-channel fabrication in polydimethylsiloxane(PDMS) elastomer

This paper describes a fabrication technique for building three-dimensional (3-D) micro-channels in polydimethylsiloxane (PDMS) elastomer. The process allows for the stacking of many thin (less than 100-μm thick) patterned PDMS layers to realize complex 3-D channel paths. The master for each layer is formed on a silicon wafer using an epoxy-based photoresist (SU 8). PDMS is cast against the master producing molded layers containing channels and openings. To realize thin layers with openings, a sandwich molding configuration was developed that allows precise control of the PDMS thickness. The master wafer is clamped within a sandwich that includes flat aluminum plates, a flexible polyester film layer, a rigid Pyrex wafer, and a rubber sheet. A parametric study is performed on PDMS surface activation in a reactive-ion-etching system and the subsequent methanol treatment for bonding and aligning very thin individual components to a substrate. Low RF power and short treatment times are better than high RF power and long treatment times, respectively, for instant bonding. Layer-to-layer alignment of less then 15 μm is achieved with manual alignment techniques that utilize surface tension driven self-alignment methods. A coring procedure is used to realize off-chip fluidic connections via the bottom PDMS layer, allowing the top layer to remain smooth and flat for complete optical access