Parameterized Algorithms for Graph Partitioning Problems

We study a broad class of graph partitioning problems, where each problem is specified by a graph $G=(V,E)$, and parameters $k$ and $p$. We seek a subset $U\subseteq V$ of size $k$, such that $\alpha_1m_1 + \alpha_2m_2$ is at most (or at least) $p$, where $\alpha_1,\alpha_2\in\mathbb{R}$ are constants defining the problem, and $m_1, m_2$ are the cardinalities of the edge sets having both endpoints, and exactly one endpoint, in $U$, respectively. This class of fixed cardinality graph partitioning problems (FGPP) encompasses Max $(k,n-k)$-Cut, Min $k$-Vertex Cover, $k$-Densest Subgraph, and $k$-Sparsest Subgraph. Our main result is an $O^*(4^{k+o(k)}\Delta^k)$ algorithm for any problem in this class, where $\Delta \geq 1$ is the maximum degree in the input graph. This resolves an open question posed by Bonnet et al. [IPEC 2013]. We obtain faster algorithms for certain subclasses of FGPPs, parameterized by $p$, or by $(k+p)$. In particular, we give an $O^*(4^{p+o(p)})$ time algorithm for Max $(k,n-k)$-Cut, thus improving significantly the best known $O^*(p^p)$ time algorithm

Covering Pairs in Directed Acyclic Graphs

The Minimum Path Cover problem on directed acyclic graphs (DAGs) is a classical problem that provides a clear and simple mathematical formulation for several applications in different areas and that has an efficient algorithmic solution. In this paper, we study the computational complexity of two constrained variants of Minimum Path Cover motivated by the recent introduction of next-generation sequencing technologies in bioinformatics. The first problem (MinPCRP), given a DAG and a set of pairs of vertices, asks for a minimum cardinality set of paths "covering" all the vertices such that both vertices of each pair belong to the same path. For this problem, we show that, while it is NP-hard to compute if there exists a solution consisting of at most three paths, it is possible to decide in polynomial time whether a solution consisting of at most two paths exists. The second problem (MaxRPSP), given a DAG and a set of pairs of vertices, asks for a path containing the maximum number of the given pairs of vertices. We show its NP-hardness and also its W[1]-hardness when parametrized by the number of covered pairs. On the positive side, we give a fixed-parameter algorithm when the parameter is the maximum overlapping degree, a natural parameter in the bioinformatics applications of the problem

Wearable devices for remote vital signs monitoring in the outpatient setting: an overview of the field

Early detection of physiological deterioration has been shown to improve patient outcomes. Due to recent improvements in technology, comprehensive outpatient vital signs monitoring is now possible. This is the first review to collate information on all wearable devices on the market for outpatient physiological monitoring. A scoping review was undertaken. The monitors reviewed were limited to those that can function in the outpatient setting with minimal restrictions on the patient’s normal lifestyle, while measuring any or all of the vital signs: heart rate, ECG, oxygen saturation, respiration rate, blood pressure and temperature. A total of 270 papers were included in the review. Thirty wearable monitors were examined: 6 patches, 3 clothing-based monitors, 4 chest straps, 2 upper arm bands and 15 wristbands. The monitoring of vital signs in the outpatient setting is a developing field with differing levels of evidence for each monitor. The most common clinical application was heart rate monitoring. Blood pressure and oxygen saturation measurements were the least common applications. There is a need for clinical validation studies in the outpatient setting to prove the potential of many of the monitors identified. Research in this area is in its infancy. Future research should look at aggregating the results of validity and reliability and patient outcome studies for each monitor and between different devices. This would provide a more holistic overview of the potential for the clinical use of each device

Light Nonaqueous-Phase Liquid Hydrocarbon Weathering at some JP-4 Fuel Release Sites

A fuel weathering study was conducted for database entries to estimate natural light, nonaqueousphase liquid weathering and source-term reduction rates for use in natural attenuation models. A range of BTEX weathering rates from mobile LNAPL plumes at eight field sites with known release dates was documented. Freephase fuel BTEX weathering rates varied among sites and were influenced by many factors. First-order weathering rate for five JP-4 fuel sites was 16%/year. Benzene and toluene exhibited higher weathering rates than ethylbenzene and xylene, as expected, because of higher water solubility. The primary weathering mechanism of mobile LNAPL was dissolution. Meaningful determination of mobile LNAPL weathering rates for BTEX in the fuels was difficult because of the large ranges of initial BTEX values

On the complexity of computing the kk-restricted edge-connectivity of a graph

The \emph{$k$-restricted edge-connectivity} of a graph $G$, denoted by $\lambda_k(G)$, is defined as the minimum size of an edge set whose removal leaves exactly two connected components each containing at least $k$ vertices. This graph invariant, which can be seen as a generalization of a minimum edge-cut, has been extensively studied from a combinatorial point of view. However, very little is known about the complexity of computing $\lambda_k(G)$. Very recently, in the parameterized complexity community the notion of \emph{good edge separation} of a graph has been defined, which happens to be essentially the same as the $k$-restricted edge-connectivity. Motivated by the relevance of this invariant from both combinatorial and algorithmic points of view, in this article we initiate a systematic study of its computational complexity, with special emphasis on its parameterized complexity for several choices of the parameters. We provide a number of NP-hardness and W[1]-hardness results, as well as FPT-algorithms.Comment: 16 pages, 4 figure

Acetic Acid Aldol Reactions in the Presence of Trimethylsilyl Trifluoromethanesulfonate

In the presence of TMSOTf and a trialkylamine base, acetic acid undergoes aldol addition to non-enolizable aldehydes under exceptionally mild conditions. Acidic workup yields the β-hydroxy carboxylic acid. The reaction appears to proceed via a three-step, one-pot process, including in situ trimethylsilyl ester formation, bis-silyl ketene acetal formation, and TMSOTf-catalyzed Mukaiyama aldol addition. Independently synthesized TMSOAc also undergoes aldol additions under similar conditions

Moderate Resolution Spectroscopy For The Space Infrared Telescope Facility (SIRTF)

A conceptual design for an infrared spectrometer capable of both low resolution (λ/Δ-λ = 50; 2.5-200 microns) and moderate resolution (1000; 4-200 microns) and moderate resolution (1000; 4-200 microns) has been developed. This facility instrument will permit the spectroscopic study in the infrared of objects ranging from within the solar system to distant galaxies. The spectroscopic capability provided by this instrument for SIRTF will give astronomers orders of magnitude greater sensitivity for the study of faint objects than had been previously available. The low resolution mode will enable detailed studies of the continuum radiation. The moderate resolution mode of the instrument will permit studies of a wide range of problems, from the infrared spectral signatures of small outer solar system bodies such as Pluto and the satellites of the giant planets, to investigations of more luminous active galaxies and QS0s at substantially greater distances. A simple design concept has been developed for the spectrometer which supports the science investigation with practical cryogenic engineering. Operational flexibility is preserved with a minimum number of mechanisms. The five modules share a common aperture, and all gratings share a single scan mechanism. High reliability is achieved through use of flight-proven hardware concepts and redundancy. The design controls the heat load into the SIRTF cryogen, with all heat sources other than the detectors operating at 7K and isolated from the 4K cold station. Two-dimensional area detector arrays are used in the 2.5-120μm bands to simultaneously monitor adjacent regions in extended objects and to measure the background near point sources

Parameterized Complexity of Asynchronous Border Minimization

Microarrays are research tools used in gene discovery as well as disease and cancer diagnostics. Two prominent but challenging problems related to microarrays are the Border Minimization Problem (BMP) and the Border Minimization Problem with given placement (P-BMP). In this paper we investigate the parameterized complexity of natural variants of BMP and P-BMP under several natural parameters. We show that BMP and P-BMP are in FPT under the following two combinations of parameters: 1) the size of the alphabet (c), the maximum length of a sequence (string) in the input (l) and the number of rows of the microarray (r); and, 2) the size of the alphabet and the size of the border length (o). Furthermore, P-BMP is in FPT when parameterized by c and l. We complement our tractability results with corresponding hardness results

Laboratory evidence of disseminated intravascular coagulation is associated with a fatal outcome in children with cerebral malaria despite an absence of clinically evident thrombosis or bleeding

Background A procoagulant state is implicated in cerebral malaria (CM ) pathogenesis, but whether disseminated intravascular coagulation (DIC ) is present or associated with a fatal outcome is unclear. Objectives To determine the frequency of overt DIC , according to ISTH criteria, in children with fatal and non‐fatal CM . Methods/patients Malawian children were recruited into a prospective cohort study in the following diagnostic groups: retinopathy‐positive CM (n = 140), retinopathy‐negative CM (n = 36), non‐malarial coma (n = 14), uncomplicated malaria (UM ), (n = 91), mild non‐malarial febrile illness (n = 85), and healthy controls (n = 36). Assays in the ISTH DIC criteria were performed, and three fibrin‐related markers, i.e. protein C, antithrombin, and soluble thrombomodulin, were measured. Results and conclusions Data enabling assignment of the presence or absence of ‘overt DIC ’ were available for 98 of 140 children with retinopathy‐positive CM . Overt DIC was present in 19 (19%), and was associated with a fatal outcome (odds ratio [OR] 3.068; 95% confidence interval [CI] 1.085–8.609; P = 0.035]. The levels of the three fibrin‐related markers and soluble thrombomodulin were higher in CM patients than in UM patients (all P < 0.001). The mean fibrin degradation product level was higher in fatal CM patients (71.3 μg mL−1 [95% CI 49.0–93.6]) than in non‐fatal CM patients (48.0 μg mL−1 [95% CI 37.7–58.2]; P = 0.032), but, in multivariate logistic regression, thrombomodulin was the only coagulation‐related marker that was independently associated with a fatal outcome (OR 1.084 for each ng mL−1 increase [95% CI 1.017–1.156]; P = 0.014). Despite these laboratory derangements, no child in the study had clinically evident bleeding or thrombosis. An overt DIC score and high thrombomodulin levels are associated with a fatal outcome in CM , but infrequently indicate a consumptive coagulopathy

Parameterized complexity of the MINCCA problem on graphs of bounded decomposability

In an edge-colored graph, the cost incurred at a vertex on a path when two incident edges with different colors are traversed is called reload or changeover cost. The "Minimum Changeover Cost Arborescence" (MINCCA) problem consists in finding an arborescence with a given root vertex such that the total changeover cost of the internal vertices is minimized. It has been recently proved by G\"oz\"upek et al. [TCS 2016] that the problem is FPT when parameterized by the treewidth and the maximum degree of the input graph. In this article we present the following results for the MINCCA problem: - the problem is W[1]-hard parameterized by the treedepth of the input graph, even on graphs of average degree at most 8. In particular, it is W[1]-hard parameterized by the treewidth of the input graph, which answers the main open problem of G\"oz\"upek et al. [TCS 2016]; - it is W[1]-hard on multigraphs parameterized by the tree-cutwidth of the input multigraph; - it is FPT parameterized by the star tree-cutwidth of the input graph, which is a slightly restricted version of tree-cutwidth. This result strictly generalizes the FPT result given in G\"oz\"upek et al. [TCS 2016]; - it remains NP-hard on planar graphs even when restricted to instances with at most 6 colors and 0/1 symmetric costs, or when restricted to instances with at most 8 colors, maximum degree bounded by 4, and 0/1 symmetric costs.Comment: 25 pages, 11 figure