A Gap-{ETH}-Tight Approximation Scheme for Euclidean {TSP}

We revisit the classic task of finding the shortest tour of $n$ points in $d$-dimensional Euclidean space, for any fixed constant $d \geq 2$. We determine the optimal dependence on $\varepsilon$ in the running time of an algorithm that computes a $(1+\varepsilon)$-approximate tour, under a plausible assumption. Specifically, we give an algorithm that runs in $2^{\mathcal{O}(1/\varepsilon^{d-1})} n\log n$ time. This improves the previously smallest dependence on $\varepsilon$ in the running time $(1/\varepsilon)^{\mathcal{O}(1/\varepsilon^{d-1})}n \log n$ of the algorithm by Rao and Smith (STOC 1998). We also show that a $2^{o(1/\varepsilon^{d-1})}\text{poly}(n)$ algorithm would violate the Gap-Exponential Time Hypothesis (Gap-ETH). Our new algorithm builds upon the celebrated quadtree-based methods initially proposed by Arora (J. ACM 1998), but it adds a simple new idea that we call \emph{sparsity-sensitive patching}. On a high level this lets the granularity with which we simplify the tour depend on how sparse it is locally. Our approach is (arguably) simpler than the one by Rao and Smith since it can work without geometric spanners. We demonstrate the technique extends easily to other problems, by showing as an example that it also yields a Gap-ETH-tight approximation scheme for Rectilinear Steiner Tree

Faster space-efficient algorithms for Subset Sum, k -Sum, and related problems

We present randomized algorithms that solve subset sum and knapsack instances with n items in O∗ (20.86n) time, where the O∗ (∙ ) notation suppresses factors polynomial in the input size, and polynomial space, assuming random read-only access to exponentially many random bits. These results can be extended to solve binary integer programming on n variables with few constraints in a similar running time. We also show that for any constant k ≥ 2, random instances of k-Sum can be solved using O(nk -0.5polylog(n)) time and O(log n) space, without the assumption of random access to random bits.Underlying these results is an algorithm that determines whether two given lists of length n with integers bounded by a polynomial in n share a common value. Assuming random read-only access to random bits, we show that this problem can be solved using O(log n) space significantly faster than the trivial O(n2) time algorithm if no value occurs too often in the same list.</p

Polynomial Kernels for Weighted Problems

Kernelization is a formalization of efficient preprocessing for NP-hard problems using the framework of parameterized complexity. Among open problems in kernelization it has been asked many times whether there are deterministic polynomial kernelizations for Subset Sum and Knapsack when parameterized by the number $n$ of items. We answer both questions affirmatively by using an algorithm for compressing numbers due to Frank and Tardos (Combinatorica 1987). This result had been first used by Marx and V\'egh (ICALP 2013) in the context of kernelization. We further illustrate its applicability by giving polynomial kernels also for weighted versions of several well-studied parameterized problems. Furthermore, when parameterized by the different item sizes we obtain a polynomial kernelization for Subset Sum and an exponential kernelization for Knapsack. Finally, we also obtain kernelization results for polynomial integer programs

A strategy for the characterization of minute chromosome rearrangements using multiple color fluorescence in situ hybridization with chromosome-specific DNA libraries and YAC clones

The identification of marker chromosomes in clinical and tumor cytogenetics by chromosome banding analysis can create problems. In this study, we present a strategy to define minute chromosomal rearrangements by multicolor fluorescence in situ hybridization (FISH) with whole chromosome painting probes derived from chromosome-specific DNA libraries and Alu-polymerase chain reaction (PCR) products of various region-specific yeast artificial chromosome (YAC) clones. To demonstrate the usefulness of this strategy for the characterization of chromosome rearrangements unidentifiable by banding techniques, an 8p+ marker chromosome with two extra bands present in the karyotype of a child with multiple anomalies, malformations, and severe mental retardation was investigated. A series of seven-color FISH experiments with sets of fluorochrome-labeled DNA library probes from flow-sorted chromosomes demonstrated that the additional segment on 8p+ was derived from chromosome 6. For a more detailed characterization of the marker chromosome, three-color FISH experiments with library probes specific to chromosomes 6 and 8 were performed in combination with newly established telomeric and subtelomeric YAC clones from 6q25, 6p23, and 8p23. These experiments demonstrated a trisomy 6pter6p22 and a monosomy 8pter8p23 in the patient. The present limitations for a broad application of this strategy and its possible improvements are discusse

Finding and counting vertex-colored subtrees

The problems studied in this article originate from the Graph Motif problem introduced by Lacroix et al. in the context of biological networks. The problem is to decide if a vertex-colored graph has a connected subgraph whose colors equal a given multiset of colors $M$. It is a graph pattern-matching problem variant, where the structure of the occurrence of the pattern is not of interest but the only requirement is the connectedness. Using an algebraic framework recently introduced by Koutis et al., we obtain new FPT algorithms for Graph Motif and variants, with improved running times. We also obtain results on the counting versions of this problem, proving that the counting problem is FPT if M is a set, but becomes W[1]-hard if M is a multiset with two colors. Finally, we present an experimental evaluation of this approach on real datasets, showing that its performance compares favorably with existing software.Comment: Conference version in International Symposium on Mathematical Foundations of Computer Science (MFCS), Brno : Czech Republic (2010) Journal Version in Algorithmic

Delineation of Chondroid Lipoma: An Immunohistochemical and Molecular Biological Analysis

Aims. Chondroid lipoma (CL) is a benign tumor that mimics a variety of soft tissue tumors and is characterized by translocation t(11;16). Here, we analyze CL and its histological mimics. Methods. CL (n = 4) was compared to a variety of histological mimics (n = 83) for morphological aspects and immunohistochemical features including cyclinD1(CCND1). Using FISH analysis, CCND1 and FUS were investigated as potential translocation partners. Results. All CLs were strongly positive for CCND1. One of 4 myoepitheliomas, CCND1, was positive. In well-differentiated lipomatous tumors and in chondrosarcomas, CCND1 was frequently expressed, but all myxoid liposarcomas were negative. FISH analysis did not give support for direct involvement of CCND1 and FUS as translocation partners. Conclusions. Chondroid lipoma is extremely rare and has several and more prevalent histological mimics. The differential diagnosis of chondroid lipomas can be unraveled using immunohistochemical and molecular support

Transformation of smallholder beef cattle production in Vietnam

This research describes and analyses how smallholder crop livestock farmers in rural Ea Kar, Vietnam, were able to take advantage of the rising demand for meat in urban centres and transform cattle production from a traditional, extensive grazing system to a more intensive, stall-fed system that supplied quality meat to urban markets. The traditional grazing system produced low-quality animals that could only be sold for local consumption. Introduction of the concept of farm-grown fodder production enabled farmers to produce fatter animals, achieving higher sale prices, and reduce labour inputs by moving from grazing to stall-feeding. These benefits convinced farmers, traders and local government that smallholder cattle production could be a viable enterprise and so stimulated stakeholder interest. Within 10 years, the way that cattle were produced and marketed changed considerably. By 2010, more than 3,000 smallholders had adopted farm-grown forages and stall-feeding, and many produced high-quality beef cattle. Traders had been able to develop access to urban markets as farmers were able to produce animals that satisfied the stringent quality requirements of urban markets. In addition to the underlying driver of strong market demand for quality meat, several factors contributed to this transition: (i) a convincing innovation – the use of farm-grown fodder – that provided immediate benefits to farmers and provided a vision for local stakeholders; (ii) a participatory, systems-oriented innovation process that emphasised capacity strengthening; (iii) a value chain approach that linked farmers and local traders to markets; (iv) the formation of a loosely structured coalition of local stakeholders that facilitated and managed the innovation process; and (v) technical support over a sufficiently long time period to allow innovation processes to become sustainable

Performance of factor IX extended half-life product measurements in external quality control assessment programs

Background: Patients with hemophilia B are increasingly treated with extended half-life (EHL) factor IX (FIX) concentrates. For the laboratory, introduction of these EHL concentrates presents a major challenge. To understand the variation in FIX activity levels, all available diagnostic assays need to be directly compared. Methods: The ECAT, UKNEQAS, and RCPAQAP have collaboratively performed a global survey to evaluate the quality of FIX measurements using FIX deficient plasma samples spiked with recombinant FIX (rFIX), rFIXFP, rFIXFc, and N9-GP to levels at typical FIX trough (6 IU/dL) and peak levels (60 IU/dL). Participants were asked to use their routine protocols, using one-stage assays (OSA) or chromogenic assays (CA). Results: In samples spiked with 6 IU/dL product, median (25%-75% range) FIX activity levels (OSA), were 8.0 IU/dL (7.0-9.2) for rFIX, 6.0 IU/dL (4.0-7.1) for rFIXFP, 6.6 IU/dL (5.5-8.0) for rFIXFc, and 4.9 IU/dL (3.5-8.4) for N9-GP. In samples spiked with 60 IU/dL, FIX activity levels measured (using OSA) was 63.0 IU/dL (59.9-67.0) for rFIX, 42.5 IU/dL (28.2-47.0) for rFIXFP, 50.0 IU/dL (45.0-55.0) for rFIXFc, and 34.0 IU/dL (24.8-67.5) for N9-GP. Considerable differences were observed between reagents for all samples. With CA, there was also quite some variation, but no differences between reagents. Conclusion: Large variation is observed in the measurement of FIX activity levels after administration of rFIX and EHL FIX products. For N9-GP, most silica-based assays show especially high levels. It is essential to standardize and improve reliability of measurements of these concentrates as diagnosis and treatment monitoring is based on these results

Dealing with critical challenges in African innovation platforms: lessons for facilitation

Innovation platforms are increasingly used by research and development initiatives to actively engage the poor in agricultural innovation processes. These platforms are forums for action and learning, where different types of actors come together to address issues of mutual concern. However, the dynamic nature of the innovation process, and the differences in interest, capacity and power among the actors involved, pose a challenge in the facilitation of these platforms. We believe that the key to success is very much linked to the attitude, skills and capacities of the innovation broker. This paper highlights seven key issues which in our view are critical to effective platform facilitation and have not received the attention they deserve: the dynamic and evolving nature of platforms; power dynamics; gender equity; external versus internal facilitation; sustainability of the process; issues of scale; and monitoring and evaluation. These issues and implications for facilitation of innovation platforms will be discussed based on examples from the field and in relation to current theories

Systems approaches to innovation in pest management: reflections and lessons learned from an integrated research program on parasitic weeds in rice

This paper provides a retrospective look at a systems-oriented research program, on the increasing occurrence of parasitic weeds in rainfed rice in sub-Saharan Africa, to qualitatively assess merits and identify challenges of such approach. We gained a broad contextual overview of the problem and different stakeholders' roles, which enabled identification of entry points for innovations in parasitic weed management. At the crop level parasitic weed infestation is associated with poor soil fertility and water management. Farmers' infrequent use of inputs to control them was caused by various factors, ranging from fears of undesired side effects (agronomic) to a lack of quality control of products (institutional). Furthermore, there may be enough extension agents, but they lack the required training on (parasitic) weed management to provide farmers with advice, while their organizations do not provide them with the necessary means for farm visits. At even higher organizational levels we observed a lack of coherent policies on parasitic weed control and implementation of them. Merits and challenges of an integrated multi-stakeholder and multi-level research project are discussed