Constant-Factor FPT Approximation for Capacitated k-Median

Capacitated k-median is one of the few outstanding optimization problems for which the existence of a polynomial time constant factor approximation algorithm remains an open problem. In a series of recent papers algorithms producing solutions violating either the number of facilities or the capacity by a multiplicative factor were obtained. However, to produce solutions without violations appears to be hard and potentially requires different algorithmic techniques. Notably, if parameterized by the number of facilities k, the problem is also W[2] hard, making the existence of an exact FPT algorithm unlikely. In this work we provide an FPT-time constant factor approximation algorithm preserving both cardinality and capacity of the facilities. The algorithm runs in time 2^O(k log k) n^O(1) and achieves an approximation ratio of 7+epsilon

When the Optimum is also Blind: a New Perspective on Universal Optimization

Consider the following variant of the set cover problem. We are given a universe U={1,...,n} and a collection of subsets C = {S_1,...,S_m} where each S_i is a subset of U. For every element u from U we need to find a set phi(u) from collection C such that u belongs to phi(u). Once we construct and fix the mapping phi from U to C a subset X from the universe U is revealed, and we need to cover all elements from X with exactly phi(X), that is {phi(u)}_{all u from X}. The goal is to find a mapping such that the cover phi(X) is as cheap as possible. This is an example of a universal problem where the solution has to be created before the actual instance to deal with is revealed. Such problems appear naturally in some settings when we need to optimize under uncertainty and it may be actually too expensive to begin finding a good solution once the input starts being revealed. A rich body of work was devoted to investigate such problems under the regime of worst case analysis, i.e., when we measure how good the solution is by looking at the worst-case ratio: universal solution for a given instance vs optimum solution for the same instance. As the universal solution is significantly more constrained, it is typical that such a worst-case ratio is actually quite big. One way to give a viewpoint on the problem that would be less vulnerable to such extreme worst-cases is to assume that the instance, for which we will have to create a solution, will be drawn randomly from some probability distribution. In this case one wants to minimize the expected value of the ratio: universal solution vs optimum solution. Here the bounds obtained are indeed smaller than when we compare to the worst-case ratio. But even in this case we still compare apples to oranges as no universal solution is able to construct the optimum solution for every possible instance. What if we would compare our approximate universal solution against an optimal universal solution that obeys the same rules as we do? We show that under this viewpoint, but still in the stochastic variant, we can indeed obtain better bounds than in the expected ratio model. For example, for the set cover problem we obtain $H_n$ approximation which matches the approximation ratio from the classic deterministic setup. Moreover, we show this for all possible probability distributions over $U$ that have a polynomially large carrier, while all previous results pertained to a model in which elements were sampled independently. Our result is based on rounding a proper configuration IP that captures the optimal universal solution, and using tools from submodular optimization. The same basic approach leads to improved approximation algorithms for other related problems, including Vertex Cover, Edge Cover, Directed Steiner Tree, Multicut, and Facility Location

High Frequency Ultrasonography of the Skin and Its Role as an Auxillary Tool in Diagnosis of Benign and Malignant Cutaneous Tumors – A Comparison of Two Clinical Cases

The number of dermatologic entities that can be studied by ultrasound examination (US) of the skin is increasing. Conventional US and high frequency US (HFUS) are considered useful additional tools in improving the diagnosis and management of common benign and malignant skin tumors. US may help in positive and differential diagnosis of primary melanocytic neoplasms and of locoregional spread in melanoma patients. US preoperative evaluation of primary melanoma thickness correlates with histologically estimated melanoma thickness, and can help determine surgical margins and indications for sentinel lymph node biopsy. It is also useful during follow-up after surgical treatment for early detection of recurrence or metastases. In this case report, we present two cases of skin lesions clinically suspicious for malignancy. The first lesion was a round nodule 3 mm in diameter, resembling a blue nevus. In HFUS it was well delimited, hypoechoic, and well vascularized. The second lesion presented as an elevated, well-circumscribed nodule, 5-6 mm in diameter, inhomogeneous in color. HFUS depicted a poorly delimited, irregular, hypoechoic lesion crossing the dermoepidermal junction. At the first exam it was not vascularized, but 6 months later a number of vascular flow signals within the lesion were found. In histopathological examination the lesions were finally diagnosed as, respectively: benign cavernous hemangioma and melanoma. In both presented cases HFUS proved to be useful in a differential diagnosis of suspicious skin lesions. Noninvasive and easy to perform, HFUS is a valuable diagnostic method in dermatology.</p

High Frequency Ultrasonography of the Skin and Its Role as an Auxillary Tool in Diagnosis of Benign and Malignant Cutaneous Tumors – A Comparison of Two Clinical Cases

The number of dermatologic entities that can be studied by ultrasound examination (US) of the skin is increasing. Conventional US and high frequency US (HFUS) are considered useful additional tools in improving the diagnosis and management of common benign and malignant skin tumors. US may help in positive and differential diagnosis of primary melanocytic neoplasms and of locoregional spread in melanoma patients. US preoperative evaluation of primary melanoma thickness correlates with histologically estimated melanoma thickness, and can help determine surgical margins and indications for sentinel lymph node biopsy. It is also useful during follow-up after surgical treatment for early detection of recurrence or metastases. In this case report, we present two cases of skin lesions clinically suspicious for malignancy. The first lesion was a round nodule 3 mm in diameter, resembling a blue nevus. In HFUS it was well delimited, hypoechoic, and well vascularized. The second lesion presented as an elevated, well-circumscribed nodule, 5-6 mm in diameter, inhomogeneous in color. HFUS depicted a poorly delimited, irregular, hypoechoic lesion crossing the dermoepidermal junction. At the first exam it was not vascularized, but 6 months later a number of vascular flow signals within the lesion were found. In histopathological examination the lesions were finally diagnosed as, respectively: benign cavernous hemangioma and melanoma. In both presented cases HFUS proved to be useful in a differential diagnosis of suspicious skin lesions. Noninvasive and easy to perform, HFUS is a valuable diagnostic method in dermatology.</p

How does management affect soil C sequestration and greenhouse gas fluxes in boreal and temperate forests? : A review

Acknowledgements This review has been supported by the grant Holistic management practices, modelling and monitoring for European forest soils – HoliSoils (EU Horizon 2020 Grant Agreement No 101000289) and the Academy of Finland Fellow project (330136, B. Adamczyk). In addition to the HoliSoils consortium partners, Dr. Abramoff contributed on this study and her work was supported by the United States Department of Energy, Office of Science, Office of Biological and Environmental Research. Oak Ridge National Laboratory is managed by UT-Battelle, LLC, for the United States Department of Energy under contract DE-AC05-00OR22725.Peer reviewedPublisher PD

Observation of associated near-side and away-side long-range correlations in √sNN=5.02 TeV proton-lead collisions with the ATLAS detector

Two-particle correlations in relative azimuthal angle (Δϕ) and pseudorapidity (Δη) are measured in √sNN=5.02  TeV p+Pb collisions using the ATLAS detector at the LHC. The measurements are performed using approximately 1  μb-1 of data as a function of transverse momentum (pT) and the transverse energy (ΣETPb) summed over 3.1<η<4.9 in the direction of the Pb beam. The correlation function, constructed from charged particles, exhibits a long-range (2<|Δη|<5) “near-side” (Δϕ∼0) correlation that grows rapidly with increasing ΣETPb. A long-range “away-side” (Δϕ∼π) correlation, obtained by subtracting the expected contributions from recoiling dijets and other sources estimated using events with small ΣETPb, is found to match the near-side correlation in magnitude, shape (in Δη and Δϕ) and ΣETPb dependence. The resultant Δϕ correlation is approximately symmetric about π/2, and is consistent with a dominant cos⁡2Δϕ modulation for all ΣETPb ranges and particle pT

Search for direct production of charginos and neutralinos in events with three leptons and missing transverse momentum in √s = 7 TeV pp collisions with the ATLAS detector

A search for the direct production of charginos and neutralinos in final states with three electrons or muons and missing transverse momentum is presented. The analysis is based on 4.7 fb−1 of proton–proton collision data delivered by the Large Hadron Collider and recorded with the ATLAS detector. Observations are consistent with Standard Model expectations in three signal regions that are either depleted or enriched in Z-boson decays. Upper limits at 95% confidence level are set in R-parity conserving phenomenological minimal supersymmetric models and in simplified models, significantly extending previous results

Measurement of χ c1 and χ c2 production with s√ = 7 TeV pp collisions at ATLAS

The prompt and non-prompt production cross-sections for the χ c1 and χ c2 charmonium states are measured in pp collisions at s√ = 7 TeV with the ATLAS detector at the LHC using 4.5 fb−1 of integrated luminosity. The χ c states are reconstructed through the radiative decay χ c → J/ψγ (with J/ψ → μ + μ −) where photons are reconstructed from γ → e + e − conversions. The production rate of the χ c2 state relative to the χ c1 state is measured for prompt and non-prompt χ c as a function of J/ψ transverse momentum. The prompt χ c cross-sections are combined with existing measurements of prompt J/ψ production to derive the fraction of prompt J/ψ produced in feed-down from χ c decays. The fractions of χ c1 and χ c2 produced in b-hadron decays are also measured

Single hadron response measurement and calorimeter jet energy scale uncertainty with the ATLAS detector at the LHC

The uncertainty on the calorimeter energy response to jets of particles is derived for the ATLAS experiment at the Large Hadron Collider (LHC). First, the calorimeter response to single isolated charged hadrons is measured and compared to the Monte Carlo simulation using proton-proton collisions at centre-of-mass energies of sqrt(s) = 900 GeV and 7 TeV collected during 2009 and 2010. Then, using the decay of K_s and Lambda particles, the calorimeter response to specific types of particles (positively and negatively charged pions, protons, and anti-protons) is measured and compared to the Monte Carlo predictions. Finally, the jet energy scale uncertainty is determined by propagating the response uncertainty for single charged and neutral particles to jets. The response uncertainty is 2-5% for central isolated hadrons and 1-3% for the final calorimeter jet energy scale.Comment: 24 pages plus author list (36 pages total), 23 figures, 1 table, submitted to European Physical Journal

Jet size dependence of single jet suppression in lead-lead collisions at sqrt(s(NN)) = 2.76 TeV with the ATLAS detector at the LHC

Measurements of inclusive jet suppression in heavy ion collisions at the LHC provide direct sensitivity to the physics of jet quenching. In a sample of lead-lead collisions at sqrt(s) = 2.76 TeV corresponding to an integrated luminosity of approximately 7 inverse microbarns, ATLAS has measured jets with a calorimeter over the pseudorapidity interval |eta| < 2.1 and over the transverse momentum range 38 < pT < 210 GeV. Jets were reconstructed using the anti-kt algorithm with values for the distance parameter that determines the nominal jet radius of R = 0.2, 0.3, 0.4 and 0.5. The centrality dependence of the jet yield is characterized by the jet "central-to-peripheral ratio," Rcp. Jet production is found to be suppressed by approximately a factor of two in the 10% most central collisions relative to peripheral collisions. Rcp varies smoothly with centrality as characterized by the number of participating nucleons. The observed suppression is only weakly dependent on jet radius and transverse momentum. These results provide the first direct measurement of inclusive jet suppression in heavy ion collisions and complement previous measurements of dijet transverse energy imbalance at the LHC.Comment: 15 pages plus author list (30 pages total), 8 figures, 2 tables, submitted to Physics Letters B. All figures including auxiliary figures are available at http://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/PAPERS/HION-2011-02