A local 2-approximation algorithm for the vertex cover problem

We present a distributed 2-approximation algorithm for the minimum vertex cover problem. The algorithm is deterministic, and it runs in (Δ + 1)2 synchronous communication rounds, where Δ is the maximum degree of the graph. For Δ = 3, we give a 2-approximation algorithm also for the weighted version of the problem.

An optimal local approximation algorithm for max-min linear programs

In a max-min LP, the objective is to maximise ω subject to Ax ≤ 1, Cx ≥ ω1, and x ≥ 0 for nonnegative matrices A and C. We present a local algorithm (constant-time distributed algorithm) for approximating max-min LPs. The approximation ratio of our algorithm is the best possible for any local algorithm; there is a matching unconditional lower bound.

Pain measurement and management in elderly patients : Clinical studies in long term hospital care and after cardiac surgery

The proportion of patients over 75 years of age, receiving all different types of healthcare, is constantly increasing. The elderly undergo surgery and anaesthetic procedures more often than middle-aged patients. Poor pain management in the elderly is still an issue. Although the elderly consumes the greatest proportion of prescribed medicines in Western Europe, most clinical pharmacological studies have been performed in healthy volunteers or middle-aged patients. The aim of this study was to investigate pain measurement and management in cognitively impaired patients in long term hospital care and in cognitively normal elderly patients after cardiac surgery. This thesis incorporated 366 patients, including 86 home-dwelling or hospitalized elderly with chronic pain and 280 patients undergoing cardiac surgery with acute pain. The mean age of patients was 77 (SD ± 8) years and approximately 8400 pain measurements were performed with four pain scales: Verbal Rating Scale (VRS), the Visual Analogue Scale (VAS), the Red Wedge Scale (RWS), and the Facial Pain Scale (FPS). Cognitive function, depression, functional ability in daily life, postoperative sedation and postoperative confusion were assessed with MMSE, GDS, Barthel Index, RASS, and CAM-ICU, respectively. The effects and plasma concentrations of fentanyl and oxycodone were measured in elderly (≥ 75 years) and middle-aged patients (≤ 60 years) and the opioid-sparing effect of pregabalin was studied after cardiac surgery. The VRS pain scores after movement correlated with the Barthel Index. The VRS was most successful in the groups of demented patients (MMSE 17-23, 11-16 and ≤ 10) and in elderly patients on the first day after cardiac surgery. The elderly had a higher plasma concentration of fentanyl at the end of surgery than younger patients. The plasma concentrations of oxycodone were comparable between the groups. Pain intensity on the VRS was lower and the sedation scores were higher in the elderly. Total oxycodone consumption during five postoperative days was reduced by 48% and the CAM-ICU scores were higher on the first postoperative day in the pregabalin group. The incidence of postoperative pain during movement was lower in the pregabalin group three months after surgery. This investigation demonstrates that chronic pain did not seem to impair daily activities in home-dwelling Finnish elderly. The VRS appeared to be applicable for elderly patients with clear cognitive dysfunction (MMSE ≤17) and it was the most feasible pain scale for the early postoperative period after cardiac surgery. After cardiac surgery, plasma concentrations of fentanyl in elderly were elevated, although oxycodone concentrations were at similar level compared to middle-aged patients. The elderly had less pain and were more sedated after doses of oxycodone. Therefore, particular attention must be given to individual dosing of the opioids in elderly surgical patients, who often need a smaller amount for adequate analgesia than middle-aged patients. The administration of pregabalin reduced postoperative oxycodone consumption after cardiac surgery. Pregabalin-treated patients had less confusion, and additionally to less postoperative pain on the first postoperative day and during movement at three months post-surgery. Pregabalin might be a new alternative as analgesic for acute postoperative and chronic pain management in the elderly. Its clinical role and safety remains to be verified in large-scale randomized and controlled studies. In the future, many clinical trials in the older category of patients will be needed to facilitate improvements in health care methods.

Unified Galerkin- and DAE-Based Approximation of Fractional Order Systems

We consider numerical solutions of nonlinear multiterm fractional integrodifferential equations, where the order of the highest derivative is fractional and positive but is otherwise arbitrary. Here, we extend and unify our previous work, where a Galerkin method was developed for efficiently approximating fractional order operators and where elements of the present differential algebraic equation (DAE) formulation were introduced. The DAE system developed here for arbitrary orders of the fractional derivative includes an added block of equations for each fractional order operator, as well as forcing terms arising from nonzero initial conditions. We motivate and explain the structure of the DAE in detail. We explain how nonzero initial conditions should be incorporated within the approximation. We point out that our approach approximates the system and not a specific solution. Consequently, some questions not easily accessible to solvers of initial value problems, such as stability analyses, can be tackled using our approach. Numerical examples show excellent accuracy. DOI: 10.1115/1.4002516]

Costs and Benefits of a Shared Digital Long-Term Preservation System

This paper describes the cost-benefit analysis of digital long-term preservation (LTP) that was carried out in the context of the Finnish National Digital Library Project (NDL) in 2010. The analysis was based on the assumption that as many as 200 archives, libraries, and museums will share an LTP system. The term ‘system’ shall be understood as encompassing not only information technology, but also human resources, organizational structures, policies and funding mechanisms. The cost analysis shows that an LTP system will incur, over the first 12 years, cumulative costs of €42 million, i.e. an average of €3.5 million per annum. Human resources and investments in information technology are the major cost factors. After the initial stages, the analysis predicts annual costs of circa €4 million. The analysis compared scenarios with and without a shared LTP system. The results indicate that a shared system will have remarkable benefits. At the development and implementation stages, a shared system shows an advantage of €30 million against the alternative scenario consisting of five independent LTP solutions. During the later stages, the advantage is estimated at €10 million per annum. The cumulative cost benefit over the first 12 years would amount to circa €100 million.

Activation barriers for d.c. conductivity in ionic glasses: Classical calculations using the small-cluster approximation

A small-cluster approximation has been used to calculate the activation barriers for the d.c. conductivity in ionic glasses. The main emphasis of this approach is on the importance of the hitherto ignored polarization energy contribution to the total activation energy. For the first time it has been demonstrated that the d.c. conductivity activation energy can be calculated by considering ionic migration to a neighbouring vacancy in a smali cluster of ions consisting of face-sharing anion polyhedra. The activation energies from the model calculations have been compared with the experimental values in the case of highly modified lithium thioborate glasses.

Long-Term Excess Mortality after Aneurysmal Subarachnoid Hemorrhage

Objective There is high case-fatality rate and loss of productive life-years related to aneurysmal subarachnoid hemorrhage (aSAH) but little data on long-term survival of SAH patients. We aim to evaluate long-term excess mortality and related risk factors after aSAH. Methods One year survivors (n=3080) after aSAH from Department of Neurosurgery in Helsinki between 1980 and 2007 were reviewed for this retrospective follow-up study. Follow-up started one year after SAH and continued until death or the end of 2008 (36 960 patient-years). Mortality and relative survival ratio (RSR) were compared with matched general population. Results After 20 years, survivors of aSAH showed 18% excess mortality compared to general population. Risk factors included: old age; poor preoperative clinical condition; conservative aneurysm treatment; multiple aneurysms; and unfavourable clinical outcome at 3 months. Conclusion Even after initially favourable recovery, patients with aSAH experience excess mortality in the long run. Cardiovascular and cerebrovascular diseases are prominent in this population.

Phase diagram of the two-dimensional disordered Hubbard model in the Hartree-Fock approximation

Ground-state properties of the two-dimensional Hubbard model with point-defect disorder are investigated numerically in the Hartree-Fock approximation. The phase diagram in the p(point defect concentration)-delta(deviation from half filling) plane exhibits antiferromagnetic, spin-density-wave, paramagnetic, and spin-glass-like phases. The disorder stabilizes the antiferromagnetic phase relative to the spin-density-wave phase. The presence of U strongly enhances the localization in the antiferromagnetic phase. The spin-density-wave and spin-glass-like phases are weakly localized.

Seasonal and short-term variation in denitrification and anammox at a coastal station on the Gulf of Finland, Baltic Sea

Benthic processes were measured at a coastal deposition area in the northern Baltic Sea, covering all seasons. The N-2 production rates, 90-400 mu mol N m(-2) d(-1), were highest in autumn-early winter and lowest in spring. Heterotrophic bacterial production peaked unexpectedly late in the year, indicating that in addition to the temperature, the availability of carbon compounds suitable for the heterotrophic bacteria also plays a major role in regulating the denitrification rate. Anaerobic ammonium oxidation (anammox) was measured in spring and autumn and contributed 10% and 15%, respectively, to the total N-2 production. The low percentage did, however, result in a significant error in the total N-2 production rate estimate, calculated using the isotope pairing technique. Anammox must be taken into account in the Gulf of Finland in future sediment nitrogen cycling research.

New Approximation Algorithms for Minimum Cycle Bases of Graphs

We consider the problem of computing an approximate minimum cycle basis of an undirected non-negative edge-weighted graph G with m edges and n vertices; the extension to directed graphs is also discussed. In this problem, a {0,1} incidence vector is associated with each cycle and the vector space over F-2 generated by these vectors is the cycle space of G. A set of cycles is called a cycle basis of G if it forms a basis for its cycle space. A cycle basis where the sum of the weights of the cycles is minimum is called a minimum cycle basis of G. Cycle bases of low weight are useful in a number of contexts, e.g. the analysis of electrical networks, structural engineering, chemistry, and surface reconstruction. Although in most such applications any cycle basis can be used, a low weight cycle basis often translates to better performance and/or numerical stability. Despite the fact that the problem can be solved exactly in polynomial time, we design approximation algorithms since the performance of the exact algorithms may be too expensive for some practical applications. We present two new algorithms to compute an approximate minimum cycle basis. For any integer k >= 1, we give (2k - 1)-approximation algorithms with expected running time O(kmn(1+2/k) + mn((1+1/k)(omega-1))) and deterministic running time O(n(3+2/k) ), respectively. Here omega is the best exponent of matrix multiplication. It is presently known that omega < 2.376. Both algorithms are o(m(omega)) for dense graphs. This is the first time that any algorithm which computes sparse cycle bases with a guarantee drops below the Theta(m(omega) ) bound. We also present a 2-approximation algorithm with expected running time O(M-omega root n log n), a linear time 2-approximation algorithm for planar graphs and an O(n(3)) time 2.42-approximation algorithm for the complete Euclidean graph in the plane.

Affine Hall-Littlewood Functions for A(1)((1)) And Some Constant Term Identities of Cherednik-Macdonald-Mehta Type

We study t-analogs of string functions for integrable highest weight representations of the affine Kac-Moody algebra A(1)((1)). We obtain closed form formulas for certain t-string functions of levels 2 and 4. As corollaries, we obtain explicit identities for the corresponding affine Hall-Littlewood functions, as well as higher level generalizations of Cherednik's Macdonald and Macdonald-Mehta constant term identities.

Decoupled three-dimensional finite element computation of thermoelastic damping using Zener's approximation

We consider three dimensional finite element computations of thermoelastic damping ratios of arbitrary bodies using Zener's approach. In our small-damping formulation, unlike existing fully coupled formulations, the calculation is split into three smaller parts. Of these, the first sub-calculation involves routine undamped modal analysis using ANSYS. The second sub-calculation takes the mode shape, and solves on the same mesh a periodic heat conduction problem. Finally, the damping coefficient is a volume integral, evaluated elementwise. In the only other decoupled three dimensional computation of thermoelastic damping reported in the literature, the heat conduction problem is solved much less efficiently, using a modal expansion. We provide numerical examples using some beam-like geometries, for which Zener's and similar formulas are valid. Among these we examine tapered beams, including the limiting case of a sharp tip. The latter's higher-mode damping ratios dramatically exceed those of a comparable uniform beam.

Stochastic Approximation Algorithms for Constrained Optimization via Simulation

We develop four algorithms for simulation-based optimization under multiple inequality constraints. Both the cost and the constraint functions are considered to be long-run averages of certain state-dependent single-stage functions. We pose the problem in the simulation optimization framework by using the Lagrange multiplier method. Two of our algorithms estimate only the gradient of the Lagrangian, while the other two estimate both the gradient and the Hessian of it. In the process, we also develop various new estimators for the gradient and Hessian. All our algorithms use two simulations each. Two of these algorithms are based on the smoothed functional (SF) technique, while the other two are based on the simultaneous perturbation stochastic approximation (SPSA) method. We prove the convergence of our algorithms and show numerical experiments on a setting involving an open Jackson network. The Newton-based SF algorithm is seen to show the best overall performance.