Approximation Algorithms for Survivable Multicommodity Flow Problems with Applications to Network Design

Multicommodity flow (MF) problems have a wide variety of applications in areas such as VLSI circuit design, network design, etc., and are therefore very well studied. The fractional MF problems are polynomial time solvable while integer versions are NP-complete. However, exact algorithms to solve the fractional MF problems have high computational complexity. Therefore approximation algorithms to solve the fractional MF problems have been explored in the literature to reduce their computational complexity. Using these approximation algorithms and the randomized rounding technique, polynomial time approximation algorithms have been explored in the literature. In the design of high-speed networks, such as optical wavelength division multiplexing (WDM) networks, providing survivability carries great significance. Survivability is the ability of the network to recover from failures. It further increases the complexity of network design and presents network designers with more formidable challenges. In this work we formulate the survivable versions of the MF problems. We build approximation algorithms for the survivable multicommodity flow (SMF) problems based on the framework of the approximation algorithms for the MF problems presented in [1] and [2]. We discuss applications of the SMF problems to solve survivable routing in capacitated networks.

Loading a K-39 crossed optical dipole trap from a magneto-optical trap

In this work, we have applied sub-Doppler laser cooling to a K-39 magneto-optical trap in order to load a 1071 nm crossed optical dipole trap. The number of atoms loaded into the dipole trap was characterized as a function of the frequency and intensity of the cooling and repump laser beams. For the optimum conditions, the dipole trap has about 2 x 10(6) atoms at an atomic density of 2 x 10(12) cm(-3), with a temperature of about 10 mu K. This technique is a very simple procedure to load a K-39 optical dipole trap without a previous magnetic evaporative cooling step and may find application in other atomic physic systems.

Measurement of the elastic electron-proton cross section and separation of the electric and magnetic form factor in the Q 2 range from 0.004 to 1 (GeV/c) 2

The electromagnetic form factors of the proton are fundamental quantities sensitive to the distribution of charge and magnetization inside the proton. Precise knowledge of the form factors, in particular of the charge and magnetization radii provide strong tests for theory in the non-perturbative regime of QCD. However, the existing data at Q^2 below 1 (GeV/c)^2 are not precise enough for a hard test of theoretical predictions.rnrnFor a more precise determination of the form factors, within this work more than 1400 cross sections of the reaction H(e,e′)p were measured at the Mainz Microtron MAMI using the 3-spectrometer-facility of the A1-collaboration. The data were taken in three periods in the years 2006 and 2007 using beam energies of 180, 315, 450, 585, 720 and 855 MeV. They cover the Q^2 region from 0.004 to 1 (GeV/c)^2 with counting rate uncertainties below 0.2% for most of the data points. The relative luminosity of the measurements was determined using one of the spectrometers as a luminosity monitor. The overlapping acceptances of the measurements maximize the internal redundancy of the data and allow, together with several additions to the standard experimental setup, for tight control of systematic uncertainties.rnTo account for the radiative processes, an event generator was developed and implemented in the simulation package of the analysis software which works without peaking approximation by explicitly calculating the Bethe-Heitler and Born Feynman diagrams for each event.rnTo separate the form factors and to determine the radii, the data were analyzed by fitting a wide selection of form factor models directly to the measured cross sections. These fits also determined the absolute normalization of the different data subsets. The validity of this method was tested with extensive simulations. The results were compared to an extraction via the standard Rosenbluth technique.rnrnThe dip structure in G_E that was seen in the analysis of the previous world data shows up in a modified form. When compared to the standard-dipole form factor as a smooth curve, the extracted G_E exhibits a strong change of the slope around 0.1 (GeV/c)^2, and in the magnetic form factor a dip around 0.2 (GeV/c)^2 is found. This may be taken as indications for a pion cloud. For higher Q^2, the fits yield larger values for G_M than previous measurements, in agreement with form factor ratios from recent precise polarized measurements in the Q2 region up to 0.6 (GeV/c)^2.rnrnThe charge and magnetic rms radii are determined as rn⟨r_e⟩=0.879 ± 0.005(stat.) ± 0.004(syst.) ± 0.002(model) ± 0.004(group) fm,rn⟨r_m⟩=0.777 ± 0.013(stat.) ± 0.009(syst.) ± 0.005(model) ± 0.002(group) fm.rnThis charge radius is significantly larger than theoretical predictions and than the radius of the standard dipole. However, it is in agreement with earlier results measured at the Mainz linear accelerator and with determinations from Hydrogen Lamb shift measurements. The extracted magnetic radius is smaller than previous determinations and than the standard-dipole value.

Probing the decay characteristics of the Pygmy Dipole Resonance in the semi-magic nucleus 140 Ce with gamma-gamma coincidence measurements

Im Rahmen dieser Arbeit wurde ein neuartiger Experimentaufbau -- das γ3 Experiment -- zur Messung von photoneninduzierten Kern-Dipolanregungen in stabilen Isotopen konzipiert und an der High Intensity γ-Ray Source (HIγS) an der Duke University installiert.rnDie hohe Energieauflösung und die hohe Nachweiseffizienz des Detektoraufbaus, welcher aus einer Kombination von LaBr Szintillatoren und hochreinen Germanium-Detektoren besteht, erlaubt erstmals die effiziente Messung von γ-γ-Koinzidenzen in Verbindung mit der Methode der Kernresonanzfluoreszenz.rnDiese Methode eröffnet den Zugang zum Zerfallsverhalten der angeregten Dipolzustände als zusätzlicher Observablen, die ein detaillierteres Verständnis der zugrunde liegenden Struktur dieser Anregungen ermöglicht.rnDer Detektoraufbau wurde bereits erfolgreich im Rahmen von zwei Experimentkampagnen in 2012 und 2013 für die Untersuchung von 13 verschiedenen Isotopen verwendet. Im Fokus dieser Arbeit stand die Analyse der Pygmy-Dipolresonanz (PDR) im Kern 140Ce im Energiebereich von 5,2 MeV bis 8,3 MeV basierend auf den mit dem γ3 Experimentaufbau gemessenen Daten. Insbesondere das Zerfallsverhalten der Zustände, die an der PDR beteiligt sind, wurde untersucht. Der Experimentaufbau, die Details der Analyse sowie die Resultate werden in der vorliegenden Arbeit präsentiert. Desweiteren erlaubt ein Vergleich der Ergebnisse mit theoretischen Rechnungen im quasi-particle phonon model (QPM) eine Interpretation des beobachteten Zerfallsverhaltens.

The \bar{B} \to X_s γγdecay: NLL QCD contribution of the Electromagnetic Dipole operator O_7

We calculate the set of O(\alpha_s) corrections to the double differential decay width d\Gamma_{77}/(ds_1 \, ds_2) for the process \bar{B} \to X_s \gamma \gamma originating from diagrams involving the electromagnetic dipole operator O_7. The kinematical variables s_1 and s_2 are defined as s_i=(p_b - q_i)^2/m_b^2, where p_b, q_1, q_2 are the momenta of b-quark and two photons. While the (renormalized) virtual corrections are worked out exactly for a certain range of s_1 and s_2, we retain in the gluon bremsstrahlung process only the leading power w.r.t. the (normalized) hadronic mass s_3=(p_b-q_1-q_2)^2/m_b^2 in the underlying triple differential decay width d\Gamma_{77}/(ds_1 ds_2 ds_3). The double differential decay width, based on this approximation, is free of infrared- and collinear singularities when combining virtual- and bremsstrahlung corrections. The corresponding results are obtained analytically. When retaining all powers in s_3, the sum of virtual- and bremstrahlung corrections contains uncanceled 1/\epsilon singularities (which are due to collinear photon emission from the s-quark) and other concepts, which go beyond perturbation theory, like parton fragmentation functions of a quark or a gluon into a photon, are needed which is beyond the scope of our paper.

Table 2 Analytical data of the samples by the "Dipole CHIM" at the Yingezhuang gold deposit

CHIM method involves extracting metal ions of electromobile forms in either anodes or cathodes, facilitated by a man-made electric field. This paper presents two newly developed CHIM alternatives that are electrified by a low voltage dipole. The firstly improved technique enables cationic ions to be extracted in a single cathode, whereas the secondly improved technique allows both anionic and cationic species to be extracted simultaneously in an anode and in a cathode. Compared with the traditional CHIM methods, the innovative techniques developed in this paper are characterized by simple instrumentation, low cost and easy operation in field, and in particular enables simultaneous extraction of anionic and cationic species of elements, from which more information can be derived with higher extraction efficiency. Field tests at several well-known mine areas in China confirm the effectiveness and efficiency of the new techniques in exploring for deeply buried ore bodies.

A Multiresolution Image Alignment Technique Based on Direct Methods for Pose Estimation of Aerial Vehicles

In this paper, we seek to expand the use of direct methods in real-time applications by proposing a vision-based strategy for pose estimation of aerial vehicles. The vast majority of approaches make use of features to estimate motion. Conversely, the strategy we propose is based on a MR (Multi-Resolution) implementation of an image registration technique (Inverse Compositional Image Alignment ICIA) using direct methods. An on-board camera in a downwards-looking configuration, and the assumption of planar scenes, are the bases of the algorithm. The motion between frames (rotation and translation) is recovered by decomposing the frame-to-frame homography obtained by the ICIA algorithm applied to a patch that covers around the 80% of the image. When the visual estimation is required (e.g. GPS drop-out), this motion is integrated with the previous known estimation of the vehicles' state, obtained from the on-board sensors (GPS/IMU), and the subsequent estimations are based only on the vision-based motion estimations. The proposed strategy is tested with real flight data in representative stages of a flight: cruise, landing, and take-off, being two of those stages considered critical: take-off and landing. The performance of the pose estimation strategy is analyzed by comparing it with the GPS/IMU estimations. Results show correlation between the visual estimation obtained with the MR-ICIA and the GPS/IMU data, that demonstrate that the visual estimation can be used to provide a good approximation of the vehicle's state when it is required (e.g. GPS drop-outs). In terms of performance, the proposed strategy is able to maintain an estimation of the vehicle's state for more than one minute, at real-time frame rates based, only on visual information.

Optimal Piecewise Linear Function Approximation for GPU-based Applications

Many computer vision and human-computer interaction applications developed in recent years need evaluating complex and continuous mathematical functions as an essential step toward proper operation. However, rigorous evaluation of this kind of functions often implies a very high computational cost, unacceptable in real-time applications. To alleviate this problem, functions are commonly approximated by simpler piecewise-polynomial representations. Following this idea, we propose a novel, efficient, and practical technique to evaluate complex and continuous functions using a nearly optimal design of two types of piecewise linear approximations in the case of a large budget of evaluation subintervals. To this end, we develop a thorough error analysis that yields asymptotically tight bounds to accurately quantify the approximation performance of both representations. It provides an improvement upon previous error estimates and allows the user to control the trade-off between the approximation error and the number of evaluation subintervals. To guarantee real-time operation, the method is suitable for, but not limited to, an efficient implementation in modern Graphics Processing Units (GPUs), where it outperforms previous alternative approaches by exploiting the fixed-function interpolation routines present in their texture units. The proposed technique is a perfect match for any application requiring the evaluation of continuous functions, we have measured in detail its quality and efficiency on several functions, and, in particular, the Gaussian function because it is extensively used in many areas of computer vision and cybernetics, and it is expensive to evaluate.

Numerical Approximation of a Fractional-In-Space Diffusion Equation (II) – with Nonhomogeneous Boundary Conditions

2000 Mathematics Subject Classification: 26A33 (primary), 35S15

Dual self-image technique for beam collimation

We propose an accurate technique for obtaining highly collimated beams, which also allows testing the collimation degree of a beam. It is based on comparing the period of two different self-images produced by a single diffraction grating. In this way, variations in the period of the diffraction grating do not affect to the measuring procedure. Self-images are acquired by two CMOS cameras and their periods are determined by fitting the variogram function of the self-images to a cosine function with polynomial envelopes. This way, loss of accuracy caused by imperfections of the measured self-images is avoided. As usual, collimation is obtained by displacing the collimation element with respect to the source along the optical axis. When the period of both self-images coincides, collimation is achieved. With this method neither a strict control of the period of the diffraction grating nor a transverse displacement, required in other techniques, are necessary. As an example, a LED considering paraxial approximation and point source illumination is collimated resulting a resolution in the divergence of the beam of σ φ = ± μrad.

Near-field diffraction-based focal length determination technique

An accurate and simple technique for determining the focal length of a lens is presented. It consists of measuring the period of the fringes produced by a diffraction grating at the near field when it is illuminated with a beam focused by the unknown lens. In paraxial approximation, the period of the fringes varies linearly with the distance. After some calculations, a simple extrapolation of data is performed to obtain the locations of the principal plane and the focal plane of the lens. Thus, the focal length is obtained as the distance between the two mentioned planes. The accuracy of the method is limited by the collimation degree of the incident beam and by the algorithm used to obtain the period of the fringes. We have checked the technique with two commercial lenses, one convergent and one divergent, with nominal focal lengths (+100±1) mm and (−100±1) mm respectively. We have experimentally obtained the focal lengths resulting into the interval given by the manufacturer but with an uncertainty of 0.1%, one order of magnitude lesser than the uncertainty given by the manufacturer.

Fracture Of Distal Humerus: Mipo Technique With Visualization Of The Radial Nerve.

To evaluate the outcomes in patients treated for humerus distal third fractures with MIPO technique and visualization of the radial nerve by an accessory approach, in those without radial palsy before surgery. The patients were treated with MIPO technique. The visualization and isolation of the radial nerve was done by an approach between the brachialis and the brachiorradialis, with an oblique incision, in the lateral side of the arm. MEPS was used to evaluate the elbow function. Seven patients were evaluated with a mean age of 29.8 years old. The average follow up was 29.85 months. The radial neuropraxis after surgery occurred in three patients. The sensorial recovery occurred after 3.16 months on average and also of the motor function, after 5.33 months on average, in all patients. We achieved fracture consolidation in all patients (M=4.22 months). The averages for flexion-extension and prono-supination were 112.85° and 145°, respectively. The MEPS average score was 86.42. There was no case of infection. This approach allowed excluding a radial nerve interposition on site of the fracture and/or under the plate, showing a high level of consolidation of the fracture and a good evolution of the range of movement of the elbow. Level of Evidence IV, Case Series.

In Vitro Effects Of Hydrogen Peroxide Combined With Different Activators For The In-office Bleaching Technique On Enamel.

Abstract Objective. The aim of this study was to evaluate the alteration of human enamel bleached with high concentrations of hydrogen peroxide associated with different activators. Materials and methods. Fifty enamel/dentin blocks (4 × 4 mm) were obtained from human third molars and randomized divided according to the bleaching procedure (n = 10): G1 = 35% hydrogen peroxide (HP - Whiteness HP Maxx); G2 = HP + Halogen lamp (HL); G3 = HP + 7% sodium bicarbonate (SB); G4 = HP + 20% sodium hydroxide (SH); and G5 = 38% hydrogen peroxide (OXB - Opalescence Xtra Boost). The bleaching treatments were performed in three sessions with a 7-day interval between them. The enamel content, before (baseline) and after bleaching, was determined using an FT-Raman spectrometer and was based on the concentration of phosphate, carbonate, and organic matrix. Statistical analysis was performed using two-way ANOVA for repeated measures and Tukey's test. Results. The results showed no significant differences between time of analysis (p = 0.5175) for most treatments and peak areas analyzed; and among bleaching treatments (p = 0.4184). The comparisons during and after bleaching revealed a significant difference in the HP group for the peak areas of carbonate and organic matrix, and for the organic matrix in OXB and HP+SH groups. Tukey's analysis determined that the difference, peak areas, and the interaction among treatment, time and peak was statistically significant (p < 0.05). Conclusion. The association of activators with hydrogen peroxide was effective in the alteration of enamel, mainly with regards to the organic matrix.

Preservation Of The External Jugular Vein In Bilateral Radical Neck Dissections: Technique In Two Cases And Review Of The Literature.

Context. The possibility of cephalic venous hypertension with the resultant facial edema and elevated cerebrospinal fluid pressure continues to challenge head and neck surgeons who perform bilateral radical neck dissections during simultaneous or staged procedures. Case Report. The staged procedure in patients who require bilateral neck dissections allows collateral venous drainage to develop, mainly through the internal and external vertebral plexuses, thereby minimizing the risks of deleterious consequences. Nevertheless, this procedure has disadvantages, such as a delay in definitive therapy, the need for a second hospitalization and anesthesia, and the risk of cutting lymphatic vessels and spreading viable cancer cells. In this paper, we discuss the rationale and feasibility of preserving the external jugular vein. Considering the limited number of similar reports in the literature, two cases in which this procedure was accomplished are described. The relevant anatomy and technique are reviewed and the patients' outcomes are discussed. Conclusion. Preservation of the EJV during bilateral neck dissections is technically feasible, fast, and safe, with clinically and radiologically demonstrated patency.

High Prevalence Of Insulin Resistance Assessed By The Glucose Clamp Technique In Hormonal And Non-hormonal Contraceptive Users.

Objective To assess the prevalence of insulin resistance (IR) and associated factors in contraceptive users. Methods A total of 47 women 18 to 40 years of age with a body mass index (kg/m(2)) < 30, fasting glucose levels < 100 mg/dl and 2-hour glucose level < 140 mg/dl after a 75-g oral glucose load were submitted to a hyperinsulinemic-euglycemic clamp. The women were distributed in tertiles regarding M-values. The analysed variables were use of combined hormonal/non-hormonal contraception, duration of use, body composition, lipid profile, glucose levels and blood pressure. Results IR was detected in 19% of the participants. The women with low M-values presented significantly higher body fat mass, waist-to-hip ratio, fasting insulin, HOMA-IR and were nulligravida, showed > 1 year of contraceptive use and higher triglyceride levels. IR was more frequent among combined oral contraceptive users, however no association was observed after regression analysis. Conclusions The prevalence of IR was high among healthy women attending a family planning clinic independent of the contraceptive method used with possible long-term negative consequences regarding their metabolic and cardiovascular health. Although an association between hormonal contraception and IR could not be found this needs further research. Family planning professionals should be proactive counselling healthy women about the importance of healthy habits.