Homotopy Method for the Large, Sparse, Real Nonsymmetric Eigenvalue Problem

A homotopy method to compute the eigenpairs, i.e., the eigenvectors and eigenvalues, of a given real matrix A1 is presented. From the eigenpairs of some real matrix A0, the eigenpairs of A(t) ≡ (1 − t)A0 + tA1 are followed at successive "times" from t = 0 to t = 1 using continuation. At t = 1, the eigenpairs of the desired matrix A1 are found. The following phenomena are present when following the eigenpairs of a general nonsymmetric matrix: • bifurcation, • ill conditioning due to nonorthogonal eigenvectors, • jumping of eigenpaths. These can present considerable computational difficulties. Since each eigenpair can be followed independently, this algorithm is ideal for concurrent computers. The homotopy method has the potential to compete with other algorithms for computing a few eigenvalues of large, sparse matrices. It may be a useful tool for determining the stability of a solution of a PDE. Some numerical results will be presented

Non-line-of-sight Node Localization based on Semi-Definite Programming in Wireless Sensor Networks

An unknown-position sensor can be localized if there are three or more anchors making time-of-arrival (TOA) measurements of a signal from it. However, the location errors can be very large due to the fact that some of the measurements are from non-line-of-sight (NLOS) paths. In this paper, we propose a semi-definite programming (SDP) based node localization algorithm in NLOS environment for ultra-wideband (UWB) wireless sensor networks. The positions of sensors can be estimated using the distance estimates from location-aware anchors as well as other sensors. However, in the absence of LOS paths, e.g., in indoor networks, the NLOS range estimates can be significantly biased. As a result, the NLOS error can remarkably decrease the location accuracy. And it is not easy to efficiently distinguish LOS from NLOS measurements. In this paper, an algorithm is proposed that achieves high location accuracy without the need of identifying NLOS and LOS measurement.Comment: submitted to IEEE ICC'1

Semiconducting-to-metallic photoconductivity crossover and temperature-dependent Drude weight in graphene

We investigated the transient photoconductivity of graphene at various gate-tuned carrier densities by optical-pump terahertz-probe spectroscopy. We demonstrated that graphene exhibits semiconducting positive photoconductivity near zero carrier density, which crosses over to metallic negative photoconductivity at high carrier density. Our observations are accounted for by considering the interplay between photo-induced changes of both the Drude weight and the carrier scattering rate. Notably, we observed multiple sign changes in the temporal photoconductivity dynamics at low carrier density. This behavior reflects the non-monotonic temperature dependence of the Drude weight, a unique property of massless Dirac fermions

The dynamics of laser droplet generation

We propose an experimental setup allowing for the characterization of laser droplet generation in terms of the underlying dynamics, primarily showing that the latter is deterministically chaotic by means of nonlinear time series analysis methods. In particular, we use a laser pulse to melt the end of a properly fed vertically placed metal wire. Due to the interplay of surface tension, gravity force and light-metal interaction, undulating pendant droplets are formed at the molten end, which eventually completely detach from the wire as a consequence of their increasing mass. We capture the dynamics of this process by employing a high-speed infrared camera, thereby indirectly measuring the temperature of the wire end and the pendant droplets. The time series is subsequently generated as the mean value over the pixel intensity of every infrared snapshot. Finally, we employ methods of nonlinear time series analysis to reconstruct the phase space from the observed variable and test it against determinism and stationarity. After establishing that the observed laser droplet generation is a deterministic and dynamically stationary process, we calculate the spectra of Lyapunov exponents. We obtain a positive largest Lyapunov exponent and a negative divergence, i.e., sum of all the exponents, thus indicating that the observed dynamics is deterministically chaotic with an attractor as solution in the phase space. In addition to characterizing the dynamics of laser droplet generation, we outline industrial applications of the process and point out the significance of our findings for future attempts at mathematical modeling.Comment: 7 two-column pages, 8 figures; accepted for publication in Chaos [supplementary material available at http://www.matjazperc.com/chaos/laser.html

Bilateral Anterior Shoulder Dislocation

Introduction: Unilateral anterior shoulder dislocation is one of the most common problems encountered in orthopedic practice. However, simultaneous bilateral anterior dislocation of the shoulders is quite rare. Case Presentation: We report a case of a 75-year-old woman presented with simultaneous bilateral anterior shoulder dislocation following a trauma, complicated with a traction injury to the posterior cord of the brachial plexus. Conclusions: Bilateral anterior shoulder dislocation is very rare. The excessive traction force during closed reduction may lead to nerve palsy. Clear documentation of neurovascular status and adequate imaging before and after a reduction should be performed

Proximal Fifth Metatarsal Fractures: Anatomy, Classification, Treatment and Complications

Context: Fractures of proximal fifth metatarsal are one of the most common fractures of the foot. Evidence Acquisition: A search of PubMed for studies on proximal fifth metatarsal fracture and Jones fracture focusing on the classification and management was performed. The reference list of the retrieved articles was searched for additional related studies. Results: The vascular supply and soft tissue anatomy of the fifth metatarsal explains the increased risk of delayed union and non-union in fractures at the metaphyseal-diaphyseal junction. Lawrence and Botte classify proximal fifth metatarsal fractures according to their location: tuberosity avulsion fractures (zone 1), fractures at metaphyseal-diaphyseal junction extending into the fourth-fifth intermetatarsal joint (zone 2) and proximal diaphyseal fractures (zone 3). Zone 1 fractures are treated conservatively with functional immobilization and early mobilization with excellent outcome. For zone 2 and zone 3 fractures, acute forms can be treated conservatively but with a risk of delayed union time and time for return to function. Therefore, early surgical fixation with intramedullary screw is advised in athletic individuals. For cases presented with signs of delayed union and non-union, surgical treatment with or without bone grafting is recommended. Complications of these fractures and their management are discussed in this report. Conclusions: Lawrence and Botte’s classification of proximal fifth metatarsal fractures is recommended by experts, due to its implication on prognosis and treatment strategy. Zone 1 fractures should be treated conservatively due to their excellent healing potential. Early operative treatment is advised for zone 2 and zone 3 fractures, especially in the athletic group. Complications of delayed union, non-union and refractures should be treated by revision fixation and bone grafting

Optimal rate assignment strategy to minimize average waiting time in wireless networks

In a wireless network that supports multiple flows, allocation of bandwidth resource among the flows is one of the critical problems. Different allocation strategies have been developed based on different optimization objectives. Unfortunately, these objectives may not reflect directly the time needed for a flow to transmit what it wants. In this paper, we define a new objective, average waiting time, that reflects the average time needed for the flows to finish their transmissions. For small networks, we develop an optimal scheme that minimizes the average waiting time. We extend the mechanism for general networks, and simulation results show that it can significantly reduce the average waiting time when compared with other existing mechanisms. © 2011 IEEE.published_or_final_versionThe 2011 IEEE Vehicular Technology Conference (VTC Fall), San Francisco, CA., 5-8 September 2011. In IEEEVTS Vehicular Technology Conference Proceedings, 2011, p. 1-