Entanglement verification with finite data

Suppose an experimentalist wishes to verify that his apparatus produces entangled quantum states. A finite amount of data cannot conclusively demonstrate entanglement, so drawing conclusions from real-world data requires statistical reasoning. We propose a reliable method to quantify the weight of evidence for (or against) entanglement, based on a likelihood ratio test. Our method is universal in that it can be applied to any sort of measurements. We demonstrate the method by applying it to two simulated experiments on two qubits. The first measures a single entanglement witness, while the second performs a tomographically complete measurement.Comment: 4 pages, 3 pretty picture

Entanglement and purity of single- and two-photon states

Whereas single- and two-photon wave packets are usually treated as pure states, in practice they will be mixed. We study how entanglement created with mixed photon wave packets is degraded. We find in particular that the entanglement of a delocalized single-photon state of the electro-magnetic field is determined simply by its purity. We also discuss entanglement for two-photon mixed states, as well as the influence of a vacuum component.Comment: 11 pages, 10 figures, 1 debuting autho

Performance of networks of artificial neurons: The role of clustering

The performance of the Hopfield neural network model is numerically studied on various complex networks, such as the Watts-Strogatz network, the Barab{\'a}si-Albert network, and the neuronal network of the C. elegans. Through the use of a systematic way of controlling the clustering coefficient, with the degree of each neuron kept unchanged, we find that the networks with the lower clustering exhibit much better performance. The results are discussed in the practical viewpoint of application, and the biological implications are also suggested.Comment: 4 pages, to appear in PRE as Rapid Com

High temperature expansion in supersymmetric matrix quantum mechanics

We formulate the high temperature expansion in supersymmetric matrix quantum mechanics with 4, 8 and 16 supercharges. The models can be obtained by dimensionally reducing N=1 U(N) super Yang-Mills theory in D=4,6,10 to 1 dimension, respectively. While the non-zero frequency modes become weakly coupled at high temperature, the zero modes remain strongly coupled. We find, however, that the integration over the zero modes that remains after integrating out all the non-zero modes perturbatively, reduces to the evaluation of connected Green's functions in the bosonic IKKT model. We perform Monte Carlo simulation to compute these Green's functions, which are then used to obtain the coefficients of the high temperature expansion for various quantities up to the next-leading order. Our results nicely reproduce the asymptotic behaviors of the recent simulation results at finite temperature. In particular, the fermionic matrices, which decouple at the leading order, give rise to substantial effects at the next-leading order, reflecting finite temperature behaviors qualitatively different from the corresponding models without fermions.Comment: 17 pages, 13 figures, (v2) some typos correcte

Vibration Control of Manipulators with Flexible Nonprismatic Links Using Piezoelectric Actuators and Sensors

This work presents a tracking control model for a flexible nonprismatic link robotic manipulator using simultaneously motor torques and piezoelectric actuators. The dynamic model of the flexible manipulator is obtained in a closed form through the Lagrange equations. The control uses the motor torques for the joints tracking control and also to reduce the low-frequency vibration induced in the manipulator links. The stability of this control is guaranteed by the Lyapunov stability theory. Piezoelectric actuators and sensors are added for controlling vibrations with frequencies beyond the reach of motor torque control. The naturals frequencies are calculated by the finite element method, and the approximated eigenfunctions are interpolated by polynomials. Three eigenfunctions are used for the dynamics of the arm, while only two are used for the control. Numerical experiments on Matlab/Simulink are used to verify the efficiency of the control model

D-brane orbiting NS5-branes

We study real time dynamics of a Dp-brane orbiting a stack of NS5-branes. It is generally known that a BPS D-brane moving in the vicinity of NS5-branes becomes unstable due to the presence of tachyonic degree of freedom induced on the D-brane. Indeed, the D-brane necessarily falls into the fivebranes due to gravitational attraction and eventually collapses into a pressureless fluid. Such a decay of the D-brane is known to be closely related to the rolling tachyon problem. In this paper we show that in special cases the decay of D-brane caused by gravitational attraction can be avoided. Namely for certain values of energy and angular momentum the D-brane orbits around the fivebranes, maintaining certain distance from the fivebranes all the time, and the process of tachyon condensation is suppressed. We show that the tachyonic degree of freedom induced on such a D-brane really disappears and the brane returns to a stable D-brane.Comment: 12 pages, latex, added referenc

Geological and Geotechnical Evaluation of Gully Erosion at Nguzu Edda, Afikpo Sub-Basin, Southeastern Nigeria

A detailed geological field mapping of Nguzu Edda has revealed that gully erosion and landslides have remained active over the years, posing serious threats to human life, agricultural land, infrastructure and socio-economic activities within the area. Consequently, twelve true representative soil samples from different locations within gully sites have been analyzed based on ASTM and British Standards, to evaluate geologic conditions and geotechnical parameters that influence the gullies problems. The results of the laboratory tests revealed that the soil at the gully sites are predominantly sands (57~99.5 % with mean of 69.7%) with low amount of fines (silt; 0.3~ 22% with average value of 14.6% and clay: 0.2 ~ 21% with average value of 13.9%). The liquid limit (LL) ranged from 15 ~ 31.50 % with mean of 23.32% and the plasticity index (PI) ranged from 2.92~14.42% with mean of 8.95%. The moisture content, permeability, bulk density, porosity, organic matter and pH have average values of 25.31%, 6.04×10-4 cm/sec, 1.55 kg/m3, 40.40, 1.26% and 5.12, respectively. The cation exchange capacity (CEC) is low, which could be attributed to low organic matter, pH and non active clay minerals. With regard to the aforementioned characteristics, the soils at gully sites are loose sands with low amount of fines fraction, hence cohesionless, and are easily exposed to agents/factors of gully erosion. Thus, provides insights about the vulnerable causes of gully erosion and landslides problems that are prevalent in the area. This research addresses, to a great extent the effects of local geology, geotechnical properties of the underlying soil and associated human activities on the formation of gully erosion, in-turn results to landslides within in the study area. Engineering-geologic aspects of soil erosion control were also recommended. Keywords: Afikpo Sub-basin, Geologic conditions, Geotechnical analysis, Gully erosion and Erosion control measures