Anomalous transport in scale-free networks

To study transport properties of scale-free and Erdos-Rényi networks, we analyze the conductance G between two arbitrarily chosen nodes of random scale-free networks with degree distribution P(k)-k(-lambda) in which all links have unit resistance. We predict a broad range of values of G, with a power-law tail distribution phi(SF)(G)-G(-g(G)), where g(G)=2lambda-1, and confirm our predictions by simulations. The power-law tail in phi(SF)(G) leads to large values of G, signaling better transport in scale-free networks compared to Erdos-Rényi networks where the tail of the conductivity distribution decays exponentially. Based on a simple physical "transport backbone" picture we show that the conductances of scale-free and Erdos-Rényi networks are well approximated by ck(A)k(B)/(k(A)+k(B)) for any pair of nodes A and B with degrees k(A) and k(B), where c emerges as the main parameter characterizing network transport.     

Melting of dense sodium

High-pressure high-temperature synchrotron diffraction measurements reveal a maximum on the melting curve of Na in the bcc phase at approximately 31 GPa and 1000 K and a steep decrease in melting temperature in its fcc phase. The results extend the melting curve by an order of magnitude up to 130 GPa. Above 103 GPa, Na crystallizes in a sequence of phases with complex structures with unusually low melting temperatures, reaching 300 K at 118 GPa, and an increased melting temperature is observed with further increases in pressure.     

Synthesis, characterization, and controlled aggregation of biotemplated polystyrene nanodisks

Cross-linked polystyrene nanodisks were prepared by controlled polymerization of styrene and divinylbenzene in the interior of bicelles, discoidal lipid aggregates. Aggregation behavior of polymer nanodisks was studied in water, organic solvents, and solid phase. Nanodisks form stable dispersions in aqueous solutions of surfactants, such as sodium dodecyl sulfate (SDS). Varying SDS/nanodisk ratio allowed us to control the size of nanodisk aggregates. Nanodisks are readily solubilized in nonpolar organic solvents, such as toluene and carbon tetrachloride, to yield stable monodisperse suspensions. These findings open opportunities for creating nanodisk-based nanocomposite materials. Stable nanodisk suspension in toluene enabled small angle neutron scattering (SANS) measurements. SANS data confirmed the nanodisk diameter and allowed accurate measurement of nanodisk thickness (19.5 ± 1.0 Å). In solid phase, nanodisks aggregate in sub-micron platelets.     

Observation of higher-order solitons in defocusing waveguide arrays

We observe experimentally higher-order solitons in waveguide arrays with defocusing saturable nonlinearity. Such solitons can comprise several in-phase bright spots and are stable above a critical power threshold. We elucidate the impact of the nonlinearity saturation on the domains of existence and stability of the observed complex soliton states.     

Entanglement generated by dissipation and steady state entanglement of two macroscopic objects

Entanglement is a striking feature of quantum mechanics and an essential ingredient in most applications in quantum information. Typically, coupling of a system to an environment inhibits entanglement, particularly in macroscopic systems. Here we report on an experiment where dissipation continuously generates entanglement between two macroscopic objects. This is achieved by engineering the dissipation using laser and magnetic fields, and leads to robust event-ready entanglement maintained for 0.04 s at room temperature. Our system consists of two ensembles containing about 10(12) atoms and separated by 0.5 m coupled to the environment composed of the vacuum modes of the electromagnetic field. By combining the dissipative mechanism with a continuous measurement, steady state entanglement is continuously generated and observed for up to 1 h.     

Matroid intersection algorithms

LetM ₁ = (E, 9₁),M ₂ = (E, 9₂) be two matroids over the same set of elementsE, and with families of independent sets 9₁, 9₂. A setI 9₁ 9₂ is said to be anintersection of the matroidsM ₁,M ₂. An important problem of combinatorial optimization is that of finding an optimal intersection ofM ₁,M ₂. In this paper three matroid intersection algorithms are presented. One algorithm computes an intersection containing a maximum number of elements. The other two algorithms compute intersections which are of maximum total weight, for a given weighting of the elements inE. One of these algorithms is primal-dual, being based on duality considerations of linear programming, and the other is primal. All three algorithms are based on the computation of an augmenting sequence of elements, a generalization of the notion of an augmenting path from network flow theory and matching theory. The running time of each algorithm is polynomial inm, the number of elements inE, and in the running times of subroutines for independence testing inM ₁,M ₂. The algorithms provide constructive proofs of various important theorems of matroid theory, such as the Matroid Intersection Duality Theorem and Edmonds' Matroid Polyhedral Intersection Theorem.Research sponsored by the Air Force Office of Scientific Research Grant 71-2076.     

k-space inherited parallel acquisition (KIPA): application on dynamic magnetic resonance imaging thermometry

In this study, a novel method for dynamic parallel image acquisition and reconstruction is presented. In this method, called k-space inherited parallel acquisition (KIPA), localized reconstruction coefficients are used to achieve higher reduction factors, and lower noise and artifact levels compared to that of generalized autocalibrating partially parallel acquisition (GRAPPA) reconstruction. In KIPA, the full k-space for the first frame and the partial k-space for later frames are required to reconstruct a whole series of images. Reconstruction coefficients calculated for different segments of k-space from the first frame data set are used to estimate missing k-space lines in corresponding k-space segments of other frames. The local determination of KIPA reconstruction coefficients is essential to adjusting them according to the local signal-to-noise ratio characteristics of k-space data. The proposed algorithm is applicable to dynamic imaging with arbitrary k-space sampling trajectories. Simulations of magnetic resonance thermometry using the KIPA method with a reduction factor of 6 and using dynamic imaging studies of human subjects with reduction factors of 4 and 6 have been performed to prove the feasibility of our method and to show apparent improvement in image quality in comparison with GRAPPA for dynamic imaging.     

Sparse Multicategory Generalized Distance Weighted Discrimination in Ultra-High Dimensions

Distance weighted discrimination (DWD) is an appealing classification method that is capable of overcoming data piling problems in high-dimensional settings. Especially when various sparsity structures are assumed in these settings, variable selection in multicategory classification poses great challenges. In this paper, we propose a multicategory generalized DWD (MgDWD) method that maintains intrinsic variable group structures during selection using a sparse group lasso penalty. Theoretically, we derive minimizer uniqueness for the penalized MgDWD loss function and consistency properties for the proposed classifier. We further develop an efficient algorithm based on the proximal operator to solve the optimization problem. The performance of MgDWD is evaluated using finite sample simulations and miRNA data from an HIV study.     

Approximate solutions of the Liouville equation. III. Variational principles and projection operators

Aspects of stationary variational principles for the Laplace-transformed Liouville equation are discussed. Projection techniques are used to derive new stationary principles applicable to the space orthogonal to the space spanned by functions occurring in the conservation laws. As a result, any trial function automatically leads to results satisfying the conservation laws. The procedure is also applied to the parity-even and parity-odd distributions which obey equations governed by the square of the Liouville operator. The technique is extended to eliminate the one-body additive contribution to the solution exactly. Finally, the ideas of the moment method, which leads to the continued-fraction representation of autocorrelation functions, are applied to variational principles. We find continued-fraction variational principles such that a zero trial function yields the usual representation. However, a trial function representing noninteracting particles contains the results of the moment method and in addition yields the exact analytic behavior for free particles.Work supported by a grant from the National Science Foundation.     

Physics and the explanation of life

It is proposed to consider present-day physics as dealing with a special situation, the situation in which the phenomena of life and consciousness play no role. It is pointed out that physical theory has often dealt, in the past, with similarly special situations. Planetary theory neglects all but gravitational forces, macroscopic physics neglects fluctuations due to the atomic structure of matter, nuclear physics disregards weak and gravitational interactions. In some of these cases, physicists were well aware of dealing with special situations, or limiting cases as they are called in the article; in other cases, they were not. It is pointed out that, even if it were true that present-day physics accurately describes the motion of the physical constituents of living bodies, it would not give the whole story. Arguments are adduced, however, to show that the laws of physics, applicable for inanimate matter, will have to be modified when dealing with the more general situation in which life and consciousness play significant roles.The present article is a somewhat revised version of the address presented by the writer at the 1969 AAAS meeting in Boston, Mass.