On Integrability of the Kontsevich Non-Abelian ODE System

We consider systems of ODEs with the right-hand side being Laurent polynomials in several non-commutative unknowns. In particular, these unknowns could be matrices of arbitrary size. An important example of such a system was proposed by M. Kontsevich (private communication). We prove the integrability of the Kontsevich system by finding a Lax pair, corresponding first integrals and commuting flows. We also provide a pre-Hamiltonian operator which maps gradients of integrals for the Kontsevich system to symmetries.     

Completeness in Supergravity Constructions

We prove that the supergravity r- and c-maps preserve completeness. As a consequence, any component \({\mathcal{H}}\) of a hypersurface {h = 1} defined by a homogeneous cubic polynomial h such that \({-\partial^2h}\) is a complete Riemannian metric on \({\mathcal{H}}\) defines a complete projective special Kähler manifold and any complete projective special Kähler manifold defines a complete quaternionic Kähler manifold of negative scalar curvature. We classify all complete quaternionic Kähler manifolds of dimension less or equal to 12 which are obtained in this way and describe some complete examples in 16 dimensions.     

Effects of word frequency, contextual diversity, and semantic distinctiveness on spoken word recognition

The relative abilities of word frequency, contextual diversity, and semantic distinctiveness to predict accuracy of spoken word recognition in noise were compared using two data sets. Word frequency is the number of times a word appears in a corpus of text. Contextual diversity is the number of different documents in which the word appears in that corpus. Semantic distinctiveness takes into account the number of different semantic contexts in which the word appears. Semantic distinctiveness and contextual diversity were both able to explain variance above and beyond that explained by word frequency, which by itself explained little unique variance.     

Sub-200 fs microjoule pulses from a monolithic linear fiber CPA system

An all-fiber-integrated linear chirped-pulse amplifier system generating microjoule pulse energies is reported. It is seeded by an all-fiber dissipative-soliton laser and incorporates a newly developed fiber stretcher, whose dispersive properties match that of the grating compressor. Pulse durations of 189 fs with energies of 2.2 μJ were achieved after compression. The average power was 9.8 W at the repetition rate of 4.5 MHz.     

The Electron Density is Smooth Away from the Nuclei

We prove that the electron densities of electronic eigenfunctions of atoms and molecules are smooth away from the nuclei.     

Confinement of nonneutral plasmas on magnetic surfaces

The confinement of a nonneutral plasma in a magnetic-surface, or stellarator, configuration is explored. The fluid equilibrium equations are derived and are found to be fundamentally different from previous results. Diocotron modes are predicted to be stable. The collisional confinement time can be very long. Possible applications include positron trapping and confinement of positron-electron plasmas. The basic physics can be addressed experimentally in the simple tabletop stellarator planned for construction at Columbia University.     

The thermal effect of urethral warming during cryosurgery

The heating effect of urethral warming during cryosurgery has been investigated theoretically, via heat transfer simulations. Two warmer configurations have been considered: (i). the clinically available urethral warmer, which has a configuration of a counter flow fluid heat exchanger; (ii). a newly designed urethral warmer, based on a temperature controlled electrical heater, termed a "cryoheater". A dramatic effect of thermal resistance to heat transfer through the heat exchanger wall has been identified, which is absent in the cryoheater. It follows that the cryoheater is expected to be more efficient in generating an unfrozen region around the urethra. It is shown that the conventional heat exchanger may fail to prevent freezing around the urethra in a significant number of prostate cases, depending on the layout of cryoprobes around the urethra. On the other hand, clinical reports exist which suggest that the heat exchanger improves in many cases the outcome of cryosurgery, in terms of long term complications. It is speculated in the current report that the cryoheater can further improve the outcome of cryosurgery, by providing protection from freezing in a wider range of cases. It is suggested that a future study be conducted to examine the correlation between the layout of cryoprobes and surgical outcome.     

Challenges in uncovering the origin of the proton's spin

One of the most fascinating challenges facing modern strong interaction physics is to understand the origin of the spin of the nucleon in terms of the spin and orbital angular momentum of the quarks and gluons. We review recent progress on this problem as well as some of the uncertainties associated with state of the art lattice QCD simulations. In particular, we explain the importance of the corrections associated with chiral extrapolation and finite volume corrections, especially for the term B(0) extracted from the appropriate low moment of the deeply virtual Compton scattering amplitude.     

Traveling Salesman Problem with Clustering

In the original traveling salesman problem, the traveling salesman has the task to find the shortest closed tour through a proposed set of nodes, touching each node exactly once and returning to the initial node at the end. For the sake of the tour length to be minimized, nodes close to each other might not be visited one after the other but separated in the tour. However, for some practical applications, it is useful to group nodes to clusters, such that all nodes of a cluster are visited contiguously. Here we present an approach which leads to an automatic clustering with a clustering parameter governing the sizes of the clusters.