Toda Fields on Riemann Surfaces: remarks on the Miura transformation

We point out that the Miura transformation is related to a holomorphic foliation in a relative flag manifold over a Riemann Surface. Certain differential operators corresponding to a free field description of $W$--algebras are thus interpreted as partial connections associated to the foliation.Comment: AmsLatex 1.1, 10 page

Laser beam steering device

Agile beam steering is a critical requirement for airborne and space based LIDAR and optical communication systems. Design and test results are presented for a compact beam steering device with low inertia which functions by dithering two complementary (positive and negative) binary optic microlens arrays relative to each other in directions orthogonal to the direction of light propagation. The miniaturized system has been demonstrated at scan frequencies as high as 300 Hz, generating a 13 x 13 spot array with a total field of view of 2.4 degrees. The design is readily extendable to a 9.5 degree field of view and a 52 x 52 scan pattern. The system is compact - less than 2 in. on a side. Further size reductions are anticipated

Strong asymptotics for Cauchy biorthogonal polynomials with application to the Cauchy two--matrix model

We apply the nonlinear steepest descent method to a class of 3x3 Riemann-Hilbert problems introduced in connection with the Cauchy two-matrix random model. The general case of two equilibrium measures supported on an arbitrary number of intervals is considered. In this case, we solve the Riemann-Hilbert problem for the outer parametrix in terms of sections of a spinorial line bundle on a three-sheeted Riemann surface of arbitrary genus and establish strong asymptotic results for the Cauchy biorthogonal polynomials.Comment: 31 pages, 12 figures. V2; typos corrected, added reference

Large-scale multielectrode recording and stimulation of neural activity

Large circuits of neurons are employed by the brain to encode and process information. How this encoding and processing is carried out is one of the central questions in neuroscience. Since individual neurons communicate with each other through electrical signals (action potentials), the recording of neural activity with arrays of extracellular electrodes is uniquely suited for the investigation of this question. Such recordings provide the combination of the best spatial (individual neurons) and temporal (individual action-potentials) resolutions compared to other large-scale imaging methods. Electrical stimulation of neural activity in turn has two very important applications: it enhances our understanding of neural circuits by allowing active interactions with them, and it is a basis for a large variety of neural prosthetic devices. Until recently, the state-of-the-art in neural activity recording systems consisted of several dozen electrodes with inter-electrode spacing ranging from tens to hundreds of microns. Using silicon microstrip detector expertise acquired in the field of high-energy physics, we created a unique neural activity readout and stimulation framework that consists of high-density electrode arrays, multi-channel custom-designed integrated circuits, a data acquisition system, and data-processing software. Using this framework we developed a number of neural readout and stimulation systems: (1) a 512-electrode system for recording the simultaneous activity of as many as hundreds of neurons, (2) a 61-electrode system for electrical stimulation and readout of neural activity in retinas and brain-tissue slices, and (3) a system with telemetry capabilities for recording neural activity in the intact brain of awake, naturally behaving animals. We will report on these systems, their various applications to the field of neurobiology, and novel scientific results obtained with some of them. We will also outline future directions

Entire curves avoiding given sets in C^n

Let $F\subset\Bbb C^n$ be a proper closed subset of $\Bbb C^n$ and $A\subset\Bbb C^n\setminus F$ at most countable ($n\geq 2$). We give conditions of $F$ and $A$, under which there exists a holomorphic immersion (or a proper holomorphic embedding) $\phi:\Bbb C\to\Bbb C^n$ with $A\subset\phi(\Bbb C)\subset\Bbb C^n\setminus F$.Comment: 10 page

Modular differential equations for characters of RCFT

We discuss methods, based on the theory of vector-valued modular forms, to determine all modular differential equations satisfied by the conformal characters of RCFT; these modular equations are related to the null vector relations of the operator algebra. Besides describing effective algorithmic procedures, we illustrate our methods on an explicit example.Comment: 13 page

Demographic patterns and outcomes of patients in level I trauma centers in three international trauma systems

Introduction: Trauma systems were developed to improve the care for the injured. The designation and elements comprising these systems vary across countries. In this study, we have compared the demographic patterns and patient outcomes of Level I trauma centers in three international trauma systems. Methods: International multicenter prospective trauma registry-based study, performed in the University Medical Center Utrecht (UMCU), Utrecht, the Netherlands, John Hunter Hospital (JHH), Newcastle, Australia, and Harborview Medical Center (HMC), Seattle, the United States. Inclusion: patients =18 years, admitted in 2012, registered in the institutional trauma registry. Results: In UMCU, JHH, and HMC, respectively, 955, 1146, and 4049 patients met the inclusion criteria of which 300, 412, and 1375 patients with Injury Severity Score (ISS) > 15. Mean ISS was higher in JHH (13.5; p < 0.001) and HMC (13.4; p < 0.001) compared to UMCU (11.7). Unadjusted mortality: UMCU = 6.5 %, JHH = 3.6 %, and HMC = 4.8 %. Adjusted odds of death: JHH = 0.498 [95 % confidence interval (CI) 0.303-0.818] and HMC = 0.473 (95 % CI 0.325-0.690) compared to UMCU. HMC compared to JHH was 1.002 (95 % CI 0.664-1.514). Odds of death patients ISS > 15: JHH = 0.507 (95 % CI 0.300-0.857) and HMC = 0.451 (95 % CI 0.297-0.683) compared to UMCU. HMC = 0.931 (95 % CI 0.608-1.425) compared to JHH. TRISS analysis: UMCU: Ws = 0.787, Z = 1.31, M = 0.87; JHH, Ws = 3.583, Z = 6.7, M = 0.89; HMC, Ws = 3.902, Z = 14.6, M = 0.84. Conclusion: This study demonstrated substantial differences across centers in patient characteristics and mortality, mainly of neurological cause. Future research must investigate whether the outcome differences remain with nonfatal and long-term outcomes. Furthermore, we must focus on the development of a more valid method to compare systems

The kernel of the edth operators on higher-genus spacelike two-surfaces

The dimension of the kernels of the edth and edth-prime operators on closed, orientable spacelike 2-surfaces with arbitrary genus is calculated, and some of its mathematical and physical consequences are discussed.Comment: 12 page

86-GBaud subcarrier multiplexed 16QAM signal generation using an electrical 90 degree hybrid and IQ mixers

We experimentally demonstrate an aggregate 86-GBaud (over three sub-bands and one polarization) signal generation based on subcarrier multiplexing technique using IQ mixers, an electrical 90 degree hybrid, and diplexers. The electrical hybrid allows transmitter-side digital signal processing to be simplified to pulse shaping and digital pre-emphasis. We verified the configuration by testing the performance of an 86-GBaud Nyquist-shaped 16 quadrature amplitude modulation signal with differential bit encoding. The implementation penalty assuming 7% hard-decision forward error correction is reduced to 2 dB by utilizing a 31-tap decision-directed least mean square based multiple-input multiple-output equalizer for sideband crosstalk mitigation