Level-Spacing Distributions and the Bessel Kernel

The level spacing distributions which arise when one rescales the Laguerre or Jacobi ensembles of hermitian matrices is studied. These distributions are expressible in terms of a Fredholm determinant of an integral operator whose kernel is expressible in terms of Bessel functions of order $\alpha$. We derive a system of partial differential equations associated with the logarithmic derivative of this Fredholm determinant when the underlying domain is a union of intervals. In the case of a single interval this Fredholm determinant is a Painleve tau function.Comment: 18 pages, resubmitted to make postscript compatible, no changes to manuscript conten

Observation of Fermi-energy dependent unitary impurity resonances in a strong topological insulator Bi2Se3 with scanning tunneling spectroscopy

Scanning tunneling spectroscopic studies of Bi2Se3 epitaxial films on Si (111) substrates reveal highly localized unitary impurity resonances associated with non-magnetic quantum impurities. The strength of the resonances depends on the energy difference between the Fermi level ({E_F}) and the Dirac point ({E_D}) and diverges as {E_F} approaches {E_D}. The Dirac-cone surface state of the host recovers within ~ 2{\AA} spatial distance from impurities, suggesting robust topological protection of the surface state of topological insulators against high-density impurities that preserve time reversal symmetry.Comment: 6 pages, 6 figures. Accepted for fast-track publication in Solid State Communications (2012

Edge overload breakdown in evolving networks

We investigate growing networks based on Barabasi and Albert's algorithm for generating scale-free networks, but with edges sensitive to overload breakdown. the load is defined through edge betweenness centrality. We focus on the situation where the average number of connections per vertex is, as the number of vertices, linearly increasing in time. After an initial stage of growth, the network undergoes avalanching breakdowns to a fragmented state from which it never recovers. This breakdown is much less violent if the growth is by random rather than preferential attachment (as defines the Barabasi and Albert model). We briefly discuss the case where the average number of connections per vertex is constant. In this case no breakdown avalanches occur. Implications to the growth of real-world communication networks are discussed.Comment: To appear in Phys. Rev.

Intercomparison in the field between the new WISP-3 and other radiometers (TriOS Ramses, ASD FieldSpec, and TACCS)

Optical close-range instruments can be applied to derive water quality parameters for monitoring purposes and for validation of optical satellite data. In situ radiometers are often difficult to deploy, especially from a small boat or a remote location. The water insight spectrometer (WISP-3) is a new hand-held radiometer for monitoring water quality, which automatically performs measurements with three radiometers (L-sky, L-u, E-d) and does not need to be connected with cables and electrical power during measurements. The instrument is described and its performance is assessed by an intercomparison to well-known radiometers, under real fieldwork conditions using a small boat and with sometimes windy and cloudy weather. Root mean squared percentage errors relative to those of the TriOS system were generally between 20% and 30% for remote sensing reflection, which was comparable to those of the other instruments included in this study. From this assessment, it can be stated that for the tested conditions, the WISP-3 can be used to obtain reflection spectra with accuracies in the same range as well-known instruments. When tuned with suitable regional algorithms, it can be used for quick scans for water quality monitoring of Chl, SPM, and aCDOM. (C) 2012 Society of Photo-Optical Instrumentation Engineers (SPIE). [DOI: 10.1117/1.JRS.6.063615

Challenges of open innovation: the paradox of firm investment in open-source software

Open innovation is a powerful framework encompassing the generation, capture, and employment of intellectual property at the firm level. We identify three fundamental challenges for firms in applying the concept of open innovation: finding creative ways to exploit internal innovation, incorporating external innovation into internal development, and motivating outsiders to supply an ongoing stream of external innovations. This latter challenge involves a paradox, why would firms spend money on R&D efforts if the results of these efforts are available to rival firms? To explore these challenges, we examine the activity of firms in opensource software to support their innovation strategies. Firms involved in open-source software often make investments that will be shared with real and potential rivals. We identify four strategies firms employ – pooled R&D/product development, spinouts, selling complements and attracting donated complements – and discuss how they address the three key challenges of open innovation. We conclude with suggestions for how similar strategies may apply in other industries and offer some possible avenues for future research on open innovation

The Solution Space of the Unitary Matrix Model String Equation and the Sato Grassmannian

The space of all solutions to the string equation of the symmetric unitary one-matrix model is determined. It is shown that the string equation is equivalent to simple conditions on points $V_1$ and $V_2$ in the big cell \Gr of the Sato Grassmannian $Gr$. This is a consequence of a well-defined continuum limit in which the string equation has the simple form \lb \cp ,\cq_- \rb =\hbox{\rm 1}, with \cp and \cq_- $2\times 2$ matrices of differential operators. These conditions on $V_1$ and $V_2$ yield a simple system of first order differential equations whose analysis determines the space of all solutions to the string equation. This geometric formulation leads directly to the Virasoro constraints \L_n\,(n\geq 0), where \L_n annihilate the two modified-KdV \t-functions whose product gives the partition function of the Unitary Matrix Model.Comment: 21 page

Universality of a double scaling limit near singular edge points in random matrix models

We consider unitary random matrix ensembles Z_{n,s,t}^{-1}e^{-n tr V_{s,t}(M)}dM on the space of Hermitian n x n matrices M, where the confining potential V_{s,t} is such that the limiting mean density of eigenvalues (as n\to\infty and s,t\to 0) vanishes like a power 5/2 at a (singular) endpoint of its support. The main purpose of this paper is to prove universality of the eigenvalue correlation kernel in a double scaling limit. The limiting kernel is built out of functions associated with a special solution of the P_I^2 equation, which is a fourth order analogue of the Painleve I equation. In order to prove our result, we use the well-known connection between the eigenvalue correlation kernel and the Riemann-Hilbert (RH) problem for orthogonal polynomials, together with the Deift/Zhou steepest descent method to analyze the RH problem asymptotically. The key step in the asymptotic analysis will be the construction of a parametrix near the singular endpoint, for which we use the model RH problem for the special solution of the P_I^2 equation. In addition, the RH method allows us to determine the asymptotics (in a double scaling limit) of the recurrence coefficients of the orthogonal polynomials with respect to the varying weights e^{-nV_{s,t}} on \mathbb{R}. The special solution of the P_I^2 equation pops up in the n^{-2/7}-term of the asymptotics.Comment: 32 pages, 3 figure

Bulk Universality and Related Properties of Hermitian Matrix Models

We give a new proof of universality properties in the bulk of spectrum of the hermitian matrix models, assuming that the potential that determines the model is globally $C^{2}$ and locally $C^{3}$ function (see Theorem \ref{t:U.t1}). The proof as our previous proof in \cite{Pa-Sh:97} is based on the orthogonal polynomial techniques but does not use asymptotics of orthogonal polynomials. Rather, we obtain the $sin$-kernel as a unique solution of a certain non-linear integro-differential equation that follows from the determinant formulas for the correlation functions of the model. We also give a simplified and strengthened version of paper \cite{BPS:95} on the existence and properties of the limiting Normalized Counting Measure of eigenvalues. We use these results in the proof of universality and we believe that they are of independent interest

Fredholm Determinants, Differential Equations and Matrix Models

Orthogonal polynomial random matrix models of NxN hermitian matrices lead to Fredholm determinants of integral operators with kernel of the form (phi(x) psi(y) - psi(x) phi(y))/x-y. This paper is concerned with the Fredholm determinants of integral operators having kernel of this form and where the underlying set is a union of open intervals. The emphasis is on the determinants thought of as functions of the end-points of these intervals. We show that these Fredholm determinants with kernels of the general form described above are expressible in terms of solutions of systems of PDE's as long as phi and psi satisfy a certain type of differentiation formula. There is also an exponential variant of this analysis which includes the circular ensembles of NxN unitary matrices.Comment: 34 pages, LaTeX using RevTeX 3.0 macros; last version changes only the abstract and decreases length of typeset versio

A Single-Lumen Central Venous Catheter for Continuous and Direct Intra-abdominal Pressure Measurement

Background: Abdominal compartment syndrome (ACS) is associated with high morbidity and mortality rates. Therefore, the need for a good diagnostic tool to predict intra-abdominal hypertension (IAH) and progression to ACS is paramount. Bladder pressure (BP) has been used for several years for intra-abdominal pressure (IAP) measurement but has the disadvantage that it is not a continuous measurement. In this study, a single-lumen central venous catheter (CVC) is placed through the abdominal wall into the abdominal cavity to continuously and directly monitor the intra-abdominal pressure (CDIAP). The aim of this study was to evaluate the use of CDIAP to measure BP as a representative of the true IAP. Methods: Both BP and CDIAP were prospectively recorded on a variety of surgical patients admitted to the intensive care unit (ICU) from March 2003 up to December 2004. At the end of the surgical procedure, the CVC was placed through the abdominal wall and connected to a pressure transducer. In addition, the BP was measured through the urine drainage port after clamping the catheter and filling the bladder with 50 ml of 0.9% saline. At least three paired measurements (BP and CDIAP) were performed for at least one day on the ICU in a standardized manner at preset time intervals on each patient. The paired measurements were compared using the Bland-Altman (B-A) method. Data are presented as mean ± standard deviation. Results: Over a period of 22 months (March 2003 until December 2004), 125 paired measurements of both BP and CDIAP were recorded on 25 patients. The mean age was 72.4 ± 6.6 years. Eighteen patients underwent central vascular surgery, and seven patients with peritonitis received laparotomy. The mean CDIAP was 11.4 ± 4.8 (range 2-30) mmHg, and the BP was 12.9 ± 5.3 (range 3-37) mmHg. The mean difference between CDIAP and BP was 1.6 ± 2.7 mmHg. There was an acceptable level of agreement (intraclass correlation 0.82) between IAP measured by BP and IAP measured via CDIAP. Conclusion: Continuous direct intra-abdominal pressure measurement proved that the BP measurement approach of Kron is representative of the IAP. CDIAP measurement is accurate and makes it easier for the nursing staff to be informed of the IAP