Harer-Zagier type recursion formula for the elliptic GinOE

We consider real eigenvalues of the elliptic Ginibre matrix indexed by the non-Hermiticity parameter $\tau \in [0,1]$, and present a Harer-Zagier type recursion formula for the even moments in the form of an $11$-term recurrence relation. For the Ginibre case when $\tau=0$, this formula simplifies to a 3-term recurrence relation. On the other hand, for the GOE case when $\tau=1$, it reduces to a 5-term recurrence relation, recovering the result established by Ledoux. For the proof, we employ the skew-orthogonal polynomial formalism and the generalised Christoffel-Darboux formula. Together with Gaussian integration by parts, these enable us to derive a seventh-order linear differential equation for the moment generating function.Comment: 36 pages, 1 figur

Effect of fibronectin on the binding of antithrombin III to immobilized heparin

An objective of this research is to verify the mechanism of anticoagulant activity of surface-immobilized heparin in the presence of plasma proteins. The competition and binding interaction between immobilized heparin and antithrombin III (ATIII)/thrombin have been described in vitro. However, the strong ionic character of heparin leads to its specific and nonspecific binding with many other plasma proteins. Most notably, fibronectin contains six active binding sites for heparin which may interfere with the subsequent binding of heparin with ATIII or thrombin. \ud Heparin was covalently immobilized through polyethylene oxide (PEO) hydrophilic spacer groups onto a model surface synthesized by random copolymerization of styrene and p-aminostyrene. The binding interaction of immobilized heparin with ATIII was then determined in the presence of different fibronectin concentrations. The binding interaction was studied by first binding immobilized heparin with ATIII, followed by the introduction of fibronectin; heparin binding with fibronectin, followed by incubation with ATIII, and simultaneous incubation of surface immobilized heparin with ATIII and fibronectin. The extent of ATIII binding to heparin in each experiment was assayed using a chromogenic substrate for ATIII, S-2238. \ud The results of this study demonstrate that the displacement of ATIII from immobilized heparin was proportional to the fibronectin concentration, and was reversible. Furthermore, the binding sequence did not play a role in the final concentration of ATIII bound to immobilized heparin

Determinantal Coulomb gas ensembles with a class of discrete rotational symmetric potentials

We consider determinantal Coulomb gas ensembles with a class of discrete rotational symmetric potentials whose droplets consist of several disconnected components. Under the insertion of a point charge at the origin, we derive the asymptotic behaviour of the correlation kernels both in the macro- and microscopic scales. In the macroscopic scale, this particularly shows that there are strong correlations among the particles on the boundary of the droplets. In the microscopic scale, this establishes the edge universality. For the proofs, we use the nonlinear steepest descent method on the matrix Riemann-Hilbert problem to derive the asymptotic behaviours of the associated planar orthogonal polynomials and their norms up to the first subleading terms.Comment: 25 pages, 5 figure

Almost-Hermitian random matrices and bandlimited point processes

We study the distribution of eigenvalues of almost-Hermitian random matrices associated with the classical Gaussian and Laguerre unitary ensembles. In the almost-Hermitian setting, which was pioneered by Fyodorov, Khoruzhenko and Sommers in the case of GUE, the eigenvalues are not confined to the real axis, but instead have imaginary parts which vary within a narrow "band" about the real line, of height proportional to $\tfrac 1 N$, where $N$ denotes the size of the matrices. We study vertical cross-sections of the 1-point density as well as microscopic scaling limits, and we compare with other results which have appeared in the literature in recent years. Our approach uses Ward's equation and a property which we call "cross-section convergence", which relates the large-$N$ limit of the cross-sections of the density of eigenvalues with the equilibrium density for the corresponding Hermitian ensemble: the semi-circle law for GUE and the Marchenko-Pastur law for LUE.Comment: 42 pages, 10 figure

The comparison of the aid allocation of Korea in the 1950s and the 1960s to that of contemporary Uganda

노트 : Prepared for Korea and World Economy Conference X

Spherical Induced Ensembles with Symplectic Symmetry

We consider the complex eigenvalues of the induced spherical Ginibre ensemble with symplectic symmetry and establish the local universality of these point processes along the real axis. We derive scaling limits of all correlation functions at regular points both in the strong and weak non-unitary regimes as well as at the origin having spectral singularity. A key ingredient of our proof is a derivation of a differential equation satisfied by the correlation kernels of the associated Pfaffian point processes, thereby allowing us to perform asymptotic analysis

Estimating Effects of Multipath Propagation on GPS Signals

Multipath Simulator Taking into Account Reflection and Diffraction (MUSTARD) is a computer program that simulates effects of multipath propagation on received Global Positioning System (GPS) signals. MUSTARD is a very efficient means of estimating multipath-induced position and phase errors as functions of time, given the positions and orientations of GPS satellites, the GPS receiver, and any structures near the receiver as functions of time. MUSTARD traces each signal from a GPS satellite to the receiver, accounting for all possible paths the signal can take, including all paths that include reflection and/or diffraction from surfaces of structures near the receiver and on the satellite. Reflection and diffraction are modeled by use of the geometrical theory of diffraction. The multipath signals are added to the direct signal after accounting for the gain of the receiving antenna. Then, in a simulation of a delay-lock tracking loop in the receiver, the multipath-induced range and phase errors as measured by the receiver are estimated. All of these computations are performed for both right circular polarization and left circular polarization of both the L1 (1.57542-GHz) and L2 (1.2276-GHz) GPS signals