Related papers: Bordering for spectrally arbitrary sign patterns
The transfer matrix is a powerful technique that can be applied to statistical mechanics systems as, for example, in the calculus of the entropy of the ice model. One interesting way to study such systems is to map it onto a 3-color…
We present applications of rectangular matrix models to various combinatorial problems, among which the enumeration of face-bicolored graphs with prescribed vertex degrees, and vertex-tricolored triangulations. We also mention possible…
We give a specific method to solve with quadratic complexity the linear systems arising in known algorithms to deal with the sign determination problem. In particular, this enable us to improve the complexity bound for sign determination in…
Diagrammatic techniques to compute perturbatively the spectral properties of Euclidean Random Matrices in the high-density regime are introduced and discussed in detail. Such techniques are developed in two alternative and very different…
A new adaptive shaping method that can generate arbitrary optical waveforms with folded-type or fan-type birefringent variable shapers is proposed in this paper. Automatic arbitrary laser temporal shaping of picosecond and femtosecond…
A numerical scheme to compute the spectrum of a large class of self-adjoint extensions of the Laplace-Beltrami operator on manifolds with boundary in any dimension is presented. The algorithm is based on the characterisation of a large…
Techniques to extract information from spectra of unresolved multi-component systems are revised, with emphasis on recent developments and practical aspects. We review the cross-correlation techniques developed to deal with such spectra,…
In this article, we compute the topological expansion of all possible mixed-traces in a hermitian two matrix model. In other words we give a recipe to compute the number of discrete surfaces of given genus, carrying an Ising model, and with…
One of the great miracles of random matrix theory is that, in the $N \to \infty$ limit, many otherwise intractable matrix problems with horrendously complicated finite-$N$ expressions admit remarkably simple and elegant asymptotic…
The Numerical Assembly Technique is extended to investigate arbitrary planar frame structures with the focus on the computation of natural frequencies. This allows us to obtain highly accurate results without resorting to spatial…
We explore a general method based on trees of elementary submodels in order to present highly simplified proofs to numerous results in infinite combinatorics. While countable elementary submodels have been employed in such settings already,…
We use a waveguide-based electro-optic phase modulator, driven by a nanosecond-timescale arbitrary waveform generator, to produce an optical spectrum with an arbitrary pattern of sidebands. A programmed sequence of linear voltage ramps,…
An $n\times n$ zero pattern $S$, which is a matrix with entries $*$ and $0$, is called spectrally arbitrary with respect to a field $F$ if any monic polynomial $f$ of degree $n$ can be realized as the characteristic polynomial of a matrix…
Boundary labeling is a technique in computational geometry used to label sets of features in an illustration. It involves placing labels along an axis-parallel bounding box and connecting each label with its corresponding feature using…
In this article, the enumeration of partial chord diagrams is discussed via matrix model techniques. In addition to the basic data such as the number of backbones and chords, we also consider the Euler characteristic, the backbone spectrum,…
A matrix approach to continuous iteration is proposed for general formal series. It leads, in particular, to an order{to{order iteration of the exponential function, and consequently to an algorithmic approach to tetration. Lower{order…
Bending of a shape-invariant optical beam is achieved so far along parabolic or circular curves. Borrowing ideas used in nonlinear optical communication, we propose such a bending along any preassigned curve or surface, controlled by the…
A new condition, the strong inner product property, is introduced and used to construct sign patterns of row orthogonal matrices. Using this property, infinite families of sign patterns allowing row orthogonality are found. These provide…
Boundary-induced pattern formation from a spatially uniform state is investigated using one-dimensional reaction-diffusion equations. The temporal oscillation is successively transformed into a spatially periodic pattern, triggered by…
We investigate invertible matrices over finite additively idempotent semirings. The main result provides a criterion for the invertibility of such matrices. We also give a construction of the inverse matrix and a formula for the number of…