Related papers: Spectral computations for birth and death chains
By considering an empirical approximation, and a new class of operators that we will call walking operators, we construct, for any positive ND-toeplitz matrix, an infinite in all dimensions matrix, for which the inverse approximates the…
As widely known, the basic reproduction number plays a key role in weighing birth/infection and death/recovery processes in several models of population dynamics. In this general setting, its characterization as the spectral radius of next…
We give some new bounds for the clique and independence numbers of a graph in terms of its eigenvalues.
Given a circulant matrix $\mathrm{circ}(c,a,0,0,...,0,a)$, $a\ne 0$, of order~$n$, we ``border'' it from left and from above by constant column and row, respectively, and we set the left top entry to be $-nc$. This way we get a~particular…
We suggest a general spectral method for calculating statistics of multi-step birth-death processes and chemical reactions of the type mA->nA (m and n are positive integers) which possess an absorbing state. The method yields accurate…
Arrangement graphs were introduced for their connection to computational networks and have since generated considerable interest in the literature. In a pair of recent articles by Chen, Ghorbani and Wong, the eigenvalues for the adjacency…
In a complex network, different groups of nodes may have existed for different amounts of time. To detect the evolutionary history of a network is of great importance. We present a general method based on spectral analysis to address this…
Any system of coupled oscillators may be characterized by its spectrum of resonance frequencies (or eigenfrequencies), which can be tuned by varying the system's parameters. The relationship between control parameters and the eigenfrequency…
A detailed discussion of semiclassical trace formulae is presented and it is demonstrated how a regularized trace formula can be derived while dealing only with finite and convergent expressions. Furthermore, several applications of trace…
This review presents an account of the major works done on spectra of adjacency matrices drawn on networks and the basic understanding attained so far. We have divided the review under three sections: (a) extremal eigenvalues, (b) bulk part…
We derive a message passing method for computing the spectra of locally tree-like networks and an approximation to it that allows us to compute closed-form expressions or fast numerical approximates for the spectral density of random graphs…
We present the spectrum of the (normalized) graph Laplacian as a systematic tool for the investigation of networks, and we describe basic properties of eigenvalues and eigenfunctions. Processes of graph formation like motif joining or…
Percolation threshold of a network is the critical value such that when nodes or edges are randomly selected with probability below the value, the network is fragmented but when the probability is above the value, a giant component…
For a large class of integral operators or second order differential operators, their isospectral (or cospectral) operators are constructed explicitly in terms of $h$-transform (duality). This provides us a simple way to extend the known…
Spectral measures arise in numerous applications such as quantum mechanics, signal processing, resonances, and fluid stability. Similarly, spectral decompositions (pure point, absolutely continuous and singular continuous) often…
All networks can be analyzed at multiple scales. A higher scale of a network is made up of macro-nodes: subgraphs that have been grouped into individual nodes. Recasting a network at higher scales can have useful effects, such as decreasing…
The full spectrum of transfer matrices of the general eight-vertex model on a square lattice is obtained by numerical diagonalization. The eigenvalue spacing distribution and the spectral rigidity are analyzed. In non-integrable regimes we…
We establish spectral estimates at a critical energy level for $h$-pseudors . Via a trace formula, we compute the contribution of isolated (non-extremum) critical points under a condition of "real principal type". The main result holds for…
In this paper, we consider an extended coined Szegedy model and discuss the existence of the point spectrum of induced quantum walks in terms of recurrence properties of the underlying birth and death process. We obtain that if the…
We give upper and lower bounds on the spectral radius of a graph in terms of the number of walks. We generalize a number of known results.