The asymptotic tails of limit distributions of continuous time Markov chains

This paper investigates tail asymptotics of stationary distributions and quasi-stationary distributions of continuous-time Markov chains on a subset of the non-negative integers. A new identity for stationary measures is established. In particular, for continuous-time Markov chains with asymptotic power-law transition rates, tail asymptotics for stationary distributions are classified into three types by three easily computable parameters: (i) Conley-Maxwell-Poisson distributions (light-tailed), (ii) exponential-tailed distributions, and (iii) heavy-tailed distributions. Similar results are derived for quasi-stationary distributions. The approach to establish tail asymptotics is different from the classical semimartingale approach. We apply our results to biochemical reaction networks (modeled as continuous-time Markov chains), a general single-cell stochastic gene expression model, an extended class of branching processes, and stochastic population processes with bursty reproduction, none of which are birth-death processes

A Computationally Efficient Tool for Assessing the Depth Resolution in Potential-Field Inversion

In potential-field inversion problems, it can be difficult to obtain reliable information about the source distribution with respect to depth. Moreover, spatial resolution of the solution decreases with depth, and in fact the more ill-posed the problem – and the more noisy the data – the less reliable the depth information. Based on early work in depth resolution, defined in terms of the singular value decomposition, we introduce a tool APPROXDRP which uses an approximation of the singular vectors obtained by the iterative Lanczos bidiagonalization algorithm, making it well suited for large-scale problems. This tool allows a computational/visual analysis of how much the depth resolution in a computational potential-field inversion problem can be obtained from the given data.We show that when used in combination with a plot of the approximate SVD quantities, APPROXDRP may successfully show the limitations of depth resolution resulting from noise in the data. This allows a reliable analysis of the retrievable depth information and effectively guides the user in choosing the optimal number of iterations, for a given problem

Comparison of delay-interferometer and time-lens-based all-optical OFDM demultiplexers

In this paper we present the first detailed numerical comparison of two promising all-optical schemes to demultiplex orthogonal frequency-division multiplexing (OFDM) signals. The investigated schemes are the optical discrete Fourier transformation (O-DFT) and the optical spectral magnification (SM) based on time lenses. In the former scheme, cascaded delay-interferometers (DIs) are used to perform the O-DFT, with subsequent active optical gating to remove the intercarrier interference (ICI). Here a reduced-complexity partial O-DFT, realized by replacing a number of DIs with optical bandpass filters, is investigated. In the latter scheme the OFDM spectrum is magnified, allowing for simple optical bandpass filtering of the individual subcarriers with reduced ICI. Ideally only a single unit consisting of two time lenses is needed, reducing the complexity and potentially the energy consumption compared to the type of O-DFT scheme relying on many active gates. The bit-error-rate is estimated down to ∼10-6 by Monte Carlo bit-error counting for a 32-subcarrier OFDM input signal, showing that a performance close to the ideal O-DFT is achievable for both the reduced-complexity O-DFT and the SM scheme.</p

Clang and Coccinelle:synergising program analysis tools for CERT C Secure Coding Standard certification

Writing correct C programs is well-known to be hard, not least due to the many language features intrinsic to C. Writing secure C programs is even harder and, at times, seemingly impossible. To improve on this situation the US CERT has developed and published a set of coding standards, the “CERT C Secure Coding Standard”, that (in the current version) enumerates 118 rules and 182 recommendations with the aim of making C programs (more) secure. The large number of rules and recommendations makes automated tool support essential for certifying that a given system is in compliance with the standard. In this paper we report on ongoing work on integrating two state of the art analysis tools, Clang and Coccinelle, into a combined tool well suited for analysing and certifying C programs according to, e.g., the CERT C Secure Coding standard or the MISRA (the Motor Industry Software Reliability Assocation) C standard. We further argue that such a tool must be highly adaptable and customisable to each software project as well as to the certification rules required by a given standard. Clang is the C frontend for the LLVM compiler/virtual machine project which includes a comprehensive set of static analyses and code checkers. Coccinelle is a program transformation tool and bug-finder developed originally for the Linux kernel, but has been successfully used to find bugs in other Open Source projects such as WINE and OpenSSL