New Optimised Estimators for the Primordial Trispectrum

Cosmic microwave background studies of non-Gaussianity involving higher-order multispectra can distinguish between early universe theories that predict nearly identical power spectra. However, the recovery of higher-order multispectra is difficult from realistic data due to their complex response to inhomogeneous noise and partial sky coverage, which are often difficult to model analytically. A traditional alternative is to use one-point cumulants of various orders, which collapse the information present in a multispectrum to one number. The disadvantage of such a radical compression of the data is a loss of information as to the source of the statistical behaviour. A recent study by Munshi & Heavens (2009) has shown how to define the skew spectrum (the power spectra of a certain cubic field, related to the bispectrum) in an optimal way and how to estimate it from realistic data. The skew spectrum retains some of the information from the full configuration-dependence of the bispectrum, and can contain all the information on non-Gaussianity. In the present study, we extend the results of the skew spectrum to the case of two degenerate power-spectra related to the trispectrum. We also explore the relationship of these power-spectra and cumulant correlators previously used to study non-Gaussianity in projected galaxy surveys or weak lensing surveys. We construct nearly optimal estimators for quick tests and generalise them to estimators which can handle realistic data with all their complexity in a completely optimal manner. We show how these higher-order statistics and the related power spectra are related to the Taylor expansion coefficients of the potential in inflation models, and demonstrate how the trispectrum can constrain both the quadratic and cubic terms.Comment: 19 pages, 2 figure

A General Transfer-Function Approach to Noise Filtering in Open-Loop Quantum Control

We present a general transfer-function approach to noise filtering in open-loop Hamiltonian engineering protocols for open quantum systems. We show how to identify a computationally tractable set of fundamental filter functions, out of which arbitrary transfer filter functions may be assembled up to arbitrary high order in principle. Besides avoiding the infinite recursive hierarchy of filter functions that arises in general control scenarios, this fundamental filter-functions set suffices to characterize the error suppression capabilities of the control protocol in both the time and frequency domain. We prove that the resulting notion of filtering order reveals conceptually distinct, albeit complementary, features of the controlled dynamics as compared to the order of error cancellation, traditionally defined in the Magnus sense. Examples and implications are discussed.Comment: Paper plus supplementary material. 10 pages, 1 figure. Unnumbered equation between 2 and 3 corrected. Results are unchange

Quantifying protein densities on cell membranes using super-resolution optical fluctuation imaging

Surface molecules, distributed in diverse patterns and clusters on cell membranes, influence vital functions of living cells. It is therefore important to understand their molecular surface organisation under different physiological and pathological conditions. Here, we present a model-free, quantitative method to determine the distribution of cell surface molecules based on TIRF illumination and super-resolution optical fluctuation imaging (SOFI). This SOFI-based approach is robust towards single emitter multiple-blinking events, high labelling densities and high blinking rates. In SOFI, the molecular density is not based on counting events, but results as an intrinsic property due to the correlation of the intensity fluctuations. The effectiveness and robustness of the method was validated using simulated data, as well as experimental data investigating the impact of palmitoylation on CD4 protein nanoscale distribution in the plasma membrane of resting T cells.Comment: 9 pages, 3 figures plus Supplementary Informatio

Detection of multiplicative noise in stationary random processes using second- and higher order statistics

This paper addresses the problem of detecting the presence of colored multiplicative noise, when the information process can be modeled as a parametric ARMA process. For the case of zero-mean multiplicative noise, a cumulant based suboptimal detector is studied. This detector tests the nullity of a specific cumulant slice. A second detector is developed when the multiplicative noise is nonzero mean. This detector consists of filtering the data by an estimated AR filter. Cumulants of the residual data are then shown to be well suited to the detection problem. Theoretical expressions for the asymptotic probability of detection are given. Simulation-derived finite-sample ROC curves are shown for different sets of model parameters

A variational approach to moment-closure approximations for the kinetics of biomolecular reaction networks

Approximate solutions of the chemical master equation and the chemical Fokker-Planck equation are an important tool in the analysis of biomolecular reaction networks. Previous studies have highlighted a number of problems with the moment-closure approach used to obtain such approximations, calling it an ad-hoc method. In this article, we give a new variational derivation of moment-closure equations which provides us with an intuitive understanding of their properties and failure modes and allows us to correct some of these problems. We use mixtures of product-Poisson distributions to obtain a flexible parametric family which solves the commonly observed problem of divergences at low system sizes. We also extend the recently introduced entropic matching approach to arbitrary ansatz distributions and Markov processes, demonstrating that it is a special case of variational moment closure. This provides us with a particularly principled approximation method. Finally, we extend the above approaches to cover the approximation of multi-time joint distributions, resulting in a viable alternative to process-level approximations which are often intractable.Comment: Minor changes and clarifications; corrected some typo