SIMEX and TLS: An equivalence result

SIMEX was introduced by Cook and Stefanski (1994) as a simulation type estimator in errors-in-variables models. The idea of the SIMEX procedure is to compensate for the effect of the measurement errors while still using naive regression estimators. Polzehl and Zwanzig (2004) defined a symmetrized version of this estimator. In this paper we establish some results relating these two simulation-extrapolation-type estimators to well known consistent estimators like the total least squares estimator (TLS) and the moment estimator (MME) in the context of errors-in-variables models. We further introduce an adaptive SIMEX (ASIMEX), which is calculated like SIMEX, but based on an estimated variance. The main result of this paper is that SYMEX, ASIMEX are equivalent to TLS. Additionally we see that SIMEX is equivalent to the moment estimator

Report of the Working Group on `W Mass and QCD' (Phenomenology Workshop on LEP2 Physics, Oxford, April 1997)

The W Mass and QCD Working Group discussed a wide variety of topics relating to present and future measurements of M(W) at LEP2, including QCD backgrounds to W+W- production. Particular attention was focused on experimental issues concerning the direct reconstruction and threshold mass measurements, and on theoretical and experimental issues concerning the four jet final state. This report summarises the main conclusions.Comment: 43 pages LaTeX and 15 encapsulated postscript figures. Uses epsfig and ioplppt macros. Full Proceedings to be published in Journal of Physics

Application of Multicanonical Multigrid Monte Carlo Method to the Two-Dimensional ϕ4\phi^4-Model: Autocorrelations and Interface Tension

We discuss the recently proposed multicanonical multigrid Monte Carlo method and apply it to the scalar $\phi^4$-model on a square lattice. To investigate the performance of the new algorithm at the field-driven first-order phase transitions between the two ordered phases we carefully analyze the autocorrelations of the Monte Carlo process. Compared with standard multicanonical simulations a real-time improvement of about one order of magnitude is established. The interface tension between the two ordered phases is extracted from high-statistics histograms of the magnetization applying histogram reweighting techniques.Comment: 49 pp. Latex incl. 14 figures (Fig.7 not included, sorry) as uuencoded compressed tar fil

Virtual Distillation for Quantum Error Mitigation

Contemporary quantum computers have relatively high levels of noise, making it difficult to use them to perform useful calculations, even with a large number of qubits. Quantum error correction is expected to eventually enable fault-tolerant quantum computation at large scales, but until then it will be necessary to use alternative strategies to mitigate the impact of errors. We propose a near-term friendly strategy to mitigate errors by entangling and measuring $M$ copies of a noisy state $\rho$. This enables us to estimate expectation values with respect to a state with dramatically reduced error, $\rho^M/ \mathrm{Tr}(\rho^M)$, without explicitly preparing it, hence the name "virtual distillation". As $M$ increases, this state approaches the closest pure state to $\rho$, exponentially quickly. We analyze the effectiveness of virtual distillation and find that it is governed in many regimes by the behavior of this pure state (corresponding to the dominant eigenvector of $\rho$). We numerically demonstrate that virtual distillation is capable of suppressing errors by multiple orders of magnitude and explain how this effect is enhanced as the system size grows. Finally, we show that this technique can improve the convergence of randomized quantum algorithms, even in the absence of device noise

Inferring the dynamics of underdamped stochastic systems

Many complex systems, ranging from migrating cells to animal groups, exhibit stochastic dynamics described by the underdamped Langevin equation. Inferring such an equation of motion from experimental data can provide profound insight into the physical laws governing the system. Here, we derive a principled framework to infer the dynamics of underdamped stochastic systems from realistic experimental trajectories, sampled at discrete times and subject to measurement errors. This framework yields an operational method, Underdamped Langevin Inference (ULI), which performs well on experimental trajectories of single migrating cells and in complex high-dimensional systems, including flocks with Viscek-like alignment interactions. Our method is robust to experimental measurement errors, and includes a self-consistent estimate of the inference error

On the reliability of negative heat capacity measurements

A global protocol for the thermostatistical analysis of hot nuclear sources is discussed. Within our method of minimization of variances we show that the abnormal kinetic energy fluctuation signal recently reported in different experimental data (M.D'Agostino et al.-Phys. Lett. B 473 (2000) 219, N. Le Neindre et al.- contr. to the XXXVIII Bormio Winter Meeting on Nucl. Phys. (2001) 404) is a genuine signal of a first order phase transition in a finite system.Comment: 15 Postscript figures, submitted to NUCL. Phys. A on 24-apr-200