Fisher information and asymptotic normality in system identification for quantum Markov chains

This paper deals with the problem of estimating the coupling constant $\theta$ of a mixing quantum Markov chain. For a repeated measurement on the chain's output we show that the outcomes' time average has an asymptotically normal (Gaussian) distribution, and we give the explicit expressions of its mean and variance. In particular we obtain a simple estimator of $\theta$ whose classical Fisher information can be optimized over different choices of measured observables. We then show that the quantum state of the output together with the system, is itself asymptotically Gaussian and compute its quantum Fisher information which sets an absolute bound to the estimation error. The classical and quantum Fisher informations are compared in a simple example. In the vicinity of $\theta=0$ we find that the quantum Fisher information has a quadratic rather than linear scaling in output size, and asymptotically the Fisher information is localised in the system, while the output is independent of the parameter.Comment: 10 pages, 2 figures. final versio

Maximum likelihood drift estimation for a threshold diffusion

We study the maximum likelihood estimator of the drift parameters of a stochastic differential equation, with both drift and diffusion coefficients constant on the positive and negative axis, yet discontinuous at zero. This threshold diffusion is called drifted Oscillating Brownian motion.For this continuously observed diffusion, the maximum likelihood estimator coincide with a quasi-likelihood estimator with constant diffusion term. We show that this estimator is the limit, as observations become dense in time, of the (quasi)-maximum likelihood estimator based on discrete observations. In long time, the asymptotic behaviors of the positive and negative occupation times rule the ones of the estimators. Differently from most known results in the literature, we do not restrict ourselves to the ergodic framework: indeed, depending on the signs of the drift, the process may be ergodic, transient or null recurrent. For each regime, we establish whether or not the estimators are consistent; if they are, we prove the convergence in long time of the properly rescaled difference of the estimators towards a normal or mixed normal distribution. These theoretical results are backed by numerical simulations

The singular continuous diffraction measure of the Thue-Morse chain

The paradigm for singular continuous spectra in symbolic dynamics and in mathematical diffraction is provided by the Thue-Morse chain, in its realisation as a binary sequence with values in $\{\pm 1\}$. We revisit this example and derive a functional equation together with an explicit form of the corresponding singular continuous diffraction measure, which is related to the known representation as a Riesz product.Comment: 6 pages, 1 figure; revised and improved versio

effects of the pre-season period

Study aim: To assess changes in physical fitness of amateur soccer players after a pre-season training period and baseline fitness dependencies. Material and methods: Twenty-one amateur soccer players were assessed during the pre-season. The following physical vari ables were assessed before and after a two-month pre-season training period: (i) cardiorespiratory fitness, (ii) strength and power, and (iii) change of direction (COD). Results: Significant decreases were found for countermovement jump (CMJ) (p < 0.001; d = 1.161), drop jump (DJ) (p = 0.014; d = 0.958), and horizontal jump (HJ) (p = 0.042; d = 0.640), while no significant changes were found for the overall variables from the beginning to the end of pre-season. Fit players revealed significant decreases for CMJ (p = 0.002; d = ?2.495), DJ (p = 0.004; d = ?1.760), HJ (p = 0.028; d = ?1.005), COD deficit (p = 0.034; d = 1.013), and maximal aerobic speed (MAS) (p = 0.026; d = ?4.053). No significant changes were found for unfit players. Conclusions: Amateur soccer coaches should consider assessing physical qualities at the beginning of pre-season and use the free-of-charge monitoring tools such as session-rate of perceived exertion (s-RPE) during the training process.D915-7373-ED16 | Cesar LeaoN/

An objective based classification of aggregation techniques for wireless sensor networks

Wireless Sensor Networks have gained immense popularity in recent years due to their ever increasing capabilities and wide range of critical applications. A huge body of research efforts has been dedicated to find ways to utilize limited resources of these sensor nodes in an efficient manner. One of the common ways to minimize energy consumption has been aggregation of input data. We note that every aggregation technique has an improvement objective to achieve with respect to the output it produces. Each technique is designed to achieve some target e.g. reduce data size, minimize transmission energy, enhance accuracy etc. This paper presents a comprehensive survey of aggregation techniques that can be used in distributed manner to improve lifetime and energy conservation of wireless sensor networks. Main contribution of this work is proposal of a novel classification of such techniques based on the type of improvement they offer when applied to WSNs. Due to the existence of a myriad of definitions of aggregation, we first review the meaning of term aggregation that can be applied to WSN. The concept is then associated with the proposed classes. Each class of techniques is divided into a number of subclasses and a brief literature review of related work in WSN for each of these is also presented

Data-driven efficient score tests for deconvolution problems

We consider testing statistical hypotheses about densities of signals in deconvolution models. A new approach to this problem is proposed. We constructed score tests for the deconvolution with the known noise density and efficient score tests for the case of unknown density. The tests are incorporated with model selection rules to choose reasonable model dimensions automatically by the data. Consistency of the tests is proved

Quantum learning: optimal classification of qubit states

Pattern recognition is a central topic in Learning Theory with numerous applications such as voice and text recognition, image analysis, computer diagnosis. The statistical set-up in classification is the following: we are given an i.i.d. training set $(X_{1},Y_{1}),... (X_{n},Y_{n})$ where $X_{i}$ represents a feature and $Y_{i}\in \{0,1\}$ is a label attached to that feature. The underlying joint distribution of $(X,Y)$ is unknown, but we can learn about it from the training set and we aim at devising low error classifiers $f:X\to Y$ used to predict the label of new incoming features. Here we solve a quantum analogue of this problem, namely the classification of two arbitrary unknown qubit states. Given a number of `training' copies from each of the states, we would like to `learn' about them by performing a measurement on the training set. The outcome is then used to design mesurements for the classification of future systems with unknown labels. We find the asymptotically optimal classification strategy and show that typically, it performs strictly better than a plug-in strategy based on state estimation. The figure of merit is the excess risk which is the difference between the probability of error and the probability of error of the optimal measurement when the states are known, that is the Helstrom measurement. We show that the excess risk has rate $n^{-1}$ and compute the exact constant of the rate.Comment: 24 pages, 4 figure

Bayesian estimation of one-parameter qubit gates

We address estimation of one-parameter unitary gates for qubit systems and seek for optimal probes and measurements. Single- and two-qubit probes are analyzed in details focusing on precision and stability of the estimation procedure. Bayesian inference is employed and compared with the ultimate quantum limits to precision, taking into account the biased nature of Bayes estimator in the non asymptotic regime. Besides, through the evaluation of the asymptotic a posteriori distribution for the gate parameter and the comparison with the results of Monte Carlo simulated experiments, we show that asymptotic optimality of Bayes estimator is actually achieved after a limited number of runs. The robustness of the estimation procedure against fluctuations of the measurement settings is investigated and the use of entanglement to improve the overall stability of the estimation scheme is also analyzed in some details.Comment: 10 pages, 5 figure

Srs2 removes deadly recombination intermediates independently of its interaction with SUMO-modified PCNA

Saccharomyces cerevisiae Srs2 helicase plays at least two distinct functions. One is to prevent recombinational repair through its recruitment by sumoylated Proliferating Cell Nuclear Antigen (PCNA), evidenced in postreplication-repair deficient cells, and a second one is to eliminate potentially lethal intermediates formed by recombination proteins. Both actions are believed to involve the capacity of Srs2 to displace Rad51 upon translocation on single-stranded DNA (ssDNA), though a role of its helicase activity may be important to remove some toxic recombination structures. Here, we described two new mutants, srs2R1 and srs2R3, that have lost the ability to hinder recombinational repair in postreplication-repair mutants, but are still able to remove toxic recombination structures. Although the mutants present very similar phenotypes, the mutated proteins are differently affected in their biochemical activities. Srs2R1 has lost its capacity to interact with sumoylated PCNA while the biochemical activities of Srs2R3 are attenuated (ATPase, helicase, DNA binding and ability to displace Rad51 from ssDNA). In addition, crossover (CO) frequencies are increased in both mutants. The different roles of Srs2, in relation to its eventual recruitment by sumoylated PCNA, are discussed