A perturbation analysis of stochastic matrix Riccati diffusions

Matrix differential Riccati equations are central in filtering and optimal control theory. The purpose of this article is to develop a perturbation theory for a class of stochastic matrix Riccati diffusions. Diffusions of this type arise, for example, in the analysis of ensemble Kalman-Bucy filters since they describe the flow of certain sample covariance estimates. In this context, the random perturbations come from the fluctuations of a mean field particle interpretation of a class of nonlinear diffusions equipped with an interacting sample covariance matrix functional. The main purpose of this article is to derive non-asymptotic Taylor-type expansions of stochastic matrix Riccati flows with respect to some perturbation parameter. These expansions rely on an original combination of stochastic differential analysis and nonlinear semigroup techniques on matrix spaces. The results here quantify the fluctuation of the stochastic flow around the limiting deterministic Riccati equation, at any order. The convergence of the interacting sample covariance matrices to the deterministic Riccati flow is proven as the number of particles tends to infinity. Also presented are refined moment estimates and sharp bias and variance estimates. These expansions are also used to deduce a functional central limit theorem at the level of the diffusion process in matrix spaces

Backward Nonlinear Smoothing Diffusions

We present a backward diffusion flow (i.e., a backward-in-time stochastic differential equation) whose marginal distribution at any (earlier) time is equal to the smoothing distribution when the terminal state (at a later time) is distributed according to the filtering distribution. This is a novel interpretation of the smoothing solution in terms of a nonlinear diffusion (stochastic) flow. This solution contrasts with, and complements, the (backward) deterministic flow of probability distributions (viz. a type of Kushner smoothing equation) studied in a number of prior works. A number of corollaries of our main result are given, including a derivation of the time-reversal of a stochastic differential equation, and an immediate derivation of the classical Rauch--Tung--Striebel smoothing equations in the linear setting

On one-dimensional Riccati diffusions

This article is concerned with the fluctuation analysis and the stability properties of a class of one-dimensional Riccati diffusions. This class of Riccati diffusion is quite general, and arises, for example, in data assimilation applications, and more particularly in ensemble (Kalman-type) filtering theory. These one-dimensional stochastic differential equations exhibit a quadratic drift function and a non-Lipschitz continuous diffusion function. We present a novel approach, combining tangent process techniques, Feynman-Kac path integration, and exponential change of measures, to derive sharp exponential decays to equilibrium. We also provide uniform estimates with respect to the time horizon, quantifying with some precision the fluctuations of these diffusions around a limiting deterministic Riccati differential equation. These results provide a stronger and almost sure version of the conventional central limit theorem. We illustrate these results in the context of ensemble Kalman-Bucy filtering. In this context, the time-uniform convergence results developed in this work do not require a stable signal. To the best of our knowledge, the exponential stability and the fluctuation analysis developed in this work are the first results of this kind for this class of nonlinear diffusions

Assessing the ability of substrate mapping techniques to guide ventricular tachycardia ablation using computational modelling

BACKGROUND: Identification of targets for ablation of post-infarction ventricular tachycardias (VTs) remains challenging, often requiring arrhythmia induction to delineate the reentrant circuit. This carries a risk for the patient and may not be feasible. Substrate mapping has emerged as a safer strategy to uncover arrhythmogenic regions. However, VT recurrence remains common. GOAL: To use computer simulations to assess the ability of different substrate mapping approaches to identify VT exit sites. METHODS: A 3D computational model of the porcine post-infarction heart was constructed to simulate VT and paced rhythm. Electroanatomical maps were constructed based on endocardial electrogram features and the reentry vulnerability index (RVI - a metric combining activation (AT) and repolarization timings to identify tissue susceptibility to reentry). Since scar transmurality in our model was not homogeneous, parameters derived from all signals (including dense scar regions) were used in the analysis. Potential ablation targets obtained from each electroanatomical map during pacing were compared to the exit site detected during VT mapping. RESULTS: Simulation data showed that voltage cut-offs applied to bipolar electrograms could delineate the scar, but not the VT circuit. Electrogram fractionation had the highest correlation with scar transmurality. The RVI identified regions closest to VT exit site but was outperformed by AT gradients combined with voltage cut-offs. The performance of all metrics was affected by pacing location. CONCLUSIONS: Substrate mapping could provide information about the infarct, but the directional dependency on activation should be considered. Activation-repolarization metrics have utility in safely identifying VT targets, even with non-transmural scars

Sequential Electro-Anatomical Mapping Methodology and Preliminary Results for Reentry Vulnerability Index Estimation

Ventricular tachycardia (VT) recurrence after catheter ablation remains frequent and improved ablation strategies are needed. The re-entry vulnerability index (RVI) is an activation-repolarization marker to localize critical sites for VT initiation. Its use is limited since current electro-anatomical mapping systems (EAMS) cannot provide global measurement of activation and repolarization times within a single beat. We carried out a simulation study to assess a simple method to measure RVI using data collected by sequential EAMS and we investigated the effect of background noise, RT variability (σRT ) and ectopics on RVI estimation. The mean correlation coefficient between single ECG beats and a representative template is used as inclusion/exclusion criterion. Localization of the vulnerable region associated with 5% bottom RVI was accurate (sensitivity80±8%, specificity> 99±1%) for moderate to large repolarization variability (5 ≤ σRT ≤ 20 ms) and moderate level of noise (SNR ≥ 10 dB) but it deteriorated for σRT ≥ 25 ms and SNR ≤ 5 dB. Sensitivity remained high even when RVI estimates were only moderately accurate (cc > 0.67 ± 0.05, MAE < 25 ± 1 ms). The number of ectopic beats did not affect the results. In the in-vivo case analyzed, the sites of low RVI and VT exit was close (5.1 mm

Observation of squeezed light from one atom excited with two photons

Single quantum emitters like atoms are well-known as non-classical light sources which can produce photons one by one at given times, with reduced intensity noise. However, the light field emitted by a single atom can exhibit much richer dynamics. A prominent example is the predicted ability for a single atom to produce quadrature-squeezed light, with sub-shot-noise amplitude or phase fluctuations. It has long been foreseen, though, that such squeezing would be "at least an order of magnitude more difficult" to observe than the emission of single photons. Squeezed beams have been generated using macroscopic and mesoscopic media down to a few tens of atoms, but despite experimental efforts, single-atom squeezing has so far escaped observation. Here we generate squeezed light with a single atom in a high-finesse optical resonator. The strong coupling of the atom to the cavity field induces a genuine quantum mechanical nonlinearity, several orders of magnitude larger than for usual macroscopic media. This produces observable quadrature squeezing with an excitation beam containing on average only two photons per system lifetime. In sharp contrast to the emission of single photons, the squeezed light stems from the quantum coherence of photon pairs emitted from the system. The ability of a single atom to induce strong coherent interactions between propagating photons opens up new perspectives for photonic quantum logic with single emittersComment: Main paper (4 pages, 3 figures) + Supplementary information (5 pages, 2 figures). Revised versio

Phylogenetically Widespread Polyembryony in Cyclostome Bryozoans and the Protracted Asynchronous Release of Clonal Brood-Mates

The file attached is the Published/publisher’s pdf version of the articl

HamLib: A library of Hamiltonians for benchmarking quantum algorithms and hardware

In order to characterize and benchmark computational hardware, software, and algorithms, it is essential to have many problem instances on-hand. This is no less true for quantum computation, where a large collection of real-world problem instances would allow for benchmarking studies that in turn help to improve both algorithms and hardware designs. To this end, here we present a large dataset of qubit-based quantum Hamiltonians. The dataset, called HamLib (for Hamiltonian Library), is freely available online and contains problem sizes ranging from 2 to 1000 qubits. HamLib includes problem instances of the Heisenberg model, Fermi-Hubbard model, Bose-Hubbard model, molecular electronic structure, molecular vibrational structure, MaxCut, Max-k-SAT, Max-k-Cut, QMaxCut, and the traveling salesperson problem. The goals of this effort are (a) to save researchers time by eliminating the need to prepare problem instances and map them to qubit representations, (b) to allow for more thorough tests of new algorithms and hardware, and (c) to allow for reproducibility and standardization across research studies

Evaluation of the Re-entry Vulnerability Index to Predict Ventricular Tachycardia Circuits Using High Density Contact Mapping

BACKGROUND: Identifying arrhythmogenic sites to improve ventricular tachycardia (VT) ablation outcomes remains unresolved. The re-entry vulnerability index (RVI) combines activation and repolarization timings to identify sites critical for re-entrant arrhythmia initiation without inducing VT. OBJECTIVE: To provide the first assessment of RVI's capability to identify VT sites of origin using high-density contact mapping and comparison with other activation-repolarization markers of functional substrate. METHODS: 18 VT ablation patients (16M, 72% ischemic) were studied. Unipolar electrograms were recorded during ventricular pacing and analysed off-line. Activation time (AT), activation-recovery interval (ARI), repolarization time (RT) were measured. Vulnerability to re-entry was mapped based on RVI and spatial distribution of AT, ARI and RT. The distance from sites identified as vulnerable to re-entry to the VT site of origin was measured, with distances 20 mm indicating accurate and inaccurate localization, respectively. RESULTS: The origin of 18 VTs was identified (n=6 entrainment, n=12 pace-mapping). RVI maps included 1012, 408-2098 (median, 1st-3rd quartiles) points/patient. RVI accurately localized 72.2% VT sites of origin, with median distance equal to 5.1, 3.2-10.1 mm. Inaccurate localization was significantly less frequent for RVI than AT (5.6% vs 33.3%, OR=0.12, P=0.035). Compared to RVI, distance to VT sites of origin was significantly larger for sites showing prolonged RT and ARI, and non-significantly larger for sites showing highest AT and ARI gradients. CONCLUSION: RVI identifies vulnerable regions closest to VT sites of origin. Activation-repolarization metrics may improve VT substrate delineation and inform novel ablation strategies

Which symptoms are linked to a delayed presentation among melanoma patients? A retrospective study

Background: The incidence of melanoma is rising. Early detection is associated with a more favourable outcome. The factors that influence the timing of a patient’s presentation for medical assessment are not fully understood. The aims of the study were to measure the nature and duration of melanoma symptoms in a group of patients diagnosed with melanoma within the preceding 18 months and to identify the symptoms and barriers associated with a delay in presentation. Methods: A questionnaire was distributed to a random sample of 200 of the 963 melanoma patients who had participated in the Cancer Patient Experience Survey 2010 and were known to be alive 1 year later. Data were collected on symptoms, duration of symptoms prior to presentation and the reasons for not attending a doctor sooner. Results: A total of 159 patients responded to the questionnaire; 74 (47%) were men; mean age was 62 (range 24–90) years. Of the 149 patients who reported a symptom, 40 (27%) had a delayed presentation (i.e. >3 months). A mole growing bigger was the most common symptom and reporting this symptom was significantly associated with a delayed presentation (odds ratio (OR) 2.04, 95% confidence interval (95% CI) 1.14–5.08). Patients aged ≥65 years were less likely to report a barrier to presentation and were less likely to delay than those under 40, although this was of borderline statistical significance (OR 0.28, 95% CI 0.08–1.00). Conclusions: This study highlights that an enlarging mole is a significant symptom influencing the timing of presentation. Increasing public awareness of the signs of melanoma and of the importance of early presentation is desirable. Health professionals should take advantage of the opportunity to educate patients on such symptoms and signs where feasible. Further exploration of the barriers to presentation in younger people should be considered