Random Measurement Research Articles

Central limit theorem of overlap for the mean field Ghatak–Sherrington model

The Ghatak–Sherrington spin glass model is a random probability measure defined on the configuration space {0,±1,±2,…,±S}N with system size N and S⩾1 finite. This generalizes the classical Sherrington–Kirkpatrick (SK) model on the boolean cube {−1, +1}N to capture more complex behaviors, including the spontaneous inverse freezing phenomenon. We give a quantitative joint central limit theorem for the overlap and self-overlap array at sufficiently high temperature under arbitrary crystal and external fields. Our proof uses the moment method combined with the cavity approach. Compared to the SK model, the main challenge comes from the non-trivial self-overlap terms that correlate with the standard overlap terms.

Deep learning for solving initial path optimization of mean-field systems with memory

We consider the problem of finding the optimal initial investment strategy for a system modelled by a linear McKean–Vlasov (mean-field) stochastic differential equation with delay, driven by Brownian motion and a pure jump Poisson random measure. The goal is to determine the optimal initial values for the system in the period [ − δ , 0 ] , where δ > 0 is a delay constant, before the system starts at t = 0. Due to the delay in the dynamics, the system will, after startup, be influenced by these initial investment values. It is known that linear stochastic delay differential equations are equivalent to stochastic Volterra integral equations. By utilizing this equivalence, we can find implicit expressions for the optimal investment. Moreover, we propose a deep neural network-based algorithm to solve the stochastic control problem with delay. Specifically, we employ a multi-layer feed-forward neural network for control modelling in the interval [ − δ , 0 ] , and use back-propagation to train the feed-forward neural network. The gradient of the loss function is computed using stochastic gradient descent (SGD) with respect to the weights of the network.

A Study on Lao Phuan Vernacular House in Ngan Area, Khoun District, Xieng Khuang Province

The study on vernacular houses of the Lao Phuan ethnic group aims to determine the area that still retains most of its original form, as defined by the fieldwork of Ngan area in Khoun District, Xieng Khouang Province as a case study. The selected area is the only one that still has a large number of traditional houses left behind. Through the study of relevant documents, physical surveys with maps and observations, random measurements of house components, and in-depth interviews with village chiefs, the elderly, and residents in the village: These Lao Phuan vernacular houses are designed and built to meet the needs of their occupations and to suit the nature or environment of the area in which they reside. Including their traditions, culture, and way of living. This can be seen from using materials that are easy to find, durable in use, and abundant locally, such as using Longleng wood as a roofing material. In addition, to being a natural sense, it is also an extra sun and rain-resistant material, making it usable for decades. At the same time, the style of the house has long eaves with small windows, which is due to the fact that the area is located in an area with high rainfall. In addition, the stilt house form will be used as a storage area for daily production equipment, firewood, fishing tools, and weaving equipment, as well as for survival and safety conditions. The use of space inside the house, in addition to allocating the area to serve a basic living, also allocated a large hall area to accommodate guests or relatives who visit regularly. Especially when there are traditional events held in the village or gift ceremonies inside the house. Another important point is that the area has to adapt to the dry season (winter). Therefore, two fireplaces have been set up; the first is in the cooking area. The second point is in the living area to use the fireplace to keep warm, the process of building a house still follows the strict traditions and beliefs that have been practiced for a long time.

Multimodal Deep Representation Learning for Quantum Cross-Platform Verification.

Cross-platform verification, a critical undertaking in the realm of early-stage quantum computing, endeavors to characterize the similarity of two imperfect quantum devices executing identical algorithms, utilizing minimal measurements. While the random measurement approach has been instrumental in this context, the quasiexponential computational demand with increasing qubit count hurdles its feasibility in large-qubit scenarios. To bridge this knowledge gap, here we introduce an innovative multimodal learning approach, recognizing that the formalism of data in this task embodies two distinct modalities: measurement outcomes and classical description of compiled circuits on explored quantum devices, both containing unique information about the quantum devices. Building upon this insight, we devise a multimodal neural network to independently extract knowledge from these modalities, followed by a fusion operation to create a comprehensive data representation. The learned representation can effectively characterize the similarity between the explored quantum devices when executing new quantum algorithms not present in the training data. We evaluate our proposal on platforms featuring diverse noise models, encompassing system sizes up to 50 qubits. The achieved results demonstrate an improvement of 3 orders of magnitude in prediction accuracy compared to the random measurements and offer compelling evidence of the complementary roles played by each modality in cross-platform verification. These findings pave the way for harnessing the power of multimodal learning to overcome challenges in wider quantum system learning tasks.

Blocked Gibbs Sampler for Hierarchical Dirichlet Processes

Posterior computation in hierarchical Dirichlet process (HDP) mixture models is an active area of research in nonparametric Bayes inference of grouped data. Existing literature almost exclusively focuses on the Chinese restaurant franchise (CRF) analogy of the marginal distribution of the parameters, which can mix poorly and has a quadratic complexity with the sample size. A recently developed slice sampler allows for efficient blocked updates of the parameters, but is shown to be statistically unstable in our article. We develop a blocked Gibbs sampler that employs a truncated approximation of the underlying random measures to sample from the posterior distribution of HDP, which produces statistically stable results, is highly scalable with respect to sample size, and is shown to have good mixing. The heart of the construction is to endow the shared concentration parameter with an appropriately chosen gamma prior that allows us to break the dependence of the shared mixing proportions and permits independent updates of certain log-concave random variables in a block. En route, we develop an efficient rejection sampler for these random variables leveraging piece-wise tangent-line approximations. Supplementary materials, which include substantive additional details and code, are available online.

Outcome of random cortisol measurement in infants <30 days old

Outcome of random cortisol measurement in infants <30 days old

Cubature Kalman Hybrid Consensus Filter for Collaborative Localization of Unmanned Surface Vehicle Cluster with Random Measurement Delay.

This paper addresses the collaborative localization problem for unmanned surface vehicle (USV) clusters with random measurement delays. We propose a Cubature Kalman Hybrid Consensus Filter (CKHCF) based on the cubature Kalman filter (CKF) for widely distributed USV clusters lacking global communication capabilities. In this approach, each USV exchanges two pairs of information with all its neighbors and recalculates the received localization data based on distance and relative angle measurements. The recalculated information is then fused with the locally filtered data and updated to obtain localization information based on global measurements. To mitigate the impact of random measurement delays, we employ one-step prediction to compensate for delayed measurements. We present the derivation of the CKHCF algorithm and prove its consistency and boundedness using mathematical induction. Finally, we validate the effectiveness of the proposed algorithm through simulation experiments.

Error mitigated metasurface-based randomized measurement schemes

Estimating properties of quantum states via randomized measurements has become a significant part of quantum information science. In this paper, we design an innovative approach leveraging metasurfaces to perform randomized measurements on photonic qubits, together with error mitigation techniques that suppress realistic metasurface measurement noise. Through fidelity and purity estimation, we confirm the capability of metasurfaces to implement randomized measurements and the unbiased nature of our error-mitigated estimator. Our findings show the potential of metasurface-based randomized measurement schemes in achieving robust and resource-efficient estimation of quantum state properties. Published by the American Physical Society 2024

Multi-Feature Extraction and Selection Method to Diagnose Burn Depth from Burn Images

Burn wound depth is a significant determinant of patient treatment. Typically, the evaluation of burn depth relies heavily on the clinical experience of doctors. Even experienced surgeons may not achieve high accuracy and speed in diagnosing burn depth. Thus, intelligent burn depth classification is useful and valuable. Here, an intelligent classification method for burn depth based on machine learning techniques is proposed. In particular, this method involves extracting color, texture, and depth features from images, and sequentially cascading these features. Then, an iterative selection method based on random forest feature importance measure is applied. The selected features are input into the random forest classifier to evaluate this proposed method using the standard burn dataset. This method classifies burn images, achieving an accuracy of 91.76% when classified into two categories and 80.74% when classified into three categories. The comprehensive experimental results indicate that this proposed method is capable of learning effective features from limited data samples and identifying burn depth effectively.

Robust state estimation for uncertain linear discrete systems with state delay and random measurement losses

Robust state estimation for uncertain linear discrete systems with state delay and random measurement losses

Random measurement and prediction errors limit the practical relevance of two velocity sensors to estimate the 1RM back squat.

While maximum strength diagnostics are applied in several sports and rehabilitative settings, dynamic strength capacity has been determined via the one-repetition maximum (1RM) testing for decades. Because the literature concerned several limitations, such as injury risk and limited practical applicability in large populations (e.g., athletic training groups), the strength prediction via the velocity profile has received increasing attention recently. Referring to relative reliability coefficients and inappropriate interpretation of agreement statistics, several previous recommendations neglected systematic and random measurement bias. This article explored the random measurement error arising from repeated testing (repeatability) and the agreement between two common sensors (vMaxPro and TENDO) within one repetition, using minimal velocity thresholds as well as the velocity = 0m/s method. Furthermore, agreement analyses were applied to the estimated and measured 1RM in 25 young elite male soccer athletes. The results reported repeatability values with an intraclass correlation coefficient (ICC) = 0.66-0.80, which was accompanied by mean absolute (percentage) errors (MAE and MAPE) of up to 0.04-0.22m/s and ≤7.5%. Agreement between the two sensors within one repetition showed a systematic lower velocity for the vMaxPro device than the Tendo, with ICCs ranging from 0.28 to 0.88, which were accompanied by an MAE/MAPE of ≤0.13m/s (11%). Almost all estimations systematically over/ underestimated the measured 1RM, with a random scattering between 4.12% and 71.6%, depending on the velocity threshold used. In agreement with most actual reviews, the presented results call for caution when using velocity profiles to estimate strength. Further approaches must be explored to minimize especially the random scattering.

Stochastic fractional integrodifferential equations with jumps: application to an averaging principle

In this work we deal with a stochastic fractional integrodifferential equation associated to a Poisson random measure. We first prove existence and uniqueness of solution in the case of Lipschitz coefficients but also in the non Lipschitz case. In the second part, we establish an averaging principle in the sense of Khasminskii approach for a class of this equation with non lipschitz coefficients and weak averaging conditions.

Stochastic gradient descent for barycenters in Wasserstein space

Abstract We present and study a novel algorithm for the computation of 2-Wasserstein population barycenters of absolutely continuous probability measures on Euclidean space. The proposed method can be seen as a stochastic gradient descent procedure in the 2-Wasserstein space, as well as a manifestation of a law of large numbers therein. The algorithm aims to find a Karcher mean or critical point in this setting, and can be implemented ‘online’, sequentially using independent and identically distributed random measures sampled from the population law. We provide natural sufficient conditions for this algorithm to almost surely converge in the Wasserstein space towards the population barycenter, and we introduce a novel, general condition which ensures uniqueness of Karcher means and, moreover, allows us to obtain explicit, parametric convergence rates for the expected optimality gap. We also study the mini-batch version of this algorithm, and discuss examples of families of population laws to which our method and results can be applied. This work expands and deepens ideas and results introduced in an early version of Backhoff-Veraguas et al. (2022), in which a statistical application (and numerical implementation) of this method is developed in the context of Bayesian learning.

Fractional stable random fields on the Sierpiński gasket

We define and study fractional stable random fields on the Sierpiński gasket. Such fields are formally defined as (−Δ)−sWK,α, where Δ is the Laplace operator on the gasket and WK,α is a stable random measure. Both Neumann and Dirichlet boundary conditions for Δ are considered. Sample paths regularity and scaling properties are obtained. The techniques we develop are general and extend to the more general setting of the Barlow fractional spaces.

On the interpretability of quantum neural networks

Interpretability of artificial intelligence (AI) methods, particularly deep neural networks, is of great interest. This heightened focus stems from the widespread use of AI-backed systems. These systems, often relying on intricate neural architectures, can exhibit behavior that is challenging to explain and comprehend. The interpretability of such models is a crucial component of building trusted systems. Many methods exist to approach this problem, but they do not apply straightforwardly to the quantum setting. Here, we explore the interpretability of quantum neural networks using local model-agnostic interpretability measures commonly utilized for classical neural networks. Following this analysis, we generalize a classical technique called LIME, introducing Q-LIME, which produces explanations of quantum neural networks. A feature of our explanations is the delineation of the region in which data samples have been given a random label, likely subjects of inherently random quantum measurements. We view this as a step toward understanding how to build responsible and accountable quantum AI models.

Quantitative analysis of soil potassium by near-infrared (NIR) spectroscopy combined with a three-step progressive hybrid variable selection strategy

Soil potassium is a crucial nutrient element necessary for crop growth, and its efficient measurement has become essential for developing rational fertilization plans and optimizing crop growth benefits. At present, data mining technology based on near-infrared (NIR) spectroscopy analysis has proven to be a powerful tool for real-time monitoring of soil potassium content. However, as technology and instruments improve, the curse of the dimensionality problem also increases accordingly. Therefore, it is urgent to develop efficient variable selection methods suitable for NIR spectroscopy analysis techniques. In this study, we proposed a three-step progressive hybrid variable selection strategy, which fully leveraged the respective strengths of several high-performance variable selection methods. By sequentially equipping synergy interval partial least squares (SiPLS), the random forest variable importance measurement (RF(VIM)), and the improved mean impact value algorithm (IMIV) into a fusion framework, a soil important potassium variable selection method was proposed, termed as SiPLS-RF(VIM)-IMIV. Finally, the optimized variables were fitted into a partial least squares (PLS) model. Experimental results demonstrated that the PLS model embedded with the hybrid strategy effectively improved the prediction performance while reducing the model complexity. The RMSET and RT on the test set were 0.01181% and 0.88246, respectively, better than the RMSET and RT of the full spectrum PLS, SiPLS, and SiPLS-RF(VIM) methods. This study demonstrated that the hybrid strategy established based on the combination of NIR spectroscopy data and the SiPLS-RF(VIM)-IMIV method could quantitatively analyze soil potassium content levels and potentially solve other issues of data-driven soil dynamic monitoring.

Stressing the Relevance of Differentiating between Systematic and Random Measurement Errors in Ultrasound Muscle Thickness Diagnostics

BackgroundThe majority of studies that explore changes in musculature following resistance training interventions or examine atrophy due to immobilization or sarcopenia use ultrasound imaging. While most studies assume acceptable to excellent reliability, there seems to be unawareness of the existing absolute measurement errors. As early as 1998, methodological research addressed a collective unawareness of the random measurement error and its practical indications. Referring to available methodological approaches, within this work, we point out the limited value of focusing on relative, correlation-based reliability indices for the interpretability in scientific research but also for clinical application by assessing 1,512 muscle thickness values from more than 400 ultrasound images. To account for intra- and inter-day repeatability, data were collected on two consecutive days within four testing sessions. Commonly-stated reliability values (ICC, CV, SEM and MDC) were calculated, while evidence-based agreement analyses were applied to provide the accompanied systematic and random measurement error.ResultsWhile ICCs in the range of 0.832 to 0.998 are in accordance with the available literature, the mean absolute percentage error ranges from 1.34 to 20.38% and the mean systematic bias from 0.78 to 4.01 mm (all p ≤ 0.013), depending on the measurement time points chosen for data processing.ConclusionsIn accordance with prior literature, a more cautious interpretation of relative reliability values should be based on included systematic and random absolute measurement scattering. Lastly, this paper discusses the rationale for including different measurement error statistics when determining the validity of pre-post changes, thus, accounting for the certainty of evidence.

Edukasi Pencegahan Stroke pada Masyarakat Desa Cigugur Girang

Stroke patients could get sequelae, and it will decrease the patient’s quality of life. Stroke could be caused by comorbid diseases such as hypertension, diabetes mellitus, and dyslipidemia. Thus, stroke could be prevented by reducing the comorbid diseases. The prevention of stroke is necessary to be done in order to reduce stroke cases, especially in Bandung’s rural area. Villagers have limited access to health information and health services. In this community service, the methods we used were to screen the two risk factors of stroke (blood pressure and blood glucose ad random measurement) in Cigugur Girang Village, West Bandung area. The aim of this community service is to find comorbid factors of stroke and give education to people who have one or more stroke risk factors. The results of the blood pressure measurement screening showed that more than 40% of the residents of Cigugur Girang village had blood pressure above normal, and 5% of the population had blood sugar levels higher than normal. The risk factor for stroke in residents of Cigugur Girang Village mainly is high blood pressure. In this community service, people with high blood pressure were educated on how to maintain normal blood pressure and how to change their lifestyle. On the other hand, some participant has high blood glucose level. High blood glucose levels will develop into diabetes mellitus. In this education program, we gave information about the complications of high blood glucose, including stroke. Thus, this education program could increase community awareness to prevent stroke.

A multilevel Monte Carlo algorithm for stochastic differential equations driven by countably dimensional Wiener process and Poisson random measure

In this paper, we investigate properties of standard and multilevel Monte Carlo methods for weak approximation of solutions of stochastic differential equations (SDEs) driven by infinite-dimensional Wiener process and Poisson random measure with Lipschitz payoff function. The error of the truncated dimension randomized numerical scheme, which depends on two parameters i.e., grid density n∈N and truncation dimension parameter M∈N, is of the order n−1/2+δ(M) such that δ(⋅) is positive and decreasing to 0. We derive a complexity model and provide proof for the complexity upper bound of the multilevel Monte Carlo method which depends on two increasing sequences of parameters for both n and M. The complexity is measured in terms of upper bound for mean-squared error and is compared with the complexity of the standard Monte Carlo algorithm. The results from numerical experiments as well as Python and CUDA C implementation details are also reported.

Collective Randomized Measurements in Quantum Information Processing.

The concept of randomized measurements on individual particles has proven to be useful for analyzing quantum systems and is central for methods like shadow tomography of quantum states. We introduce collective randomized measurements as a tool in quantum information processing. Our idea is to perform measurements of collective angular momentum on a quantum system and actively rotate the directions using simultaneous multilateral unitaries. Based on the moments of the resulting probability distribution, we propose systematic approaches to characterize quantum entanglement in a collective-reference-frame-independent manner. First, we show that existing spin-squeezing inequalities can be accessible in this scenario. Next, we present an entanglement criterion based on three-body correlations, going beyond spin-squeezing inequalities with two-body correlations. Finally, we apply our method to characterize entanglement between spatially separated two ensembles.