Discrete Measurements Research Articles

Glycemic variability after mechanical thrombectomy for anterior circulation acute ischemic stroke.

Morbidity remains high among patients who undergo successful mechanical thrombectomy (MT) for anterior circulation large vessel occlusion (LVO). Stress hyperglycemia worsens the prognosis after acute ischemic stroke (AIS), but aggressively treating hyperglycemia does not improve the outcome. There is no consensus on how to best manage glycemia after AIS. Glycemic variability (GV) reflects glycemic fluctuations over time and could be the culprit. We aimed to elucidate how GV impacts outcome of AIS patients treated with MT. This was a single-center retrospective study. We consecutively included AIS patients who received MT for anterior circulation LVO. We recorded discrete blood glucose measurements within the first 24 hours post thrombectomy, from which we calculated two measures of GV: standard deviation (SD) and coefficient of variation. Univariate and multivariate analyses were conducted to identify predictors of poor functional outcome (modified Ranking scale score 3-6) and mortality at 3-month follow-up. We included 657 patients. Patients with poor functional outcome (42.5%) and patients that died (14.8%) had significantly higher GV as measured by SD. In a multivariable model adjusted for confounders, higher SD was associated with mortality -adjusted odds ratio: 1.020 (95% CI 1.001-1.040)- but not with functional outcome -adjusted odds ratio for modified Ranking scale score 3-6: 1.007 (95% CI 0.990-1.025)-. Our results suggest that higher GV after MT for anterior circulation AIS is an independent risk factor for 3-month mortality. Future trials should evaluate the benefit of reducing GV in this setting.

A note on the general moment problem

In this note we show that given an indeterminate Hamburger moment sequence, it is possible to perturb the first moment in such way that the obtained sequence remains an indeterminate Hamburger moment sequence. As a consequence we prove that every sequence of real numbers is a moment sequence for a signed discrete measure supported in \(\mathbb{R}_+\).

Environmental constituent of the petrochemical complex sustainable development

This article studies the ongoing processes of environmental safety formation in the context of sustainable development of companies. It is hypothesized that during changes most companies in the petrochemical industry of the Republic of Tatarstan underestimate the need for a comprehensive modernization of the environmental component of sustainable development. In conditions of disturbances and uncertainty in the external environment it leads to increased entropy and loss of effectiveness of discrete measures to improve the environmental safety of enterprises. The study carried out an analysis with a depth of study of more than five years, which is characterized by the emergence of economic and social risks of a global nature and reveals the degree of their influence on the environmental safety of a complex strategically important for the republic. In conclusion, it is concluded that increasing systematicity in environmental safety management under conditions of uncertainty leads to an increase in the rate of sustainable development and the effect of production activities.

Diffuse reflectance spectroscopy and digital soil mapping for assessing soil-associated off-road vehicle mobility risk

Soil attributes such as granulometric fractions and Atterberg limits (LL: liquid limit, PL: plastic limit, and PI: plasticity index) are needed to assess off-road vehicle mobility (OVM) risks. Parameters describing these attributes are generally measured in soil samples collected from a few locations through cumbersome laboratory methods. Although diffuse reflectance spectroscopy (DRS) can rapidly yield estimates for soil attributes in samples collected from specific locations and digital soil mapping (DSM) can transform such discrete measurements into spatially-continuous inference systems, these two technologies are rarely used for assessing OVM risks. In this study, we combined the DRS and DSM approaches for deriving spatially-continuous estimates for the key vehicle mobility parameters (gravel, sand, and fine particles; Cu: coefficients of uniformity; Cc: coefficient of curvature; LL; and PI) and classified soils using the Unified Soil Classification System (USCS). A total of 204 soil samples were collected from the north-eastern Himalayan state of Sikkim for measuring these parameters along with spectral reflectance over the visible and near-infrared region. Results of the chemometric models in the DRS approach showed that the USCS parameters may be estimated with the coefficient of determination (R2) values as high as 0.72. The fine (<2 mm diameter) fraction spectra provided the best estimates for the Atterberg limits while a combination of spectra collected from fine and coarse (>2 mm diameter) fractions was effective in estimating other granulometric fractions except for sand, which was best estimated using the coarse fraction spectra. With the DSM approach allowing effective mapping of these parameters, a spatially-continuous framework to quantify soil-associated OVM risks was developed for Sikkim for the first time.

The Potential of Isotopic Tracers for Precise and Environmentally Clean Stream Discharge Measurements

Accurate discharge measurement is mandatory for any hydrological study. While the “velocity” measurement method is adapted to laminar flows, the “dilution” method is more appropriate for turbulent streams. As most low-gradient streams worldwide are neither laminar nor turbulent, a methodological gap appears. In this study, we demonstrate that the application of the “dilution” method to a low-gradient small stream gives very satisfactory results in addition to revealing surface/subsurface processes. A variety of chemical and isotopic tracers were injected into the stream (anions, fluorescent dyes, and chloride and hydrogen isotopes). We report the first use of 37Cl for stream discharge measurement and show that 37Cl and 2H can be reliably used as quantitative tracers. Discharge uncertainty calculations show that deuterium is the most accurate tracer method used. We also compare the differences in the tailing part of the restitution curves of tracers and investigate the role of transient surface and hyporheic zones in solute transport in light of a simple transport modelling approach. We conclude that isotopic tracers can be used as “environmentally friendly” tracers for discrete stream discharge measurements and that the application of multi-tracers tests in rivers opens the path to a better understanding of surface–subsurface interaction processes.

Using crystal-lattice distortion data for geological investigations: the weighted Burgers vector method

Distorted crystals carry useful information on processes involved in their formation, deformation and growth. The distortions are accommodated by geometrically necessary dislocations, and therefore characterising those dislocations is an informative task, to assist in, for example, deducing the slip systems that produced the dislocations. Electron backscatter diffraction (EBSD) allows detailed quantification of distorted crystals and we summarise here a method for extracting information on dislocations from such data. The weighted Burgers vector (WBV) method calculates a vector at each point on an EBSD map, or an average over a region. The vector is a weighted average of the Burgers vectors of dislocation lines intersecting the map surface. It is weighted towards dislocation lines at a high angle to the map but that can be accounted for in interpretation. The method is fast and does not involve specific assumptions about dislocation types; it assumes only that elastic strains have little effect on the calculation. It can be used, with care, to analyse subgrain walls (sharp orientation changes) as well as gradational orientation changes within individual grains. There are four linked parts to this contribution. 1We describe the mathematical background to the WBV and then how it is modified to deal with spaced, discrete orientation measurements. 2EBSD orientation data have angular errors, and so does the WBV. We present a new analysis of these angular errors, showing there is a trade-off between directional accuracy and area sampled. Angular errors can now be accounted for during testing of hypotheses about dislocation types. 3We present new studies on olivine and plagioclase to illustrate how to use the method. 4We discuss published studies on ice and titanite to further illustrate the method.We note that the methods discussed here are applicable to any crystalline material encompassing minerals (including ice), metals and ceramics.

3D tomographic phase retrieval and unwrapping

This paper develops uniqueness theory for 3D phase retrieval with finite, discrete measurement data for strong phase objects and weak phase objects, including: (i) Unique determination of (phase) projections from diffraction patterns—General measurement schemes with coded and uncoded apertures are proposed and shown to ensure unique reduction of diffraction patterns to the phase projection for a strong phase object (respectively, the projection for a weak phase object) in each direction separately without the knowledge of relative orientations and locations. (ii) Uniqueness for 3D phase unwrapping—General conditions for unique determination of a 3D strong phase object from its phase projection data are established, including, but not limited to, random tilt schemes densely sampled from a spherical triangle of vertexes in three orthogonal directions and other deterministic tilt schemes. (iii) Uniqueness for projection tomography—Unique determination of an object of n 3 voxels from generic n projections or n + 1 coded diffraction patterns is proved. This approach of reducing 3D phase retrieval to the problem of (phase) projection tomography has the practical implication of enabling classification and alignment, when relative orientations are unknown, to be carried out in terms of (phase) projections, instead of diffraction patterns. The applications with the measurement schemes such as single-axis tilt, conical tilt, dual-axis tilt, random conical tilt and general random tilt are discussed.

Spectrometric Characterization for Triple‐Junction Solar Cells

Spectrometric characterization allows for accurate determination of the current matching point and investigation of sub‐cell properties of multi‐junction solar cells. It is widely used for dual‐junction solar cells. Although the concept is suggested for triple‐junction solar cells, it is only applied for the variation of two sub‐cells. In this work, the applicability and evaluation procedure for a systematic variation of all three sub‐cells of a triple‐junction solar cell are presented. Clearly defined measurement conditions are derived which allow for meaningful characterization and comparisons of different triple‐junction devices. The presented procedure is exemplarily tested on a III–V on silicon triple‐junction solar cell using an light‐emitting diode‐based solar simulator where all needed spectral conditions can be calculated in advance and accordingly adjusted. Spectral conditions around the air mass 1.5 global spectrum are chosen and a fit routine to determine the current matching point from the discrete measurement points is proposed and validated by a measurement with a higher resolution around the current matching point. Finally, it is shown that the spectral conditions applied during the measurement also reflect outdoor conditions. This highlights the relevance of the presented procedure beyond the determination of the current‐matching conditions.

Evaluation of the Thermal Performance of Two Passive Facade System Solutions for Sustainable Development

Sustainable development is essential for the future of the planet. Using passive elements, like ventilated facades based on insulation and air chambers, or living walls, which are solutions based on nature, is a powerful strategy for cities to improve their thermal environment, reduce energy consumption, and mitigate the effects of climate change. This approach allows for the quantification of the influence of passive surfaces on energy fluxes compared to bare surfaces. In addition, it delves into understanding how the incorporation of vegetation on building facades alters surface energy fluxes, involving a combination of physical and biochemical processes. This comprehensive investigation seeks to harness the potential of passive and natural solutions to address the pressing challenges of urban sustainability and climate resilience. This research uses a surface energy balance model to analyze the thermal performance of two facades using experimental data from a PASLINK test cell. This study uses the grey box RC model, which links continuous-time ordinary differential equations with discrete measurement data points. This model provides insight into the complex interplay among factors that influence the thermal behavior of building facades, with the goal of comprehensively understanding how ventilated and green facades affect the dynamics of energy flow compared to conventional facades. The initial thermal resistance of the bare facade was 0.75 (°C m2)/W. The introduction of a ventilated facade significantly increased this thermal resistance to 2.47 (°C m2)/W due to the insulating capacity of the air chamber and its insulating layer (1.70 (°C m2)/W). Regarding the modular living wall, it obtained a thermal resistance value of 1.22 (°C m2)/W (this vegetated facade does not have an insulating layer). In this context, the modular living wall proved to be effective in reducing convective energy by 68% compared with the non-green facade. It is crucial to highlight that evapotranspiration was the primary mechanism for energy dissipation in the green facade. The experiments conclusively show that both the modular living wall and open-ventilated facade significantly reduce solar heat loads compared with non-passive bare wall facades, demonstrating their effectiveness in enhancing thermal performance and minimizing heat absorption.

A Functional Approach to Interpreting the Role of the Adjoint Equation in Machine Learning

The connection between numerical methods for solving differential equations and machine learning has been revealed recently. Differential equations have been proposed as continuous analogues of deep neural networks, and then used in handling certain tasks, such as image recognition, where the training of a model includes learning the parameters of systems of ODEs from certain points along their trajectories. Treating this inverse problem of determining the parameters of a dynamical system that minimize the difference between data and trajectory by a gradient-based optimization method presents the solution of the adjoint equation as the continuous analogue of backpropagation that yields the appropriate gradients. The paper explores an abstract approach that can be used to construct a family of loss functions with the aim of fitting the solution of an initial value problem to a set of discrete or continuous measurements. It is shown, that an extension of the adjoint equation can be used to derive the gradient of the loss function as a continuous analogue of backpropagation in machine learning. Numerical evidence is presented that under reasonably controlled circumstances the gradients obtained this way can be used in a gradient descent to fit the solution of an initial value problem to a set of continuous noisy measurements, and a set of discrete noisy measurements that are recorded at uncertain times.

Recovering critical parameter for nonlinear Allen–Cahn equation by fully discrete continuous data assimilation algorithms *

The purpose of this study is to recover the diffuse interface width parameter for nonlinear Allen–Cahn equation by a continuous data assimilation algorithm proposed recently. We obtain the large-time error between the true solution of the Allen–Cahn equation and the data assimilated solution produced by implicit–explicit one-leg fully discrete finite element methods due to discrepancy between an approximate diffuse interface width and the physical interface width. The strongly A-stability of the one-leg methods plays key roles in proving the exponential decay of initial error. Based on the long-time error estimates, we develop several algorithms to recover both the true solution and the true diffuse interface width using only spatially discrete phase field function measurements. Numerical experiments confirm our theoretical results and verify the effectiveness of the proposed methods.

Associations between balance, strength and incident dementia in older men: the Health in Men Study

AbstractBackgroundIncreased amount of physical activity has been associated with reduced incidence of dementia. It is less clear whether the discrete physical performance measures of balance and strength are associated with dementia incidence. We investigated whether baseline measures of balance and strength were associated with incident dementia.MethodA cohort of 1,314 men with no recorded history of dementia, aged 79‐97 underwent physical performance assessments between 2011 and 2013. These assessments were performed during wave 4 of the Health in Men Study, initially recruiting participants 1996‐9 in Perth, Australia. Balance was assessed with a modified Balance Outcome Measure for Elder Rehabilitation (mBOOMER) score: a combination of three tests, the Timed Up and Go, Step and Functional Reach Tests. Strength was tested using knee extension with a spring dynamometer, measured in kilograms. Incident dementia was identified up to December 2017 from the Western Australian Data Linkage System and the national Aged Care Assessment Program. Data were analysed using Cox proportional hazards models. Balance and strength measures were entered as restricted cubic splines to allow for non‐linear relationships. Models were adjusted for sociodemographic, lifestyle and health variables, including hours of physical activity.ResultA total of 187 (14.2%) incident cases of dementia were identified. Higher (better) mBOOMER scores were associated with decreased risk of incident dementia, with greater changes in risk occurring at higher scores (1 vs 0: HR 0.91, 95% CI 0.81‐1.01, 6 vs 5: HR 0.91, 95% CI 0.81‐1.01, 9 vs 8: HR 0.77, 95% CI 0.70‐0.84, 12 vs 11: HR 0.51, 95% CI 0.37‐0.69). Higher knee extension strength was associated with a decreased risk of incident dementia, with greater changes occurring at lower levels then plateauing at around 25 kilograms (5kg vs 4kg: HR 0.93, 95% CI 0.89‐0.97, 15kg vs 14kg: HR 0.93, 95% CI 0.89‐0.97, 25kg vs 24kg: HR 0.99, 95% CI 0.95‐1.02, 35kg to 34kg: HR 1.00, 95% CI 0.95‐1.06). Relationships remained after excluding those with a dementia diagnosis within two years of baseline physical performance assessment.ConclusionBetter balance and strength are both associated with decreased risk of developing dementia, thus representing potentially modifiable risk factors.

Autonomous exploration for radioactive sources localization based on radiation field reconstruction

In recent years, unmanned ground vehicles (UGVs) have been used to search for lost or stolen radioactive sources to avoid radiation exposure for operators. To achieve autonomous localization of radioactive sources, the UGVs must have the ability to automatically determine the next radiation measurement location instead of following a predefined path. Also, the radiation field of radioactive sources has to be reconstructed or inverted utilizing discrete measurements to obtain the radiation intensity distribution in the area of interest. In this study, we propose an effective source localization framework and method, in which UGVs are able to autonomously explore in the radiation area to determine the location of radioactive sources through an iterative process: path planning, radiation field reconstruction and estimation of source location. In the search process, the next radiation measurement point of the UGVs is fully predicted by the design path planning algorithm. After obtaining the measurement points and their radiation measurements, the radiation field of radioactive sources is reconstructed by the Gaussian process regression (GPR) model based on machine learning method. Based on the reconstructed radiation field, the locations of radioactive sources can be determined by the peak analysis method. The proposed method is verified through extensive simulation experiments, and the real source localization experiment on a Cs-137 point source shows that the proposed method can accurately locate the radioactive source with an error of approximately 0.30 m. The experimental results reveal the important practicality of our proposed method for source autonomous localization tasks.

Quantification of fossil fuel CO2 from combined CO, δ13CO2 and Δ14CO2 observations

Abstract. We present a new method for partitioning observed CO2 enhancements (CO2xs) into fossil and biospheric fractions (Cff and Cbio) based on measurements of CO and δ13CO2, complemented by flask-based Δ14CO2 measurements. This method additionally partitions the fossil fraction into natural gas and petroleum fractions (when coal combustion is insignificant). Although here we apply the method only to discrete flask air measurements, the advantage of this method (CO- and δ13CO2-based method) is that CO2xs partitioning can be applied at high frequency when continuous measurements of CO and δ13CO2 are available. High-frequency partitioning of CO2xs into Cff and Cbio has already been demonstrated using continuous measurements of CO (CO-based method) and Δ14CO2 measurements from flask air samples. We find that the uncertainty in Cff estimated from the CO- and δ13CO2-based method averages 3.2 ppm (23 % of the mean Cff of 14.2 ppm estimated directly from Δ14CO2), which is significantly less than the CO-based method which has an average uncertainty of 4.8 ppm (34 % of the mean Cff). Using measurements of CO, δ13CO2 and Δ14CO2 from flask air samples at three sites in the greater Los Angeles (LA) region, we find large contributions of biogenic sources that vary by season. On a monthly average, the biogenic signal accounts for −14 to +25 % of CO2xs with larger and positive contributions in winter and smaller and negative contributions in summer due to net respiration and net photosynthesis, respectively. Partitioning Cff into petroleum and natural gas combustion fractions reveals that the largest contribution of natural gas combustion generally occurs in summer, which is likely related to increased electricity generation in LA power plants for air-conditioning.

Development and Evaluation of a Natural Language Processing System for Curating a Trans-Thoracic Echocardiogram (TTE) Database.

Although electronic health records (EHR) provide useful insights into disease patterns and patient treatment optimisation, their reliance on unstructured data presents a difficulty. Echocardiography reports, which provide extensive pathology information for cardiovascular patients, are particularly challenging to extract and analyse, because of their narrative structure. Although natural language processing (NLP) has been utilised successfully in a variety of medical fields, it is not commonly used in echocardiography analysis. To develop an NLP-based approach for extracting and categorising data from echocardiography reports by accurately converting continuous (e.g., LVOT VTI, AV VTI and TR Vmax) and discrete (e.g., regurgitation severity) outcomes in a semi-structured narrative format into a structured and categorised format, allowing for future research or clinical use. 135,062 Trans-Thoracic Echocardiogram (TTE) reports were derived from 146967 baseline echocardiogram reports and split into three cohorts: Training and Validation (n = 1075), Test Dataset (n = 98) and Application Dataset (n = 133,889). The NLP system was developed and was iteratively refined using medical expert knowledge. The system was used to curate a moderate-fidelity database from extractions of 133,889 reports. A hold-out validation set of 98 reports was blindly annotated and extracted by two clinicians for comparison with the NLP extraction. Agreement, discrimination, accuracy and calibration of outcome measure extractions were evaluated. Continuous outcomes including LVOT VTI, AV VTI and TR Vmax exhibited perfect inter-rater reliability using intra-class correlation scores (ICC = 1.00, p < 0.05) alongside high R2 values, demonstrating an ideal alignment between the NLP system and clinicians. A good level (ICC = 0.75-0.9, p < 0.05) of inter-rater reliability was observed for outcomes such as LVOT Diam, Lateral MAPSE, Peak E Velocity, Lateral E' Velocity, PV Vmax, Sinuses of Valsalva and Ascending Aorta diameters. Furthermore, the accuracy rate for discrete outcome measures was 91.38% in the confusion matrix analysis, indicating effective performance. The NLP-based technique yielded good results when it came to extracting and categorising data from echocardiography reports. The system demonstrated a high degree of agreement and concordance with clinician extractions. This study contributes to the effective use of semi-structured data by providing a useful tool for converting semi-structured text to a structured echo report that can be used for data management. Additional validation and implementation in healthcare settings can improve data availability and support research and clinical decision-making.

PulsarX: A new pulsar searching package

Context. Pulsar surveys with modern radio telescopes are becoming increasingly computationally demanding. This is particularly true for wide field-of-view pulsar surveys with radio interferometers and those conducted in real or quasi-real time. These demands result in data analysis bottlenecks that can limit the parameter space covered by the surveys and diminish their scientific return. Aims. In this paper we address the computational challenge of ‘candidate folding’ in pulsar searching, presenting a novel, efficient approach designed to optimise the simultaneous folding of large numbers of pulsar candidates. We provide a complete folding pipeline appropriate for large-scale pulsar surveys that includes radio frequency interference mitigation, de-dispersion, folding, and parameter optimisation. Methods. By leveraging the fast discrete dispersion measure transform (FDMT) algorithm, we have developed an optimised and cache-friendly implementation that we term the pruned FDMT (pFDMT). This implementation is specifically designed for candidate folding scenarios where the candidates are broadly distributed in dispersion measure space. The pFDMT approach efficiently reuses intermediate processing results and prunes the unused computation paths, resulting in a significant reduction in arithmetic operations. In addition, we propose a novel folding algorithm based on the Tikhonov-regularised least squares method that can improve the time resolution of the pulsar profile. Results. We present the performance of its real-world application as an integral part of two major pulsar search projects conducted with the MeerKAT telescope: the MPIfR-MeerKAT Galactic Plane Survey (MMGPS) and the Transients and Pulsars with MeerKAT (TRAPUM) project. In our processing of approximately 500 candidates, the theoretical number of de-dispersion operations can be reduced by a factor of around 50 when compared to brute-force de-dispersion, which scales with the number of candidates.

Distributed Multiagent-Based Event-Driven Fault-Tolerant Control of Islanded Microgrids.

This article proposes an observer-based event-driven fault-tolerant (OBEDFT) secondary control strategy for AC microgrids (MGs) to achieve load voltage regulation. First, the input-output feedback linearization method transforms the voltage regulation issue into an output feedback tracking problem for linear multiagent systems (MASs) with nonlinear dynamics. This transformation provides the necessary preprocessing for load voltage regulation. Then, an OBEDFT secondary control protocol that considers full-state immeasurability is proposed. The actuators of distributed generators (DGs) may experience partial loss of effectiveness (PLOE) and bias faults, and these fault parameters may be heterogeneous and time-varying. The protocol introduces adaptive techniques to avoid information related to fault parameters while using event-driven mechanisms to achieve discrete measurements of neighboring DG. Additionally, the protocol uses boundary layers to construct smooth controllers that prevent the chattering effect caused by nonsmooth controllers. Finally, simulation results confirm the effectiveness of this load voltage regulation strategy.

Picture hesitant fuzzy grey compromise relational bidirectional projection method with application in multi-attribute recommendation

In view of the technical defects of the existing grey relational projection method, a new grey compromise relational bidirectional projection method is proposed. By incorporating the information expression advantage of picture hesitant fuzzy number, the distance formula of picture hesitant fuzzy statistics is constructed based on the centralized trend measurement and discrete trend measurement in descriptive statistics. On this basis, a multi-attribute recommendation method of picture hesitant fuzzy grey compromise relational bidirectional projection is proposed by combining compromise idea and bidirectional projection technology. The validity and advantage of this method are verified by numerical analysis, which also suggested the rationality of the picture hesitant fuzzy statistical distance and the grey compromise relational bidirectional projection method.

Relationship Between Kinetic and Kinematic Measures of the Countermovement Jump and National Weightlifting Performance

Abstract Purpose The association between vertical jump and weightlifting performance have been well established often using discrete performance measures such as jump height or peak power which provides little insight into temporal strategies. The purpose of this investigation was to identify currently unassessed temporal countermovement jump metrics and their reliability and relationship to national weightlifting performance. Methods A total of 42 national weightlifting athletes (n = 30 females and 12 males), were recruited for this study. Countermovement jump was measured using a force plate following a national and international competition. Vertical ground reaction force and time data were analyzed using a custom script where temporal metrics relating to specific phases of the jump were extracted. Snatch, Clean and Jerk and Total weightlifting performance was obtained following each competition. Reliability of jump metrics were determined using coefficient of variation and interclass correlation coefficient. A Spearman’s Rho, non-parametric bivariate correlation was used to determine the relationship between the jump metrics and weightlifting performance. Results From a total of 15 metrics, 13 were deemed reliable, with propulsive impulse showing the greatest level of reliability. Correlational analysis showed strong to very strong (r = 0.676–0.817) relationships between all absolute measures of weightlifting performance and propulsive impulse for both women and men. Conclusion This novel finding suggests that practitioners may wish to use propulsive impulse as it may provide more insight into changes of force capabilities following training. Additionally, it may also be used as a talent identification tool given its strong relationship to performance.

Soft Quantization Using Entropic Regularization.

The quantization problem aims to find the best possible approximation of probability measures on Rd using finite and discrete measures. The Wasserstein distance is a typical choice to measure the quality of the approximation. This contribution investigates the properties and robustness of the entropy-regularized quantization problem, which relaxes the standard quantization problem. The proposed approximation technique naturally adopts the softmin function, which is well known for its robustness from both theoretical and practicability standpoints. Moreover, we use the entropy-regularized Wasserstein distance to evaluate the quality of the soft quantization problem's approximation, and we implement a stochastic gradient approach to achieve the optimal solutions. The control parameter in our proposed method allows for the adjustment of the optimization problem's difficulty level, providing significant advantages when dealing with exceptionally challenging problems of interest. As well, this contribution empirically illustrates the performance of the method in various expositions.