Minimum Uncertainty Research Articles

Fast and universal single-molecule localization using multi-dimensional point spread functions

The recent development of single-molecule imaging techniques has enabled not only high accuracy spatial resolution imaging but also information rich functional imaging. Abundant information about single molecules can be encoded in its diffraction pattern and be extracted precisely (e.g. 3D position, wavelength, dipole orientation). However, sophisticated high dimensional point spread function (PSF) modeling and analyzing methods have greatly impeded the broad accessibility of these techniques. Here, we present a graphics processing unit (GPU) -based B-spline PSF modeling method that could flexibly model high dimensional PSFs with arbitrary shape without greatly increasing the model parameters. Our B-spline fitter achieves 100 times speed improvement and minimal uncertainty for each dimension, enabling efficient high dimensional single-molecule analysis. We demonstrated, both in simulations and experiments, the universality and flexibility of our B-spline fitter to accurately extract the abundant information from different types of high dimensional single-molecule data, including multicolor PSF (3D + color), multi-channel four-dimensional 4Pi-PSF (3D + interference phase) and five-dimensional vortex PSF (3D + dipole orientation).

Accurate 3D single-molecule localization via vectorial in situ point spread function retrieval and aberration assessment

Single-molecule localization microscopy (SMLM) gradually plays an important role in deep tissue imaging. However, current SMLM methods primarily rely on fiducial marks, neglecting aberrations introduced by thick samples, thereby resulting in decreased image quality in deep tissues. Here, we introduce vectorial in situ point spread function (PSF) retrieval (VISPR), a method that retrieves a precise PSF model considering both system- and sample-induced aberrations under SMLM conditions. By employing the theory of vectorial PSF model and maximum likelihood estimation (MLE) phase retrieval, VISPR is capable of reconstructing an accurate in situ 3D PSF model achieving the theoretically minimum uncertainty and accurately reflecting three-dimensional information of single molecules. This capability enables accurate 3D super-resolution reconstruction in deep regions away from the coverslips. Additionally, VISPR demonstrates applicability in low signal-to-noise ratio scenarios and compatibility with various SMLM microscope modalities. From both simulations and experiments, we verified the superiority and effectiveness of VISPR. We anticipate that VISPR will become a pivotal tool for advancing deep tissue SMLM imaging.

Distributed salinity sensor based on optical frequency domain reflectometry with polyimide coated single mode fiber

A distributed optical fiber sensor for salinity sensing is proposed and analyzed. The sensor uses a single mode fiber coated with polyimide and is based on optical frequency domain reflectometry. By applying the polyimide solution to the surface of the fiber, a layer of polyimide film is formed by heating. As the polyimide coating is very sensitive to changes in the salinity of the external solution, the polyimide film will expand or shrink as the external concentration changes. This converts the value of salt concentration into the frequency shift in the spectrum through cross-correlation. To characterize the sensor, four polyimide-coated sensors with different average coating thicknesses of 126 µm, 170 µm, 192 µm and 249 µm were fabricated. The sensitivities of -21.71 GHz/(mol/L), -28.55 GHz/(mol/L), -29.97 GHz/(mol/L) and -42.78 GHz/(mol/L) were achieved when the salinity was measured from 0 mol/L to 3.09 mol/L, respectively. The sensitivity and response time of polyimide fibers with different diameters were measured. The minimum salinity measurement uncertainty of the sensor is 0.05 mol/L. The sensor has high sensitivity and has promising applications in observing ocean parameters and ion chemical sensing.

Teleportation of a qubit using quasi-Bell states

In this paper, we study the exotic Landau problem at the classical level where two conserved quantities are derived. At the quantum level, the corresponding quantum operators of the conserved quantities provide two oscillator representations from which we derive two Boson Fock spaces. Using the normalized coherent states which are the minimum uncertainty states on noncommutative configuration space isomorphic to each of the boson Fock space, we form entangled coherent states which are Bell- like states labeled quasi-Bell states. The effect of non-maximality of a quasi-Bell state based quantum channel is investigated in the context of a teleportation of a qubit.

Outlier detection based on multisource information fusion in incomplete mixed data

Multisource incomplete mixed data fusion (MsIMDF) plays a crucial role in outlier detection by utilizing complementary, informative, interpretative, and less noisy single-source data to identify unexpected errors or behaviors. However, existing multisource data fusion approaches only consider homogeneous data and single uncertain information,overlooking the mixed heterogeneous data and diverse uncertainty information. This limitation can negatively impact the performance of outlier detection. To address this issue, we propose MsIMDF-USF, a novel two-stage model that fully leverages the rich multisource knowledge and uncertainty information in incomplete mixed data. During the information fusion stage, the MsIMDF model combines multisource data into new single-source data using the minimum uncertainty strategy based on rough and fuzzy information. Subsequently, in the outlier detection stage, we reconstruct a neighborhood information network under a united-similar-fuzzy (USF) relationship using the new fused data. This reconstruction aims to strengthen the connections between similar objects while weakening relationships among dissimilar ones by considering single-attribute and multi-attribute information. Outlier scores are obtained based on the stationary distribution of the reconstructed networks using a Markov random walk. Experimental results on 16 real datasets demonstrate that the MsIMDF-USF model effectively extracts higher-quality data, exhibiting high applicability and robustness in outlier detection tasks.

Evaluation of MCP Correlation Algorithms Applied to Wind Data Series

This work aimed to develop methodologies for analysing statistical correlations among wind data series using various Measure-Correlate-Predict (MCP) methods, with the goal of selecting the most suitable method for extrapolating long-term data with minimal associated uncertainty. It was analysed the minimum time required for a wind measurement campaign when applying this methodology. Fifteen local wind measurement stations were selected. The long-term wind data reanalysis series that exhibited the strongest correlation with the measured wind data at each station was then chosen. Multiple tests were conducted with different simultaneous periods between the measured data series and the long-term series. Fifteen correlation algorithms were tested for each concurrent period. The performance of each model was evaluated using the RMSE (Root Mean Square Error) and MBE (Mean Bias Error) associated with each MCP. Analysis of the errors identified measurement periods with the lowest associated error ranging from 1 to 5 years and a single-factor ANOVA analysis was conducted. Finally, t-significance tests were performed. The study concluded that the Neural Network was the most effective MCP method. Additionally, it was determined that the minimum number of years required for a local measurement campaign should be between 2 and 3 years.

Intensity-Product-Based Optical Sensing to Beat the Diffraction Limit in an Interferometer.

The classically defined minimum uncertainty of the optical phase is known as the standard quantum limit or shot-noise limit (SNL), originating in the uncertainty principle of quantum mechanics. Based on the SNL, the phase sensitivity is inversely proportional to K, where K is the number of interfering photons or statistically measured events. Thus, using a high-power laser is advantageous to enhance sensitivity due to the K gain in the signal-to-noise ratio. In a typical interferometer, however, the resolution remains in the diffraction limit of the K = 1 case unless the interfering photons are resolved as in quantum sensing. Here, a projection measurement method in quantum sensing is adapted for classical sensing to achieve an additional K gain in the resolution. To understand the projection measurements, several types of conventional interferometers based on N-wave interference are coherently analyzed as a classical reference and numerically compared with the proposed method. As a result, the Kth-order intensity product applied to the N-wave spectrometer exceeds the diffraction limit in classical sensing and the Heisenberg limit in quantum sensing, where the classical N-slit system inherently satisfies the Heisenberg limit of π/N in resolution.

Data-driven surrogate modeling and optimization of supercritical jet into supersonic crossflow

For the design and optimization of advanced aero-engines, the prohibitively computational resources required for numerical simulations pose a significant challenge, due to the extensive exploration of design parameters across a vast design space. Surrogate modeling techniques offer a viable alternative for efficiently emulating numerical results within a notably compressed timeframe. This study introduces parametric Reduced-Order Models (ROMs) based on Convolutional AutoEncoders (CAE), Fully Connected AutoEncoders (FCAE), and Proper Orthogonal Decomposition (POD) to fast emulate spatial distributions of physical variables for a supercritical jet into a supersonic crossflow under different operating conditions. To further accelerate the decision-making process, an optimization model is developed to enhance fuel-oxidizer mixing efficiency while minimizing total pressure loss. Results indicate that CAE-based ROMs exhibit superior prediction accuracy while FCAE-based ROMs show inferior predictive accuracy but minimal uncertainty. The latter may be ascribed to the markedly greater number of hyperparameters. POD-based ROMs underperform in regions of strong nonlinear flow dynamics, coupled with higher overall prediction uncertainties. Both AE- and POD-based ROMs achieve online predictions approximately 9 orders of magnitude faster than conventional simulations. The established optimization model enables the attainment of Pareto-optimal frontiers for spatial mixing deficiencies and total pressure recovery coefficient.

Regulating the redshift of the charge transfer band edge and antithermal quenching by ion substitution strategy in YP1-xVxO4:Eu3+ phosphor

The redshift of the charge transfer band (CTB) edge of phosphor induced by temperature rise is pervasively accompanied by antithermal quenching. Accordingly, exploring the mechanism of the CTB redshift is thus not only propitious for optimizing the sensitivity of optical thermometry but also tenders a new idea for the design of antithermal quenching phosphors. Herein, a family of YP1-xVxO4:Eu3+ phosphors were designed via the V5+/P5+ ion substitution strategy. With the increase of the V5+ ratio, the relative integral intensity of the 5D0→7F2 transition multiplies from 1.25 to 28.67 times under CTB edge excitation. Moreover, by Gaussian fitting, the reduction degree of vanadate band gap energy 1E (1T1)→1B2 (1T2), 1A2 (1T1)→1B2 (1T2) increased from 0.122 eV and 0.065 eV to0.162 eV and 0.083 eV, respectively, in the range of 303–523 K. Both reveal an enhance in redshift of the excitation spectra. The decrease of charge transfer state (CTS) energy level and the alteration of photoelectron thermal population are two mechanisms that induce CTB redshift. Specifically, the decrease of the CTS level is dominant in the YPO4:Eu3+ sample, and the thermal population of the higher vibrational levels of the VO43−ground state is dominant in the presence of a tiny amount of V5+ doping. In addition, according to the experimental phenomenon, a dual-mode temperature sensing scheme based on excitation intensity ratio (EIR) and single band ratiometric (SBR) is proposed. Y0.9P0.1V0.9O4:0.1Eu3+ achieves a maximum sensitivity of Sr-max = 4.040 % K−1 and a minimum temperature determination uncertainty of δT = 0.124 K at 323 K, which excellent performance indicates that this is a promising non-contact optical thermometer.

On quantum states for angular position and angular momentum of light

In the present paper we construct a properly defined quantum state ψ(θ) expressed in terms of elliptic Jacobi theta functions for the self-adjoint observables angular position θ and the corresponding angular momentum operator L=−id/dθ in units of ℏ=1 . The quantum uncertainties Δθ and ΔL for the state are well-defined and are shown to give a lower value of the uncertainty product ΔθΔL in contrast to the so called minimal uncertainty states as discussed in Franke-Arnold et al (2004 New J. Phys. 6 103-1-8). The mean value ⟨L⟩ of the state ψ(θ) is not required to be an integer. In the case of any half-integer mean value ⟨L⟩ the state constructed exhibits a remarkable critical behavior with upper and lower bounds Δθ=π2/3−2 and ΔL=1/2 .

Convergence, sampling and total order estimator effects on parameter orthogonality in global sensitivity analysis.

Dynamical system models typically involve numerous input parameters whose "effects" and orthogonality need to be quantified through sensitivity analysis, to identify inputs contributing the greatest uncertainty. Whilst prior art has compared total-order estimators' role in recovering "true" effects, assessing their ability to recover robust parameter orthogonality for use in identifiability metrics has not been investigated. In this paper, we perform: (i) an assessment using a different class of numerical models representing the cardiovascular system, (ii) a wider evaluation of sampling methodologies and their interactions with estimators, (iii) an investigation of the consequences of permuting estimators and sampling methodologies on input parameter orthogonality, (iv) a study of sample convergence through resampling, and (v) an assessment of whether positive outcomes are sustained when model input dimensionality increases. Our results indicate that Jansen or Janon estimators display efficient convergence with minimum uncertainty when coupled with Sobol and the lattice rule sampling methods, making them prime choices for calculating parameter orthogonality and influence. This study reveals that global sensitivity analysis is convergence driven. Unconverged indices are subject to error and therefore the true influence or orthogonality of the input parameters are not recovered. This investigation importantly clarifies the interactions of the estimator and the sampling methodology by reducing the associated ambiguities, defining novel practices for modelling in the life sciences.

Circuits implementations using carbon nanotube field-effect transistor nanotechnology

Device scaling is a pivotal aspect in the field of electronics, aimed at enhancing the performance of integrated circuits (ICs) by reducing the dimensions of transistors. The device scaling presents the short channel effects (SCEs) in the nanoscale regime. To address the SCEs, nanometer IC designers have turned to the carbon nanotube field-effect transistor (CNTFET) technology, which offers unique properties and mitigates the challenges associated with transistor scaling. In this research work, a leakage reduction technique known as the input-dependent (INDEP) method is suggested to tackle the leakage current issue at the nanoscale regime using CNTFET technology. The INDEP method involves the incorporation of two additional transistors within the logic circuit. To evaluate the efficacy of the INDEP method, a CNTFET-based 7-stage inverter chain is meticulously designed at 32 nm CNTFET technology node. Subsequent comparative analysis against alternative designs is conducted, assessing performance metrics such as power dissipation, delay, and power delay product (PDP). The suggested INDEP method reduces power dissipation by 83.75% and improves PDP by 78.44%. Furthermore, the study delves into the impact of process, voltage, and temperature (PVT) variations. Additionally, the investigation explores the influence of parameters such as the number of carbon nanotubes, temperature, supply voltage, and chiral indices on the performance of the 7-stage inverter chain. The simulation results demonstrate that the CNTFET-based INDEP technique yields promising outcomes, characterized by low power dissipation, precise output, and minimal uncertainty across all evaluated metrics.

Weakly q-deformed Heisenberg algebra and non-Hermitian Hamiltonians: Application in statistical physics

We have investigated a weakly q-deformed algebra, which leads to non-Hermitian operators. It has been explicitly shown that the harmonic oscillator Hamiltonian is quasi-Hermitian, and that the corresponding physical Hilbert-space metric Θ differs from that obtained in Ref. [1], by hermitizing the position operator. The reality of the Hamiltonian eigenvalues has been illustrated by analytically computing the first order correction to the energy spectrum of the harmonic oscillator (HO). Furthermore, we have shown that this q-deformation leads to a GUP with minimal uncertainties in both position and momentum measurements. Moreover, the physical implications of this q-deformation, have been investigated by studying the thermostatistics of a system of HOs and an ideal gas. For both systems, we computed the partition function, and then we derived some thermodynamic functions. In addition, for the ideal gas, a modified equation of state and a generalized Mayer's equation, consistent with the real behavior of gases, have been established. The obtained results show that the impact of this model would be significant at high temperatures. However, unlike earlier research, we observe that this q-deformation induced the similar corrections regardless of the system under study.

Extended uncertainty principle: A deeper insight into the Hubble tension?

The standard cosmological model, known as the ΛCDM model, has been successful in many respects, but it has some significant discrepancies, some of which have not been resolved yet. In measuring the Hubble-Lemaître parameter, there is an apparent discrepancy which is known as the Hubble tension, defined as differences in values of this parameter measured by the Type Ia Supernovae (SNeIa) data (a model-independent method) and by the Cosmic Microwave Background (CMB) radiation maps (a model-dependent method). Although many potential solutions have been proposed, the issue still remains unresolved. Recently, it was observed that the Hubble tension can be due to the concept of uncertainty in measuring cosmological parameters at large distance scales through applying the Heisenberg Uncertainty Principle (HUP) in cosmological setups. Extending this pioneering idea, in the present study we plan to incorporate the Extended Uncertainty Principle (EUP) containing a minimal fundamental measurable momentum (or equivalently, a maximal fundamental measurable length) as a candidate setup for describing large-scale effects of Quantum Gravity (QG) to address the Hubble tension and constrain the EUP length scale. In this regard, by finding a relevant formula for the effective photon rest mass in terms of the present-time value of the Hubble-Lemaître parameter, we see that discrepancies in the value of photon rest mass associated with the Hubble-Lemaître parameter values estimated from model-independent and model-dependent methods perhaps is the cause of Hubble tension. We show explicitly that the presence of a non-zero minimal uncertainty in momentum (or non-zero maximal uncertainty in position) measurements as a consequence of the large distance quantum gravity effect addresses the Hubble tension satisfactorily without having to invoke new physics. Moreover, we use the formula for the effective photon rest mass to find some relevant lower bounds on the EUP length scale.

Spatial mapping and driving factor Identification for salt-affected soils at continental scale using Machine learning methods

Soil salinization is one of the most serious land-degrading threats globally, particularly in Asia, where there are 21 countries, e.g., Kazakhstan, China, Iran, and Indonesia, lack of accurate spatial information of salt-affected soils currently. Mapping the distribution of salt-affected soils and identifying their main driving factors is critical for sustainable development. Current studies for mapping the spatial distribution of salt-affected soils focused on recognizing the soil salinity by using the indicator of electrical conductivity of saturated soil paste extract (ECe), while cannot distinguish the soil sodicity. Meanwhile, the absence of uncertainty assessment is another problem for large-scale studies. To address these gaps, we developed an effective spatial prediction model that considered both soil salinity and sodicity using machine learning (ML) models and soil salinization data. This study used ECe, pH, and exchangeable sodium percent (ESP) as indicators, with sample sizes of 22,803, 30,821, and 12,961, respectively, to produce salt-affected soil maps with uncertainty assessments in Asia, and conducted the analysis of the drivers of soil salinization. The ML models involved cubist, random forest, quantile regression forest, quantile regression neural network, and a simple multiple linear regression model for comparison. The results showed that among these models, quantile regression forest exhibited the best performance, with mean absolute percentage error values of 2.54 %∼52.06 %, coefficient of determination values of 0.40 ∼ 0.74, and Nash-Sutcliffe efficiency values of 0.36 ∼ 0.71. The predicted maps, with 1 km resolution, demonstrated minimal uncertainty across over 60.4 % of the study area. Approximately 466.36 million hectares of topsoil (0–30 cm) and 377.68 million hectares of subsoil (30–100 cm) in Asia are salt-affected, mainly concentrated in arid, semi-arid, and coastal regions. Climatic factors (the annual precipitation and maximum temperature), topography (digital elevation model and slope), and salinity index V (SI5) were identified as the main drivers of soil salinization. Overall, this study provides important guidelines for soil salinization management and achieving ecological sustainability.

Algebraic solution and thermodynamic properties for the one- and two-dimensional Dirac oscillator with minimal length uncertainty relations

We study the quantum characteristics of the Dirac oscillator within the framework of Heisenberg's generalized uncertainty principle. This principle leads to the appearance of a minimal length of the order of the Planck length. Hidden symmetries are identified to solve the model algebraically. The presence of the minimal length leads to a quadratic dependence of the energy spectrum on the quantum number n, implying the hard confinement property of the system. Thermodynamic properties are calculated using the canonical partition function. The latter is well determined by the method based on Epstein's zeta function. The results reveal that the minimal length has a significant effect on the thermodynamic properties.

Expanding the Toolbox for Industrial Luminescent Primary Thermometry: Er3+-doped SrMoO4

We herein demonstrate the feasibility of employing strontium molybdate as host matrix for trivalent erbium ions for the developing of an optical temperature sensor operating in a wide temperature range suitable for industrial applications. This class of metal molybdate, known for its chemical and thermal capabilities, works as primary luminescent thermometer, relying on the thermally coupled levels of Er3+ arising from downshifting processes, neglecting first, the requirement of calibration curve acquisition and second, the excitation induced heating on the sample typically observed in upconverting luminescent thermometers. The synthesised primary optical thermometer displays a maximum temperature relative sensitivity of 1.13 %. K−1 and minimum temperature uncertainty and 0.09 K. These values make the performance of the Er3+-doped strontium molybdate as optical temperature sensor competitive with the existing luminescent primary thermometers, including a wide operating temperature range up to 413 K and high accuracy as main features. Moreover, it can be easily scaled up and produced due to straightforwardness and cost-effectiveness of the ceramic synthesis method, matching the requirements for its usage in industrial environments.

Enhancing groundwater quality assessment in coastal area: A hybrid modeling approach

Monitoring of groundwater (GW) resources in coastal areas is vital for human needs, agriculture, ecosystems, securing water supply, biodiversity, and environmental sustainability. Although the utilization of water quality index (WQI) models has proven effective in monitoring GW resources, it has faced substantial criticism due to its inconsistent outcomes, prompting the need for more reliable assessment methods. Therefore, this study addressed this concern by employing the data-driven root mean squared (RMS) models to evaluate groundwater quality (GWQ) in the coastal Bhola district near the Bay of Bengal, Bangladesh. To enhance the reliability of the RMS-WQI model, the research incorporated the extreme gradient boosting (XGBoost) machine learning (ML) algorithm. For the assessment of GWQ, the study utilized eleven crucial indicators, including turbidity (TURB), electric conductivity (EC), pH, total dissolved solids (TDS), nitrate (NO3−), ammonium (NH4+), sodium (Na), potassium (K), magnesium (Mg), calcium (Ca), and iron (Fe). In terms of the GW indicators, concentration of K, Ca and Mg exceeded the guideline limit in the collected GW samples. The computed RMS-WQI scores ranged from 54.3 to 72.1, with an average of 65.2, categorizing all sampling sites' GWQ as “fair.” In terms of model reliability, XGBoost demonstrated exceptional sensitivity (R2 = 0.97) in predicting GWQ accurately. Furthermore, the RMS-WQI model exhibited minimal uncertainty (<1 %) in predicting WQI scores. These findings implied the efficacy of the RMS-WQI model in accurately assessing GWQ in coastal areas, that would ultimately assist regional environmental managers and strategic planners for effective monitoring and sustainable management of coastal GW resources.

Black hole interior quantization: a minimal uncertainty approach

In a previous work we studied the interior of the Schwarzschild black hole implementing an effective minimal length, by applying a modification to the Poisson brackets of the theory. In this work we perform a proper quantization of such a system. Specifically, we quantize the interior of the Schwarzschild black hole in two ways: once by using the standard quantum theory, and once by following a minimal uncertainty approach. Then, we compare the obtained results from the two approaches. We show that, as expected, the wave function in the standard approach diverges in the region where classical singularity is located and the expectation value of the Kretschmann scalar also blows up on this state in that region. On the other hand, by following a minimal uncertainty quantization approach, we obtain 5 new and important results as follows. (1) All the interior states remain well-defined and square-integrable. (2) The expectation value of the Kretschmann scalar on the states remains finite over the whole interior region, particularly where used to be the classical singularity, therefore signaling the resolution of the black hole singularity. (3) A new quantum number is found which plays a crucial role in determining the convergence of the norm of states, as well as the convergence and finiteness of the expectation value of the Kretschmann scalar. (4) A minimum for the radius of the (2-spheres in the) black holes is found (5) By demanding square-integrability of states in the whole interior region, an exact relation between the Barbero-Immirzi parameter and the minimal uncertainty scale is found.

Semiclassical resolution of the black hole singularity inspired in the minimal uncertainty approach

We propose a new lapse function that simplifies the Hamiltonian constraint, describing the interior of the black hole in terms of the Ashtekar-Barbero variables, into a more straightforward form. The new Hamiltonian leads to different equations of motion than those found in the literature, but through a suitable transformation between temporal parameters, it is found that such a choice leads us to the classical solutions of the Schwarzschild metric, still preserving the physical singularity. In order to resolve this singularity, and inspired by the minimal uncertainty approach, we modify the classical algebra between the dynamic variables of the model, imposing an effective dynamics within the black hole. As a consequence, one of the dynamic variables, denoted by pb, acquires a minimum value at the singularity t=0, and on the other hand, the variable related to the radius of the 2-sphere, pc, leads to the resolution of the classical singularity of the black hole by replacing it with a bounce that connects the interior of the black hole with the interior of the white hole. This bounce occurs in the Planck-scale region, where a new event horizon manifests. Upon crossing this horizon, the nature of the interval changes from spatial to temporal outside the white hole.