Length Uncertainty Research Articles

Calibrated uncertainty estimation for interpretable proton computed tomography image correction using Bayesian deep learning

Integrated-type proton computed tomography (pCT) measures proton stopping power ratio (SPR) images for proton therapy treatment planning, but its image quality is degraded due to noise and scatter. Although several correction methods have been proposed, techniques that include estimation of uncertainty are limited. This study proposes a novel uncertainty-aware pCT image correction method using a Bayesian convolutional neural network (BCNN). A DenseNet-based BCNN was constructed to predict both a corrected SPR image and its uncertainty from a noisy SPR image. A total 432 noisy SPR images of 6 non-anthropomorphic and 3 head phantoms were collected with Monte Carlo simulations, while true noise-free images were calculated with known geometric and chemical components. Heteroscedastic loss and deep ensemble techniques were performed to estimate aleatoric and epistemic uncertainties by training 25 unique BCNN models. 200-epoch end-to-end training was performed for each model independently. Feasibility of the predicted uncertainty was demonstrated after applying two post-hoc calibrations and calculating spot-specific path length uncertainty distribution. For evaluation, accuracy of head SPR images and water-equivalent thickness (WET) corrected by the trained BCNN models was compared with a conventional method and non-Bayesian CNN model. BCNN-corrected SPR images represent noise-free images with high accuracy. Mean absolute error in test data was improved from 0.263 for uncorrected images to 0.0538 for BCNN-corrected images. Moreover, the calibrated uncertainty represents accurate confidence levels, and the BCNN-corrected calibrated WET was more accurate than non-Bayesian CNN with high statistical significance. Computation time for calculating one image and its uncertainties with 25 BCNN models is 0.7 s with a consumer grade GPU. Our model is able to predict accurate pCT images as well as two types of uncertainty. These uncertainties will be useful to identify potential cause of SPR errors and develop a spot-specific range margin criterion, toward elaboration of uncertainty-guided proton therapy.

Design of a mathematical model and a simulation-optimization approach for master surgical scheduling considering uncertainty in length of stay, demands and duration of surgery

Design of a mathematical model and a simulation-optimization approach for master surgical scheduling considering uncertainty in length of stay, demands and duration of surgery

Consequences of minimal length discretization on line element, metric tensor, and geodesic equation

When minimal length uncertainty emerging from a generalized uncertainty principle (GUP) is thoughtfully implemented, it is of great interest to consider its impacts on gravitational Einstein field equations (gEFEs) and to try to assess consequential modifications in metric manifesting properties of quantum geometry due to quantum gravity. GUP takes into account the gravitational impacts on the noncommutation relations of length (distance) and momentum operators or time and energy operators and so on. On the other hand, gEFE relates classical geometry or general relativity gravity to the energy–momentum tensors, that is, proposing quantum equations of state. Despite the technical difficulties, we intend to insert GUP into the metric tensor so that the line element and the geodesic equation in flat and curved space are accordingly modified. The latter apparently encompasses acceleration, jerk, and snap (jounce) of a particle in the quasi‐quantized gravitational field. Finite higher orders of acceleration apparently manifest phenomena such as accelerating expansion and transitions between different radii of curvature and so on.

A minimal length uncertainty approach to cosmological constant problem

AbstractBased on quantum mechanical framework for the minimal length uncertainty, we demonstrate that the generalized uncertainty principle (GUP) parameter could be best constrained by recent gravitational waves observations on one hand. On the other hand, this suggests modified dispersion relations (MDRs) enabling an estimation for the difference between the group velocity of gravitons and that of photons. Utilizing features of the UV/IR correspondence and the obvious similarities between GUP (including non‐gravitating and gravitating impacts on Heisenberg uncertainty principle) and the discrepancy between the theoretical and the observed cosmological constant (apparently manifesting gravitational influences on the vacuum energy density), we suggest a possible solution for the cosmological constant problem.

Effect of Member Length Uncertainty and Backlash on Deformation Accuracy for a High-Precision Space Truss Structure

Effect of Member Length Uncertainty and Backlash on Deformation Accuracy for a High-Precision Space Truss Structure

Self-Limiting Polymerization of DNA Origami Subunits with Strain Accumulation.

Biology demonstrates how a near infinite array of complex systems and structures at many scales can originate from the self-assembly of component parts on the nanoscale. But to fully exploit the benefits of self-assembly for nanotechnology, a crucial challenge remains: How do we rationally encode well-defined global architectures in subunits that are much smaller than their assemblies? Strain accumulation via geometric frustration is one mechanism that has been used to explain the self-assembly of global architectures in diverse and complex systems a posteriori. Here we take the next step and use strain accumulation as a rational design principle to control the length distributions of self-assembling polymers. We use the DNA origami method to design and synthesize a molecular subunit known as the PolyBrick, which perturbs its shape in response to local interactions via flexible allosteric blocking domains. These perturbations accumulate at the ends of polymers during growth, until the deformation becomes incompatible with further extension. We demonstrate that the key thermodynamic factors for controlling length distributions are the intersubunit binding free energy and the fundamental strain free energy, both which can be rationally encoded in a PolyBrick subunit. While passive polymerization yields geometrical distributions, which have the highest statistical length uncertainty for a given mean, the PolyBrick yields polymers that approach Gaussian length distributions whose variance is entirely determined by the strain free energy. We also show how strain accumulation can in principle yield length distributions that become tighter with increasing subunit affinity and approach distributions with uniform polymer lengths. Finally, coarse-grained molecular dynamics and Monte Carlo simulations delineate and quantify the dominant forces influencing strain accumulation in a molecular system. This study constitutes a fundamental investigation of the use of strain accumulation as a rational design principle in molecular self-assembly.

Accurately Mapping Image Charge and Calibrating Ion Velocity in Charge Detection Mass Spectrometry.

Image charge detection is the foundation of charge detection mass spectrometry (CDMS). The mass-to-charge ratio, m/z, of a highly charged ion or particle is determined by measuring the particle's charge and velocity. Charge is typically determined from a calibrated image charge signal, and the particle velocity is calculated using the peaks from the shaped signal as they relate to the particle position and time-of-flight through a detector of known length. Although much has been done to improve the charge accuracy in CDMS, little has been done to address the inconsistencies in the particle velocity measurements and the interpretation of peak position and effective electrode length. In this work, we combine SIMION ion trajectory software and the Shockley-Ramo theorem to accurately determine the effective electrode length, peak position, and shape of the signal peaks. Six model charge detector geometries were examined with this method and evaluated in laboratory experiments. Experimental results in all cases agreed with the simulations. Using a charge detector with multiple, 12.7 mm-long cylindrical electrodes, experimental velocities across and between electrodes agreed within 0.25% relative standard deviation (RSD) when this method was used to correct for effective electrode lengths, corresponding to an uncertainty in the effective electrode length of only 40 μm. For a detector with multiple electrodes and varied electrode spacing, experiments showed that the peak amplitude and shape vary with the geometry and with the particle path through the detector, whereas all peak areas agreed to within 2.3% RSD. For a charge detector made of two printed circuit boards, the velocities agreed within 0.44% RSD using the calculated effective electrode length.

Understanding Mass Resolution of Foil‐Based Time‐of‐Flight Mass Spectrometry

AbstractThe fractional mass uncertainty of linear, foil‐based time‐of‐flight space instruments is affected by the energy, path length, and timing uncertainties. Carbon foils are typically used in time‐of‐flight instruments to generate secondary electrons, but carbon foils also add unwanted effects to the instrument response. We present a complete characterization that studies the extent to which carbon foils degrade the mass resolution by parameterizing each component of the fractional mass uncertainty. Using the parametrization, the limiting factors of the fractional mass resolution are determined for a range of incident ion energies. The parametrization can be used as a tool for instrument developers to quickly assess the mass resolution and possibly mitigate the limiting factors of the mass resolution.

Generalised Uncertainty Relations for Angular Momentum and Spin in Quantum Geometry

We derive generalised uncertainty relations (GURs) for orbital angular momentum and spin in the recently proposed smeared-space model of quantum geometry. The model implements a minimum length and a minimum linear momentum and recovers both the generalised uncertainty principle (GUP) and extended uncertainty principle (EUP), previously proposed in the quantum gravity literature, within a single formalism. In this paper, we investigate the consequences of these results for particles with extrinsic and intrinsic angular momentum and obtain generalisations of the canonical so ( 3 ) and su ( 2 ) algebras. We find that, although SO ( 3 ) symmetry is preserved on three-dimensional slices of an enlarged phase space, corresponding to a superposition of background geometries, individual subcomponents of the generalised generators obey nontrivial subalgebras. These give rise to GURs for orbital angular momentum while leaving the canonical commutation relations intact except for a simple rescaling, ħ → ħ + β . The value of the new parameter, β ≃ ħ × 10 − 61 , is determined by the ratio of the dark energy density to the Planck density, and its existence is required by the presence of both minimum length and momentum uncertainties. Here, we assume the former to be of the order of the Planck length and the latter to be of the order of the de Sitter momentum ∼ ħ Λ , where Λ is the cosmological constant, which is consistent with the existence of a finite cosmological horizon. In the smeared-space model, ħ and β are interpreted as the quantisation scales for matter and geometry, respectively, and a quantum state vector is associated with the spatial background. We show that this also gives rise to a rescaled Lie algebra for generalised spin operators, together with associated subalgebras that are analogous to those for orbital angular momentum. Remarkably, consistency of the algebraic structure requires the quantum state associated with a flat background to be fermionic, with spin eigenvalues ± β / 2 . Finally, the modified spin algebra leads to GURs for spin measurements. The potential implications of these results for cosmology and high-energy physics, and for the description of spin and angular momentum in relativistic theories of quantum gravity, including dark energy, are briefly discussed.

Forensic PSHA: Benchmarking Canada’s Fifth Generation seismic hazard model using the OpenQuake-engine

This article explores the implementation of the Natural Resources Canada’s Fifth Generation national seismic hazard model as developed for the National Building Code of Canada (NBCC), within the OpenQuake-engine. It also describes the reconciliation of the differences in hazard estimates relative to the published NBCC values, calculated using GSCFRISK. Source and ground-motion input models developed for the GSCFRISK software were translated to the OpenQuake-engine format for the hazard comparison. In order to successfully undertake this process, several adjustments to the OpenQuake code were needed to mimic the behavior of GSCFRISK. This required the development of new functions for earthquake-rupture scaling and ground-motion interpolation. Hazard values estimated using the OpenQuake-engine are generally in good agreement with the 2015 NBCC national-scale hazard values, with differences less than 2%–3% typically achieved. Where larger differences arise, they can be rationalized in terms of differences between the behaviors of the two software engines with respect to earthquake-rupture length uncertainty and maximum ground-motion integration distance.

High-efficiency sub-microscale uncertainty measurement method using pattern recognition

This study presents a fast precision measurement method that uses pattern recognition. First, a specific micro-structured surface was designed and manufactured, providing a unique pattern for recognition and matching. Second, a measurement system was proposed based on the algorithms of circle Hough transform (CHT), neural classifier (NC), template matching (TM) and sub-pixel interpolation (SI). Then, a series of experiments were carried out from three aspects: circle detection, length uncertainty, and measurement speed and range. The results showed the correct circle classification percentage was more than 96% and the CHT search accuracy was within a two-pixel level. The length uncertainty test demonstrated the method was able to achieve 90-nm length uncertainty, and a comparison of measurement speeds showed it helped to speed up measurements by a factor of 1000 compared to the original one.

Robust load transport by an overhead crane with respect to cable length uncertainties

We exploit a Fourier method to inverse engineer fast load transport protocols for an overhead crane, which is robust with respect to the deviation of cable length, corresponding to an ideal value. In the small oscillations regime, the protocols guarantee final adiabatic energies, i.e. null excitation with respect to the initial energy, regardless of the initial conditions. We demonstrate with calculations for the exact dynamics the stability of this result.

A first realization of ASTM E3125-17 test procedures for laser scanner performance evaluation

Spherical coordinate three-dimensional (3D) imaging systems, such as Terrestrial Laser Scanners (TLS), are already used widely in different fields. Their measurement performance evaluation is a topic of active research. In 2017, the first comprehensive documentary standard describing performance evaluation methods and procedures for TLS systems, the ASTM E3125-17, was released. In this paper, we report on the first realization of the test procedures per that standard. We briefly discuss the test procedures and then describe the materials and methods used to realize the tests. We then discuss the test measurands (the quantities of interest in the testing procedure), present the test values (the measured values of the test measurands), and the test value uncertainties (uncertainties in the testing process, which is typically the uncertainty in the reference length). The work described in this paper will serve as a useful reference for understanding and implementing the ASTM E3125-17 standard.

Effective hydraulic conductivity of discrete fracture network with aperture-length correlation

Determining effective hydraulic conductivity is critical to understand groundwater flow behavior in fractured rock masses and is required for large-scale numerical simulations. A new approach is developed to estimate the effective hydraulic conductivity of a discrete fracture network with aperture and trace length being stochastic and correlated. The aperture and length are assumed to follow a joint lognormal distribution. The average flowrate through the network is determined by integrating flowrate in the fracture ensemble with the laminar flow and non-linear flow being separately considered based on the Reynolds number. The effective hydraulic conductivity of the discrete fracture network is then determined from the idea that Darcy’s law still applies to the overall flow behavior through the network. For comparison, the simple average hydraulic conductivity is also developed based on the assumption that flow in all fractures is laminar and aperture and trace length are uncorrelated. Based on the developed approach, the effects of aperture and trace length uncertainty, their correlation degree, and non-linear flow characteristics on the ratio of effective hydraulic conductivity over simple average hydraulic conductivity are examined. The results demonstrate that the effective hydraulic conductivity can be either larger than or smaller than the simple average hydraulic conductivity depending on correlation level between aperture and trace length and the degree of non-linear effect in the network. Non-linear flow reduces the effective hydraulic conductivity of the fracture network. Correlation between aperture and trace length increases the effective hydraulic conductivity. Aperture uncertainty tends to reduce the effective hydraulic conductivity.

Thermodynamics of the Schwarzschild and Reissner\u2013Nordstr\xf6m black holes under the Snyder\u2013de Sitter model

This paper examines the effects of a new form of the extended generalized uncertainty principle in the Snyder–de Sitter model on the thermodynamics of the Schwarzschild and Reissner–Nordström black holes. Firstly, we present a generalization of the minimal length uncertainty relation with two deformation parameters. Then we obtain the corrected mass–temperature relation, entropy and heat capacity for Schwarzschild black hole. Also we investigate the effect of the corrected uncertainty principle on the thermodynamics of the charged black holes. Our discussion of the corrected entropy involves a heuristic analysis of a particle which is absorbed by the black hole. Finally, we compare the thermodynamics of a charged black hole with the thermodynamics of a Schwarzschild black hole and with the usual forms, that is, without corrections to the uncertainty principle.

Thermal relativity, modified Hawking radiation, and the generalized uncertainty principle

After a brief review of the thermal relativistic corrections to the Schwarzschild black hole entropy, it is shown how the Stefan–Boltzman law furnishes large modifications to the evaporation times of Planck-size mini-black holes, and which might furnish important clues to the nature of dark matter and dark energy since one of the novel consequences of thermal relativity is that black holes do not completely evaporate but leave a Planck size remnant. Equating the expression for the modified entropy (due to thermal relativity corrections) with Wald’s entropy should, in principle, determine the functional form of the modified gravitational Lagrangian [Formula: see text]. We proceed to derive the generalized uncertainty relation which corresponds to the effective temperature [Formula: see text] associated with thermal relativity and given in terms of the Hawking ([Formula: see text]) and Planck ([Formula: see text]) temperature, respectively. Such modified uncertainty relation agrees with the one provided by string theory up to first order in the expansion in powers of [Formula: see text]. Both lead to a minimal length (Planck size) uncertainty. Finally, an explicit analytical expression is found for the modifications to the purely thermal spectrum of Hawking radiation which could cast some light into the resolution of the black hole information paradox.

Potential algebra approach to quantum mechanics with generalized uncertainty principle

In this note, we study the potential algebra for several models arising out of quantum mechanics with generalized uncertainty principle. We first show that the eigenvalue equation corresponding to the momentum-space HamiltonianH=−(1+βp2)ddp(1+βp2)ddp+g(g−1)β2p2−gβ, which is associated with some one-dimensional models with minimal length uncertainty, can be solved by the unitary representations of the Lie algebra su(2) if g∈{12,1,32,2,⋯}. We then apply this result to spectral problems for the non-relativistic harmonic oscillator as well as the relativistic Dirac oscillator in the presence of a minimal length and show that these problems can be solved solely in terms of su(2).

Reference points for the length-based indicator Lmax5% for use in the assessment of data-limited stocks

Abstract In the absence of abundance indices from scientific surveys or commercial sources, reliable length frequency data from sampled commercial catches can be used to provide an indirect assessment of fishing mortality. Length-based indicators are simple metrics which describe length frequency distributions. The length-based indicator Lmax5%, the mean length of the largest 5% of individuals in the catch, combined with appropriately selected reference points, can be used to evaluate the presence of very large individuals in the catch and hence determine exploitation level. Using analytical per-recruit models, we derive reference points consistent with a spawning potential ratio of 40%. The reference points depend on the life history parameters for natural mortality, maturity, and growth (M, Lmat, L∞, k, CVL∞). Using available simulation tools, we investigate the sensitivity of the reference points to errors in these parameters and explore the usefulness of particular reference points for management purposes for stocks with different life histories. The proposed reference points are robust to uncertainty in length at first capture, Lc, and take into account the maturation schedule of a species. For those stocks with high M/k ratios (>1), Lmax5%, combined with the appropriate reference point, can be used to provide a data-limited stock assessment.

An IBBCEAS system for atmospheric measurements of glyoxal and methylglyoxal in the presence of high NO<sub>2</sub> concentrations

Abstract. A system based on incoherent broadband cavity-enhanced absorption spectroscopy (IBBCEAS) has been developed for simultaneous measurement of nitrogen dioxide (NO2), glyoxal (GLY), and methylglyoxal (MGLY). In this system, the measured light absorption at around 460 nm is spectrally resolved. The concentration of absorbers is determined from a multicomponent fit. At an integration time of 100 s, the measurement sensitivity (2σ) for NO2, GLY, and MGLY is 18, 30, and 100 ppt, respectively. The measurement uncertainty, which mainly originates from path length calibration, sampling loss, and uncertainty of absorption cross sections is estimated to be 8 % for NO2, 8 % for GLY, and 16 % for MGLY. When deploying the instrument during field observations, we found significant influence of NO2 on the spectra fitting for retrieving GLY and MGLY concentrations, which is caused by the fact that NO2 has a higher absorption cross section and higher ambient concentration. In order to minimize such an effect, a NO2 photolytic convertor (NPC), which removes sampled NO2 at an efficiency of 76 %, was integrated on the IBBCEAS system. Since sampled GLY and MGLY are mostly (≥95 %) conserved after passing through the NPC, the quality of the spectra fitting and the measurement accuracy of ambient GLY and MGLY under NO2-rich environments could be improved.

Single-world consistent interpretation of quantum mechanics from fundamental time and length uncertainties

Within ordinary ---unitary--- quantum mechanics there exist global protocols that allow to verify that no definite event ---an outcome to which a probability can be associated--- occurs. Instead, states that start in a coherent superposition over possible outcomes always remain as a superposition. We show that, when taking into account fundamental errors in measuring length and time intervals, that have been put forward as a consequence of a conjunction of quantum mechanical and general relativity arguments, there are instances in which such global protocols no longer allow to distinguish whether the state is in a superposition or not. All predictions become identical as if one of the outcomes occurs, with probability determined by the state. We use this as a criteria to define events, as put forward in the Montevideo Interpretation of Quantum Mechanics. We analyze in detail the occurrence of events in the paradigmatic case of a particle in a superposition of two different locations. We argue that our approach provides a consistent (C) single-world (S) picture of the universe, thus allowing an economical way out of the limitations imposed by a recent theorem by Frauchiger and Renner showing that having a self-consistent single-world description of the universe is incompatible with quantum theory. In fact, the main observation of this paper may be stated as follows: If quantum mechanics is extended to include gravitational effects to a QG theory, then QG, S, and C are satisfied.