Hyperbolic Curve Fit Research Articles

Millimeter accuracy depth estimation in concrete using smartphone-equipped handheld GPR and hyperbolic curve fitting with antenna distance consideration

In the management and maintenance of structural facilities, knowing the cover thickness of rebar and the depth of buried objects is of paramount importance. Currently, Smartphone-Equipped Handheld Ground Penetrating Radars (GPR) are primarily used for detecting rebar, yet the Electromagnetic Induction (EMI) method remains the sole available technique for determining the cover thickness of rebar. This necessitates the use of two separate devices to understand the subsurface condition of rebar. In this study, we introduce a new algorithm that utilizes Hyperbolic Curve Fitting to determine depth and relative permittivity from reflection images derived from a single GPR measurement, using metal depth estimation as an exemplar. Our contributions include the automatic detection of the hyperbola's centerline before curve fitting, separation of the hyperbola into left and right for enhanced fitting accuracy by removing points near the vertex, and incorporating a rigorous theoretical model that took into account the distance between the transmitting and receiving antennas, known as the inter-antenna distance. This algorithm had enabled us to meet the performance requirements for the EMI method as stipulated by the Japanese Society for Non-Destructive Inspection (JSNDI). Notably, our method retained its accuracy even at depths exceeding the 100 mm limitation of the EMI method.

Conserved mammalian muscle mechanics during eccentric contractions.

Skeletal muscle has a broad range of biomechanical functions, including power generation and energy absorption. These roles are underpinned by the force-velocity relationship, which comprises two distinct components: a concentric and an eccentric force-velocity relationship. The concentric component has been extensively studied across a wide range of muscles with different muscle properties. However, to date, little progress has been made in accurately characterising the eccentric force-velocity relationship in mammalian muscle with varying muscle properties. Consequently, mathematical models of this muscle behaviour are based on a poorly understood phenomenon. Here, we present a comprehensive assessment of the concentric force-velocity and eccentric force-velocity relationships of four mammalian muscles (soleus, extensor digitorum longus, diaphragm and digastric) with varying biomechanical functions, spanning three orders of magnitude in body mass (mouse, rat and rabbits). The force-velocity relationship was characterised using a hyperbolic-linear equation for the concentric component a hyperbolic equation for the eccentric component, at the same time as measuring the rate of force development in the two phases of force development in relation to eccentric lengthening velocity. We demonstrate that, despite differences in the curvature and plateau height of the eccentric force-velocity relationship, the rates of relative force development were consistent for the two phases of the force-time response during isovelocity lengthening ramps, in relation to lengthening velocity, in the four muscles studied. Our data support the hypothesis that this relationship depends on cross-bridge and titin activation. Hill-type musculoskeletal models of the eccentric force-velocity relationship for mammalian muscles should incorporate this biphasic force response. KEY POINTS: The capacity of skeletal muscle to generate mechanical work and absorb energy is underpinned by the force-velocity relationship. Despite identification of the lengthening (eccentric) force-velocity relationship over 80years ago, no comprehensive study has been undertaken to characterise this relationship in skeletal muscle. We show that the biphasic force response seen during active muscle lengthening is conserved over three orders of magnitude of mammalian skeletal muscle mass. Using mice with a small deletion in titin, we show that part of this biphasic force profile in response to muscle lengthening is reliant on normal titin activation. The rate of force development during muscle stretch may be a more reliable way to describe the forces experienced during eccentric muscle contractions compared to the traditional hyperbolic curve fitting, and functions as a novel predictor of force-velocity characteristics that may be used to better inform hill-type musculoskeletal models and assess pathophysiological remodelling.

Verification of Commercial Near-Infrared Spectroscopy Measurement and Fresh Weight Diversity Modeling in Brix% for Small Tomato Fruits with Various Cultivars and Growth Conditions

The use of non-destructive commercial near-infrared (NIR) spectroscopy to estimate Brix% was verified using all samples of cherry tomato ‘TY Chika’, currant tomato ‘Microbeads’, and the M&S or market-purchased and supplemental local source tomatoes. Additionally, the relationship between fresh weight and Brix% of all samples was examined. These tomatoes had a diversity of cultivars, growing methods, harvest timing, and production locations and varied widely from 4.0% to 14.2% for Brix% and 1.25 g to 95.84 g for fresh weight. Regardless of the diversity of all samples, it was revealed that the refractometer-based Brix% (y) was practically estimated from the NIR-derived Brix% value (x) using a relationship of y = x (RMSE = 0.747 Brix%) after only a one-time calibration for the NIR spectrometer offset. An inverse relationship between fresh weight and Brix% could be modeled using a hyperbolic curve fit, and the model showed an R2 of 0.809 except for ‘Microbeads’. The Brix% of ‘TY Chika’ was highest on average (9.5%) and had a large difference from 6.2 to 14.2% among the samples. Data distribution of cherry tomato groups such as ‘TY Chika’ and M&S cherry tomatoes was closer, indicating a roughly linear correlation between fresh weight and Brix%.

A Complement to Decline Curve Analysis

Summary Decline curve analysis (DCA) has been the mainstay in unconventional reservoir evaluation. Because of the extremely low matrix permeability, each well is evaluated economically for ultimate recovery as if it were its own reservoir. Classification and normalization of well potential is difficult because of ever-changing stimulation total contact area and a hyperbolic curve fit parameter that is disconnected from any traditional reservoir characterization descriptor. A new discrete fracture model approach allows direct modeling of inflow performance in terms of fracture geometry, drainage volume shape, and matrix permeability. Running such a model with variable geometrical input to match the data in lieu of standard regression techniques allows extraction of a meaningful parameter set for reservoir characterization, an expected outcome from all conventional well testing. Because the entirety of unconventional well operation is in transient mode, the discrete fractured well solution to the diffusivity equation is used to model temporal well performance. The analytical solution to the diffusivity equation for a line source or a 2D fracture operating under constrained bottomhole pressure consists of a sum of terms, each with exponential damping with time. Each of these terms has a relationship with the constant rate, semisteady-state solution for inflow, although the well is not operated with constant rate, nor will this flow regime ever be realized. The new model is compared with known literature models, and sensitivity analyses are presented for variable geometry to illustrate the depiction of different time regimes naturally falling out of the unified diffusivity equation solution for discrete fractures. We demonstrate that apparent hyperbolic character transitioning to exponential decline can be modeled directly with this new methodology without the need to define any crossover point. The mathematical solution to the physical problem captures the rate transient functionality and any and all transitions. Each exponential term in the model is related to the various possible interferences that may develop, each occurring at a different time, thus yielding geometrical information about the drainage pattern or development of fracture interference within the context of ultralow matrix permeability. Previous results analyzed by traditional DCA can be reinterpreted with this model to yield an alternate set of descriptors. The approach can be used to characterize the efficacy of evolving stimulation practices in terms of geometry within the same field and thus contribute to the current type curve analyses subject to binning. It enables the possibility of intermixing of vertical and horizontal well performance information as simply gathering systems of different geometry operating in the same reservoir. The new method will assist in reservoir characterization and evaluation of evolving stimulation technologies in the same field and allow classification of new type curves.

Hyperbolic models for a 2-D backfill and reinforcement pullout

ABSTRACT: A series of direct shear tests were performed using an idealised two-dimensional test medium consisting of rhombically stacked steel rods to facilitate displacement computations for reinforced slopes using a force-equilibrium-based finite-displacement method. A series of pullout tests using extensible and stiff reinforcement with various embedment lengths (Lt) were also performed. Modelling for the non-linear behaviour of shear stress–displacement and pullout force–displacement relationships was performed using hyperbolic models. In modelling shear stress–displacement relationships for the steel rod backfill, a linear Mohr–Coulomb failure envelope was assumed for the investigated range of confining pressures. It was found that model parameters for the initial shear stiffness, namely K and n, are significantly different from those for ordinary soils because of the regular and dense packing of the steel rods, but are advantageous as a backfill material for model tests because of its consistency and repeatability. Results of hyperbolic curve fitting for the pullout force–displacement relationship indicate that the model parameters describing non-linear and pressure-dependent behaviour of reinforcement pullout, namely Kt, m, and Rt, are functions of Lt. The modelled hyperbolic shear stress–displacement relationships and the pullout force–displacement relationships are in good agreement with the experimental ones and are applicable for simulating the behaviour of model slopes consisting of steel rod assemblies.

Analysis and modeling for fiber-optic gyroscope scale factor based on environment temperature

To explore and reduce the nonlinear error and temperature dependency of fiber-optic gyroscope (FOG) scale factor, a scale factor modeling method based on temperature is presented in this paper. A hyperbolic curve fitting is proposed according to the characteristic of scale factor under stable temperature at first. Compared to traditional modeling methods, it shows that a higher precision model of scale factor can be obtained. Then the influence of temperature on scale factor is analyzed and then the hyperbolic curve fitting method is extended based on temperature, making it possible to work over the whole potential temperature range of the FOG without degrading the performance. This paper also provides the experimental and verification results. It can be seen that a high precision model of scale factor has been established, the temperature dependency of scale factor has been reduced effectively, and the error due to environment temperature is reduced by one order at least.

New models for retrieving and partitioning the colored dissolved organic matter in the global ocean: Implications for remote sensing

Despite the importance of CDOM to upper ocean biogeochemical processes and optics, our current understanding of its spatial and temporal distributions and the factors controlling these distributions is very limited. This eventually prevents an understanding of its relationship to the pool of dissolved organic carbon in coastal and open oceans. This work aims to present a new approach for accurate modeling of absorption spectra of CDOM (a cdom) and deriving information on its composition in global ocean waters. The modeling approach uses measurements (in situ) of the remote sensing reflectances at two wavelengths (denoted 443 555 R rs ) to estimate a cdom(350) and a cdom(412), applies them to determine two spectral slopes of an exponential curve fit (S) and a hyperbolic curve fit ( γ), derives an appropriate parameter ( γ o) for grading the CDOM compositional changes from a cdom (350) and γ, and finally employs a cdom(350), S, and γ o in a modified exponential model to describe a cdom(λ) as a function of wavelength. The robustness of this model was rigorously tested on three independent datasets, such as NOMAD in situ data, NOMAD SeaWiFS match-ups data and IOCCG simulated data (all of them contain a cdom(λ) and R rs(λ)), which represent a variety of waters within coastal and offshore regions around the world. Accuracy of the retrievals found with the new models was generally excellent, with MRE (mean relative error) and RMSE (root mean square error) of − 5.64–3.55% and 0.203–0.318 for the NOMAD in situ datasets, and − 5.63 to −0.98% and 0.136–0.241 for the NOMAD satellite datasets respectively (for λ 412 to λ 670). When used with SeaWiFS images collected over the regional and global waters, the new model showed the highest surface abundances of CDOM within the subpolar gyres and continental shelves dominated by terrestrial inputs (and perhaps local production) of colored dissolved materials, and the lowest surface abundances of CDOM in the central subtropical gyres and the open oceans presumably regulated by photobleaching phenomenon, bacterial activity and local processes. Significant interseasonal and interannual seasonal changes in the terrestrially-derived CDOM distributions were noticed from these new products that closely corresponded with the global mean runoff/river discharge induced by climate change/warming scenarios.

Sulfoacetate Is Degraded via a Novel Pathway Involving Sulfoacetyl-CoA and Sulfoacetaldehyde in Cupriavidus necator H16

Bacterial degradation of sulfoacetate, a widespread natural product, proceeds via sulfoacetaldehyde and requires a considerable initial energy input. Whereas the fate of sulfoacetaldehyde in Cupriavidus necator (Ralstonia eutropha) H16 is known, the pathway from sulfoacetate to sulfoacetaldehyde is not. The genome sequence of the organism enabled us to hypothesize that the inducible pathway, which initiates sau (sulfoacetate utilization), involved a four-gene cluster (sauRSTU; H16_A2746 to H16_A2749). The sauR gene, divergently orientated to the other three genes, probably encodes the transcriptional regulator of the presumed sauSTU operon, which is subject to inducible transcription. SauU was tentatively identified as a transporter of the major facilitator superfamily, and SauT was deduced to be a sulfoacetate-CoA ligase. SauT was a labile protein, but it could be separated and shown to generate AMP and an unknown, labile CoA-derivative from sulfoacetate, CoA, and ATP. This unknown compound, analyzed by MALDI-TOF-MS, had a relative molecular mass of 889.7, which identified it as protonated sulfoacetyl-CoA (calculated 889.6). SauS was deduced to be sulfoacetaldehyde dehydrogenase (acylating). The enzyme was purified 175-fold to homogeneity and characterized. Peptide mass fingerprinting confirmed the sauS locus (H16_A2747). SauS converted sulfoacetyl-CoA and NADPH to sulfoacetaldehyde, CoA, and NADP(+), thus confirming the hypothesis.

Feedback of the Kinesin-1 Neck-linker Position on the Catalytic Site

Kinesin-1 motor proteins step along microtubules by a mechanism in which the heads cycle through microtubule-bound and unbound states in an interlaced fashion. An important contribution to head-head coordination arises from the action of the neck-linker that docks onto the core motor domain upon ATP binding. We show here that the docked neck-linker not only guides the microtubule-unbound head to the next microtubule binding site but also signals its position to the head to which it is attached. Cross-linking studies on mutated kinesin constructs reveal that residues at the interface motor core/docked neck-linker, among them most importantly a conserved tyrosine, are involved in this feedback. The primary effect of the docked neck-linker is a reduced microtubule binding affinity in the ADP state.

Mechanistic Insights into the Suppression of Drug Resistance by Human Immunodeficiency Virus Type 1 Reverse Transcriptase Using α-Boranophosphate Nucleoside Analogs

A class of amino acid substitutions in drug-resistant HIV-1 reverse transcriptase (RT) is responsible for the selectively impaired incorporation of the nucleotide analog inhibitor into DNA. We have shown previously that alpha-boranophosphate nucleoside analogs suppress RT-mediated resistance when the catalytic rate is responsible for drug resistance such as in the case of K65R and dideoxy (dd)NTPs, and Q151M toward AZTTP and ddNTPs. Here, we extend this property to BH3-d4TTP and BH3-3TCTP toward their clinically relevant mutants Q151M and M184V, respectively. Pre-steady-state kinetics on mutants of the Q151M RT family reveal a 3-5-fold resistance to d4TTP. This resistance is suppressed using BH3-d4TTP. Likewise, resistance to 3TCTP by M184V RT (30-fold) and K65R/M184V RT (180-fold) is suppressed using BH3-3TCTP because of a 160-fold acceleration of the catalytic constant kpol. Mechanistic insights into the rate enhancement were obtained using various alpha-boranophosphate nucleotides. The presence of the BH3 group renders kpol independent of amino acid substitutions present in RT. Indeed, the approximately 100-fold decrease in polymerase activity caused by the R72A substitution is restored to wild-type levels using BH3-dTTP. Metal ion titration studies show that alpha-boranophosphate nucleoside analogs enhance 3-8-fold the binding of Mg2+ ions to the active site of the RT.DNA.dNTP complex and alleviate the requirement of critical amino acids involved in phosphodiester bond formation. To our knowledge, this is the first example of rescue of polymerase activity by means of a nucleotide analog.

Selective modifiers of glutathione biosynthesis and 'repriming' of vascular smooth muscle photorelaxation.

Photorelaxation of vascular smooth muscle (VSM) is caused by the release of nitric oxide (NO) from a finite molecular store that can be depleted by irradiating pre-contracted arteries with visible light. The ability of an 'exhausted' vessel to respond to a further period of illumination is lost temporarily but then recovers slowly as the photosensitive store is reconstituted in the dark. The recovery process, termed repriming, displays an absolute requirement for endothelium-derived NO and is inhibited by pre-treating arteries with ethacrynic acid, a thiol-alkylating agent. Here we demonstrate that agents that up- or down-regulate glutathione (GSH) biosynthesis influence the extent to which the store is regenerated in the dark. Isolated rat tail arteries (RTAs) were perfused internally with Krebs solution containing phenylephrine (PE; mean [PE] +/- s.e.mean: 5. 78+/-0.46 microM) and periodically exposed to laser light (lambda=514.5 nm, 6.3 mW cm(-2) for 6 min). Photorelaxations of control RTAs were compared with those from either (a) vessels taken from animals previously injected i.p. with buthionine sulphoximine (BSO), an inhibitor of gamma-glutamylcysteine synthetase (three injections, 100 mg kg(-1) at 8 h intervals); or (b) isolated RTAs that were perfused ex vivo with oxothiazolidine (OXO), a precursor of cysteine (10(-4) M OXO for 60 min). RTAs from BSO-treated animals exhibited attenuated photorelaxations: the mean (+/-s.e.mean) amplitude of the response recorded after 72 min recovery in the dark was 12.4+/-1.6% versus 21.4+/-2.9% for control arteries (n=5; P<0. 01). Conversely RTAs treated with OXO and allowed to recover for a similar period showed enhanced photorelaxations, 32.6+/-6.3% as compared to 21.4+/-2.9% for control arteries (n=5; P<0.01). A hyperbolic curve fit to repriming curves for BSO-treated and control arteries returned asymptote values (maximum photorelaxations) of (mean +/- s.e.mean) 24.2+/-3.2% and 55.2+/-8.5%, respectively. The level of GSH in RTA extracts was measured by high-pressure liquid chromatography (HPLC). Injecting animals with BSO decreased GSH to 85% of control levels (P<0.05) while treatment of isolated vessels with OXO resulted in a 31% increase above control levels (P<0.05). Thus, drug-induced changes in RTA GSH levels were positively correlated with altered photorelaxations. The results lead us to postulate that the photosensitive store in VSM is generated, at least in part, from intracellular GSH which becomes converted to S-nitrosoglutathione (GSNO) by nitrosating species that are formed ultimately from endothelium-derived NO. The possible physiological significance of a photolabile store of NO in VSM is discussed briefly.

Target detection for low ambient backgrounds

A prediction of human visual target detection performance is important for many military and civilian applications. A previous paper by the authors in this journal develops an extensive numerical hyperbolic curve fitting routine for the Blackwell-McCready (BM) laboratory contrast threshold data set. The BM data set is extended to real world scenes by developing a new operational definition of ambient luminance. The pro- cess involves an empirically derived formula for computing the diurnal ambient luminance as a function of solar position, time of day and ob- server location on the earth. An analytical methodology predicts prob- ability of detection Pd for various target areas, contrast levels and back- ground ambient luminance. A subsequent analysis shows that Pd is a very sensitive function of target parameters during the twilight region before dawn and after dusk. Several numerical examples illustrate the utility of this formalism to various target detection applications involving aided and unaided optics. © 1998 Society of Photo-Optical Instrumentation Engi- neers. (S0091-3286(98)01607-9)

Regulation of early gestational corpus luteum function in spontaneous and follicular stimulated conceptions

To determine the regulatory role of hCG on P secretion in normal and abnormal (abortive and ectopic) first trimester pregnancies. The number of doublings of hCG per day (1/DT; reciprocal of hCG doubling time) was correlated with serum P using linear and nonlinear models in normal intrauterine pregnancies, spontaneous abortions, and ectopic pregnancies (EPs) conceived spontaneously or after clomiphene citrate (CC). Linear correlations between P and 1/DTs of hCG were poor. In contrast, nonlinear modeling with a hyperbolic curve fit the data well and allowed all of the data to be included for analysis regardless of the pregnancy type. Furthermore, this model could be used to explain the differential P concentrations seen in normal and abnormal first trimester pregnancies. The nonlinear hyperbolic model demonstrated that follicular events determine the maximal P production during early gestation. Human chorionic gonadotropin 1/DTs approximately equal to 0.5 sustain maximal P production. Progesterone production is then sustained by the rate of change of hCG. Nonlinear correlation analysis suggests that P production in early gestations is regulated by prior follicular events and the rate of hCG production.

Computer-Automated Linac Diagnostics and Data Acquisition

Computer interactive diagnostics have been developed and tested for measuring RF Linac electron beam position and emittance. Electron beam position is measured with ferrite-loaded stripline monitors. The measured signals are processed by an APPLE-II computer, displayed and updated (at the Linac repetition rate) on a monitor. Data to determine emittance is collected by measuring electron beam spot size (using the wire scanner technique) as the focal strength of a quadrupole triplet is adjusted around the focus at the scanner. The emittance is calculated by the APPLE-II making a hyperbolic curve fit to these data.