Points Of Curve Research Articles

Learning curve analysis of single-port thoracoscopic combined subsegmental resections.

Combined subsegmental surgery (CSS) is considered to be a safe and effective resection modality for early-stage lung cancer. However, there is a lack of a clear definition of the technical difficulty classification of this surgical case, as well as a lack of reported analyzes of the learning curve of this technically demanding surgical approach. We performed a retrospective study of single-port thoracoscopic CSS performed by the same surgeon between April 2016 and September 2019. The combined subsegmental resections were divided into simple and complex groups according to the difference in the number of arteries or bronchi which need to be dissected. The operative time, bleeding and complications were analyzed in both groups. Learning curves were obtained using the cumulative sum (CUSUM) method and divided into different phases to assess changes in the surgical characteristics of the entire case cohort at each phase. The study included 149 cases, including 79 in the simple group and 70 in the complex group. The median operative time in the two groups was 179min (IQR, 159-209) and 235min (IQR, 219-247) p < 0.001, respectively. And the median postoperative drainage was 435 mL (IQR, 279-573) and 476 mL (IQR, 330-750), respectively, with significant differences in postoperative extubation time and postoperative length of stay. According to the CUSUM analysis, the learning curve for the simple group was divided by the inflection point into 3 phases: Phase I, learning phase (1st to 13th operation); Phase II, consolidation phase (14th to 27th operation), and Phase III, experience phase (28th to 79th operation), with differences in operative time, intraoperative bleeding, and length of hospital stay in each phase. The curve inflection points of the learning curve for the complex group were located in the 17th and 44th cases, with significant differences in operative time and postoperative drainage between the stages. The technical difficulties of the simple group of single-port thoracoscopic CSS could be overcome after 27 cases, while the technical ability of the complex group of CSS to ensure feasible perioperative outcomes was achieved after 44 operations.

Nonlinear Vibrations of Carbon Nanotubes with Thermal-Electro-Mechanical Coupling

Carbon nanotubes (CNTs) have wide-ranging applications due to their excellent mechanical and electrical properties. However, there is little research on the nonlinear mechanical properties of thermal-electro-mechanical coupling. In this paper, we study the nonlinear vibrations of CNTs by a thermal-electro-mechanical coupling beam theory. The Galerkin method is used to discretize the partial differential equation and obtain two nonlinear ordinary differential equations that describe the first- and second-order mode vibrations. Then, we obtain the approximate analytical solutions of the two equations for the primary resonance and the subharmonic resonance using the multi-scale method. The results indicate the following three points. Firstly, the temperature and electric fields have a significant influence on the first-mode vibration, while they have little influence on the second-mode vibration. Under the primary resonance, when the load amplitude of the second mode is 20 times that of the first mode, the maximal vibrational amplitude of the second is only one-fifth of the first. Under the subharmonic resonance, it is more difficult to excite the subharmonic vibration at the second-order mode than that of the first mode for the same parameters. Secondly, because the coefficient of electrical expansion (CEE) is much bigger than the coefficient of thermal expansion (CTE), CNTs are more sensitive to changes in the electric field than the temperature field. Finally, under the primary resonance, there are two bifurcation points in the frequency response curves and the load-amplitude curves. As a result, they will induce the jump phenomenon of vibrational amplitude. When the subharmonic vibration is excited, the free vibration term does not disappear, and the steady-state vibration includes two compositions.

Dynamical stability from quasi normal modes in 2nd, 1st and 0th order holographic superfluid phase transitions

We study a simple extension of the original Hartnoll, Herzog and Horowitz (HHH) holographic superfluid model with two nonlinear scalar self-interaction terms λ|ψ|4 and τ|ψ|6 in the probe limit. Depending on the value of λ and τ, this setup allows us to realize a large spectrum of holographic phase transitions which are 2nd, 1st and 0th order as well as the “cave of wind” phase transition. We speculate the landscape pictures and explore the near equilibrium dynamics of the lowest quasinormal modes (QNMs) across the whole phase diagram at both zero and finite wave-vector. We find that the zero wave-vector results of QNMs correctly present the stability of the system under homogeneous perturbations and perfectly agree with the landscape analysis of homogeneous configurations in canonical ensemble. The zero wave-vector results also show that a 0th order phase transition cannot occur since it always corresponds to a global instability of the whole system. The finite wave-vector results show that under inhomogeneous perturbations, the unstable region is larger than that under only homogeneous perturbations, and the new boundary of instability match with the turning point of condensate curve in grand canonical ensemble, indicating a new explanation from the subsystem point of view. The additional unstable section also perfectly match the section with negative value of charge susceptibility.

Smooth magnetotelluric impedance estimation by optimization

In urban and industrialised areas, magnetotelluric (MT) recordings often contain a significant amount of high-power near-field noise which, constituting non-Gaussian noise for most of the recording length, may lead to the failure of the common transfer functions (TF) estimation methods. The most evident consequence of this is the appearance of sharp points in the TF curves versus frequency, deteriorating their inherent smoothness. The TF's smoothness is in fact one of the main criteria adopted by MT practitioners to evaluate the data quality and effectiveness of the estimation procedure; when not reached by the estimation, it may be a-posteriori introduced by splines or filtering procedures, but these approaches lack physical soundness. We propose a new heuristic algorithm aimed at obtaining the maximum TF versus frequency smoothness, through an optimization scheme rejecting EM events in frequency-domain. The algorithm searches for frequency-dependent power thresholds to be applied to the events, rejecting those making the TF sharp. The TF's smoothness is the objective function to be minimized, and the model space is constituted by the infinite set of threshold vectors for each analysed frequency. After the process, the Ordinaly Least Squares (OLS) residual distribution is much closer to a Rayleigh one, allowing for an unbiased estimation. We applied the procedure both to synthetic and real MT data. Measured data has been collected for a geothermal exploration project in the East Africa Rift, where strong coherent noise affected the recordings. The combination of the technique with the remote-reference technique effectively reduced the bias due to the artificial signal. The physical consistency of the resulting TF has been tested by dispersion relationships.

Tipping point in North American Arctic-Boreal carbon sink persists in new generation Earth system models despite reduced uncertainty

Estimating the impacts of climate change on the global carbon cycle relies on projections from Earth system models (ESMs). While ESMs currently project large warming in the high northern latitudes, the magnitude and sign of the future carbon balance of Arctic-Boreal ecosystems are highly uncertain. The new generation of increased complexity ESMs in the Intergovernmental Panel on Climate Change Sixth Assessment Report (IPCC AR6) is intended to improve future climate projections. Here, we benchmark the Coupled Model Intercomparison Project (CMIP) 5 and 6 (8 CMIP5 members and 12 CMIP6 members) with the International Land Model Benchmarking (ILAMB) tool over the region of NASA’s Arctic-Boreal vulnerability experiment (ABoVE) in North America. We show that the projected average net biome production (NBP) in 2100 from CMIP6 is higher than that from CMIP5 in the ABoVE domain, despite the model spread being slightly narrower. Overall, CMIP6 shows better agreement with contemporary observed carbon cycle variables (photosynthesis, respiration, biomass) than CMIP5, except for soil carbon and turnover time. Although both CMIP ensemble members project the ABoVE domain will remain a carbon sink by the end of the 21st century, the sink strength in CMIP6 increases with CO2 emissions. CMIP5 and CMIP6 ensembles indicate a tipping point defined here as a negative inflection point in the NBP curve by 2050–2080 independently of the shared socioeconomic pathway (SSP) for CMIP6 or representative concentration pathway (RCP) for CMIP5. The model ensembles therefore suggest that, if the carbon sink strength keeps declining throughout the 21st century, the Arctic-Boreal ecosystems in North America may become a carbon source over the next century.

Research on fatigue crack quantitative monitoring based on eddy current sensor with an interactive induction coil layout

To reduce the number of sensor channels, this paper proposes an eddy current sensor with an interactive induction coil layout. First, the crack monitoring principle of the sensor is analyzed, and fatigue crack monitoring experiment is carried out. It is found that the cracks can be quantified according to the characteristic points of the sensitivity variation curve. Then, a permalloy plate is used for reinforcing the sensor, and the crack monitoring accuracy test is carried out, which shows that the crack monitoring accuracy error of the sensor is no more than 0.1 mm. Finally, the sensor network is built by the sensor according to the dangerous parts of the butt joint structure determined by the finite element analysis. And fatigue crack monitoring experiment is carried out, which shows that the sensor network can determine the position and length of the fatigue crack, and the error is no more than 0.1 mm.

Effects of thermal boundary conditions on the performance of spray dryers

In this paper, three kinds of wall conditions are numerically simulated to investigate deposition, powder recovery and energy aspects of spray dryers. A co-current dryer with a pressure nozzle is chosen as a base dryer and two dryers with fully insulated, and cooled walls are compared with the base one. Governing equations of a transient flow field are solved through the Eulerian approach, while Lagrangian particle tracking predicts particles’ motion. The sticky point curve is employed as a criterion of bouncing or stickiness to model the deposition pattern of skim milk particles on the surfaces. Results show that the spray dryer with cooled walls has better deposition characteristics, while the dryer with insulated surfaces works with higher drying efficiency. Overall, it is observed that the wall conditions can be changed to improve the drying efficiency and wall deposition. However, changing the thermal boundary conditions does not seem to be effective in improving the powder recovery. • The performance of dryers was investigated in three different dryers. • The sticky point curve was considered on the walls. • Maximum powder recovery obtained in the base dryer. • Significant deposition reduction observed in the cooled-walls dryer.

Analytical solutions of the magnetic and stress fields on a soft ferromagnetic material containing a smooth rigid inclusion in two-dimensional space

The analytical investigations on a rigid inclusion embedded in a soft ferromagnetic material in two-dimensional space subjected to uniform magnetic load at infinity have been carried out, with the magnetic insulation boundary of the rigid inclusion. In our study, explicit solutions of the magnetic and stress fields are obtained based on linear magnetoelastic theory and complex variable theory. The relative rigid-body displacement of the rigid inclusion is considered to ensure the boundary condition and constraint satisfied accurately. It is found that the analytic solutions of Kolosov-Muskhelishvili (K-M) potentials have a compact form when the shape of rigid inclusion is characterized by Laurent polynomial with finite terms. As examples, the rigid-body displacement, magnetic flux and stress on the boundary of elliptic and polygonal rigid inclusions are analyzed, respectively. Our results show that the rigid-body displacement caused by a non-strong magnetic load is small, while the orientation and contour curvature of the rigid inclusions have significant effects on the distribution of the stress and magnetic flux fields. In addition, the maximum magnetic flux and maximum stress do not always occur at the maximum curvature point. For polygonal rigid inclusions, the orientations in which the extreme concentration is obtained are closely related to the number of tips of the inclusions.

Insight into the critical morphological characteristics of earthquake-induced sequential rock avalanches in weathered-fractured rock cliffs

Rock avalanches are a significant threat to transportation or hydraulic infrastructure, as they can also cause catastrophic secondary destruction in large practical engineering or to nearby residents. Earthquake-induced rock avalanches have been the most common and prominent natural hazard phenomena among geological hazards in recent years. Earthquake-induced rock avalanche events usually begin when a massive rock mass or multiple rock masses separate from a rock slope, progressively fragmenting and transforming into fast-moving, cohesionless rock falls. Earthquake-induced sequential collapse often occurs on weathered and fractured rock cliffs in horizontal strata, and its kinematic dynamics and destabilization mechanism are significantly different from those of isolated collapse due to weathering. In this study, the failure characteristics of the initiation and movement process of the avalanche are revealed in detail, through physical model experiments and analytical solutions, thereby obtaining an earthquake-controlled mechanical model equation. Our methods use the inflection points of the displacement time curve at the top of the rock wall and the digital images acquired by the shaking test bench to quantify the critical damage time point and to characterize the critical morphology of continuous collapse. A mathematical model of analytical solution is proposed, which aims to address the kinematic mechanics mechanism of sequential collapse under translational and rotational motion models. The comparative analysis results of the experiment and analytical solutions reveal that the transformed motion pattern is controlled by the ratio between the model stacking height, the rock block size, and the seismic acceleration. Whereas the rotational motion pattern is mainly influenced by the nodal dip angle, model stacking height, and seismic acceleration. The results of the study are of great scientific importance to elucidate the destruction mechanism of the earthquake-induced sequential collapse of rock avalanches and to determine the evolution characteristic of subsequent rockfalls motion of dangerous rocks. The proposed framework for the analysis of rock avalanches can be applied to understand the critical topographic features and mechanical mechanism behavior of analogous geological hazards.

Analysis of Shear Stagger Deformation of Existing Shield Tunnel below Induced by Quasirectangular Shield Tunneling

To use urban underground space more efficiently is a research hotspot of urban underground development. Compared with conventional circular tunnels, quasirectangular tunnels have the characteristics of larger space utilization and higher economic benefits, gradually used in urban rail engineering in recent years. But the ground disturbance induced by the quasirectangular tunneling needs further researches. This paper derives the calculation formula of the additional stress of existing shield tunnel below caused by the quasirectangular shield tunneling by mirror image method and Mindlin solution. The existing shield tunnel is simplified as an elastic foundation short beam connected by tensile springs and shear springs. This paper establishes the energy-deformation coupling equation by principle of minimum potential energy so that the disturbance induced by quasirectangular tunneling to the existing shield tunnel below can be analyzed. The FEM is established with the actual engineering as the background. It is by comparing the numerical simulation results and field monitoring data that the theoretical prediction formula is verified. The research results show that the theoretical calculation results consist highly with numerical simulation results and field monitoring data, verifying practicality of formulas in this paper. Calculation results of shear stagger model are more accurate, which can be also used to analyze the staggered and splayed amount between segments. As the tunnel construction proceeds, uplift deformation, segment stagger, shear force, and segment splay of existing shield tunnel gradually increase, which are symmetrical about the central axis of new tunnel. After the shield machine passes through the central axis of the existing shield tunnel for 20 meters, stable disturbance to the existing shield tunnel occurs. Stagger amount and shear force between segments reach the minimum at the position with maximum uplift deformation of existing shield tunnel and reach the maximum at inflection point of the uplift deformation curve.

Thermodynamic insights into phase behavior a new aqueous two-phase system at different temperatures: Experimental equilibria, data correlation and modeling

In the current research, a novel aqueous ternary-two-phase system (ATPS) containing a deep eutectic solvent (DES formed by mixing choline chloride with polyethylene glycol 400) and the non-ionic surfactant Triton X-100 was designed. The phase behavior of this system including phase diagrams (binodal curves) and tie-line compositions was thermodynamically investigated at the temperature range of 298.15 to 316.15 K under atmospheric pressure. This system presented a DES-rich top phase and a surfactant-rich bottom phase. The plait point of binodal diagrams together with the tie-lines length (TLL) and the slope of tie-lines (STL) were determined at each of the operational temperatures. The influence of temperature on the binodal curves and the tie-lines was analyzed from which it was found that an increase in the temperature expands the two-phase region in the binodal curve as well as increases the length of the tie-lines. Moreover, the binodal curves data and the tie-line compositions were successfully correlated using a series of semi-empirical models with satisfactory results. Finally, the molar Gibbs energy, molar enthalpy and molar entropy of the cloud points of binodal curve were calculated and the results showed that the formation of the two-phase system is spontaneous and endothermic as well as the entropy is its driving force.

Experimental Analysis of Hysteresis in the Motion of a Two-Input Piezoelectric Bimorph Actuator

This article presents a comparison of hysteresis courses in the motion of a two-input actuator (bimorph) and hysteresis in the motion of a single-input actuator (unimorph). The comparison was based on the results of laboratory and numerical experiments, the subject of which was an actuator built of three layers: a carrier layer from a glass-reinforced epoxy laminate and two piezoelectric layers from Macro Fiber Composite. The layers were glued together, and electrodes in the Macro Fiber Composite layers were connected to a system that included an analogue/digital board and a voltage amplifier. The main purpose of this research was to compare the characteristic points of the hysteresis curves of the displacement of the bimorph actuator with the characteristic points of the hysteresis curves of the unimorph actuator. Based on the research results, it was noticed that, in the bimorph, the maximum hysteresis and mean hysteresis values increase faster than the maximum displacement of a beam tip. However, values of characteristic input voltages for hysteresis loops—voltage corresponding to a maximum displacement of the actuator beam tip and voltage corresponding to maximum hysteresis—are almost the same for the bimorph and unimorph. From a practical point of view, it was noticed that the unimorph is a better choice compared to the bimorph in applications in which high changes in frequencies of input voltages appear.

Video Grading of Pancreatic Anastomoses During Robotic Pancreatoduodenectomy to Assess Both Learning Curve and the Risk of Pancreatic Fistula: A Post Hoc Analysis of the LAELAPS-3 Training Program.

To assess the learning curve of pancreaticojejunostomy during robotic pancreatoduodenectomy (RPD) and to predict the risk of postoperative pancreatic fistula (POPF) by using the objective structured assessment of technical skills (OSATS), taking the fistula risk into account. RPD is a challenging procedure that requires extensive training and confirmation of adequate surgical performance. Video grading, modified for RPD, of the pancreatic anastomosis could assess the learning curve of RPD and predict the risk of POPF. Post hoc assessment of patients prospectively included in 4 Dutch centers in a nationwide LAELAPS-3 training program for RPD. Video grading of the pancreaticojejunostomy was performed by 2 graders using OSATS (attainable score: 12-60). The main outcomes were the combined OSATS of the 2 graders and POPF (grade B/C). Cumulative sum analyzed a turning point in the learning curve for surgical skill. Logistic regression determined the cutoff for OSATS. Patients were categorized for POPF risk (ie, low, intermediate, and high) based on the updated alternative fistula risk scores. Videos from 153 pancreatic anastomoses were included. Median OSATS score was 48 (interquartile range: 41-52) points and with a turning point at 33 procedures. POPF occurred in 39 patients (25.5%). An OSATS score below 49, present in 77 patients (50.3%), was associated with an increased risk of POPF (odds ratio: 4.01, P =0.004). The POPF rate was 43.6% with OSATS < 49 versus 15.8% with OSATS ≥49. The updated alternative fistula risk scores category "soft pancreatic texture" was the second strongest prognostic factor of POPF (odds ratio: 3.37, P =0.040). Median cumulative surgical experience was 17 years (interquartile range: 8-21). Video grading of the pancreatic anastomosis in RPD using OSATS identified a learning curve and a reduced risk of POPF in case of better surgical performance. Video grading may provide a valid method to surgical training, quality control, and improvement.

Study on the pore structure characteristics and damage constitutive model of sandstone under freeze-thaw conditions

Rocks in Northwest China are often affected by the combined action of freeze-thaw and load erosion. Therefore, in order to better understand the mechanical properties of rocks in seasonal frozen areas and the meso-damage caused by freeze-thaw erosion, uniaxial compression tests, electron microscope scanning tests, X-ray diffraction tests (XRD) and mercury intrusion tests (MIP) were carried out on five sandstone samples with different freeze-thaw times, and the mechanical parameters and meso-damage characteristics of sandstone samples with different freeze-thaw times were obtained. Fractal theory was used to analyze the change in pore volume of sandstone after freeze-thaw cycles. Finally, the damage constitutive equation under the coupling action of freeze-thaw damage and load was established based on Lemaitre’s equivalent effect variation criterion. The results showed that the type of sandstone is a porous coarse-grained sandstone. With the increased freeze-thaw times, the compressive strength and cohesion of sandstone gradually decreased, and the closed pores in sandstone gradually connected, leading to the visible internal macroscopic cracks. Affected by freeze-thaw times, the volume proportion of large pores (100–1,000 µm) in sandstone gradually increased, while the volume proportion of micropores (.05–100 µm) gradually decreased. With the increased freeze-thaw times, the fractal dimension of pore volume decreased from 1.94 to 1.59. The theoretical curve can better fit the characteristic points of the stress-strain curve, which can further reveal the damage mechanism of sandstone under the coupling effects of freeze-thaw and load. The minimum error between the peak point of the experimental curve and the theoretical curve is 3.3%.

Sensitivity of uterine artery Doppler pulsatility index in screening for adverse pregnancy outcome in first and second trimesters.

In a poor resource country where screening for adverse pregnancy outcomes using maternal biomarkers seems unattainable, there is a need to search for credible alternatives. This study is, therefore, aimed at determining the sensitivity of uterine artery Doppler pulsatility index (UtAD-PI) in predicting pregnancy outcomesin the first and second trimesters and to establish any statistical difference in mean UtAD-PI in first and second trimesters screening of women with normal and abnormal pregnancy outcomes respectively. This clinical-based, longitudinal, and unpaired cohort study involved 500 pregnant women, who were screened for adverse outcomes using UtAD-PI and delivered in the hospital. These were divided into two groups, each having a training set and a test set. The training set was used to generate the receiver operator characteristic curve and cut-off point while the test set was used to test for sensitivity and specificity of the Ut-ADI in each trimester. The sensitivity and specificity of UtAD-PI in first-trimester screening are 97% and 76.5% while second-trimester gave sensitivity and specificity of 57.5% and 63.3% respectively. The uterine artery Doppler pulsatility index shows statistically significant differences between normal pregnancy and pregnancy with adverse outcomes (p-value = 0.000). The uterine artery Doppler pulsatility index is a good screening tool for adverse pregnancy outcomes. First-trimester screening of patients for adverse outcomes is more sensitive than the second-trimester screening using UtAD-PI. There is also a statistically significant difference between mean UtAD-PI between normal pregnancy and pregnancy with adverse pregnancy outcomes.

CT-guided percutaneous transthoracic needle biopsy (PTNB): A thoracic surgeon's learning curve and experience summary.

Few studies have investigated the learning process of percutaneous transthoracic needle biopsy (PTNB). Here, we aimed to evaluate the number of cases required to achieve proficiency by plotting the learning curve of PTNB. Data were collected from 94 consecutive patients who underwent computed tomography-guided PTNB by a thoracic surgeon at the Affiliated Hospital of Xuzhou Medical University between May 2021 and February 2022. The data collected included patient information, relevant examination results, intraoperative parameters, postoperative complications, and diagnostic results. The inflection points of the cumulative sum curve were around cases 13 and 24, according to which three phases were identified, including phase I, phase II, and phase III. A significant downtrend was observed regarding operative time (phase I, 26.53 ± 9.13 min vs. phase III, 18.42 ± 4.29 min, p < 0.05), rate of false-negative (phase I, 15.4% vs. phase III, 5.7%; p < 0.05), rate of pneumothorax (phase I, 30.8% vs. phase III, 12.9%; p < 0.05), and rate of hemoptysis (phase I, 15.4% vs. phase III, 2.9%; p < 0.05). Thirteen cases were accumulated to lay the technical foundation, and 24 cases were required to achieve proficiency. In this study we summarize our own experience and provide specific guidance for young doctors with no experience in biopsy.

Algebraic curves admitting non-collinear Galois points

This paper presents a criterion for the existence of a birational embedding into a projective plane with non-collinear Galois points for algebraic curves and describes its application via a novel example of a plane curve with non-collinear Galois points. In addition, this paper presents a new characterisation of the Fermat curve in terms of non-collinear Galois points.

Study of MFL signal identification in pipelines based on non-uniform magnetic charge distribution patterns

Magnetic flux leakage (MFL), a pipeline internal detection, is the mainstream technology for international oil and gas pipeline safety maintenance. To address the problem of large errors in the assessment of defects in pipeline inspection by existing theoretical analysis models, this paper introduces the charge density parameter to establish a mathematical model of non-uniform magnetic charge for pipeline leakage detection and calculates the non-uniform distribution pattern of magnetic charge on the defect side wall. The contour plot method is proposed to visually analyze the size of defects. To compare the error between uniform and non-uniform models, and verify the correctness of the theoretical model, experiments were systematically conducted on the X70 pipeline with internal MFL technology. The results show that: the magnetic charge distribution curve is symmetrically shaped at the center of the defect, with a valley at the center and two peaks at the defect edge. As the defect depth and width increase, the magnetic charge density increases sharply near the surface and edge. The peak-to-valley spacing and peak-to-valley values in the contour map of the MFL signal can directly reflect the location and size of defects. The signal characteristic values follow the trend of a first-order decreasing exponential function as the value of the lift-off increases. The first-order derivative of the signal characteristic value tends to decrease and then increase as the mesh size decreases, and the extreme point of the derivative curve is the best mesh size.

The Ernesto Cave, northern Italy, as a candidate auxiliary reference section for the definition of the Anthropocene series

Annually laminated stalagmites ER77 and ER78 from Grotta di Ernesto provide an accurate annual record of environmental and anthropogenic signals for the last ~200 years. Two major transitions are recorded in the stalagmites. The first coincides with the year 1840 CE, when a change from porous and impurity-rich-laminae to clean, translucent laminae occurs. This is accompanied by a steady increase in the growth rate, a decrease in fluorescence and a sharp increase in δ13C values. These changes concur with the end of the Little Ice Age. The second transition takes place around the year 1960 CE and corresponds with an increase in both annual growth rate and sulfur concentration in stalagmite ER78 at 4.2 mm from the top, and with the deflection point in the 14C activity curve in stalagmite ER77 at 4.8 mm from the top. This latter is the stratigraphic signal proposed as the primary guide for the definition of the Anthropocene series. The following shift toward depleted δ34S–SO4 in stalagmite ER78 suggests that industrial pollution is a major source of sulfur. The interpretation of atmospheric signals (S, δ34S, 14C) in the stalagmites is affected by attenuation and time lags and the environmental signals are influenced by soil and ecosystem processes, while other anthropogenic signals (δ15N, 239Pu) are not recorded. For these reasons, the stalagmite record is here proposed as an auxiliary (reference) section rather than a global standard. In summary, Grotta di Ernesto contains one of the best stalagmite records documenting the Anthropocene, and one of only two stalagmite records where the S peak has been measured at high resolution.

Photovoltaic single-diode model parametrization. An application to the calculus of the Euclidean distance to an [formula omitted]–[formula omitted] curve

In this paper we provide a new parametrization of the characteristic curve (I-V curve) associated to the photovoltaic (PV) single-diode model (SDM), which is the most common model in the literature to analyze the behavior of a PV panel. The SDM relates the voltage with the current, through a transcendental equation with five parameters to be determined. There are many methodologies to extract the SDM parameters and some of them are based on obtaining the best fit of the SDM model on a voltage–current dataset through the ordinary least squares method. However, the fact that errors affect not only the current but also the voltage indicates that the maximum likelihood estimation (MLE) of the parameters is obtained by the total least squares method, also called orthogonal distance regression (ODR). The main difficulty in performing ODR lies in obtaining the Euclidean distance from a point to the SDM I-V curve which is in general a hard mathematical problem; in our particular case it is noticeably more difficult due to the implicit nature of the SDM equation and the fact that solution candidates might not be unique. This paper proposes a new parametrization that allows reduction of the calculus of the Euclidean distance from any point to the I-V curve to solving a single-variable equation. An in-depth mathematical analysis determines the number of possible candidates where the Euclidean distance can be attained. Moreover, a full casuistry alongside a geometrical study based on the curvature of the I-V curve and the Maximum Curvature Point, permits identification and classification of all these candidates. This enables for the first time a complete algorithm to compute the Euclidean distance from a point to an I-V curve at any condition and, thus, to perform a reliable ODR to obtain the MLE of the SDM parameters. Using the obtained theoretical background, it is demonstrated that two existing methodologies to compute the Euclidean distance fail in some cases, whereas the proposed algorithm is execution-proof and runs faster.