Number Of Curves Research Articles

The a-number of yn = xm + x over finite fields

This paper presents a formula for the [Formula: see text]-number of certain maximal curves characterized by the equation [Formula: see text] over the finite field [Formula: see text]. [Formula: see text]-number serves as an invariant for the isomorphism class of the [Formula: see text]-torsion group scheme. By utilizing the action of the Cartier operator on [Formula: see text], we establish a closed formula for the [Formula: see text]-number of [Formula: see text].

Functional Time Series Analysis and Visualization Based on Records

In many phenomena, data are collected on a large scale and at different frequencies. In this context, functional data analysis (FDA) has become an important statistical methodology for analyzing and modeling such data. The approach of FDA is to assume that data are continuous functions and that each continuous function is considered as a single observation. Thus, FDA deals with large-scale and complex data. However, visualization and exploratory data analysis, which are very important in practice, can be challenging due to the complexity of the continuous functions. Here we introduce a type of record concept for functional data, and we propose some nonparametric tools based on the record concept for functional data observed over time (functional time series). We study the properties of the trajectory of the number of record curves under different scenarios. Also, we propose a unit root test based on the number of records. The trajectory of the number of records over time and the unit root test can be used for visualization and exploratory data analysis. We illustrate the advantages of our proposal through a Monte Carlo simulation study. We also illustrate our method on two different datasets: Daily wind speed curves at Yanbu, Saudi Arabia and annual mortality rates in France. Overall, we can identify the type of functional time series being studied based on the number of record curves observed. Supplementary materials for this article are available online.

A Novel Approach to Automatically Digitize Analog Seismograms

Abstract Before the widespread adoption of the digital seismographs, seismic records were stored in analog form on paper and manually read by analysts. These analog seismograms contained various useful information and were crucial for seismic research. To meet the demands of the modern computational analysis, researchers must digitize historical analog seismograms and extract information. In this article, we present a novel approach to automatically digitize analog seismograms. Initially, Otsu threshold segmentation was applied to the analog seismograms to remove underlying noise and improve their clarity. Subsequently, a novel dynamic distributed seismic waveform onset-point-search algorithm was implemented, which automatically locates the onset point of each seismic waveform baseline in analog seismograms and accurately determines the total number of seismic waveform curves. To address the complexity and diversity of seismic waveforms, we implemented an innovative seismic waveform classification algorithm that can distinguish between complex waveforms and smooth waveforms, and further implemented a new smooth waveform removal method to eliminate interference from smooth waveforms during complex waveform extraction. Then, we used a YOLOv9s-based model to identify time markers within the seismic waveforms for removal. In addition, in the seismic waveform digitization extraction and reconstruction phase, we implemented a novel method for extracting significant seismic waveform features and geometric restoration for peak and trough feature extraction and geometric restoration, as well as vertical feature extraction of seismic waveforms. Finally, we implemented a new waveform sequence integration and time mapping model, which can effectively reconstruct seismic waveform data based on the extracted features and map arrival times to each waveform point. Experiments have verified the significant superiority and stability of the methods implemented in this article for digitizing analog seismograms.

Mean and covariance estimation for discretely observed high-dimensional functional data: Rates of convergence and division of observational regimes

Estimation of the mean and covariance parameters for functional data is a critical task, with local linear smoothing being a popular choice. In recent years, many scientific domains are producing multivariate functional data for which p, the number of curves per subject, is often much larger than the sample size n. In this setting of high-dimensional functional data, much of developed methodology relies on preliminary estimates of the unknown mean functions and the auto- and cross-covariance functions. This paper investigates the convergence rates of local linear estimators in terms of the maximal error across components and pairs of components for mean and covariance functions, respectively, in both L2 and uniform metrics. The local linear estimators utilize a generic weighting scheme that can adjust for differing numbers of discrete observations Nij across curves j and subjects i, where the Nij vary with n. Particular attention is given to the equal weight per observation (OBS) and equal weight per subject (SUBJ) weighting schemes. The theoretical results utilize novel applications of concentration inequalities for functional data and demonstrate that, similar to univariate functional data, the order of the Nij relative to p and n divides high-dimensional functional data into three regimes (sparse, dense, and ultra-dense), with the high-dimensional parametric convergence rate of log(p)/n1/2 being attainable in the latter two.

Tjurina number of a local complete intersection curve

In contrast to the Milnor number, there was no known formula relating the Tjurina number of a reducible curve to the Tjurina numbers of its components. In this work we exhibit such a formula relating Tjurina number of a complete intersection algebroid (or analytic) curve over an algebraically closed field of characteristic zero (or over C ) to the Tjurina numbers of its components, involving the intersection indices among the components and numerical analytic invariants extracted from modules of Kähler differentials on unions of branches of the curve.

NotPlaNET: Removing False Positives from Planet Hunters TESS with Machine Learning

Differentiating between real transit events and false-positive signals in photometric time-series data is a bottleneck in the identification of transiting exoplanets, particularly long-period planets. This differentiation typically requires visual inspection of a large number of transit-like signals to rule out instrumental and astrophysical false positives that mimic planetary transit signals. We build a one-dimensional convolutional neural network (CNN) to separate eclipsing binaries and other false positives from potential planet candidates, reducing the number of light curves that require human vetting. Our CNN is trained using the TESS light curves that were identified by Planet Hunters citizen scientists as likely containing a transit. We also include the background flux and centroid information. The light curves are visually inspected and labeled by project scientists and are minimally preprocessed, with only normalization and data augmentation taking place before training. The median percentage of contaminants flagged across the test sectors is 18% with a maximum of 37% and a minimum of 10%. Our model keeps 100% of the planets for 16 of the 18 test sectors, while incorrectly flagging one planet candidate (0.3%) for one sector and two (0.6%) for the remaining sector. Our method shows potential to reduce the number of light curves requiring manual vetting by up to a third with minimal misclassification of planet candidates.

Photometric and Spectroscopic Study of Ten Low Mass Ratio Contact Binary Systems: Orbital Stability, O’Connell Effect and Infrared Calcium Line Filling

Low mass ratio contact binary systems are more likely to have unstable orbits and potentially merge. In addition, such systems exhibit characteristics such as starspots and high energy emissions (UV) suggestive of chromospheric and magnetic activity. Light curve modeling of ten contact binary systems is reported. All were found to be of extreme low mass ratio ranging from 0.122 to 0.24 and three were found to be potentially unstable and possible merger candidates. Filling of the infrared calcium absorption lines is a marker of increased chromospheric activity. We use the available Large Sky Area Multi-Object Fiber Spectroscopic Telescope spectra along with matched standard spectra (broadened for rotation) to measure the excess filling of the central core depression flux of the two main infrared calcium absorption lines λ8542 and λ8662. We find that all reported contact binaries have excess filling of the core flux in the infrared calcium lines. Three of the systems reported were also observed by the Galaxy Evolution Explorer mission and we find that all three have features of excess ultraviolet emissions further adding evidence for increased chromospheric activity in low mass ratio contact binaries. Analysis of both orbital stability and absorption line filling is dependent on the determination of geometric and absolute parameters from light curve modeling. Not an insignificant number of contact binary light curves exhibit the O’Connell effect, usually attributed to starspots. We discuss the inclusion of starspots in light curve solutions and how they influence the geometric and absolute parameters.

A Method of Rapidly Deriving Late-type Contact Binary Parameters and Its Application in the Catalina Sky Survey

With the continuous development of large optical surveys, a large number of light curves of late-type contact binary systems (CBs) have been released. Deriving parameters for CBs using the the Wilson–Devinney program and the PHOEBE program poses a challenge. Therefore, this study developed a method for rapidly deriving light curves based on the Neural Networks model combined with the Hamiltonian Monte Carlo (HMC) algorithm (NNHMC). The neural network was employed to establish the mapping relationship between the parameters and the pregenerated light curves by the PHOEBE program, and the HMC algorithm was used to obtain the posterior distribution of the parameters. The NNHMC method was applied to a large contact binary sample from the Catalina Sky Survey, and a total of 19,104 late-type contact binary parameters were derived. Among them, 5172 have an inclination greater than 70° and a temperature difference less than 400 K. The obtained results were compared with the previous studies for 30 CBs, and there was an essentially consistent goodness-of-fit (R 2) distribution between them. The NNHMC method possesses the capability to simultaneously derive parameters for a vast number of targets. Furthermore, it can provide an extremely efficient tool for the rapid derivation of parameters in future sky surveys involving large samples of CBs.

SurvdigitizeR: an algorithm for automated survival curve digitization

BackgroundDecision analytic models and meta-analyses often rely on survival probabilities that are digitized from published Kaplan–Meier (KM) curves. However, manually extracting these probabilities from KM curves is time-consuming, expensive, and error-prone. We developed an efficient and accurate algorithm that automates extraction of survival probabilities from KM curves.MethodsThe automated digitization algorithm processes images from a JPG or PNG format, converts them in their hue, saturation, and lightness scale and uses optical character recognition to detect axis location and labels. It also uses a k-medoids clustering algorithm to separate multiple overlapping curves on the same figure. To validate performance, we generated survival plots form random time-to-event data from a sample size of 25, 50, 150, and 250, 1000 individuals split into 1,2, or 3 treatment arms. We assumed an exponential distribution and applied random censoring. We compared automated digitization and manual digitization performed by well-trained researchers. We calculated the root mean squared error (RMSE) at 100-time points for both methods. The algorithm’s performance was also evaluated by Bland–Altman analysis for the agreement between automated and manual digitization on a real-world set of published KM curves.ResultsThe automated digitizer accurately identified survival probabilities over time in the simulated KM curves. The average RMSE for automated digitization was 0.012, while manual digitization had an average RMSE of 0.014. Its performance was negatively correlated with the number of curves in a figure and the presence of censoring markers. In real-world scenarios, automated digitization and manual digitization showed very close agreement.ConclusionsThe algorithm streamlines the digitization process and requires minimal user input. It effectively digitized KM curves in simulated and real-world scenarios, demonstrating accuracy comparable to conventional manual digitization. The algorithm has been developed as an open-source R package and as a Shiny application and is available on GitHub: https://github.com/Pechli-Lab/SurvdigitizeR and https://pechlilab.shinyapps.io/SurvdigitizeR/.

Battery degradation evaluation based on impedance spectra using a limited number of voltage-capacity curves

Degradation prediction is crucial for ensuring safe and reliable operation of batteries. However, relying solely on capacity to characterize aging cannot comprehensively represent the health status of the battery. This work explores the potential of using a limited number of partial voltage-capacity curves to evaluate battery degradation with the aid of deep learning approaches, which can be used for onboard applications. A sequence-to-sequence model is proposed to predict the electrochemical impedance spectra during battery degradation. It only uses capacity sequences within a specific voltage range at fixed voltage increments from a limited number of cycles, which can be flexibly adapted to different life stages in an end-to-end manner. The proposed method has been validated based on the developed degradation dataset. The root mean square errors for the prediction of impedance spectra are less than 1.48 mΩ. Capacities and resistances associated with electrochemical processes can be further extracted from the obtained impedance spectra, facilitating a comprehensive evaluation of battery degradation. As a limited number of measured data are needed, the proposed method can reduce data storage requirements and computational demands, which enables fast and comprehensive aging diagnosis.

On the Algebraic Geometry of Multiview

We study the multiviews of algebraic space curves X from n pin-hole cameras of a real or complex projective space. We assume the pin-hole centers to be known, i.e., we do not reconstruct them. Our tools are algebro-geometric. We give some general theorems, e.g., we prove that a projective curve (over complex or real numbers) may be reconstructed using four general cameras. Several examples show that no number of badly placed cameras can make a reconstruction possible. The tools are powerful, but we warn the reader (with examples) that over real numbers, just using them correctly, but in a bad way, may give ghosts: real curves which are images of the emptyset. We prove that ghosts do not occur if the cameras are general. Most of this paper is devoted to three important cases of space curves: unions of a prescribed number of lines (using the Grassmannian of all lines in a 3-dimensional projective space), plane curves, and curves of low degree. In these cases, we also see when two cameras may reconstruct the curve, but different curves need different pairs of cameras.

Two-dimensional Eclipse Mapping of the Hot-Jupiter WASP-43b with JWST MIRI/LRS

We present eclipse maps of the two-dimensional thermal emission from the dayside of the hot-Jupiter WASP-43b, derived from an observation of a phase curve with the JWST MIRI/LRS instrument. The observed eclipse shapes deviate significantly from those expected for a planet emitting uniformly over its surface. We fit a map to this deviation, constructed from spherical harmonics up to order ℓmax=2 , alongside the planetary, orbital, stellar, and systematic parameters. This yields a map with a meridionally averaged eastward hot-spot shift of (7.75 ± 0.36)°, with no significant degeneracy between the map and the additional parameters. We show the latitudinal and longitudinal contributions of the dayside emission structure to the eclipse shape, finding a latitudinal signal of ∼200 ppm and a longitudinal signal of ∼250 ppm. To investigate the sensitivity of the map to the method, we fix the parameters not used for mapping and derive an “eigenmap” fitted with an optimized number of orthogonal phase curves, which yields a similar map to the ℓmax=2 map. We also fit a map up to ℓmax=3 , which shows a smaller hot-spot shift, with a larger uncertainty. These maps are similar to those produced by atmospheric simulations. We conclude that there is a significant mapping signal which constrains the spherical harmonic components of our model up to ℓmax=2 . Alternative mapping models may derive different structures with smaller-scale features; we suggest that further observations of WASP-43b and other planets will drive the development of more robust methods and more accurate maps.

Arterial Input Function (AIF) Correction Using AIF Plus Tissue Inputs with a Bi-LSTM Network.

Background: The arterial input function (AIF) is vital for myocardial blood flow quantification in cardiac MRI to indicate the input time-concentration curve of a contrast agent. Inaccurate AIFs can significantly affect perfusion quantification. Purpose: When only saturated and biased AIFs are measured, this work investigates multiple ways of leveraging tissue curve information, including using AIF + tissue curves as inputs and optimizing the loss function for deep neural network training. Methods: Simulated data were generated using a 12-parameter AIF mathematical model for the AIF. Tissue curves were created from true AIFs combined with compartment-model parameters from a random distribution. Using Bloch simulations, a dictionary was constructed for a saturation-recovery 3D radial stack-of-stars sequence, accounting for deviations such as flip angle, T2* effects, and residual longitudinal magnetization after the saturation. A preliminary simulation study established the optimal tissue curve number using a bidirectional long short-term memory (Bi-LSTM) network with just AIF loss. Further optimization of the loss function involves comparing just AIF loss, AIF with compartment-model-based parameter loss, and AIF with compartment-model tissue loss. The optimized network was examined with both simulation and hybrid data, which included in vivo 3D stack-of-star datasets for testing. The AIF peak value accuracy and ktrans results were assessed. Results: Increasing the number of tissue curves can be beneficial when added tissue curves can provide extra information. Using just the AIF loss outperforms the other two proposed losses, including adding either a compartment-model-based tissue loss or a compartment-model parameter loss to the AIF loss. With the simulated data, the Bi-LSTM network reduced the AIF peak error from -23.6 ± 24.4% of the AIF using the dictionary method to 0.2 ± 7.2% (AIF input only) and 0.3 ± 2.5% (AIF + ten tissue curve inputs) of the network AIF. The corresponding ktrans error was reduced from -13.5 ± 8.8% to -0.6 ± 6.6% and 0.3 ± 2.1%. With the hybrid data (simulated data for training; in vivo data for testing), the AIF peak error was 15.0 ± 5.3% and the corresponding ktrans error was 20.7 ± 11.6% for the AIF using the dictionary method. The hybrid data revealed that using the AIF + tissue inputs reduced errors, with peak error (1.3 ± 11.1%) and ktrans error (-2.4 ± 6.7%). Conclusions: Integrating tissue curves with AIF curves into network inputs improves the precision of AI-driven AIF corrections. This result was seen both with simulated data and with applying the network trained only on simulated data to a limited in vivo test dataset.

Data mining algorithm in the identification of accounting fraud by smart city information technology

The identification of accounting fraud is an important measure to safeguard the interests of stakeholders and ensure the long-term development of the company. The current traditional methods for identifying accounting fraud rely on manual review and judgment, lacking objectivity and accuracy. In order to improve the accuracy of accounting fraud identification, improve identification efficiency and objectivity, this article combines smart city information technology to conduct in-depth research on data mining algorithms for accounting fraud identification. This article first provides a brief overview of smart cities and information technology, then introduces the basic theory of accounting fraud identification, and finally implements accounting fraud identification through k-means clustering mining algorithm. The data is divided into k clusters, and abnormal clusters are identified by checking the characteristics and attributes of each cluster. Compared with traditional rule-based and pattern based methods, this approach can more flexibly adapt to different types and forms of fraud, and can discover unknown patterns of fraud. In the experiment, this article used electronic data collection, analysis, and retrieval systems on the websites of the Shanghai Stock Exchange and Shenzhen Stock Exchange to collect 641 annual reports and financial characteristics from 62 listed companies that engaged in financial statement fraud and 84 companies that were not reported to have financial statement fraud from 2012 to 2021 as test samples. The results were tested and analyzed from several aspects, including the number of misjudgments, misjudgment rate, and ROC curve. The final test results show that compared to traditional accounting fraud identification methods, the comprehensive misjudgment rate of data mining algorithms based on smart cities has decreased by 3 %. The conclusion indicates that data mining algorithms used in smart city information technology to identify accounting fraud can help improve the accuracy of accounting fraud, improve audit objectivity and effectiveness.

Implementation of FRET Spectrometry Using Temporally Resolved Fluorescence: A Feasibility Study.

Förster resonance energy transfer (FRET) spectrometry is a method for determining the quaternary structure of protein oligomers from distributions of FRET efficiencies that are drawn from pixels of fluorescence images of cells expressing the proteins of interest. FRET spectrometry protocols currently rely on obtaining spectrally resolved fluorescence data from intensity-based experiments. Another imaging method, fluorescence lifetime imaging microscopy (FLIM), is a widely used alternative to compute FRET efficiencies for each pixel in an image from the reduction of the fluorescence lifetime of the donors caused by FRET. In FLIM studies of oligomers with different proportions of donors and acceptors, the donor lifetimes may be obtained by fitting the temporally resolved fluorescence decay data with a predetermined number of exponential decay curves. However, this requires knowledge of the number and the relative arrangement of the fluorescent proteins in the sample, which is precisely the goal of FRET spectrometry, thus creating a conundrum that has prevented users of FLIM instruments from performing FRET spectrometry. Here, we describe an attempt to implement FRET spectrometry on temporally resolved fluorescence microscopes by using an integration-based method of computing the FRET efficiency from fluorescence decay curves. This method, which we dubbed time-integrated FRET (or tiFRET), was tested on oligomeric fluorescent protein constructs expressed in the cytoplasm of living cells. The present results show that tiFRET is a promising way of implementing FRET spectrometry and suggest potential instrument adjustments for increasing accuracy and resolution in this kind of study.

Counting elliptic curves with a rational N-isogeny for small N

We count the number of rational elliptic curves of bounded naive height that have a rational N-isogeny, for N∈{2,3,4,5,6,8,9,12,16,18}. For some N, this is done by generalizing a method of Harron and Snowden. For the remaining cases, we use the framework of Ellenberg, Satriano and Zureick-Brown, in which the naive height of an elliptic curve is the height of the corresponding point on a moduli stack.

A protein network refinement method based on module discovery and biological information

BackgroundThe identification of essential proteins can help in understanding the minimum requirements for cell survival and development to discover drug targets and prevent disease. Nowadays, node ranking methods are a common way to identify essential proteins, but the poor data quality of the underlying PIN has somewhat hindered the identification accuracy of essential proteins for these methods in the PIN. Therefore, researchers constructed refinement networks by considering certain biological properties of interacting protein pairs to improve the performance of node ranking methods in the PIN. Studies show that proteins in a complex are more likely to be essential than proteins not present in the complex. However, the modularity is usually ignored for the refinement methods of the PINs.MethodsBased on this, we proposed a network refinement method based on module discovery and biological information. The idea is, first, to extract the maximal connected subgraph in the PIN, and to divide it into different modules by using Fast-unfolding algorithm; then, to detect critical modules according to the orthologous information, subcellular localization information and topology information within each module; finally, to construct a more refined network (CM-PIN) by using the identified critical modules.ResultsTo evaluate the effectiveness of the proposed method, we used 12 typical node ranking methods (LAC, DC, DMNC, NC, TP, LID, CC, BC, PR, LR, PeC, WDC) to compare the overall performance of the CM-PIN with those on the S-PIN, D-PIN and RD-PIN. The experimental results showed that the CM-PIN was optimal in terms of the identification number of essential proteins, precision-recall curve, Jackknifing method and other criteria, and can help to identify essential proteins more accurately.

Studying Transient Phenomena in Thin Films with Reinforcement Learning.

Neutron reflectometry has long been a powerful tool to study the interfacial properties of energy materials. Recently, time-resolved neutron reflectometry has been used to better understand transient phenomena in electrochemical systems. Those measurements often comprise a large number of reflectivity curves acquired over a narrow q range, with each individual curve having lower information content compared to a typical steady-state measurement. In this work, we present an approach that leverages existing reinforcement learning tools to model time-resolved data to extract the time evolution of structure parameters. By mapping the reflectivity curves taken at different times as individual states, we use the Soft Actor-Critic algorithm to optimize the time series of structure parameters that best represent the evolution of an electrochemical system. We show that this approach constitutes an elegant solution to the modeling of time-resolved neutron reflectometry data.

Modeling of Risk Factors for Vulnerable Road Users’ Crashes on National Highways Passing through Medium-sized Indian Cities

The safety of vulnerable road users, such as pedestrians, bicyclists and motorised twowheelers, on national highways passing through urban areas has been a significant concern in developing countries like India. This study analyzes Visakhapatnam police crash data (2014-2017) to identify high-risk road segments to vulnerable road users. Establishing negative binomial models helps analyze risk variables for fatal and injury crashes concerning several susceptible road users on mid-block sections. Further, this study focuses on site-specific information collected from road-safety audits, speed, average daily traffic, length of road section and percentage of two-wheelers, also considered to fully help understand the likelihood of a crash. The statistical analysis of this paper identified the risk variables, like length of road segment, presence of service roads, land-use type (i.e., commercial/mixed land use), number of curves and average daily traffic associated with the incidence of fatal and injury crashes of vulnerable road users in Visakhapatnam city, India. The conclusions highlight the crucial safety measures that transportation planners and policymakers must take to create a more secure environment for road users. Keywords: Vulnerable road users, Mid-block sections, Negative binomial models, Crash, Count-data models, Safety measures.

A comprehensive methodology to estimate the fatigue life of S-shaped integral squeeze film damper

The Integral Squeeze Film Damper (ISFD) finds widespread application in various rotating machinery, such as gas turbines, turbochargers, and high-speed rotors, to dampen vibrations and improve operational stability. This study presents a comprehensive methodology to predict the fatigue life of an Integral Squeeze Film Damper (ISFD) by combining Low Cycle Fatigue (LCF), High Cycle Fatigue (HCF) test, and Finite Element (FE) simulations. An S-shaped spring specimen is designed and tested under high-cycle fatigue loading to develop the stress amplitude versus the number of the cycles curve. LCF tests are performed to obtain fatigue parameters, and a Chaboche kinematic hardening model is employed for cyclic plasticity FE simulations. FE analysis of the ISFD is conducted to establish its dynamic characteristics, aiding in identifying critical locations based on maximum von Mises stress. The integration of local stress–strain states from FE simulations with experimental fatigue parameters is carried out to predict fatigue life of ISFD. The validity of the methodology is confirmed through experimental and stress analyses, providing valuable insights for optimizing the fatigue performance of ISFD components.