Function Function Research Articles

A Volterra edge dislocation problem in second-order elasticity theory

A displacement function technique has been developed to study plane strain problems in second-order elasticity theory for incompressible elastic materials. The formulation culminates in the development of a single inhomogeneous biharmonic equation of the form [Formula: see text] for the second-order displacement function [Formula: see text]. In the second-order, the isotropic stress associated with constitutive behaviour is governed by an inhomogeneous harmonic equation of the form [Formula: see text]. Both functions [Formula: see text] and [Formula: see text] depend only on the solution to the analogous problem in classical elasticity. While there are similarities to the Airy stress function, the displacement function approach enables the evaluation of the first- and second-order displacement fields purely through its derivatives, thus eliminating the introduction of arbitrary rigid body terms normally associated with formulations where the strains derived from a stress function approach need to be integrated. The displacement function approach is applied to develop a second-order elasticity solution to the problem of a Volterra edge dislocation.

Statistical analysis of bistable feature in a 1.55-[formula omitted] vertical cavity emitting laser

Optical bistability in telecom-band lasers has attracted significant attention because of its immense potential for applications in the fields of optical communications and optical computing. In this paper, we report on an experimental investigation of the statistical properties of a 1.55-μm bistable VCSEL. The VCSEL exhibits mode switching at a current of 5.41 mA and 4.15 mA when the pump continuously increases and decreases, respectively. Both of these switching exhibit a bistable region, indicating a polarization bistability induced by the gain saturation. By calculation of second-order autocorrelation functions with injection current, we identify different regions associated with the dynamics of different dominant modes. In particular, the statistical analysis reveals more properties of the bistable laser, such as the intensity fluctuations induced by different kinds of noise.

Phase retrieval in incoherent diffractive imaging using higher-order photon correlation functions

To obtain spatial information about an arbitrary atomic distribution in x-ray structure analysis, e.g. in molecules or proteins, the standard method is to measure the intensity in the far field, i.e. the first-order photon correlation function of the coherently scattered x-ray photons (coherent diffractive imaging). Recently, it was suggested to record alternatively the incoherently scattered photons and measure the second-order photon correlation function to reconstruct the geometry of the unknown atomic distribution (incoherent diffractive imaging). Yet, besides various advantages of the latter method, both techniques suffer from the so-called phase retrieval problem. Lately, an ab-initio phase retrieval algorithm to reconstruct the phase of the so-called structure factor of the scattering objects based on the third-order photon correlation function was reported. The algorithm makes use of the closure phase, which contains important, yet incomplete phase information, well-known from triple correlations and their bispectrum in speckle masking and astronomy applications. Here, we provide a detailed analysis of the underlying scheme and quantities in the context of x-ray structure analysis. In particular, we explicitly calculate for the first time the third-order photon correlation function for single photon emitters in a full quantum mechanical treatment and discuss the uniqueness of the closure phase equations constructed from. In this context, we recapitulate the sign problem of the closure phase and how it can be lifted using redundant information. We further show how the algorithm can be improved using even higher-order photon correlation functions produced by single photon emitters, e.g. the fourth-order correlation function, delivering new phase relations appearing in the four-point correlations.

Functional Bayesian Model Average Regression Based on Derivative Information

Functional data regression models based on basis function expansion have been widely used in economic, financial, and environmental fields. However, determining the appropriate type and quantity of basis functions, such as KL expansion and B-spline, has remained a challenge to overcome. Additionally, when two curves are similar, constructing an effective regression model can prove to be difficult. On top of that, this paper suggests a functional Bayesian model average regression model, which is based on the KL expansion of the derivative function. On the one hand, the method uses the first and second-order derivative function information as predictors to capture the curve's fluctuation trend more comprehensively. On the other hand, the method applies model averaging to dynamically determine the appropriate number of basis functions to use, which can effectively alleviate the overfitting and underfitting problems of the model. The experiments and corresponding data analysis demonstrate that the proposed method has higher prediction accuracy and robustness than the comparative methods.

Upper limit of mineral-associated organic carbon in temperate and sub-tropical soils: How far is it?

Soil organic carbon (SOC) is the main terrestrial C pool and is roughly divided into stable mineral-associated organic carbon (MAOC) and particulate organic matter carbon (POC). However, the sequestration capacity of MAOC remains unquantified. Currently, soils are considered to have a limited capacity to accumulate MAOC, primarily due to the presence of fine fractions, i.e. silt and clay particles. However, it is unlikely that saturation will occur in all soils due to land use. Therefore it is necessary to investigate whether soils from different latitudes and their silt and clay fractions that comprise MAOC are saturated. We selected 71 soil samples that were physically fractionated from a Mexican inventory of vegetation with a wide range of SOC (4–186 g kg−1 soil) and clay (126–777 g kg−1 soil) contents. Soils were grouped into non-volcanic soils and allophanic Andosols. In the first group, we found a positive and highly significant linear relationship between SOC and MAOC contents, but no upper limit was detected. We found a common slope of 0.86 (R2 = 0.97, p < 0.01), i.e. 86% of the SOC was contained in MAOC irrespective of soil types and management, a value very similar to that in other studies. Conversely, for allophanic Andosols, which had SOC content twice that of non-volcanic soils, a second-order polynomial function (R2 = 0.98, p < 0.01) was established, the upper limit of which exceeded 186 g SOC kg−1 for a MAOC of 134 g kg−1. This was also supported by an increasing polynomial function of particulate organic carbon (POC) as the SOC increased. In both types of soils, maximum MAOCs were found between 700 and 800 g kg−1 of silt and clay in medium-textured soils. The amount of silt and clay particles was limited by SOC accumulation in the silt fraction as clay became saturated. These results are influenced by the mass proportion of silt and clay that follows a unique pattern in allophanic Andosols and non-volcanic soils. An investigation of a comprehensive database comprising 21,315 soil profiles sampled 0–30 cm across Mexico showed that most soils are below 186 g SOC kg−1 the bending point above which the upper limit does exist.

On Second-Order Cone Functions

We consider the second-order cone function (SOCF) f:Rn⟶R defined by fx=cTx+d−Ax+b, with parameters c∈Rn, d∈R, A∈Rm×n, and b∈Rm. Every SOCF is concave. We give necessary and sufficient conditions for strict concavity of f. The parameters A and b are not uniquely determined. We show that every SOCF can be written in the form fx=cTx+d−δ2+x−x∗TMx−x∗. We give necessary and sufficient conditions for the parameters c, d, δ, M=ATA, and x∗ to be uniquely determined. We also give necessary and sufficient conditions for f to be bounded above.

Functional Principal Component Regression Model Based on FIrst-order Boosting and Model Averaging

Functional regression model has always been an important research direction in the field of functional data analysis, in which functional principal component analysis as a common method of functional regression modeling, the determination of the number of truncations of the eigenfunctions has always been a problem to be solved. Based on this, this paper proposes a functional principal component regression model based on the idea of model averaging, which uses Bayesian model averaging instead of model selection, determines the number of truncations adaptively and balances the prediction error with the training error. In addition, the original function curves do not effectively capture the information of their functional characteristics. In this paper, the first-order derivative function is used as the supplementary information of the original function curve to jointly characterize the predictor variables. In the efficiency test, this paper averages the Bayesian model as the benchmark model and conducts real data analysis on several benchmark datasets. The results show that the proposed method has higher predictive accuracy and robustness than commonly used models.

Accelerometer-based swimming metabolism of smallmouth bass (Micropterus dolomieu).

Bioenergetics is informative for a range of fundamental and applied resource management questions, but findings are often constrained by a lack of ecological realism due to the challenges of remotely estimating key parameters such as metabolic rate. To enable field applications, we conducted a calibration study with smallmouth bass (Micropterus dolomieu, 0.7-2 kg) surgically implanted with accelerometer transmitters and exposed to a ramp-Ucrit swimming protocol in a swim tunnel respirometer across a range of water temperatures (6, 12, 18, and 24°C). There was an exponential increase in fish acceleration with swimming speed, and acceleration per speed was higher in smaller fish and female fish, and at colder temperatures. Mass-specific fish metabolic rate (MO2; mg O2 kg-1 h-1) increased with swimming speed, acceleration, and temperature, and decreased with fish mass, which when combined were strong predictors of MO2. Maximum metabolic rate (MMR) was estimated to peak at 22°C, but maximum sustained swimming speed (Ucrit) remained high at c. 90-100 m s-1 above 20°C, based on second-order polynomial functions. Aerobic scope (AS) estimates peaked at 20°C (>90% AS at 17-24°C; >50% AS at 11-28°C). Males exhibited marginally higher MMR, AS, and Ucrit than females at higher temperatures. Larger fish generally exhibited higher Ucrit, but smaller fish had a marginally broader performance range (AS, Ucrit) among temperatures, benefiting from higher MMR despite a steeper increase in resting metabolic rate with temperature. These findings enable field studies to estimate metabolic metrics of smallmouth bass in situ to characterize their ecological energetics and inform bioenergetics models.

Negative Differential Resistance in Conical Nanopore Iontronic Memristors.

Emerging ion transport dynamics with memory effects at nanoscale solution-substrate interfaces offers a unique opportunity to overcome the bottlenecks in traditional computational architectures, trade-offs in selectivity and throughput in separation, and electrochemical energy conversions. Negative differential resistance (NDR), a decrease in conductance with increasing potential, constitutes a new function from the perspective of time-dependent instead of steady-state nanoscale electrokinetic ion transport but remains unexplored in ionotronics to develop higher-order complexity and advanced capabilities. Herein, NDR is introduced in hysteretic and rectified ion transport through single conical nanopipettes (NPs) as ionic memristors. Deterministic and chaotic behaviors are controlled via an electric field as the sole stimulus. The NDR arises fundamentally from the availability and redistribution of the ionic charges during the hysteretic and rectified transport at asymmetric nanointerfaces. The elucidated mechanism is generalizable, and the drastically simplified operations enable tunable state-switching dynamics with higher-order complexity besides the first-order synaptic functions in multiple excitatory and inhibitory states.

Computations on fall of the leaning tower with considering air resistance

The free fall of a sphere was studied by considering air buoyancy and resistance. After selecting the reasonable drag coefficient formula recommended by the literature, partial differential formulas on the motion of balls falling in the Leaning Tower of Pisa are solved. The variation process of acceleration, velocity and displacement over time during the falling process of two spheres is obtained. The research results indicate that the kinematics of free fall considering air resistance is different from that neglecting air resistance. Air Resistance must be considered in the free fall of the solid ball after 0.3005 seconds. In the free fall of the leaning tower, air resistance makes the solid ball land at 0.4418 seconds which is earlier than the hollow. The variation of the acceleration of a solid ball with time can be described by a second-order function a=-0.115t2 -0.022t+9.801. Velocity does not satisfy the product of acceleration and time but can be described as a polynomial function of the velocity variation with time v = c1t2 + c2t + c3 . About the relationship between displacement and time, for a solid sphere, displacement is proportional to 1.9526 power of time h=5.4945t1.9526 , while for a hollow sphere, it cannot be expressed by a function. The relationship between air resistance and velocity during the falling process of an iron ball satisfies a polynomial function Fd =c1v2 -c2v+c3 rather than a simple relationship where air resistance is directly proportional to the first or second power of speed, which was used in many papers as a reasonable assumption.

Development and Application of an IoT-Based System for Soil Water Status Monitoring in a Soil Profile.

Soil water content (θ), matric potential (h) and hydraulic conductivity (K) are key parameters for hydrological and environmental processes. Several sensors have been developed for measuring soil θ-h-K relationships. The cost of such commercially available sensors may vary over several orders of magnitude. In recent years, some sensors have been designed in the framework of Internet of Things (i.e., IoT) systems to make remote real-time soil data acquisition more straightforward, enabling low-cost field-scale monitoring at high spatio-temporal scales. In this paper, we introduce a new multi-parameter sensor designed for the simultaneous estimation of θ and h at different soil depths and, due to the sensor's specific layout, the soil hydraulic conductivity function via the instantaneous profile method (IPM). Our findings indicate that a second-order polynomial function is the most suitable model (R2 = 0.99) for capturing the behavior of the capacitive-based sensor in estimating θ in the examined soil, which has a silty-loam texture. The effectiveness of low-cost capacitive sensors, coupled with the IPM method, was confirmed as a viable alternative to time domain reflectometry (TDR) probes. Notably, the layout of the sensor makes the IPM method less labor-intensive to implement. The proposed monitoring system consistently demonstrated robust performance throughout extended periods of data acquisition and is highly suitable for ongoing monitoring of soil water status.

Experimental investigation of brain contusion characteristics and dynamic response in low-age children using an animal model

IntroductionBrain contusion is a prevalent traumatic brain injury (TBI) in low-age children, bearing the potential for coma and fatality. Hence, it is imperative to undertake comprehensive research in this field. MethodsThis study employed 4-week-old piglets as surrogates for children and introduced self-designed devices for both free-fall drop impact tests and drop-hammer impact tests. The study explored the characteristics of brain contusion and dynamic responses of brain under these distinct testing conditions. ResultsBrain contusions induced by free-fall and drop-hammer conditions both were categorized as the coup injury, except that slight difference in the contusion location was observed, with contusion occurring mainly in the surrounding regions beneath the impact location under free-fall condition and the region just right beneath the impact location under drop-hammer condition. Analysis of impact force and intracranial pressure (ICP) curves indicated similar trends in impact forces under both conditions, yet different trends in ICPs. Further examination of the peak impact forces and ICPs elucidated that, with increasing impact energy, the former followed a combined power and first-order polynomial function, while the latter adhered to a power function. The brain contusion was induced at the height (energy) of 2 m (17.2 J), but not at the heights of 0.4, 0.7, 1, 1.35 and 1.7 m, when the vertex of the piglet head collided with a rigid plate. In the case of a cylindrical rigid hammer (cross-sectional area constituting 40 % of the parietal bone) striking the head, the brain contusion was observed under the energy of 21.9 J, but not under energies of 8.1 J, 12.7 J and 20.3 J. Notably, the incidence of brain contusion was more pronounced under the free-fall condition. ConclusionsThese findings not only facilitate a comprehensive understanding of brain contusion dynamics in pediatric TBIs, but also contribute to the validation of theories and finite element models for piglet heads, which are commonly employed as surrogates for children.

Real-time Gait Event Tracker (RGET): An Innovative Approach to Digital Human Modeling through Integration of Inertial Measurement Unit and Dynamic Feature Extraction

The advancement of digital human modeling technology underscores the importance of accurately representing human characteristics and behaviors using motion capture technologies. This paper introduces the Real-time Gait Event Tracker (RGET), an advanced method aimed at precisely detecting gait events via an Inertial Measurement Unit (IMU), thereby supporting high-precision digital human modeling. RGET integrates planning techniques into continuous states and action spaces, utilizing first-order difference functions and sliding window techniques to effectively identify four key gait events: Heel Strike (HS), Toe Off (TO), Walking Start (WS), and Walking Pause (WP). The system efficiently manages IMU gait signal data through real-time queuing techniques and extracts dynamic features within time frames using positive/negative windowed first-order difference integrations. By adopting weighted sleep time methods and adaptive threshold decision rules, RGET accurately extracts gait event features from sequences. Not only does RGET support precise gait segmentation with an F1 score of 95.9%, but it also provides an innovative method for digital human modeling and its applications.

A novel kriging-improved high-dimensional model representation metamodelling technique for approximating high-dimensional problems

Aiming to address the issue of the ‘curse of dimensionality’ encountered in approximating high-dimensional problems using surrogate-based methods, high-dimensional model representation (HDMR), decomposing the high-dimensional problem into summands of different-order component functions, has been widely studied. To reduce the computational demands of the current HDMR metamodelling techniques, an improved high-dimensional model representation framework (iHDMR) is presented, taking full advantage of the relationships between the first-order and second-order component functions in the Cut-HDMR theory. then, a novel metamodelling technique, termed kriging (KRG)-iHDMR, is implemented by integrating the kriging technique and the suggested surface-axes alternating sampling strategy into the iHDMR framework. The accuracy and efficiency of KRG-iHDMR are demonstrated by various numerical and engineering examples with different dimensions. Finally, an optimization problem of the multi-stage solid launch vehicle propulsion system is introduced to verify the engineering feasibility of the KRG-iHDMR metamodelling technique.

Error Bounds for Fractional Integral Inequalities with Applications

Fractional calculus has been a concept used to obtain new variants of some well-known integral inequalities. In this study, our main goal is to establish the new fractional Hermite–Hadamard, and Simpson’s type estimates by employing a differentiable function. Furthermore, a novel class of fractional integral related to prominent fractional operator (Caputo–Fabrizio) for differentiable convex functions of first order is proven. Then, taking this equality into account as an auxiliary result, some new estimation of the Hermite–Hadamard and Simpson’s type inequalities as generalization is presented. Moreover, few inequalities for concave function are obtained as well. It is observed that newly established outcomes are the extension of comparable inequalities existing in the literature. Additionally, we discuss the applications to special means, matrix inequalities, and the q-digamma function.

Aero-engine Degradation Evaluation Based on First-Order Transition Function and Gaussian Mapping Networks

Aero-engine Degradation Evaluation Based on First-Order Transition Function and Gaussian Mapping Networks

Minimum contrast for the first-order intensity estimation of spatial and spatio-temporal point processes

In this paper, we harness a result in point process theory, specifically the expectation of the weighted K-function, where the weighting is done by the true first-order intensity function. This theoretical result can be employed as an estimation method to derive parameter estimates for a particular model assumed for the data. The underlying motivation is to avoid the difficulties associated with dealing with complex likelihoods in point process models and their maximization. The exploited result makes our method theoretically applicable to any model specification. In this paper, we restrict our study to Poisson models, whose likelihood represents the base for many more complex point process models. In this context, our proposed method can estimate the vector of local parameters that correspond to the points within the analyzed point pattern without introducing any additional complexity compared to the global estimation. We illustrate the method through simulation studies for both purely spatial and spatio-temporal point processes and show complex scenarios based on the Poisson model through the analysis of two real datasets concerning environmental problems.

Non-Gaussian Correlations in the Steady State of Driven-Dissipative Clouds of Two-Level Atoms.

We report experimental measurements of the second-order coherence function g^{(2)}(τ) of the light emitted by a laser-driven dense ensemble of ^{87}Rb atoms. We observe a clear departure from the Siegert relation valid for Gaussian chaotic light. Measuring intensity and first-order coherence, we conclude that the violation is not due to the emergence of a coherent field. This indicates that the light obeys non-Gaussian statistics, stemming from non-Gaussian correlations in the atomic medium. More specifically, the steady state of this driven-dissipative many-body system sustains high-order correlations in the absence of first-order coherence. These findings call for new theoretical and experimental explorations to uncover their origin, and they open new perspectives for the realization of non-Gaussian states of light.

Augmented-Resolution Digital image correlation algorithm for vibration measurements

Digital Image Correlation (DIC) is a widespread technique, and many different implementations were developed in the literature to optimize the algorithm performance. In this paper, a new DIC algorithm is optimized for vibration measurements, where the displacement amplitude drastically decreases with the increase in frequency. Even if high-resolution cameras are used, it is mandatory to use a DIC algorithm with reliable sub-pixel performance. DIC algorithms are generally optimized for large complex displacement fields, and they solve the sub-pixel problem by fitting correlation data through a second-order polynomial function. An innovative solution is proposed to push the sub-pixel accuracy and increase the signal-to-noise ratio of the measurement, by exploiting image resizing to achieve virtual higher resolutions and by adopting a quartic polynomial function to interpolate the displacement map with an increased number of interpolation points. The proposed algorithm is validated through synthetic and experimental data and compared to literature DIC algorithms.

Abstract 891: Turning data into information: Using PD3D® models to guide colorectal cancer therapy by Optim.AITM

Abstract Colorectal cancer (CRC) is one of the most prevalent and lethal malignancies globally with up to 50 % of patients eventually progressing to metastatic disease. The mitogen-activated-protein kinase (MAPK) pathway emerges as a key player, being one of the most frequently mutated signaling pathways in the oncogenesis of CRC. However, given the numerous genomic aberrations and tumor heterogeneity in CRC, patients may benefit from combinatorial therapies, particularly those who have inoperable or metastatic tumors. In the present study, we investigated the feasibility of combining two platforms, patient-derived 3D (PD3D®) models with Optim.AI™, to identify more effective cancer therapies. PD3D® models can robustly retain the genotypic and histopathologic features of the primary patient tumor, model tumor heterogeneity and were shown to predict a patient’s drug response. Optim.AI™ is a hybrid computational-experimental platform that uses small data sets to rationally converge to optimal drug combinations within a defined drug search space. By mapping experimental data points to a second-order quadratic function, Optim.AI™ can predict every possible 531k data points and thus the cell-killing efficacy for all other possible combinations without testing each individual drug-dose combination. Two CRC PD3D® models with different mutation profiles were tested with 155 different combinations of 12 drugs at variant concentrations. The post-treatment cell viability was measured and used for Optim.AI™ analysis to evaluate and compare the best therapies. Optim.AI™ analysis revealed differential drug sensitivity between tested CRC PD3Ds®. The top-ranked drug combinations included SN-38, active compound of commonly used chemotherapeutic irinotecan, paired with MEK-inhibitors trametinib or cobimetinib which we could confirm with both platforms. With this study, we successfully demonstrated the feasibility, the robustness, and the efficiency of combining PD3Ds® and Optim.AI™ in identifying effective drug combination therapies, here for CRC, within one month. This combined technology provides precise insights into tumor treatability and its functional causes of treatment outcomes, leading to new treatment combinations and accelerating the development of new cancer drugs in a time- and cost-effective manner. Citation Format: Ulrike Pfohl, Masturah Mohd Abdul Rashid, Jhin Jieh Lim, Juergen Loskutov, Lena Wedeken, Edward Kai-Hua Chow, Hugo Saavedra, Christoph Reinhard, Christian R. Regenbrecht. Turning data into information: Using PD3D® models to guide colorectal cancer therapy by Optim.AITM [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2024; Part 1 (Regular Abstracts); 2024 Apr 5-10; San Diego, CA. Philadelphia (PA): AACR; Cancer Res 2024;84(6_Suppl):Abstract nr 891.