We have implemented quantum modeling mainly based on Bohmian Mechanics to study time series that contain strong coupling between their events. Compared to time series with normal densities, such time series are associated with rare events. Hence, employing Gaussian statistics drastically underestimates the occurrence of their rare events. The central objective of this study is to investigate the effects of rare events in the probability densities of time series from the point of view of quantum measurements. For this purpose, we first model the non-Gaussian behavior of time series using the multifractal random walk (MRW) approach. Then, we examine the role of the key parameter of MRW, λ, which controls the degree of non-Gaussianity, in quantum potentials derived for time series. Our Bohmian quantum analysis shows that the derived potential takes some negative values in high frequencies (its mean values), then substantially increases, and the value drops again for rare events. Thus, rare events can generate a potential barrier in the high-frequency region of the quantum potential, and the effect of such a barrier becomes prominent when the system transverses it. Finally, as an example of applying quantum potential beyond the microscopic world, we compute quantum potentials for the S&P financial market time series to verify the presence of rare events in the non-Gaussian densities and demonstrate deviation from the Gaussian case.

Accurate streamflow forecasting is crucial for effectively managing water resources, particularly in countries like Colombia, where hydroelectric power generation significantly contributes to the national energy grid. Although highly interpretable, traditional deterministic, physically-driven models often suffer from complexity and require extensive parameterization. Data-driven models like Linear Autoregressive (LAR) and Long Short-Term Memory (LSTM) networks offer simplicity and performance but cannot quantify uncertainty. This work introduces Sparse Variational Gaussian Processes (SVGPs) for forecasting streamflow contributions. The proposed SVGP model reduces computational complexity compared to traditional Gaussian Processes, making it highly scalable for large datasets. The methodology employs optimal hyperparameters and shared inducing points to capture short-term and long-term relationships among reservoirs. Training, validation, and analysis of the proposed approach consider the streamflow dataset from 23 geographically dispersed reservoirs recorded during twelve years in Colombia. Performance assessment reveals that the proposal outperforms baseline Linear Autoregressive (LAR) and Long Short-Term Memory (LSTM) models in three key aspects: adaptability to changing dynamics, provision of informative confidence intervals through Bayesian inference, and enhanced forecasting accuracy. Therefore, the SVGP-based forecasting methodology offers a scalable and interpretable solution for multi-output streamflow forecasting, thereby contributing to more effective water resource management and hydroelectric planning.

A vast majority of the countries is under the economic and health crises due to the current epidemic of coronavirus disease 2019 (COVID-19). The present study analyzes the COVID-19 using time series, which is an essential gizmo for knowing the enlargement of infection and its changing behavior, especially the trending model. We have considered an autoregressive model with a non-linear time trend component that approximately converted into the linear trend using the spline function. The spline function split the COVID-19 series into different piecewise segments between respective knots and fitted the linear time trend. First, we obtain the number of knots with its locations in the COVID-19 series and then the estimation of the best-fitted model parameters are determined under Bayesian setup. The results advocate that the proposed model/methodology is a useful procedure to convert the non-linear time trend into a linear pattern of newly coronavirus case for various countries in the pandemic situation of COVID-19.

Suitable measures of grazing impacts on ground cover, that enable separation of the effects of climatic variations, are needed to inform land managers and policy makers across the arid rangelands of the Northern Territory of Australia. This work developed and tested a time-series, change-point detection method for application to time series of vegetation fractional cover derived from Landsat data to identify irregular and episodic ground-cover growth cycles. These cycles were classified to distinguish grazing impacts from that of climate variability. A measure of grazing impact was developed using a multivariate technique to quantify the rate and degree of ground cover change. The method was successful in detecting both long term (> 3 years) and short term (< 3 years) growth cycles. Growth cycle detection was assessed against rainfall surplus measures indicating a relationship with high rainfall periods. Ground cover change associated with grazing impacts was also assessed against field measurements of ground cover indicating a relationship between both field and remotely sensed ground cover. Cause and effects between grazing practices and ground cover resilience can now be explored in isolation to climatic drivers. This is important to the long term balance between ground cover utilisation and overall landscape function and resilience.

We study a conformation of an albumin protein in the temperature range of 300K-315K, i.e. in the physiological range of temperature. Using simulations we calculate values of two backbone angles, that carry most of information about positioning of the protein chain in a conformational space. Given these, we calculate energy components of such protein. Further, using the Flory theory we determine the temperature in which investigated albumin chain model is closest to the free joined chain model. Near the Flory temperature, we study energy components and the conformational entropy, both derived from two angles that reflect most of the chain dynamics in a conformational space. We show that the conformational entropy is an oscillating function of time in considered range of temperature. Our finding is that, the only regular oscillation pattern appears near the Flory temperature.

Gradual disability worsening in Multiple Sclerosis (MS) is indicative of confirmed progression that mostly involves progression independent of relapse activity (PIRA) and is associated with neurodegeneration. Insights from pathology reveal grey matter involvement (neocortex, hippocampus, spinal cord, and deep grey matter structures) and microglia activation in early stages of MS. Cortical lesions result in thinning and atrophy and are considered accurate predictors of disability progression and cognitive decline.Neuroimaging biomarkers, such as high-resolution 7T MR images and TSPO-PET, have been examined for the detection of cortical pathology linked to cognitive deficits and thus progression, but are limited in clinical practice due to availability, time constraints, and cost.Electroencephalography (EEG) emerges as a non-invasive, cost-effective tool that reflects cortical activity in MS. Its potential in monitoring cognitive impairment is explored by focusing on nonlinear EEG analysis. The MuST PREDICT^TM project aims to extract linear and nonlinear EEG features, investigating their role in predicting disease progression and optimizing treatment. The study employs retrospective, cross-sectional, and prospective designs, utilizing EEGs from various MS forms, cognitive assessments, serum/cerebrospinal fluid biomarkers and neuroimaging. The methodology involves time-based and spectral feature extraction, employing artificial intelligence classifiers and brain criticality-based approaches.The conceptual framework of an innovative modality is herein presented, that would EEG for early MS progression detection. Standardization of the methodology could lead to the creation of a digital tool for better prognostication and treatment strategy optimization.

In this paper, we present Binet's formulas, generating functions, and the summation formulas for generalized Pentanacci numbers, and as special cases, we investigate Pentanacci and Pentanacci-Lucas numbers with their properties. Also, we define Gaussian generalized Pentanacci numbers and as special cases, we investigate Gaussian Pentanacci and Gaussian Pentanacci-Lucas numbers with their properties. Moreover, we give some identities for these numbers. Furthermore, we present matrix formulations of generalized Pentanacci numbers and Gaussian generalized Pentanacci numbers.

In wireless sensor networks (WSNs), each sensor node can estimate the global parameter from the local data in distributed manner. This paper proposed a robust diffusion estimation algorithm based on minimum error entropy criterion with self-adjusting step-size, which are referred to as diffusion MEE-SAS (DMEE-SAS) algorithm. The DMEE-SAS algorithm has fast speed of convergence and is robust against non-Gaussian noise in the measurements. The detailed performance analysis of the DMEE-SAS algorithm is performed. By combining the DMEE-SAS with diffusion minimum error entropy (DMEE) algorithms, an Improving DMEE-SAS algorithm is proposed, in non-stationary environment where tracking is very important. The Improving DMEE-SAS algorithm can avoid insensitivity of the DMEE-SAS algorithm due to the small effective step-size near the optimal estimator, and obtain a fast convergence speed. Numerical simulations are given to verify the effectiveness and advantages of these proposed algorithms.

In this study, the generality and prediction accuracy of a generalised series model for large eddy simulation of premixed and non-premixed turbulent combustion is explored. The model is based on Taylor series expansion of the chemical source term in scalar space and implemented into OpenFOAM. The mathematical model does not depend on the combustion regimes, and has the correct limiting behaviour. The numerical error sources are outlined and analysed. The model is first applied to a piloted methane/air non-premixed jet flame (Sandia Flame D). The statistical (time-averaged and RMS) results agree well with experimental measurements, particularly with regard to the mixture fraction, velocity, temperature, and concentrations of major species CH4, CO2, H2O, and O2. The concentrations of intermediates CO and H2 are over-predicted, due to the limitations of the reduced reaction mechanism employed. Then, a Bunsen piloted flame is simulated. Most of the statistical properties of both reactive species and progress variable are well reproduced. The only major discrepancy evident is in the temperature, which is attributed to the experimental uncertainties of temperature fields in the pilot stream. These findings have demonstrated the model`s generality for both premixed and non-premixed combustion simulation, as well as the accuracy of prediction of reactive species distribution.

Small bowel non-Meckelian diverticulosis is a rare condition with only few published cases despite being described over 200 years ago. In the midst of the COVID-19 pandemic, studies suggested that a lot of patients may experience gastrointestinal manifestations. Intestinal symptoms could worsen the inflammation and infection associated with small bowel diverticulitis. Here, we present two cases: one with inflammation and rupture in a COVID-19 patient and the other as an asymptomatic detection. Furthermore, we provide a mini-review of the literature to emphasize the importance of considering this entity in the differential diagnosis of an acute abdomen.

In our investigation of the time evolution of energy states Einstein’s interpretation from more than a century ago is found to have greater internal consistency than that of non-relativistic quantum mechanics. We choose to align more closely with his methods by abandoning the non-relativistic Hamiltonian method, which has been the standard for nearly a century, in favor of a relativistically correct Lagrangian method. Integral equations of motion for the absorption and emission of radiation are derived that underlie and anticipate the differentially motivated Schrödinger equation. This new interpretation applies to a large volume of experimental evidence of both classical and quantum mechanical origin. Among the examples discussed in support are Planck’s law describing black body radiation, matrix mechanics, the function of the simplest quantum mechanical system an electron cyclotron, chaos theory, and evolutionary biology.

This study demonstrates a global, non-parametric, non-iterative optimization of time-mean value of a kind of index vibrated by time-varying forcing. It is based on the fact that the (steady) forced vibration of non-autonomous ordinary differential equation systems is well approximated by an analytical solution when the amplitude of forcing is sufficiently small and its base state without forcing is linearly stable and steady. It is applied to optimize a time-averaged heat-transfer rate on a two-dimensional thermal convection field in a square cavity with horizontal temperature difference, and the globally optimal way of vibrational forcing, i.e. the globally optimal, spatial distribution of vibrational heat and vorticity sources, is first obtained. The maximized vibrational thermal convection corresponds well to the state of internal gravity wave resonance. In contrast, the minimized thermal convection is weak, keeping the boundary layers on both sidewalls thick.

In many industrial, automotive, and aerospace applications, electro-mechanical systems are subjected to random vibration excitations, and the most critical components are required to undergo qualification tests to verify their suitability. Measured field data are commonly considered as reference for the synthesis of random stationary signals used as shaker input excitations in laboratory tests. For the most popular procedures of random-control testing, the user sets the input profiles in terms of power spectral density (PSD) associated with randomized phases generated by the shaker controller to finally provide the physical motion. As a result, the overall probability distribution of the test signal tends toward Gaussian, whereas many real-life random excitations prove non-Gaussian due to distinctive bursts and peaks. The quantitative estimate of the number and amplitudes of peaks present in a certain signal is usually made through the statistical parameter known as kurtosis. The so-called kurtosis control methods presented in the literature are conceived to perform qualification tests with random and non-Gaussian vibration excitations. In this paper, two novel algorithms able to synthesize shaker input signals for random-control testing with prescribed PSD and kurtosis value are proposed, and the results of their application are comparatively discussed to assess their effectiveness and potentialities in different kinds of qualification testing, including accelerated fatigue-life tests.

Phenomenon of vacuum fluctuations of virtual particles in high energy physics has been mathematically modeled by a third order differential equation. Aim of present theory is to unravel underlying mathematical equation capable of explaining microscopic phenomenon of vacuum fluctuations. Solution of such a differential equation after applying appropriate boundary conditions gives an acceptable wave function i.e. . Operation of energy and time operator on this wave function proves that these operators do not hold commutative property. Time energy uncertainty principle has been derived by calculating variance of energy and time for the same wave function.

This paper focuses on the problem of finite-time stabilization of homogeneous, non-Lipschitz systems with dilations. A key contribution of this paper is the design of a virtual recursive Hölder, non-Lipschitz state feedback which renders the non-Lipschitz systems in the special case dominated by a lower-triangular nonlinear system, finite-time stable. The proof is based on a recursive design algorithm developed recently, to construct the virtual Hölder continuous, finite-time stabilizer as well as a C¹ positive definite and proper Lyapunov function that guarantees finite-time stability of the non-Lipschitz non-linear systems.

This article describes an algorithm for estimation the variance of Gaussian noise. The data is smoothed using the Savitsky-Golay polynomial filter. Absolute differences between original and smoothed data are sorted in ascending order. The initial part of this sequence is selected for analysis. The result of calculation mean value of differences can be used to estimate the variance of the noise. By selecting points for analysis, the impact of cosmic ray noise and other artifacts can be reduced. The use of the proposed method for artificial and real spectra shows the ability to effectively estimate the noise variance. The algorithm contains no user-defined parameters.

Night-time lights interact with human physiology through different pathways starting at the retinal layers of the eye, from the signals provided by the rods, the S-, L- and M-cones, and the intrinsically photosensitive retinal ganglion cells (ipRGC). These individual photic channels combine in complex ways to modulate important physiological processes, among them the daily entrainment of the neural master oscillator that regulates circadian rhythms. Evaluating the relative excitation of each type of photoreceptor generally requires full knowledge of the spectral power distribution of the incoming light, information that is not easily available in many practical applications. One such instance is wide area sensing of public outdoor lighting; present-day radiometers onboard Earth-orbiting platforms with sufficient nighttime sensitivity are generally panchromatic and lack the required spectral discrimination capacity. In this paper we show that RGB imagery acquired with off-the-shelf digital single-lens reflex cameras (DSLR) can be a useful tool to evaluate, with reasonable accuracy and high angular resolution, the photoreceptoral inputs associated with a wide range of lamp technologies. The method is based on linear regressions of these inputs against optimum combinations of the associated R, G, and B signals, built for a large set of artificial light sources by means of synthetic photometry. Given the widespread use of RGB imaging devices, this approach is expected to facilitate the monitoring of the physiological effects of light pollution, from ground and space alike, using standard imaging technology.

All the arguments of a wavefunction are defined at the same instant implying a notion of simultaneity. In a somewhat related matter, certain phenomena in quantum mechanics seem to have non-local causal relations. Both concepts are in contradiction with special relativity. We propose to define the wavefunction with respect to the invariant proper time of special relativity instead of standard time. Moreover, we shall adopt the original idea of Schrodinger suggesting that the wavefunction represents an ontological cloud-like object that we shall call ‘individual fabric’ that has a finite density amplitude vanishing at infinity. Consequently, measurement can be assimilated to a confining potential that triggers an inherent non-local mechanism within the individual fabric. It is formalised by multiplying the wavefunction with a localising gaussian as in the GRW theory but in a deterministic manner.

Atmospheric correction is the processes of converting radiance measured at a spectral 1 sensor to the reflectance of the materials in a multispectral or hyperspectral image. This is an 2 important step for detecting or identifying the materials present in the pixel spectra. We present 3 two machine learning models for atmospheric correction trained and tested on 100,000 batches of 40 4 reflectance spectra converted to radiance using MODTRAN, so the machine learning model learns 5 the radiative transfer physics from MODTRAN. We created a theoretically interpretable Bayesian 6 Gaussian process model and a deep learning autoencoder treating the atmosphere as noise. We 7 compare both methods for estimating gain in the correction model to the well-know QUAC method 8 of assuming a constant mean endmember reflectance. Prediction of reflectance using the Gaussian 9 process model outperforms the other methods in terms of both accuracy and reliability.

Non-orthogonal multiple access (NOMA) has been investigated to support massive connectivity for Internet-of-things (IoT) networks. However, since most IoT devices suffer from limited power and decoding capabilities, it is not desirable to pair a large number of devices simultaneously, which encourages two-user NOMA grouping. Additionally, most existing techniques have not considered the diversity in the target QoS of IoT devices, which may lead to spectrum inefficiency. Few investigations have partially considered that issue by using an order-based power allocation (OPA) approach, where the power is allocated according to the order to the user's target throughput within a priority-based NOMA (PNOMA) group. However, this does not fully capture the effects of diversity in the values of the users' target throughputs. In this work, we handle both problems by considering a throughput-based power allocation (TPA) approach, that captures the QoS diversity, within a three-users PNOMA group as a compromise between spectral efficiency and complexity. Specifically, we investigate the performance of a time-division PNOMA (TD-PNOMA) scheme, where the transmission time is divided into two-time slots with two-users per PNOMA group. The performance of such TD-PNOMA is compared with a fully PNOMA (F-PNOMA) scheme, where the three users share the whole transmission time, in terms of the ergodic capacity under imperfect successive interference cancellation (SIC). The results reveal the superiority of TPA compared with OPA approach in both schemes, besides that the throughput of both schemes can outperform each other under imperfect SIC based on the transmit signal-to-noise ratio and the deployment scenarios.

Outliers can influence regression model parameters and change the direction of the estimated effect, over-estimating or under-estimating the strength of the association between a response variable and an exposure of interest. Identifying visit-level outliers from longitudinal data with continuous time-dependent covariates is important especially when the distribution of such variable is highly skewed at follow-up visits. The primary objective was to identify potential outliers at follow-up visits using interquartile range (IQR) statistic, motivated by a large TEDDY dietary longitudinal and time-to-event data with a continuous time varying vitamin B12 intake as the exposure of interest and time to developing Islet Autoimmunity (IA) as the response variable. The IQR method was also applied to simulated data. To assess the impact of IQR-method detected outliers, data was analyzed using Cox-proportional hazard model with robust sandwich estimator. Partial residual diagnostic plots were used to detect highly influential outliers. Results showed how some of the detected outliers had large influence on the Cox regression model and changed both the direction of hazard ratios and the strength of association with the risk of developing IA. In conclusion, the IQR method is useful in identifying potential outliers at visit-level which can be further investigated.

Many systems in nature and laboratories are far from equilibrium and exhibit significant fluc- tuations, invalidating the key assumptions of small fluctuations and short memory time in or near equilibrium. A full knowledge of Probability Distribution Functions (PDFs), especially time- dependent PDFs, becomes essential in understanding far-from-equilibrium processes. We consider a stochastic logistic model with multiplicative noise, which has gamma distributions as stationary PDFs. We numerically solve the transient relaxation problem, and show that as the strength of the stochastic noise increases the time-dependent PDFs increasingly deviate from gamma distributions. For sufficiently strong noise a transition occurs whereby the PDF never reaches a stationary state, but instead forms a peak that becomes ever more narrowly concentrated at the origin. The addition of an arbitrarily small amount of additive noise regularizes these solutions, and re-establishes the existence of stationary solutions. In addition to diagnostic quantities such as mean value, standard deviation, skewness and kurtosis, the transitions between different solutions are analyzed in terms of entropy and information length, the total number of statistically distinguishable states that a system passes through in time.

We study the propagation of a particular field that we call Gaussian-top-hat that presents self-focusing and maintains its shape for some propagation distances.

This study presents a novel technique utilizing high frequency vibration to shorten treatment time and preserve alveolar bone in challenging orthodontic cases treated with Invisalign® clear aligners. Four non-growing orthodontic patients (age range 14-47 years old) with Class II skeletal patterns (convex profiles with retrognathic mandibles) who sought correction of their crowded teeth and non-surgical correction of their convex profiles were included in this study. These patients were treated using Invisalign clear aligners together with high frequency vibration (HFV) devices (120 Hz) (VPro5™) that were used by all patients for five minutes per day during active orthodontic treatment. Vertical control and forward rotation of the mandible for each patient was achieved through pre-programming the Invisalign to produce posterior teeth intrusion. Successful forward rotation of the mandibles achieved in all patients led to improvement of their facial convex profiles (ANB improved 2.1 + 0.5 degrees; FMA improved 1.2 +1.1 degrees). Dental decompensation was achieved by lingual tipping of the lower incisors and palatal root torque of upper incisors. The use of HFV together with Invisalign facilitated achieving these results within a 12+6 month period. In addition, more bone labial to the lower incisors after their lingual movement was noted. In conclusion, the use of HFV concurrent with SmartTrack Invisalign aligners allowed complex tooth movement and forward projection without surgery in non-growing patients with skeletal Class II relationships. The clinical impact and implications of this case series is that the use of HFV facilitates complex orthodontic tooth movement including posterior teeth intrusion and incisor decompensation in addition to increased bone formation labial to lower incisors that may minimize future gum recession due to their labial inclination.

The up-to-date challenge towards clean road transport are non-exhaust emissions. Important advances regarding measurement systems, including well defined characterisation techniques, as well as regulation, will happen in the next few years. In this work we present detailed results of particle emissions from a test bed for wheel suspension and brakes, consisting of aerosol (size distribution, particle number (PN) and mass (PM)) and electron microscopy measurements (EM) under different load conditions. Standard tyres and brakes from series production were tested with a high-load driving cycle while particle measurements were conducted by gravimetric measurements and with a TSI SMPS, a TSI APS and a GRIMM OPS. Furthermore, samples were analyzed by electron microscopy. A bimodal particle size distribution (PSD) was obtained with the SMPS, with peaks at 20nm and around 400nm. EM analysis of &gt;1400 single particles from the electrostatic sampler matches the PSD results. EM analysis also showed ultrafine particles, mainly from O, Fe, Si, Ba, Mg and S and also fractal particles with high C fractions. Our results suggest, in agreement with previously published literature, that particulate emissions are related to brake disc temperature and occur in significant amounts above a threshold temperature.

Heel pain in the “funnel-shaped” space between the calcaneus, talus, and talocalcaneonavicular and subtalar joints may be representative of Sinus Tarsi syndrome. The pain is often characterized by a burning, numbness, or tingling sensation that can stem from strains and tears on the ligaments in that area. Injury treatment typically includes balance training, muscle exercises, bracing, foot orthosis, and non-steroidal anti-inflammatory drugs (NSAIDs). This study presents Wharton Jelly (WJ) tissue allografts as an alternative intervention for patients who fail standard-care treatments. WJ targets tissue defects, unlike other therapies, which aim to reduce swelling and symptomatic pain. This study includes five female patients who have previously failed standard-of-care treatment. Each received extracorporeal pulse-activated therapy (EPAT), WJ, laser therapy, and an orthotic. After an average of 80 days, the cohort had an overall 85.29% improvement in pain. The study's limitations include a small cohort size and a non-blinded design. Given the significant improvement in pain, WJ tissue allograft, combined with other techniques, presents an optimal patient care plan for tissue defects associated with Sinus Tarsi syndrome when standard-of-care treatments fail. These results provide evidence for a more extensive, randomized study to define dosage protocols further and confirm safety and efficacy.

Surface activity of humic acid (HA) and its six sub-fractions isolated from forest soil were characterized by surface tension measurements, dynamic light scattering, and laser doppler electrophoresis. The surface tension of HA sub-fractions decreased from 72.4 mN·m-1 to 36.8 mN·m-1 with the increasing concentration from 0 to 20000 mg·L-1. The critical micelle concentration (CMC) of HA and its sub-fractions ranged from 216 to 1024 mg·L-1 with the multiple linear regression equation of CMC = 18896–6.9×C–296×alkyl-C–331×aromatic-C–17019×H/C+4054×HB/HI (p &lt; 0.05). The Z-average particle size ranges from 108.2 nm to 186.9 nm. The maximum particle size was 5000 nm after filtered with a membrane of 0.45 μm, indicating HA and its sub-fractions progressed self-assembly during 2000 mg·L-1, pH = 6.86. The number-base particle size distribution of HA sub-fractions was identified as four peaks by Gaussian model, and the aggregate sizes were mainly in six clusters including 2 ± 1 nm, 5 ± 2 nm, 10 ± 3 nm, 21 ± 8 nm, 40 ± 10 nm, and &gt; 50 nm indicating multiple aggregations of different particle sizes in the HA fractions solution.

Physical-law based models are widely utilized in the aerospace industry. One such use is to provide flight dynamics models for use in flight simulators. For human-in-the-loop use, such simulators must run in real-time. Due to the complex physics of rotorcraft flight, to meet this real-time requirement, simplifications to the underlying physics sometimes have to be applied to the model, leading to model response errors in the predictions compared to the real vehicle. This study investigated whether a machine-learning technique could be employed to provide rotorcraft dynamic response predictions, with the ultimate aim of this model taking over when the physics-based model's accuracy degrades. In the current work, a machine-learning technique was employed to train a model to predict the dynamic response of a rotorcraft. Machine learning was facilitated using a Gaussian Process (GP) non-linear autoregressive model, which predicted the on-axis pitch rate, roll rate, yaw rate and heave responses of a Bo105 rotorcraft. A variational sparse GP model was then developed to reduce the computational cost of implementing the approach on large data sets. It was found that both of the GP models were able to provide accurate on-axis response predictions, particularly when the input contained all four control inceptors and one lagged on-axis response term. The predictions made showed improvement compared to a corresponding physics-based model. The reduction of training data to one-third (rotational axes) or one-half (heave axis) resulted in only minor degradation of the GP model predictions.

We provide a comprehensive framework for forecasting five minute load using Gaussian processes with a positive definite kernel specifically designed for load forecasts. Gaussian processes are probabilistic, enabling us to draw samples from a posterior distribution and provide rigorous uncertainty estimates to complement the point forecast, an important benefit for forecast consumers. As part of the modeling process, we discuss various methods for dimension reduction and explore their use in effectively incorporating weather data to the load forecast. We provide guidance for every step of the modeling process, from model construction through optimization and model combination. We provide results on data from the PJMISO for various periods in 2018. The process is transparent, mathematically motivated, and reproducible. The resulting model provides a probability density of five-minute forecasts for 24 hours.

Mycobacterium avium ssp paratuberculosis (MAP) is the causative agent of Johne’s disease (JD) in animals and a suspected cause of Crohn’s disease (CD) in humans. Crohn’s Disease is a progressive, detrimental granulomatous enteritis of which common therapies are targeted to suppressing certain components of the immune system. The efficacy of these treatments can be variable and temporary with no clear process of selection for the individual patient. However, diagnosis of MAP has been elusive in patients with Crohn’s Disease. In animals it can be detected by several different techniques, including bacterial cell culture, polymerase chain reaction (PCR), and immunological targets. To move to an understanding of the possible pathogenicity of MAP and the sup-posed cause of CD in humans, it is necessary to demonstrate the presence of cell wall deficient mycobacterial (CWDM) forms of MAP in blood and tissue cultures from patients with CD. From this, more tailored and accurate therapies can be implemented and be developed to eradicate this infectious organism from humans. Current anti-mycobacterial antibiotics have limited efficacy as MAP is subtly different from tuberculosis. Newer methods, such as vaccination and gut microbiome remediation will be essential as part of combination therapies.

A small phylogenetically conserved sequence of 11,231 bp termed FAM247 is repeated in human chromosome 22 by segmental duplications. This sequence forms part of diverse genes that span evolutionary time, the protein genes being the earliest as they are present in zebrafish and/or mice genomes, the long non-coding RNA genes and pseudogenes the most recent as they appear to be present only in the human genome. We propose that the conserved sequence provides a nucleation site for new gene development at evolutionary conserved chromosomal loci where the FAM247 sequences reside. The FAM247 sequence also carries information in its open reading frames that provides protein exon amino acid sequences; one exon plays an integral role in immune system regulation, specifically, the function of ubiquitin specific protease (USP18) in the regulation of interferon. An analysis of this multifaceted sequence and the genesis of genes that contain it are presented.

Motivated by the intriguing discovery of $X(6900)$ by LHCb Collaboration, we undertake a comprehensive study of the $s\bar{s}s\bar{s}$ tetraquark system in positive parity, employing the Gaussian expansion within the chiral quark model method. We consider two structures, diquark-antidiquark ($ss$-$\bar{s}\bar{s}$) structure and meson-meson ($s\bar{s}$-$s\bar{s}$)strcuture, encompassing all conceivable color and spin configurations. Despite the absence of bound states in our calculations, we have identified potential resonant states with $J^P=0^{+}$, namely $R(0,2150)$ and $R(0,2915)$, as well as a resonant state with $J^P=1^{+}$ denoted as $R(1,2950)$, and a resonant state with $J^P=2^{+}$ denoted as $R(2,2850)$, utilizing the real-scaling method. Through a comparison of their energies and widths, we propose that $R(0,2915)$ and $R(1,2950)$ may share characteristics with $X(6900)$, while $R(0,2150)$ could be a promising experimental candidate for $f_0(2100)$. We strongly advocate for experimental investigations to shed light on the existence and properties of these resonant states.

High PM10 concentrations are still a significant problem in many parts of the world. In many countries, including Poland, 50μg/m3 is the permissible threshold for a daily averaged PM10 concentration. The number of people affected by this threshold’s exceedance is challenging to estimate and requires high-resolution concentration maps. This paper presents an application of random forests for downscaling regional model air quality results. As policymakers and other end users are eager to receive a detailed resolution PM10 concentration maps, we propose a technique which utilizes the results of regional CTM (GEM-AQ, with 2.5km resolution) and local Gaussian plume model. As a result, we receive a detailed, 250-meter resolution PM10 distribution, which resembles the complex emission pattern in a foothill area in southern Poland. The random forest results are highly consistent with the GEM-AQ and observed concentration. We also discuss different strategies of data training random forest - using additional features and selecting target variables.

A class of models for non-Gaussian spatial random fields is explored for spatial field reconstruction in environmental and sensor network monitoring. The family of models explored utilises a class of transformation functions known as the Tukey g-and-h transformations to create a family of warped spatial Gaussian process models which can support various desirable features such as flexible marginal distributions, which can be skewed, leptokurtic and/or heavy-tailed. The resulting model is widely applicable in a range of spatial field reconstruction applications. To utilise the model in applications in practice, it is important to carefully characterise the statistical properties of the Tukey g-and-h random fields. In this work, we both study the properties of the resulting warped Gaussian processes as well as using the characterising statistical properties of the warped processes to obtain flexible spatial field reconstructions. In this regard, we derive five different estimators for various important quantities often considered in spatial field reconstruction problems. These include the multi-point Minimum Mean Squared Error (MMSE) estimators; the multiple point Maximum A-Posteriori (MAP) estimators; an efficient class of multiple-point linear estimators based on the Spatial-Best Linear Unbiased (S-BLUE) estimators; and two multi-point threshold exceedance based estimators, namely the Spatial Regional and Level Exceedance estimators. Simulation results and real data examples show the benefits of using the Tukey g-and-h transformation as opposed to standard Gaussian spatial random fields in a real data application for environmental monitoring.

The objective of this study was to correlate the binding of drugs on a very popular nanoparticulate polymeric matrix; PLGA nanoparticles with their main constitutional, electronic and physico-chemical descriptors. Gaussian Processes (GPs) was the artificial intelligence machine learning method that was utilized to fulfil this task. The method could successfully model the results where optimum values of the investigated descriptors of the loaded drugs were deduced. A percentage bias of 12.68 % ± 2.1 was obtained in predicting the binding energies of a group of test drugs. As a conclusion, GPs could successfully model the drugs-PLGA interactions associated with a good predicting power. The GPs-predicted binding energies (ΔG) can easily be projected to the drugs loading as was previously proven. Adopting the “Pharmaceutics Informatics” approach can save the pharmaceutical industry and the drug delivery scientists a lot of exerted resources, efforts and time.

The statistics of grain displacements probability distribution function (pdf) during the shear of a granular medium displays an unusual dependence with the shear increment upscaling as recently evinced [Phys. Rev. Lett. 115 238301 2015]. Basically, the pdf of grain displacements has clear nonextensive ($q$-Gaussian) features at small scales but approaches to Gaussian characteristics at large shear window scales -- the granulence effect. Here, we extend this analysis studying a larger system (more grains considered in the experimental setup) which exhibits a severe shear band fault during the macroscopic straining. We calculate the pdf of grain displacements and the dependency of the $q$-statistics with the shear increment. This analysis have shown a singular behavior of $q$ at large scales, displaying a non-monotonic dependence with the shear increment. By means of an independent image analysis, we demonstrate that this singular non-monotonicity could be associated with the emergence of a shear band within the confined system. We show that the exact point where the $q$-value inverts its tendency coincides with the emergence of a giant percolation cluster along the system, caused by the shear band. We believe that this original approach using Statistical Mechanics tools to identify shear bands can be a very useful piece to solve the complex puzzle of the rheology of dense granular systems.

In this article we derive a closed form expression for the symmetric logarithmic derivative of Fermionic Gaussian states. This provides a direct way of computing the quantum Fisher Information for Fermionic Gaussian states. Applications range from quantum Metrology with thermal states to non-equilibrium steady states with Fermionic many-body systems.

In this paper, a complete tool for real-time detection of atypical energy behaviors of airplanes is presented. The methodology extends in real time an existing offline process using Dubins trajectories as a predictor of the remaining distance to the runway threshold. Two major contributions are presented in this paper. First, a real-time measure of the aircraft energy behaviour is defined, indicating whether the aircraft is in good condition to intercept the extended runway centreline from its current position. Secondly, a 2D trajectory suggestion is given, allowing safe management of the approach path according to atypical criteria of historical data. Finally, this document proposes a comprehensive tool for air traffic controllers, which is a major step forward in understanding, becoming aware of and resolving critical situations that could lead to accidents.

There must exist a reformulation of quantum field theory which does not refer to classical time. We propose a pre-quantum, pre-spacetime theory, which is a matrix-valued Lagrangian dynamics for gravity, Yang-Mills fields, and fermions. The definition of spin in this theory leads us to an eight dimensional octonionic space-time. The algebra of the octonions reveals the standard model; model parameters are determined by roots of the cubic characteristic equation of the exceptional Jordan algebra. We derive the asymptotic low energy value 1/137 of the fine structure constant, and predict the existence of universally interacting spin one Lorentz bosons, which replace the hypothesised graviton. Gravity is not to be quantized, but is an emergent four-dimensional classical phenomenon, precipitated by the spontaneous localisation of highly entangled fermions.

Worldwide, the cesarean section rate has steadily increased from 6.7% in 1990 to 21.1% in 2018 and is expected to rise even more. World Health Organization propose the adoption of the Robson classification system as a global standard for monitoring, evaluating, and comparing delivery rates. The purpose of the current study is to use the Robson classification system to investigate how, independently of medical factors, the day of the week and time of delivery may affect the mode of birth. In the sample analysis, we included the records of 8572 women giving birth in one private health facility in Greece. Over 60% of deliveries during the study period were performed by a cesarean section and 8.5% of deliveries were performed by operative vaginal delivery. The results of this study indicate that the lowest birth rates are observed on Monday, Saturday, and Sunday. In Robson category 1 women are 73% more likely to deliver by cesarean section between 08:00 a.m. - 03:59 p.m. compared to those who give birth between 12:00 a.m. - 07:59 a.m. Also, women in group 5.1 are 16.7 times more likely to deliver by cesarean section in the morning compared to overnight deliveries. These result point out two non-clinical variables that influences the CS rate. The Robson classification system was a useful tool for the above comparisons.

The purpose of this work was to evaluate a novel methodology developed by Digital Blood Corporation (DBC) to calculate critical blood values using four non-invasive measured values as input. The values obtained using a point-of-care testing (POCT) device were utilized for comparison and reference. Radial arterial blood was collected for the POCT comparator analysis using the Abbott i-STAT^® device. The non-invasive methodology from DBC requires four parameters to be directly measured: temperature, hemoglobin, pO2, and pCO2. Subsequently, sodium, potassium, chloride, ionized calcium, total carbon dioxide, pH, bicarbonate, and oxygen saturation are calculated using an algorithm. The agreement between the POCT and DBC’s methodology was analyzed using Bland-Altman difference plots. For a second data set, pO2 and pCO2 values collected with the POCT were used as input for DBC’s algorithm to test its robustness. Data from 37 healthy ambulatory individuals, mean age: 42.4 + 13 years; range: 18-64 years, were included in the primary analysis. In the case of the non-invasive gained four input values the greatest variation between POCT and DBC’s approach was observed for pO2 and consequently for algorithm values that depend upon pO2 precision. Replacing transcutaneous pO2 and pCO2 with POCT values demonstrates the principal ability of DBC’s algorithm to predict the additional 8 blood values in sufficient agreement with a standard POCT device in healthy patients. The algorithm developed by DBC appears to be robust in the case of healthy patients but does need the four measured input values with preciseness comparable to a POCT device to give reliable and clinically relevant results. The present study thus serves as a proof of concept to facilitate future study and further development of this methodology into a non-invasive device.

Background: This study explores the impact of a gluten-free diet (GFD) on regional gastrointestinal (GI) transit times in individuals with celiac disease (CD) and non-celiac gluten sensitivity (NGCS). While a GFD is established for managing CD and wheat allergy, its effects on NGCS remain controversial due to inconclusive evidence. Methods: Utilizing a wireless motility and pH capsule (WMC) to assess regional and whole gut transit, newly diagnosed CD (n=12) and NGCS (n=12) patients underwent baseline evaluations, including measurements of gastric, small bowel, and colonic transit times. Results: At baseline conditions, individuals diagnosed with CD exhibited prolonged colonic and intestinal transit times when compared to those with NGCS (p&lt;0.05). Following a 4-week GFD, CD patients experienced significant reductions in both intestinal and colonic transit times, along with enhanced small intestine contractility. NGCS individuals showed improvements in intestinal transit time and contractility with a GFD, although the colon exhibited no discernible effect. The GFD did not significantly impact intragastric, intestinal, or colonic pH. Conclusions: This study, employing WMC for the first time, provides novel insights into the positive effects of a GFD on intestinal and colonic transit, as well as contractility, in CD patients, and to a lesser extent, in those with NGCS.

The abilities of quantitative description of noise are restricted due to its origin and only the statistical and spectral analysis methods can be applied while an exact time evolution cannot be defined or predicted. It emphasizes the challenges faced in many applications including communication systems where noise can play, on one hand, a vital role impacting signal-to-noise ratio but possessing, on the other hand, unique properties such as infinite entropy (infinite information capacity), exponentially decaying correlation function and so on. Despite the deterministic nature of chaotic systems, the predictability of chaotic signals is limited for a short time window putting them close to random noise. In this article, we propose and experimentally verify an approach to achieve Gaussian-distributed chaotic signals by processing the outputs of chaotic systems. The mathematical criteria, on which the main idea of the study is based on, is the Central Limit Theorem which states that the sum of a large number of independent random variables with similar variances approaches a Gaussian distribution. The study involves more than 40 mostly three-dimensional continuous-time chaotic systems (Chua’s, Lorenz’s, Sprott’s, memristor-based, etc.) whose output signals are analyzed according to criteria that encompass the probability density functions of a chaotic signal itself and its envelope and phase, statistical and entropy-based metrics such as skewness, kurtosis, and entropy power. We found that two chaotic signals of Chua’s and Lorenz’s systems exhibited superior performance across the chosen metrics. Furthermore, our focus extended to determining the minimum number of independent chaotic signals necessary to yield a Gaussian-distributed combined signal. The analytic and experimental results indicate that the sum of at least three non-Gaussian chaotic signals closely approximates Gaussian distribution. It allows generation of reproducible Gaussian-distributed deterministic chaos by modeling simple chaotic systems.

Femur length (FL) is a biometric measurement of ultrasound images used to identify the growth patterns and abnormalities of the foetus. Automatic segmentation of FL can improve the efficiency and convenience of inexperienced users. The femur region in a low-cost ultrasound image is a small area with low contrast intensity compared with the non-femur region. This study proposed a fully automated framework for segmenting and measuring the FL in a portable ultrasound image. We utilized statistical modeling, employing Gaussian mixture functions for thresholding to extract the femur area from the background. We also used the localizing region-based active contour method to segment the femur region accurately. We also proposed a refinement step in this framework to obtain a more accurate femur area in the ultrasound image. Because the length and position of the femur are the main factors affecting foetal biometric measurement accuracy, we not only evaluated segmentation results using region-based methods, such as sensitivity, specificity, and dice similarity. We also applied the FL measurement approach to evaluate the angle and length accuracy relative to the ground truth. In terms of region-based segmentation performance, the proposed method provided the best average performance with a sensitivity of 0.78, specificity of 0.87, and dice similarity of 0.81. For FL measurement performance, the proposed framework achieved an average angle accuracy of 0.99, distance accuracy of 0.88, and length accuracy of 0.93.

The Gol'denveizer problem of a torus was studied analytically by Audoly and Pomeau (2002), and the accuracy of the Audoly and Pomeau linear law was confirmed numerically by Sun (2021). However, the law does not include the major radius R of the torus. To find the influence of the major radius, we used finite element numerical simulation to simulate different cases, and we propose a modified Audoly and Pomeau linear law for vertical deformation, which includes R. A linear law of horizontal deformation is presented as well. Our studies show that the Audoly and Pomeau linear law has high accuracy. With modified vertical and horizontal deformation, a displacement-compatible relation between them is formulated.

This paper presents the application of optimal control problem in modeling of stirred tank heater temperature control. The analysis of the open loop system shows that the system is not efficient without a controller. Linear Quadratic Gaussian (LQG) and Linear Quadratic Integral (LQI) controllers are used to increase the performance of the system. Comparison of the closed loop system with the proposed controllers have been done with Matlab/Simulink Toolbox and a promising results have been analyzed.

We proposed a deep learning based chemometric data analysis technique. We trained L2 regularized sparse autoencoder end-to-end for reducing the size of the feature vector to handle the classic problem of curse of dimensionality in chemometric data analysis. We introduce a novel technique of automatic selection of nodes inside hidden layer of an autoencoder through pareto optimization. Moreover, linear regression, ϵ-SVR , and Gaussian process regressor are applied on the reduced size feature vector for the regression. We evaluated our technique on orange juice and wine dataset and results are compared against state-of-the-art methods. Quantitative results are shown on Normalized Mean Square Error (NMSE) and the results show considerable improvement in the state-of- the-art.

Multi-task Gaussian processes (MTGPs) are a powerful approach for modeling structured dependencies among multiple tasks. Researchers on MTGPs have contributed to enhance this approach in various ways. Current MTGP methods, however, cannot model nonlinear task correlations in a general way. In this paper we address this problem. We focus on spectral mixture (SM) based kernels and propose an enhancement of this type of kernels, called multi-task generalized convolution spectral mixture (MT-GCSM) kernel. The MT-GCSM kernel can model nonlinear task correlations and mixtures dependency, including time and phase delay, not only between different tasks but also within a task at the spectral mixture level. Each task in MT-GCSM has its own generalized convolution spectral mixture kernel (GCSM) with a different number of convolution structures and all spectral mixtures from different tasks are dependent. Furthermore, the proposed kernel uses inner and outer full cross convolution between base spectral mixtures, so that the base spectral mixtures in the tasks are not necessarily aligned. Extensive experiments on synthetic and real-life datasets illustrate the difference between MT-GCSM and other kernels as well as the practical effectiveness of MT-GCSM.

Developed countries have shown a time trend towards a younger age at menarche (AAM), which is associated with increased risk of later obesity and non-communicable diseases. We aimed to assess whether a time trend in AAM with associated disease risk is also present in Mexico. For this, we used data of 30,826 women from the Mexican National Health Survey (2000). Linear and log binomial regression was used for nutritional and disease outcomes, whereas Welch-ANOVA was used to test for a time trend. AAM decreased over time (p < 0.001), with a maximal difference of 0.99 years between the 1920s (13.6 years) and 1980s (12.6 years). AAM (in years) was negatively associated with weight (β = -1.01 kg; 95 % CI -1.006, -1,004) and BMI (β = -1.01 kg/m2; -1.007, -1.006), and positively with height (β = 0.18 cm; 0.112, 0.231). AAM was associated with diabetes (RR = 0.95; 0.93, 0.98) and hypercholesterolemia (RR = 0.93; 0.90, 0.95), but not with hypertension, breast cancer or arthritis. In Mexico, AAM decreased significantly during the 20th century. AAM was inversely associated with adult weight and BMI, and positively with height. Women with a later AAM had a lower risk of diabetes and hypercholesterolemia.

In the broader landscape of cryptocurrency risk management, this study delves into the nuanced estimation of Value at Risk (VaR) for a uniformly weighted portfolio of cryptocurrencies, employing the bivariate Normal Inverse Gaussian distribution renowned for its semi-heavy tails. Utilizing high-frequency data spanning from January 1st, 2017, to October 25th, 2022, with a primary focus on Bitcoin and Ethereum, our research seeks to accentuate the resilience of VaR methodology as a paramount risk assessment tool. The essence of our investigation lies in advancing the comprehension of VaR accuracy by quantitatively comparing observed returns of both cryptocurrencies with their corresponding estimated values, with a central theme being the endorsement of the Normal Inverse Gaussian distribution as a potent model for risk measurement, particularly in the domain of high-frequency data. To bolster the statistical reliability of our results, we adopt a forward test methodology, showcasing not only a contribution to the evolution of risk assessment techniques in Finance but also underscoring the practicality of sophisticated distributional models in econometrics. Our findings not only contribute to the refinement of risk assessment methods but also highlight the applicability of such models in precisely modeling and forecasting financial risk within the dynamic realm of cryptocurrencies, epitomized by the case study of Bitcoin and Ethereum.

Due to the great threat of torpedo against surface warships, an efficient hydroacoustic countermeasure system must output realtime strategies that can accommodate varied antagonizing scenarios. Aiming at the decision-making problem in the anti-torpedo hydroacoustic countermeasure cases, this paper proposes an intelligent adversarial strategy based on the game theory. By discretizing the strategy space of both sides, a matrix game model is established with the payoff characterized by the capture probability of attacking torpedo. An improved simplex algorithm is then developed to get the mixed-strategy Nash equilibrium of the game model, with which preferred avoiding strategies can be obtained to minimize the risk of being captured by the attacking torpedo. Based on the probabilistic view of preferred adversarial strategy, the launching strategy of floating acoustic decoy can be achieved, and the evasion trajectory of warship can be confirmed simultaneously. Numerical simulation demonstrates that the proposed method can generate realtime intelligent antagonizing strategy, and consequently, can improve the survival rate of surface warships in the of anti-torpedo countermeasure scenarios.

This paper explores the use of different deep learning models for predicting precipitation in 56 meteorological stations in Jilin Province, China. The models used include Stacked-LSTM, Transformer, and SVR, and Gaussian noise is added to the data to improve their robustness. Results show that the Stacked-LSTM model performs the best, achieving high prediction accuracy and stability. The study also conducts variable attribution analysis using LightGBM and finds that temperature, dew point, precipitation in previous days, and air pressure are the most important factors affecting precipitation prediction, which is consistent with traditional meteorological theory. The paper provides detailed information on the data processing, model training, and parameter settings, which can serve as a reference for future precipitation prediction tasks. The findings suggest that adding Gaussian noise to the dataset can improve the model's generalization ability, especially for predicting days with zero precipitation. Overall, this study provides useful insights into the application of deep learning models in precipitation prediction and can contribute to the development of meteorological forecasting and applications.

Background: Functional Movement Screening (FMS) allows for rapid assessment of an individual’s physical activity level and timely detection of sports injury risk. However, traditional functional movement screening often requires on-site assessment by experts, which is time-consuming and prone to subjective bias. Therefore, the study of automated functional movement screening has become increasingly important. Methods: In this study, we propose an automated assessment method for FMS based on the improved Gaussian Mixture Model (GMM). First, the oversampling of minority samples is conducted, the movement features are manually extracted from the FMS dataset collected with two Azure Kinect depth sensors, then we train the Gaussian mixture model with different scores (1 point, 2 points, 3 points) of feature data separately, finally, we conducted FMS assessment by the Maximum Likelihood estimation. Results: The improved GMM has a higher scoring accuracy (Improved GMM:0.8) compared to other models (Traditional GMM=0.38, Adaboost.M1=0.7, Naïve-Bayes=0.75), and the scoring results of improved GMM have a high level of agreement with the expert scoring (kappa=0.67). Conclusions: The results show that the proposed method based on the improved Gaussian mixture model can effectively perform the FMS assessment task and it is potentially feasible to use depth cameras for FMS assessment.

Weaving is an ancient and effective structural forming technique characterized by the ability to convert two-dimensional ribbons to three-dimensional structures. However, most 3D structures woven from straight ribbons have topological defects. Baek et al. proposed a method to weave smoother continuous 3D surface structures using naturally curved (in-plane) ribbons, obtained a new surface structure with relatively continuous variation of Gaussian curvature, and analyzed its geometric properties. We believe that this new 3D surface structure with smooth geometric properties must correspond to new mechanical properties. To this end, we investigated a 3D surface structure using naturally curved (in-plane) ribbon weaving, and the results of calculations and experiments show that such structures have better buckling stability than those woven with straight ribbons. It is observed that the number of ribbons influences the buckling behavior of different types of woven structures.

This work addresses the problem of sampling from Gaussian probability distributions by means of uniform samples obtained deterministically and directly from space-filling curves (SFCs), a purely topological concept. To that end, the well-known inverse cumulative distribution function method is used, with the help of the probit function,which is the inverse of the cumulative distribution function of the standard normal distribution. Mainly due to the central limit theorem, the Gaussian distribution plays a fundamental role in probability theory and related areas, and that is why it has been chosen to be studied in the present paper. Numerical distributions (histograms) obtained with the proposed method, and in several levels of granularity, are compared to the theoretical normal PDF, along with other already established sampling methods, all using the cited probit function. Final results are validated with the Kullback-Leibler and two other divergence measures, and it will be possible to draw conclusions about the adequacy of the presented paradigm. As is amply known, the generation of uniform random numbers is a deterministic simulation of randomness using numerical operations. That said, sequences resulting from this kind of procedure are not truly random. Even so, and to be coherent with the literature, the expression ”random number” will be used along the text to mean ”pseudo-random number”.

In this work, Gaussian Tribonacci functions are defined and investigated on the set of real numbers $\mathbb{R},$ \textit{i.e}., functions $f_{G}$ $:$ $\mathbb{R}\rightarrow \mathbb{C}$ such that for all $% x\in \mathbb{R},$ $n\in \mathbb{Z},$ $f_{G}(x+n)=f(x+n)+if(x+n-1)$ where $f$ $:$ $\mathbb{R}\rightarrow \mathbb{R}$ is a Tribonacci function which is given as $f(x+3)=f(x+2)+f(x+1)+f(x)$ for all $x\in \mathbb{R}$. Then the concept of Gaussian Tribonacci functions by using the concept of $f$-even and $f$-odd functions is developed. Also, we present linear sum formulas of Gaussian Tribonacci functions. Moreover, it is showed that if $f_{G}$ is a Gaussian Tribonacci function with Tribonacci function $f$, then $% \lim\limits_{x\rightarrow \infty }\frac{f_{G}(x+1)}{f_{G}(x)}=\alpha \ $and\ $\lim\limits_{x\rightarrow \infty }\frac{f_{G}(x)}{f(x)}=\alpha +i,$ where $% \alpha $ is the positive real root of equation $x^{3}-x^{2}-x-1=0$ for which $\alpha >1$. Finally, matrix formulations of Tribonacci functions and Gaussian Tribonacci functions are given. In the literature, there are several studies on the functions of linear recurrent sequences such as Fibonacci functions and Tribonacci functions. However, there are no study on Gaussian functions of linear recurrent sequences such as Gaussian Tribonacci and Gaussian Tetranacci functions and they are waiting for the investigating. We also present linear sum formulas and matrix formulations of Tribonacci functions which have not been studied in the literature.

Deep coal beds have been suggested as possible usable underground geological locations for carbon dioxide storage. Furthermore, injecting carbon dioxide into coal beds can improve the methane recovery. Due to importance of this issue, a novel investigation has been done on adsorption of carbon dioxide on various types of coal seam. This study has proposed four types of Gaussian Process Regression (GPR) approaches with different kernel functions to estimate excess adsorption of carbon dioxide in terms of temperature, pressure and composition of coal seams. The comparison of GPR outputs and actual excess adsorption expresses that proposed models have interesting accuracy and also the Exponential GPR approach has better performance than other ones. For this structure, R2=1, MRE=0.01542, MSE=0, RMSE=0.00019 and STD=0.00014 have been determined. Additionally, the impacts of effective parameters on excess adsorption capacity have been studied for the first time in literature. According to these results, the present work has valuable and useful tools for petroleum and chemical engineers who dealing with enhancement of recovery and environment protection.

The asymmetric bimodal exponential power (ABEP) distribution is an extension of the generalized gamma distribution to the real line via adding two parameters which fit the shape of peakedness in bimodality on real line. The special values of peakedness parameters of the distribution are combination of half Laplace and half normal distributions on real line. The distribution has two parameters fitting the height of bimodality, so capacity of bimodality is enhanced by using these parameters. Adding a skewness parameter is considered to model asymmetry in data. The location-scale form of this distribution is proposed. The Fisher information matrix of these parameters in ABEP is obtained explicitly. Properties of ABEP are examined. Real data examples are given to illustrate the modelling capacity of ABEP. The replicated artificial data from maximum likelihood estimates of parameters of ABEP and distributions having an algorithm for artificial data generation procedure are provided to test the similarity with real data.

In this study, the multi-relaxation-time lattice Boltzmann method is applied to investigate the oscillatory instability of lid-driven flows in two-dimensional semi-elliptical cavities with different vertical to horizontal aspect ratios K in the range of 1.0--3.0. The program implemented in this study is parallelized using CUDA (compute unified device architecture), a parallel computing platform, and computations are carried out on NVIDIA Tesla K40c GPU. To carry out precise calculations, the CUDA algorithm is extensively investigated, and its parallel efficiency indicates that the maximum speedup is 47.6 times faster. Furthermore, the steady--oscillatory Reynolds numbers are predicted by implementing the CUDA-based programs. The amplitude coefficient is defined to quantify the time-dependent oscillation of the velocity magnitude at the monitoring point. The simulation results indicate that the transition Reynolds numbers correlate negatively with the aspect ratio of the semi-elliptical cavity, and are smaller than those of the rectangular cavity at the same aspect ratio. In addition, the detailed vortex structures of the semi-elliptical cavity within a single period are also investigated when the Reynolds number is larger than the steady--oscillatory value to determine the effects of periodic oscillation of the velocity magnitude.

Dormancy is a physiological state that confers winter hardiness to and orchestrates phenological phase progression in temperate perennial plants. Weather fluctuations caused by climate change increasingly disturb dormancy onset and release in many plant species including tree crops leading to aberrant growth, flowering, and fruiting. Currently, research in this field is impeded by the lack of affordable non-invasive methods for on-line monitoring of dormancy. We report on an automatic framework for low-cost, long-term, and scalable dormancy studies in deciduous plants. The proposed method is based on continuous near-field sensing of the photosynthetic activity of shoots via pulse-amplitude modulated chlorophyll fluorescence sensors connected remotely to a data processing system. The resulting high-resolution time series of JIP-test parameters indicative of the responsiveness of the photosynthetic apparatus to environmental stimuli are subjected to frequency-domain analysis. The proposed approach allows to overcome the variance coming from diurnal changes of insolation and to derive estimations on the depth of dormancy. Our approach was validated over three seasons in an experimental apple (Malus × domestica Borkh.) orchard by collating the non-invasive estimations with the results of traditional methods (growing of the cuttings obtained from the tress at different phases of dormancy) and the output of commonly used chilling requirement models. We discuss the advantages of the proposed monitoring framework such as prompt detection of freeze damages along with its potential limitations.

Interactions between mobile robots and human operators in common areas require a high safety especially in terms of trajectory planning, obstacle avoidance and mutual cooperation. In this connection the crossings of planned trajectories, their uncertainty based on model fluctuations, system noise and sensor noise,play an outstanding role. This paper discusses the calculation of expected areas of interactions du ring human-robot navigation with respect to fuzzy and noisy information. Expected crossing points of possible trajectories are nonlinearily associated with positions and orientations of robot and human. The nonlinear transformation of a noisy system input, such as directions of motion of human and robot, to a system output, the expected area of intersection of their trajectories, is done by two methods: statistical linearization and the sigma-point-transformation. For both approaches fuzzy approximations are presented and the inverse problem is discussed where the input distribution parameters are computed from given output distribution parameters.

Machine learning forks into three main branches such as supervised learning, unsupervised learning, and reinforcement learning where reinforcement learning is much potential to artificial intelligence (AI) applications because it solves real problems by progressive process in which possible solutions are improved and finetuned continuously. The progressive approach, which reflects ability of adaptation, is appropriate to the real world where most events occur and change continuously and unexpectedly. Moreover, data is getting too huge for supervised learning and unsupervised learning to draw valuable knowledge from such huge data at one time. Bayesian optimization (BO) models an optimization problem as a probabilistic form called surrogate model and then directly maximizes an acquisition function created from such surrogate model in order to maximize implicitly and indirectly the target function for finding out solution of the optimization problem. A popular surrogate model is Gaussian process regression model. The process of maximizing acquisition function is based on updating posterior probability of surrogate model repeatedly, which is improved after every iteration. Taking advantages of acquisition function or utility function is also common in decision theory but the semantic meaning behind BO is that BO solves problems by progressive and adaptive approach via updating surrogate model from a small piece of data at each time, according to ideology of reinforcement learning. Undoubtedly, BO is a reinforcement learning algorithm with many potential applications and thus it is surveyed in this research with attention to its mathematical ideas. Moreover, the solution of optimization problem is important to not only applied mathematics but also AI.

Musculoskeletal models (MSKMs) are used to estimate the muscle and joint forces involved in human locomotion, often associated with the onset of degenerative musculoskeletal pathologies (e.g. osteoarthritis). Subject-specific MSKMs offer more accurate predictions than their scaled-generic counterparts. This accuracy is achieved through time-consuming personalisation of models and manual tuning procedures that suffers from potential repeatability errors, hence limiting the wider application of this modelling approach. In this work we have developed a methodology for identifying and ranking the muscles that are more important to the determination of the joint forces, thus producing reduced but still accurate representation of the musculoskeletal system in shorter timeframes. The methodology hinges on Sobol's sensitivity analysis (SSA) for ranking the muscle importance. The thousands of data points required for SSA are generated using Gaussian Process emulators, a Bayesian technique to infer the input-output relationship between nonlinear models from a limited number of observations. Results show that there is a pool of muscles whose personalisation has little effects on the model predictions. Furthermore, joint forces in subject generic and subject generic models are influenced by different set of muscles, suggesting the existence of a model specific component of the sensitivity analysis.

This paper presents a novel method to extract local features, which instead of calculating local extrema computes global maxima in a discretized scale-space representation. To avoid obtaining precise scales by interpolation and to achieve perfect rotation invariance, two essential techniques, increasing the width of kernels in pixel and utilizing disk-shaped convolution template are adopted in this method. Since the size of a convolution template is finite and finite templates can introduce computational error into convolution, we sufficiently discuss this problem and work out an upper bound of the computational error. The upper bound is utilized in the method to ensure that all features obtained are computed under a given tolerance. Besides, the technique of relative threshold to determine features is adopted to reinforce the robustness for the scene of changing illumination. Simulations show that this new method attains high performance of repeatability in various situations including scale change, rotation, blur, JPEG compression, illumination change and even viewpoint change.

Many scientific and technological problems are studied with the help of computer codes that simulate the phenomena of interest rather than via traditional laboratory experiments. Such models play an important role in neuroscience where they are used to mimic brain function from the sub-cellular to the macroscopic level. Exploration with computer models carries with it a number of statistical challenges: where to sample the input space for the simulator, how to make sense of the data that is generated, how to estimate unknown parameters in the model, how to validate a model. The simulator setting also has some unique problems and possibilities. This review paper describes statistical research on these issues and how that work might be applied to neural simulations.

Abstract: Background: Non-invasive acquistion of beat-to-beat pulse transit time (PTT) via piezoelectric/piezocapacitive sensors (PES/PCS) may expand perioperative hemodynamic monitoring. This study evaluated the ability for PTT via PES/PCS to correlate with systolic, diastolic, and mean invasive blood pressure (SBPIBP, DBPIBP, and MAPIBP) and to detect SBPIBP fluctuations. Methods: PES/PCS and IBP measurements were performed in 20 patients undergoing abdominal, urological, and cardiac surgery. A Pearson’s correlation analysis (r) between 1/PTT and IBP was performed. The predictive ability of 1/PTT with changes in SBPIBP was determined by area under the curve (reported as AUC, sensitivity, specificity). Results: Significant correlations between 1/PTT and SBPIBP were found for PES (r=0.64) and PCS (r=0.55) (p<0.01), as well as MAPIBP/DBPIBP for PES (r=0.6/0.55) and PCS (r=0.5/0.45) (p<0.05). A 7% decrease in 1/PTTPES predicted a 30% SBPIBP decrease(0.82, 0.76, 0.76), while a 5.6% increase predicted a 30% SBPIBP increase (0.75, 0.7, 0.68). A 6.6% decrease in 1/PTTPCS detected a 30% SBPIBP decrease (0.81, 0.72, 0.8), while a 4.8% 1/PTTPCS increase detected a 30% SBPIBP increase (0.73, 0.64, 0.68). Conclusions: Non-invasive beat-to-beat PTT via PES/PCS demonstrated significant correlations with IBP and detected significant changes in SBPIBP. Thus PES/PCS as a novel sensor technology may augment intraoperative hemodynamic monitoring during major surgery.

Let a,b,c be positive integers such that a²+b²=c², 2|b,gcd(a,b)=1. In 1956, Jesmanowicz conjectured that for any positive integer w, the only solution of (aw)^x+(bw)^y=(cw)^z in positive integers is (x, y, z) = (2, 2, 2). In this paper, based on Gaussian integer ring, we show that Je$\acute{s}$manowicz' conjecture is true for any positive integer

Optical communications are described and analyzed by shaped beams; we challenge the ‎effects of parameters that impact the profile of a Flat Top Gaussian (FTG) beam. When ‎the laser beam propagates throughout the atmosphere, it can be influenced by different ‎optical phenomena including scattering, absorption, and turbulence due to changes in the ‎scintillation index and the forms of intensity that are displayed in the source and receiver ‎planes. In this project, the FTG laser beam that propagates through a weak turbulent ‎region is numerically investigated using open-source software. This simulation will be ‎performed according to a mathematical model based on the split-step beam propagation ‎method. Intensity distributions at the source plane and the received average intensity in ‎atmospheric turbulence are calculated, and additional contour is in the transducer plane. ‎The scintillation index, structure constant, source size, and other parameters, are applied ‎in the Rytov method to quantify the weak turbulent model. Moreover, these parameters ‎are analyzed in near-field propagation. Also, the effects of the beam’s scintillation and ‎beam wander are determined. All results simulated are discussed and compared with the ‎TEM00 Gaussian beam. Finally, these results are compared to measurements in the ‎experimental part of the work.

The two-parameter Wright special function is an interesting mathematical object that arises in the theory of the space and time-fractional diffusion equations. Moreover, many other special functions are particular instantiations of the Wright function. The article demonstrates finite representations of the Wright function in terms of sums of generalized hypergeometric functions, which in turn provide connections with the theory of the Gaussian, Airy, Bessel, and Error functions, etc. The main application of the presented results is envisioned in computer algebra for testing numerical algorithms for the evaluation of the Wright function.

Due to the high computational burden and the high nonlinearity of the responses, crashworthiness optimizations are notoriously hard-to-solve challenges. Among various approaches, methods like the Successive Response Surface Method (SRSM) have stood out for their efficiency in enhancing baseline designs within a few iterations. However, these methods have limitations that restrict their application. Their minimum iterative resampling required is often computationally prohibitive. Furthermore, surrogate models are conventionally constructed using Polynomial Response Surface (PRS), a method that is poorly versatile, prone to overfitting, and incapable of quantifying uncertainty. Furthermore, the lack of continuity between successive response surfaces results in suboptimal predictions. This paper introduces the Multi-Fidelity Successive Response Surface (MF-SRS), a Gaussian process-based method, which leverages a nonlinear multi-fidelity approach for more accurate and efficient predictions compared to SRSM. After initial testing on synthetic problems, this method is applied to a real-world crashworthiness task: optimizing a bumper crossmember and crash box system. Results, benchmarked against SRSM and the Gaussian Process Successive Response Surface (GP-SRS) – a single-fidelity Gaussian process-driven extension of SRSM, show that MF-SRS offers distinct advantages. Specifically, it improves upon the specific energy absorbed optimum value achieved by SRSM by 14.1 %, revealing its potential for future applications.

Oriented object detection is a challenging task in scene text detection and remote sensing image analysis, which has attracted extensive attention in recent years with the development of deep learning. Currently, mainstream oriented object detectors are based on preset anchor boxes. This method increases the computational load of the network and cause a large amount of anchor box redundancy. To solve this problem, we propose anchor-free oriented object detection based on the Gaussian centerness(AOGC), a single-stage anchor-free detection method. Our method uses contextual attention FPN(CAFPN) to obtain the contextual information of the target. Then we design a label assignment method for oriented objects. Finally, we develop a Gaussian kernel-based centerness branch, which can effectively determine the significance of different anchors. AOGC achieves mAP of 74.30% on the DOTA-1.0 datasets and 89.80% on the HRSC2016 datasets, respectively. AOGC exhibits superior performance to other methods in oriented anchor-free object detection methods.

The treatment of insulin-dependent diabetes mellitus is characterized by artificial supplementation of pancreatic β-cell ability to regulate sugar levels in the blood. Even though various insulin analogs are crucial for reasonable glycemic control, understanding the dynamic mechanism of the insulin analogs may help to improve the best-protracted insulin analog to assist people with Type 1 Diabetes (T1D) to live comfortably while maintaining tight glycemic control. Here we present the high-resolution crystal structure of NN304, known as insulin detemir, to 1.7 A resolution at cryogenic temperature. We computationally further investigated our crystal structure's monomeric-dimeric conformation and dynamic profile by comparing it with a previously available detemir structure (PDB ID: 1XDA). Our structure (PDB ID: 8HGZ) obtained at elevated pH provides a distinct alternative dimeric conformation compared to the previous structure, suggesting it might induce an intermediate state in the dissociation pathway of the insulin detemir’s hexamer:dihexamer equilibrium. Combined with orientational cross-correlation analysis by Gaussian Network Model (GNM), this alternate oligomeric conformation offers the distinct cooperative motions of a protracted insulin analog that has not been previously observed.

Gol'denveizer's problem of a torus has been analyzed by Audoly and Pomeau (2002) and Sun (2021). However, all of the investigations of Gol'denveizer's problem of an elastic torus have been linear. In this paper, the finite element method is used to more accurately address this problem. Furthermore, Sun (2021) cannot be solved by nonlinear analysis. We research the nonlinear mechanical properties of Gol'denveizer's problem of circular and elliptic tori, and relevant nephograms are given. We study the buckling of Gol'denveizer's problem of an elastic torus, and propose failure patterns and force-displacement curves of tori in the nonlinear range. Investigations reveal that circular tori have more rich buckling phenomena as the parameter a increases. Gol'denveizer's problem of the buckling of an elliptic torus is analyzed, and we find a new buckling phenomenon called a "skirt." As a/b increases, the collapse load of an elliptic torus of the Gol'denveizer problem is enhanced gradually.

Performing predictive maintenance (PdM) is challenging for many reasons. Dealing with large datasets which may not contain run-to-failure data (R2F) complicates PdM even more. When no R2F data are available, identifying condition indicators (CIs), estimating the health index (HI), and thereafter, calculating a degradation model for predicting the remaining useful lifetime (RUL) are merely impossible using supervised learning. In this paper, a 3 dof delta robot used for pick and place task is studied. In the proposed method, autoencoders (AEs) are used to predict when maintenance is required based on the signal sequence distribution and anomaly detection, which is vital when no R2F data is available. Due to the sequential nature of the data, non-linearity of the system, and correlations between parameter time series, convolutional layers are used for feature extraction. Thereafter, a sigmoid function is used to predict the probability of having an anomaly given CIs acquired from AEs. This function can be manually tuned given the sensitivity of the system or optimized by solving a minimax problem. Moreover, the proposed architecture can be used for fault localization for the specified system. Additionally, the proposed method is capable of calculating RUL using Gaussian process (GP), as a degradation model, given HI values as its input.

Imperceptible vibratory noise stimulation has shown to be an effective means of improving stability for both whole body postural control and simple motor control tasks. While the physiological mechanism affording this improvement is uncertain, it is suspected that sensory noise stimulation may elicit a stochastic resonance-like effect within the somatosensory system. A stochastic resonance effect describes the phenomenon in which noise added to a non-linear system improves signal detection rather than degrading it. One hallmark of stochastic resonance is the existence of an optimal noise level which elicits the best system performance. There is disagreement in the literature regarding the presence of an optimal stimulation level for motor stability in humans. The goals of this study were to: 1) determine optimal stimulation level as a function of an individual’s sub-sensory threshold level, and 2) to determine whether performance of a force stability task was significantly better when subjects received stimulation at this identified optimal level compared to other sub-sensory threshold stimulation levels. Eighteen (18) participants completed an isometric finger flexion task with visual feedback while receiving noise stimulation scaled to varying percentages of their individual sub-sensory threshold level. Performance for this force stabilization task was quantified as the root-mean-square (RMS) error between the target force and the actual generated force values. Despite controlling all other signal properties and varying only amplitude, optimal noise stimulation values still varied widely across participants (10-100% sub-sensory threshold level). Statistical modeling revealed a significant improvement in task performance with optimal noise stimulation compared to other sub-sensory stimulation levels (p ≤ 0.019) with estimated marginal mean differences in force errors ranging from 0.13 to 0.23 N. Moderate significant Spearman correlations (r_s = 0.49 and r_s = 0.56, respectively) were found between finger flexion maximal voluntary contraction (MVC) and sub-sensory threshold level and MVC and optimal stimulation level. A strong, significant Spearman correlation (r_s = 0.65) was observed between sub-sensory threshold level and optimal stimulation level. Although these correlations do not provide a means to predict optimal stimulation level as a function of these other measures, optimal stimulation level appears to increase with sub-sensory threshold and MVC.

The VLSI industry is facing parasitic effects that trouble development in the nanoscale domain. However, instead of replacing the traditional MOSFET design, it would be more advantageous to apply different doping profiles and discerning which deal with specific parasitic effects the best. With a review of Gaussian doping, Uniform doping, and Delta doping profiles and analysis of the FET technology characteristics that use these doping profiles, a comparison can be made among them for integrated circuit design engineers. These doping profiles are compared based on how well they perform against non-ideal and ideal environments. Also, both digital and analog performance are measured to ensure the uniqueness of each doping profile that is present. After getting a list of benefits from each doping profile, it is derived to determine which doping profile works best against a host of parasitic effects and what type of application do these doping profiles have

In this paper, a method is developed for presenting a novel virtual torque sensor based on precise model and position measurements avoids the need of traditional strain gauges and amplifiers. More specifically, the harmonic drive compliance model and the Gaussian process regression (GPR) technique are used together to achieve virtual torque sensor measurement. While the harmonic drive compliance model provides the analytic part, the Gaussian process regression method is used to reconstruct the unmolded part based on motor-side and link-side joint angles as well as motor current. After an automatic offline calibration, the method allows for a lean online implementation. The virtual torque sensor measurement is compared with measurements of a commercial torque sensor, and the results have attested the effectiveness of the proposed method.

Due to the highly nonlinear, multi-stage, and strongly time-varying marine lysozyme fermentation process, it is difficult to assure the stability and prediction accuracy of the traditional single global soft sensor model on a global scale. This study innovatively proposed a soft sensor model based on an improved seagull optimization algorithm (ISOA) combined with Gaussian process regression (GPR) weighted ensemble learning. First, the sample data set is divided into multiple local sample subsets by the improved density peak clustering algorithm (ADPC). Second, the Gaussian process regression model is optimally altered with an improved seagull optimization algorithm for the purpose of establishing the corresponding sub-prediction model. Finally, the prediction model's fusion strategy is ultimately determined depending on the degree of connection between the test samples and a subset of local pieces. Simulation results show that the proposed soft sensor model, which searches GPR based on ISOA and combines various sub-models, can predict the key biochemical parameters of the marine lysozyme fermentation process better with less prediction error under the condition of fewer training data, and it can be expanded to the soft sensor models of general nonlinear systems, according to simulation results.

This article describes techniques employed in the production of a synthetic dataset of driver telematics emulated from a similar real insurance dataset. The synthetic dataset generated has 100,000 policies that included observations about driver’s claims experience together with associated classical risk variables and telematics-related variables. This work is aimed to produce a resource that can be used to advance models to assess risks for usage-based insurance. It follows a three-stage process using machine learning algorithms. The first stage is simulating values for the number of claims as multiple binary classifications applying feedforward neural networks. The second stage is simulating values for aggregated amount of claims as regression using feedforward neural networks, with number of claims included in the set of feature variables. In the final stage, a synthetic portfolio of the space of feature variables is generated applying an extended SMOTE algorithm. The resulting dataset is evaluated by comparing the synthetic and real datasets when Poisson and gamma regression models are fitted to the respective data. Other visualization and data summarization produce remarkable similar statistics between the two datasets. We hope that researchers interested in obtaining telematics datasets to calibrate models or learning algorithms will find our work valuable.

The eruption of COVID-19 patients in 215 countries worldwide has urged for robust predictive methods that can detect as early as possible the size and duration of the contagious disease and also providing precision predictions. In much recent literature reported on COVID-19, one or more essential parts of such investigation were missed. One of the crucial elements for any predictive method is that such methods should fit simultaneously as much data as possible; these data could be total infected cases, daily hospitalized cases, cumulative recovered cases, and deceased cases, and so on. Other crucial elements include sensitivity and precision of such predictive methods on the amount of data as the contagious disease evolved day by day. To show the importance of these aspects, we have evaluated the standard SIRD model and a newly introduced Gaussian-SIRD model on the development of COVID-19 in Kuwait. It is observed that the SIRD model quickly picks up the main trends of COVID-19 development, but the Gaussian-SIRD model provides precise prediction a longer period of time.

In this paper, closed forms of the summation formulas for generalized Fibonacci numbers are presented. As special cases, we give summation formulas of Fibonacci, Lucas, Pell, Pell-Lucas, Jacobsthal, Jacobsthal-Lucas numbers.

We consider rotational hypersurface in the four dimensional Euclidean space. We calculate the mean curvature and the Gaussian curvature, and some relations of the rotational hypersurface. Moreover, we define the third Laplace-Beltrami operator and apply it to the rotational hypersurface.

Dietary polyphenols exist in two forms; extractable polyphenols (EPP) or compounds solubilised by aqueous/organic solvents, and non-extractable polyphenols (NEPP) or compounds remain in the corresponding residues after the extraction. At present, most researchers focus on EEP fractions, while NEPP is neglected. Thus, this study aimed to release NEPP from the remaining powder residue of Barhi date palm kernels (BDPK) with acid hydrolysis. The related extraction conditions were determined and optimised using response surface methodology (RSM) for maximisation of NEPP with highest cytotoxic and antioxidant activities. The face-centred central composite design (FCCCD) was used to establish treatments based on three independent variables, namely; extraction temperature, time, and solvent/sample ratio. Under the optimal conditions, the experimental values for DPPH radical-scavenging capacity of NEPP (IC50=57.52µg/mL), and cytotoxicity of NEPP against A549 and HT29 cells were IC50=17.4 µg/mL and 31.4µg/mL, respectively. The experimental values were in agreement with those predicted by RSM models, confirming the suitability of the model employed and the success of RSM for optimisation of the extraction conditions for NEPP from BDPK. These results indicate that NEPP from industrial date fruit waste could be a promising candidate as natural antioxidants with significant antiproliferation effect against A549 and HT29 cancer cells in-vitro.

Plasma technology shows tremendous potential for revolutionizing oncology research and treatment. Reactive oxygen and nitrogen species, electromagnetic emissions generated through gas plasma jets, have attracted significant attention due to their selective cytotoxicity towards cancer cells. To leverage the full potential of plasma medicine, researchers have explored the use of mathematical models and various subsets of machine learning, such as reinforcement learning, and deep learning. This review emphasizes the significant application of AI algorithms in the adaptive plasma system, paving the way for precision and dynamic cancer treatment. Realizing the full potential of AI in plasma medicine, requires research efforts, data sharing and interdisciplinary collaborations. Unravelling the complex mechanisms, developing real-time diagnostics, and optimizing AI models will be crucial to harness the true power of plasma technology in oncology. The integration of personalized and dynamic plasma therapies, alongside AI and diagnostic sensors, presents a transformative approach to cancer treatment with the potential to improve outcomes globally.

Vegetation classifications on large geographic scales are necessary to inform conservation decisions and monitor keystone, invasive, and endangered species. These classifications are often effectively achieved by applying models to imaging spectroscopy, a type of remote sensing, data, but such undertakings are often limited in spatial extent. Here we provide accurate, high-resolution spatial data on the keystone species Metrosideros polymorpha, a highly polymorphic tree species distributed across bioclimatic zones and environmental gradients on Hawai'i island, using airborne imaging spectroscopy and LiDAR. We compare two tree species classification techniques, support vector machine (SVM) and spectral mixture analysis (SMA), to assess their ability to map M. polymorpha over 28,000 square kilometers where differences in topography, background vegetation, sun angle relative to the aircraft, and day of data collection, among others, challenge accurate classification. To capture spatial variability in model performance, we applied gaussian process classification (GPC) to estimate the spatial probability density of M. polymorpha occurrence using only training sample locations. We found that, while SVM and SMA models exhibit similar raw score accuracy over the test set (96.0% and 93.4%, respectively), SVM better reproduces the spatial distribution of M. polymorpha than SMA. We developed a final 2 m x 2 m M. polymorpha presence dataset and a 30 m x 30 m M. polymorpha density dataset using SVM classifications that have been made publicly available for use in conservation applications. Accurate, large-scale species classifications are achievable, but metrics for model performance assessments must account for spatial variation of model accuracy.

In the broad field of Inverse Analysis and Structural Identification, it is nowadays of a large interest the study of Gaussian Processes, as a reliable and efficient optimisation method, particularly helpful toward the identification of a global optimum point, under the conditions of complicated functions to be optimised. In the present contribution, a specific case study is considered, focusing on a historical road reinforced concrete arched bridge, located in Northern Italy, employing dynamic modal properties, deciphered from in-situ measurements, previously acquired under operational traffic conditions, by a standard wired accelerometer system, placed at the deck level. Aiming at the identification and diagnosis of the bridge structure, three main methodological steps are herein considered: the adoption of a FEM model of the structure (in the linear dynamic framework), the definition of an appropriate discrepancy function, based on measured and numerically computed quantities (natural frequencies and mode shapes of the bridge), and the investigation of such a discrepancy function, toward a consistent selection of an optimisation strategy for the identification of sought parameters (Young’s moduli and mass densities of diverse elements of the structure). The presented developments, within the framework of methodological optimisation approach by Gaussian Processes, and achieved results display a rather efficient perspective, with reference to the considered case study, toward inverse analysis for structural diagnosis, in the context of strategic (historical) infrastructures.

Spike-and-wave discharge (SWD) pattern detection in electroencephalography (EEG) signals is a key signal processing problem. It is particularly important for overcoming time-consuming, difficult, and error-prone manual analysis of long-term EEG recordings. This paper presents a new SWD method with a low computational complexity that can be easily trained with data from standard medical protocols. Precisely, EEG signals are divided into time segments for which the Morlet 1-D decomposition is applied. The generalized Gaussian distribution (GGD) statistical model is fitted to the resulting wavelet coefficients. A k-nearest neighbors (k-NN) self-supervised classifier is trained using the GGD parameters to detect the spike-and-wave pattern. Experiments were conducted using 106 spike-and-wave signals and 106 non-spike-and-wave signals for training and another 96 annotated EEG segments from six human subjects for testing. The proposed SWD classification methodology achieved 95 % sensitivity (True positive rate), 87% specificity (True Negative Rate), and 92% accuracy. These results set the path to new research to study causes underlying the so-called absence epilepsy in long-term EEG recordings.

Estimation and planning play a vital role in the construction of an autonomous navigation framework. However, these problems are often considered separately, while planning gives robot a free-collision path towards the desired goal, estimation algorithm presents the executed trajectory in the sense that it has to be closed to the ground truth path as much as possible. Recently, a unified probabilistic framework, which supports solving these problems simultaneously, dubbed STEAP has been proposed. Nevertheless, its current version is only designated for an omni wheels robot, which allows robot to move and turn in vertical direction. Differential drive robot, on the other hand, though limited to move along only one direction, has been used in various situations due to its flexibility and lower cost in hardware designing. Thus, in this extension, our aim is to control a differential drive robot via STEAP. Moreover, in a more complicated environment such as labyrinth or maze, the original STEAP sometimes fails to find a path. Indeed, this problem is mainly caused by the poor initialization and the non-linearity in optimizer constraints. In our implementation, instead of dealing with these constraints, we employ a global planner algorithm such as Dijkstra or RRT to treat STEAP as an effective local planner module that focus on following the global path. Consequently, the experimental results show that the extended STEAP not only able to navigate a differential drive robot but also in a more complicated and unstructured environment.

This study aims to develop an elderly care system for improving the interpersonal relationship of the elderly with mild cognitive impairment (MCI) by employing the speaker recognition technique and association functionality of social network platforms. Firstly, the speaker recognition units based on the Gaussian Mixture Model (GMM) and Gaussian Mixture Model-Universal Background Model (GMM-UBM) are implemented to identify the visitor via individual input utterance. After the visitor is identified, the proposed system will be linked to the private database and social network platforms to extract the associated message of two parties. Experimental results indicate that the speaker recognition unit based on GMM-UBM achieves the best performance. Finally, five elderly persons are invited to measure the usability of the proposed system. A questionnaire is used to survey the five elderly persons, and the result indicates that the proposed system is highly potentially applicable in improving the interpersonal relationship of the elderly with MCI.

Reporting on CSR activities has become the essence of reporting for modern business entities. In this regard, particular attention is paid to public interest companies. Therefore, the following paper aims to answer the question of whether there are differences in the linguistic structure of the studied CSR reports in three selected industry indices on the Warsaw Stock Exchange (WSE) in Poland, i.e. WIG-energy index, WIG-fuel index, WIG-mining index and their relationship with the performance of selected companies. The study was conducted on a purposely selected sample of companies between 2013 and 2018. A total of 138 CSR reports and 138 annual separate financial statements prepared in accordance with international balance sheet law were collected. The study was carried out based on a panel regression model. It was found that CSR reports contained similar average percentages of parts of speech such as nouns and adjectives. When linking the economic performance of companies, expressed with selected indices, to the information on the implementation of CSR concepts, it was revealed that the results are more likely to describe business performance when it is satisfactory.

Carbon Capture and Storage (CCS) stands as a pivotal technological stride toward a sustainable future, with the practice of injecting supercritical CO2 into subsurface formations having already been an established practice for enhanced oil recovery operations. The overarching objective of CCS is to protract the operational viability and sustainability of platforms and oilfields, thereby facilitating a seamless transition towards sustainable practices. This study introduces a comprehensive framework for optimizing well placements in CCS operations, employing a derivative-free method known as Bayesian optimization. The development plan is tailored for scenarios featuring aquifers devoid of flow boundaries, incorporating production wells tasked with controlling pressure buildup and injection wells dedicated to CO2 sequestration. Notably, the wells operate under group control, signifying predefined injection and production targets and constraints that must be adhered to throughout the project’s lifespan. As a result, the objective function remains invariant under specific permutations of the well locations. Our investigation delves into the efficacy of Bayesian optimization under the introduced permutation invariance. The results reveal that it demonstrates critical efficiency in handling the optimization task extremely fast. In essence, this study advocates for the efficacy of Bayesian optimization in the context of optimizing well placements for CCS operations, emphasizing its potential as a preferred methodology for enhancing sustainability in the energy sector.

Surface roughness prediction is a pivotal aspect of the manufacturing industry, as it directly influences product quality and process optimization. This study introduces a predictive model for surface roughness in the turning of complex-structured workpieces, utilizing Gaussian Process Regression (GPR) informed by vibration signals. The model captures parameters from both the time and frequency domains of the turning tool, encompassing the mean, median, standard deviation (STD), and root mean square (RMS) values. The signal is from the time to frequency domain is executed using Welch's method, complemented by time-frequency domain analysis employing three levels of Daubechies Wavelet Packet Transform (WPT). The selected features are then utilized as inputs for the GPR model to forecast surface roughness. Empirical evidence indicates that the GPR model can accurately predict the surface roughness of turned complex-structured workpieces. This predictive strategy has the potential to improve product quality, streamline manufacturing processes, and minimize waste within the industry.

Bayesian techniques for engineering problems, that rely on Gaussian process (GP) regression, are known for their ability to quantify epistemic and aleatory uncertainties and for being data efficient. The mathematical elegance of applying these methods usually comes at a high computational cost when compared to deterministic and empirical Bayesian methods. Furthermore, using these methods becomes practically infeasible in scenarios characterized by a large number of inputs and thousands of training data. The focus of this work is on enhancing Gaussian Process-based metamodeling and model calibration tasks, when the size of the training datasets is significantly large. To achieve this goal, we employ a stochastic variational inference algorithm that enables rapid statistical learning of the calibration parameters and hyperparameter tuning, while retaining the rigor of Bayesian inference. The numerical performance of the algorithm is demonstrated on multiple metamodeling and model calibration problems with thousands of training data.

Industrial dynamical systems often exhibit multi-scale response due to material heterogeneities, operation conditions and complex environmental loadings. In such problems, it is the case that the smallest length-scale of the systems dynamics controls the numerical resolution required to effectively resolve the embedded physics. In practice however, high numerical resolutions is only required in a confined region of the system where fast dynamics or localized material variability are exhibited, whereas a coarser discretization can be sufficient in the rest majority of the system. To this end, a unified computational scheme with uniform spatio-temporal resolutions for uncertainty quantification can be very computationally demanding. Partitioning the complex dynamical system into smaller easier-to-solve problems based of the localized dynamics and material variability can reduce the overall computational cost. However, identifying the region of interest for high-resolution and intensive uncertainty quantification can be a problem dependent. The region of interest can be specified based on the localization features of the solution, user interest, and correlation length of the random material properties. For problems where a region of interest is not evident, Bayesian inference can provide a feasible solution. In this work, we employ a Bayesian framework to update our prior knowledge on the localized region of interest using measurements and system response. To address the computational cost of the Bayesian inference, we construct a Gaussian process surrogate for the forward model. Once, the localized region of interest is identified, we use polynomial chaos expansion to propagate the localization uncertainty. We demonstrate our framework through numerical experiments on a three-dimensional elastodynamic problem

The most common index for representing structural condition of the pavement is the structural number. The current procedure for determining structural numbers involves utilizing falling weight deflectometer and ground-penetrating radar tests, recording pavement surface deflections, and analyzing recorded deflections by back-calculation manners. This procedure has two drawbacks: 1. falling weight deflectometer and ground-penetrating radar are expensive tests, 2. back-calculation ways has some inherent shortcomings compared to exact methods as they adopt a trial and error approach. In this study, three machine learning methods entitled Gaussian process regression, m5p model tree, and random forest used for the prediction of structural numbers in flexible pavements. Dataset of this paper is related to 759 flexible pavement sections at Semnan and Khuzestan provinces in Iran and includes “structural number” as output and “surface deflections and surface temperature” as inputs. The accuracy of results was examined based on three criteria of R, MAE, and RMSE. Among the methods employed in this paper, random forest is the most accurate as it yields the best values for above criteria (R=0.841, MAE=0.592, and RMSE=0.760). The proposed method does not require to use ground penetrating radar test, which in turn reduce costs and work difficulty. Using machine learning methods instead of back-calculation improves the calculation process quality and accuracy.

Inspired by the forward and the reverse channels from the image-size characterization problem in network information theory, we introduce a functional inequality which unifies both the Brascamp-Lieb inequality and Barthe's inequality, which is a reverse form of the Brascamp-Lieb inequality. For Polish spaces, we prove its equivalent entropic formulation using the Legendre-Fenchel duality theory. Capitalizing on the entropic formulation, we elaborate on a "doubling trick" used by Lieb and Geng-Nair to prove the Gaussian optimality in this inequality for the case of Gaussian reference measures.

This article shortly introduces Gaussian processes as a new approach for modelling time series in the field of blazar physics. In the second part of the paper, recent results from an application of GP modelling to the multi-wavelength light curves of the blazar PKS 1502+106 are discussed.

In a single-center, retrospective study, 22 cases were enrolled and divided into two groups: those who underwent surgical wide excision (group A) and those who did not (group B). The study included 13 cases in group A and 9 cases in group B. In group A, 6 cases solely underwent surgical wide excision, while 7 cases received additional treatments like radiotherapy or chemotherapy. Conversely, in group B, 4 cases received chemotherapy, 4 cases received radiotherapy, and 1 case was managed through observation alone. The mean follow-up time was 60.15 months in group A and 43.44 months in group B, with no significant difference observed. In group A, 9 cases resulted in mortality, whereas 6 cases died within the follow-up period in group B. Lesion-free intervals post-operation were observed predominantly in group A, while 7 cases in group B never experienced freedom from skin lesions. Kaplan-Meier survival curve analysis demonstrated a significant difference between the survival curves of the two groups (P = 0.046). Among non-HIV Kaposi’s sarcoma patients, surgical wide excision appears to have a role in treatment. Patients in group A exhibit a more favorable outcome in the survival curve analysis.

Natural image matting is an essential technique for image processing that enables various applications, such as image synthesis, video editing, and target tracking. However, the existing image matting methods may fail to produce satisfactory results when computing resources are limited. Sampling-based methods can reduce the dimensionality of the decision space and therefore reduce computational resources by employing different sampling strategies. While these approaches reduce computational consumption, they may miss an optimal pixel pair when the number of available high-quality pixel pairs is limited. To address this shortcoming, we propose a novel multi-criterion sampling strategy that avoids missing high-quality pixel pairs by incorporating multi-range pixel pair sampling and high-quality samples selection method. This strategy is employed to develop a multi-criterion matting algorithm via Gaussian process, which searches for the optimal pixel pair by using the Gaussian process fitting model instead of solving the original pixel pair objective function. Experimental results demonstrate that our proposed algorithm outperforms other methods even with 1% computing resources, and achieves alpha matte results comparable to those yielded by the state-of-the-art optimization algorithms.

This paper proposes a novel efficient multistage algorithm to extract source speech signals from a noisy convolutive mixture. The proposed approach comprises of two stages named Blind Source Separation (BSS) and De-noising. A hybrid source prior model separates the source signals from the noisy reverberant mixture in the BSS stage. Moreover, we model the low and high-energy components by generalized multivariate Gaussian and super-Gaussian models, respectively. We use Minimum Mean Square Error (MMSE) to reduce noise in the noisy convolutive mixture signal in the de-noising stage. Furthermore, two proposed models investigate the performance gain. In the first model, the speech signal is separated from the observed noisy convolutive mixture in the BSS stage, followed by suppression of noise in the estimated source signals in the de-noising module. In the second approach, the noise is reduced using the MMSE filtering technique in the received noisy convolutive mixture at the de-noising stage, followed by separation of source signals from the de-noised reverberant mixture at the BSS stage. We evaluate the performance of the proposed scheme in terms of signal-to-distortion ratio (SDR) with respect to other well-known multistage BSS methods. The results show the superior performance of the proposed algorithm over the other state-of-the-art methods.