On the Power of Standard Information for Tractability for L2- Approximation in the Randomized Setting

We study the approximation of multivariate functions from a separable Hilbert space in the randomized setting with the error measured in the weighted L2 norm. We consider algorithms that use standard information Λstd consisting of function values or general linear information Λall consisting of arbitrary linear functionals. We investigate the equivalences of various notions of algebraic and exponential tractability in the randomized setting for Λstd and Λall for the normalized or absolute error criterion. For the normalized error criterion, we show that the power of Λstd is the same as that of Λall for all notions of exponential tractability and some notions of algebraic tractability without any condition. For the absolute error criterion, we show that the power of Λstd is the same as that of Λall for all notions of algebraic and exponential tractability without any condition. Specifically, we solve Open Problems 98, 101, 102 and almost solve Open Problem 100 as posed by E.Novak and H.Wo´zniakowski in the book: Tractability of Multivariate Problems, Volume III: Standard Information for Operators, EMS Tracts in Mathematics, Zürich, 2012.

Assessing the Relevance of Opinions in Uncertainty and Info-Incompleteness Conditions

Researchers are interested in defining decision support systems that can act in contexts characterized by uncertainty and info-incompleteness. The present study proposes a learning model for assessing the relevance of probability, plausibility, credibility, and possibility opinions in the conditions above. The solution consists of an Artificial Neural Network acquiring input features related to the considered set of opinions and other relevant attributes. The model provides the weights for minimizing the error between the expected outcome and the ground truth concerning a given phenomenon of interest. A custom loss function was defined to minimize the Mean Best Price Error (MBPE), while the evaluation of football players’ was chosen as a case study for testing the model. A custom dataset was constructed by scraping the Transfermarkt, Football Manager, and FIFA21 information sources and by computing a sentiment score through BERT, obtaining a total of 398 occurrences, of which 85% were employed for training the proposed model. The results show that the probability opinion represents the best choice in conditions of info-completeness, predicting the best price with 0.86 MBPE (0.61% of normalized error), while an arbitrary set composed of plausibility, credibility, and possibility opinions was considered for deciding successfully in info-incompleteness, achieving a confidence score of 2.47±0.188 MBPE (1.89±0.15% of normalized error). The proposed solution provided high performance in predicting the transfer cost of a football player in conditions of both info-completeness and info-incompleteness, revealing the significance of extending the feature space to opinions concerning the quantity to predict. Furthermore, the assumptions of the theoretical background were confirmed, as well as the observations found in the state of the art regarding football player evaluation.

The effect of the carrier frequency estimation erroron the quality of receiving signals with OFDM modulation.

The article discusses the features and main stages of the formation of OFDM signals. Analytical models of signals with orthogonal frequency multiplexing in the time and frequency domains are presented in the absence and presence of a mismatch in the carrier frequency of the transmitter and receiver. The analysis of the models allowed us to identify the parameters that affect the frequency and phase spectrum of signals. The study was carried out and the dependences of the reception quality of OFDM signals (the ratio of signal power to the power of equivalent noise) on the normalized error of the carrier frequency estimation were obtained.

Improving the Quality Degradation of Dynamically Configurable Approximate Multipliers via Data Correlation

In the last few years, dynamically configurable approximate multipliers have been explored to tune the energy-quality trade-off in error-tolerant applications at runtime. Typically, the multiplier accuracy is adjusted by adding a constant correction factor equal to the multiplier mean error to the result, which is found offline assuming a predetermined input distribution. This paper describes a simple approach to update the correction term at runtime, thus adapting it to the actual incoming inputs. It takes advantage of the spatial and/or temporal correlation typically shown by input data in error-tolerant applications, such as image and video processing. When applied to a typical case study implemented with a commercial UTBB FDSOI 28 nm technology, the proposed approach shows an energy reduction of up to 34% at iso-quality and a quality improvement of up to +9 dB, −4× and +35% at iso-energy, in terms of peak-to-noise ratio (PSNR), normalized error distance (NED) and structural similarity index metric (SSIM) respectively, compared to the traditional technique based on a constant correction factor.

Determination of best-fit isotherm model for the sorption of Lead (II) and Manganese (II) ions onto acid-activated shale using selected non-linear error functions

The focus of this research is to apply the selected error function equation to establish the equilibrium isotherm model that best describes the adsorption of Pb2+ and Mn2+ onto acid-activated shale. Data collected from the batch experiment were analyzed using selected isotherm models (Langmuir, Freundlich, Temkin, Dubinin-Radushkevich, Sips and Redlich-Peterson). To compute the isotherm parameters used in choosing the best-fit isotherm model, selected non-linear error functions, namely, error sum of the square, normalized standard deviation, hybrid error function, root mean square error and Marquardt’s percent standard deviation were employed. From the scanning electron microscope results, it was observed that the surface characteristics of the shale change considerably with calcination and acid treatment but the acid-treated shale shows better uneven porous surface characteristics. Error function computation shows that the Dubinin-Radushkevich isotherm model had the least sum of normalized error of 0.3623 for Pb2+ adsorption and 0.5465 for Mn2+ adsorption; hence, it was selected as the best isotherm model for explaining the sorption of Pb(II) and Mn(II) ions unto acid-activated shale.

Anatomical 3D Modeling Using IR Sensors and Radiometric Processing Based on Structure from Motion: Towards a Tool for the Diabetic Foot Diagnosis

Medical infrared thermography has proven to be a complementary procedure to physiological disorders, such as the diabetic foot. However, the technique remains essentially based on 2D images that display partial anatomy. In this context, a 3D thermal model provides improved visualization and faster inspection. This paper presents a 3D reconstruction method associated with temperature information. The proposed solution is based on a Structure from Motion and Multi-view Stereo approach, exploiting a set of multimodal merged images. The infrared images were obtained by automatically processing the radiometric data to remove thermal interferences, segment the RoI, enhance false-color contrast, and for multimodal co-registration under a controlled environment and a ∆T < 2.6% between the RoI and thermal interferences. The geometric verification accuracy was 77% ± 2%. Moreover, a normalized error was adjusted per sample based on a linear model to compensate for the curvature emissivity (error ≈ 10% near to 90°). The 3D models were displayed with temperature information and interaction controls to observe any point of view. The temperature sidebar values were assigned with information retrieved only from the RoI. The results have proven the feasibility of the 3D multimodal construction to be used as a promising tool in the diagnosis of diabetic foot.

Prediction of Approximate Multiplier for 16-Bit DICOM Image Contrast Scaling Using Classical Machine Learning Approach

The role of approximate arithmetic are involved when the processors are used for multimedia signal processing application. The impact of multiplier is very important in many processes done by these processors. The compressors are the core architecture for reduction stage if the multiplier width is increased. Later approximations are done in the compressor to limited error without affecting the signal standard. The design of scalable-split compressor is designed in this work and a counter matching method has been developed for approximation. The design of 32x32 and 16x16 multiplier with these new compressors are synthesised in 45nm Synopsis Design Compiler and shows an improvement of 25 % of Chip area and 27% power. The split-scalable architecture attempts to reduce the delay with trade-off in area and power. Mean Error Distance (MED) and Normalized Error Distance (NED) are the parameters that ensure the quality of any approximate arithmetic based design. 16-bit medical images are processed with both existing and proposed multipliers then the Peak Signal to Noise Ratio (PSNR) is compared. Finally with several input nature and targeted PSNR the best system is identified using classical machine learning model.

Circadian Rhythm of Blood Pressure of Dipper and Non-dipper Patients With Essential Hypertension: A Mathematical Modeling Approach

Blood pressure in humans presents a circadian variation profile with a morning increase, a small postprandial valley, and a deeper descent during night-time rest. Under certain conditions, the nocturnal decline in blood pressure can be reduced or even reversed (non-dipper), which is related to a significantly worse prognosis than a normal fall pattern (dipper). Despite several advances in recent years, our understanding of blood pressure's temporal structure, its sources and mechanisms is far from complete. In this work, we developed an ordinary differential equation-based mathematical model capable of capturing the circadian rhythm of blood pressure in dipper and non-dipper patients with arterial hypertension. The model was calibrated by means of global optimization, using 24-h data of systolic and diastolic blood pressure, physical activity, heart rate, blood glucose and norepinephrine, obtained from the literature. After fitting the model, the mean of the normalized error for each data point was &lt;0.2%, and confidence intervals indicate that all parameters were identifiable. Sensitivity analysis allowed identifying the most relevant parameters and therefore inferring the most important blood pressure regulatory mechanisms involved in the non-dipper status, namely, increase in sympathetic over parasympathetic nervous tone, lower influence of physical activity on heart rate and greater influence of physical activity and glucose on the systemic vascular resistance. In summary, this model allows explaining the circadian rhythm of blood pressure and deepening the understanding of the underlying mechanisms and interactions integrating the results of previous works.

BICGSTAB-FFT Method of Moments with NURBS for Analysis of Planar Generic Layouts Embedded in Large Multilayer Structures

BICGSTAB-FFT method of moment (MM) scheme is proposed to analyze several levels of planar generic layouts embedded in large multilayer structures when the layout geometries are modeled by NURBS surfaces. In this scheme, efficient computation of normalized error defined in iterative bi-conjugate gradient stabilized (BICGSTAB) method for large multilayer structure analysis problems is implemented. The efficient computation is based on pulse expansion with dense equi-spaced mesh of generalized rooftop basis functions (BFs) defined on NURBS surfaces and equivalent periodic problem (EPP) in order to apply fast Fourier transforms (FFT). Moreover, efficient computation of Green’s functions for multilayer structure is implemented for near and far field regions. Experimental and numerical validations of whole printed reflect array antennas of electrical size between 8 and 16 times the vacuum wavelengths are shown. In these validations, CPU time consumptions of the proposed method are obtained with results between few minutes and half an hour using a conventional laptop.

Integrated MASW and ERT Imaging for Geological Definition of an Unconfined Alluvial Aquifer Sustaining a Coastal Groundwater-Dependent Ecosystem in Southwest Portugal

This paper integrates multichannel analysis of surface waves (MASW) and time-lapse electrical resistivity tomography (ERT) to define aquifer geometry and identify transient groundwater features of the Cascalheira Stream Basin Holocene alluvial aquifer (aquifer H), which contributes to the Santo André Lagoon, part of a coastal groundwater-dependent ecosystem (GDE), located in southwest Portugal. MASW measures shear-wave velocity (VS), allowing one to obtain steady geological models of the subsurface, and ERT measures subsurface electrical resistivity (ER), being subjected to ambient changes. MASW enables disambiguation of geological structures in low ER environments, such as coastal areas. This research covered one natural year and involved one MASW campaign, four ERT campaigns, and additional geological field surveys and groundwater monitoring to assist interpretation of results. In the area, the conjugate NW–SE and NE–SW strike-slip fault systems determine compartmentalization of geological structures and subsequent accommodation space for Holocene sedimentation. MASW and ERT surveys show how the NW–SE system deepens these structures toward the coast, whereas the NE–SW system generates small horsts and grabens, being one of these occupied by aquifer H. From upstream to downstream, aquifer H thickness and width increase from 10 m to 12 m and from 140 m to 240 m, respectively. Performance of VS and ER models was satisfactory, with a normalized error of the VR and ER models in the 0.01–0.09 range, meaning that a quantitative quota of uncertainty can be segregated from the overall uncertainty of groundwater models without substantially affecting its simulations accuracy. This methodology seeks to improve the design of shallow groundwater research in GDE preservation policies.