In assessing the energy performance of buildings, the thermal performance of the structural components and building materials is crucial. Although reference catalogs are used to determine the thermal properties of construction materials, the use of novel materials or non-homogeneous mixtures, particularly with biomaterials, demands the development of new instruments that are capable of performing rapid, accurate and cost-effective thermal characterization. This study introduces the ambient hot-box, a new tool for measuring the thermal properties of construction components and heterogeneous materials. The paper provides a methodology for measuring a sample’s benchmark and fresh materials using a streamlined hot-box-based instrument. Utilizing samples as a benchmark material, the new instrument is assessed, yielding transmittance values with errors below 4%. The electronic circuits, measurements techniques and instrument implementation are all described. In a context of climate change and energy cost increments, one of the largest energy waste challenges in today’s smart and sustainable cities models are related to reducing the energy demand of buildings. Specifically for the EU-28 countries, according to reports published by the Directorate General for Energy of the European Commission , approxiA building’s energy demand is influenced by several factors , includiAmong these, the building envelope’s insulation performance has a significant impact on the total energy performance of the building and a near zero energy strategy is growing to overcome this situation . Energy The thermal performance of structural elements and materials are continuously analyzed and improved to reduce heat losses and increase the efficiency of building projects . The theIn addition, the use of natural materials, such as straw or masonry walls, are clear examples of materials with high transmittance variability due to their intrinsic heterogeneity. In general, this circumstance is solved by applying a thermal transmittance average value. Although, this straightforward assumption is useful as an initial approximation, the heterogenous structure of the natural material may substantially modify the thermal transmittance final value .Other construction elements that present this problem are those based on composite materials, such as mud-straw compressed blocks, where even if the proportions of the material remain the same, small physical variations in the different material used  lead to significant variations in the final thermal transmittance value . ExperimThe method based on hot-box methodology were proposed as international standard in ISO 8990:1994  and ASTMFinally, the ISO 9869 standard  and ASTMAccurate and fast thermal resistance estimation;Adaptability to regular and irregular samples with fast and low-cost rebuilding of the proposed hot box;Fulfilling the existing constructive material characterization regulation;Reducing measurement setup complexity maintaining estimation error below the maximum allowed by regulation.The aim of this paper is to propose an electronic instrumentation system that allows obtaining a thermal resistance value of a building element, either a simple material or a complex building element, in a simple, appropriate duration and cost-effective way. The proposed apparatus simplifies hot-box instruments to offer:The rest of the paper is organized in the following sections: 2·K and thermal mass J/K, although current legislation and regulations pay special attention only to the transmittance of enclosing wall elements. Thermal transmittance  is defined as the amount of heat flow that can pass through a surface per unit of time, when that surface is exposed to a thermal gradient of 1 K, Equation (1).The thermal characteristics of a building element are mainly defined by their thermal transmittance W/mThe operation of the hot-box instrumentation system is based on two principles, a first one established by EN ISO 8990  and ASTMThe main parts of a hot-box instrument are defined in the different methodology standards presenting some similarities summarized in This paper proposes a simplification of the calibrated and hot plate hot-box methodology and analyzes the advantages and disadvantages of the proposed aHB. The simplified aHB uses only one stable and controlled temperature source to define the temperature in one side of the sample, while leaving an uncontrolled temperature source, ambient temperature, in the other sample side. In this way, both the cost and the complexity of the measuring instrument are substantially reduced obtaining, by contrast, the thermal resistance estimation with enough accuracy for building applications.The new aHB instrument introduces the sample under test in the metering chamber. The main difference between a hot-box standard design and the proposed aHB instrument is the absence of a climatic chamber. The main goal of a climatic chamber is to create an ambient environment with stable temperature and very reduced wind speed offering a completely stable steady state, Using a thermal gradient between the sample’s faces and the methodology outlined in ISO 8302 , it is pThe aHB instrument does not have a cold focus of known value (climatic chamber), using instead the surrounding environment to dissipate the heat from the material site. This difference reduces the time required to stabilize the cold focus, the energy required, and the equipment involved. Since the cold temperature cannot be available beforehand, there is no previous information on the thermal characteristics and range of magnitudes of the thermal gradient between the faces of the sample under study. Therefore, it is necessary to continuously measure all thermal variables  from the pre-heat initial conditions and while the hot source is creating the thermal gradient.Q is the heat flux measured on the opposite face in contact with ambient environment, FLQ are the paths of flanking heat-flux losses and LQ are the paths of lateral heat-flux losses.The new aHB should minimize the impact of thermal losses, so it is necessary to characterize all error sources present during the test. Q will be equal to the heat flux induced by the hot plate. But in a real setup, the value of FLQ is equal to the flowing heat flux though the insulating material used to adapt the instrument to different sample sizes and shapes, and the LQ value is equal to the flowing heat flux though the lateral and lower instrument walls. In this sense, minimizing the values of FLQ and LQ, the Q value will remain stable over time and equal to the heat flux generated by the hot plate. When this condition happens, the sample is thermally stable, and the thermal transmittance can be obtained using Equation (1). Ideally, without heat-flux losses, the value This thermal characterization procedure is applied in this work, where a real aHB instrument is constructed and a control electronic circuit is implemented to automatically measure the U-value using a calibrated aHB instrument, where both the sample thermal conditioning time and the complexity of the whole instrument are reduced compared with existing commercial equipment.In the next section, the ambient hot-box implementation and the electronic circuit are described in detail.HP–temperature of hot plate) installed in the lower part of the housing. The hot plate (HP), which acts as a heat source and is positioned over this sensor, creates a temperature gradient between the two sides of the sample. Above the HP a metal guard (MG) is installed to isolate the sample from the HP and reduce contact thermal conductivity between the sample under test and the HP. The hot temperature (TH) sensor is located on top of the MG layer and under the sample. The TH sensor monitors the temperature on the hot side of the sample under test.The aHB instrument consists of a well-calibrated metering chamber formed by insulating walls that isolate the interior space from the outside environment. 3. In this way, the width of the insulation (ExIn + EPSIn) between the sample and the external ambient is increased while better adaptation to the specific shape and surface irregularities of the sample is achieved.When the sample material or element is in place on the TH sensor, the space between the sample and the ExIn walls is filled with backfill material. This backfill material  is collocated in the upper side of the sample. An additional temperature sensor is located directly above the EPSIn material to estimate the flanking temperature losses (TFL). The aHB instrument is equipped with three sensors installed in the upper side: a thermal flux sensor (FS–Flux sensor) with a temperature sensor , sensing area of 0.0008 m2, sensitivity nominal of 60 mV/(W/m2), and uncertainty of calibration of ±3%.The aHB instrument is monitored using temperature sensors and a heat flux sensor. The temperature sensors selected were based on NTC thermistors (NTCLG100E2104JB) with glass encapsulated, 100 KOhm of resistance value at 25 °C, tolerance of ±5%, and quick response time (<0.9 s). The heat-flux sensor selected was the HFP01-05 from Hukseflux with a wide measurement range , adaptation circuits, ADC, microcontroller, and data-collected server is presented in The FS signal is pre-amplified using an instrumentation amplifier circuit with a fixed amplification factor (G = 10). The pre-amplification stage adapts noisy FS signal to the next filter stages. The filter stages minimize the electromagnetic noise produced by the HP element and power supply. The next step adds a DC offset voltage (2.5 DCV), shifting the analog input signal to the midpoint of the voltage range of the A/D converter (5 VDC). Finally, the last amplification stage adapts the signal to maximize the total input range of the ADC. A variable-gain buffer amplifier (from G = 150 to G = 750) is used to adapt the signal acquisition to different sample materials, maximizing the final FS signal precision.The NTC temperature sensors are connected to the ADC inputs using the typical adaptative stage based on voltage divider schema and using the manufacturer coefficients and circuit design recommendations.The final aHB implementation is shown in 2·s). Therefore, the ADC sampling frequency is defined around 10 Hz to achieve enough accuracy values. This sampling frequency is easily accessible for most embedded ADCs in embedded microcontroller systems.A new aHB test algorithm is proposed to accurately estimate the U-value. Although the temporal requirements of the aHB test are not as important as the final U-value precision, there are some time-related features which should be observed: the ambient and the inside temperatures change slowly  and the heat flux has similar variability  during the stable period. The rest of sensor data stored during the test could be important for estimating the thermal behavior of the constructive element, because these data could be related to the thermal capacity of the materials forming the constructive element and may be considered as inertial mass in thermal comfort studies in building projects.Read initial temperature valuesWhile (not STOP Command){  Power on HP;if (Tc < GradientTemp) then{  read and store sensors data;}if (Tc = GradientTemp) then{  Maintain Tc value; }}Power off HPWhile { read and store sensors data;}The hot-plate power-on process is implemented using a switching power transistor configured like a motor driver due to the inductive component of the heater.Although there are numerous modifications in the form and use of the hot-box element itself, in relation to the description of the standard, the physical and material characteristics of the system described are still known. If the details and materials that compose the hot box are known, it is possible to establish, by corrective calculations, the magnitudes of losses produced by the non-ideality of the system itself.INQ) should be equal to the energy transmitted through the sample  can be substantially reduced increasing the EPS width by covering the part of the EPS near the HP and exposed to the ambient with vacuum-insulated panels like the ones used for instrument walls.Thermal losses due to heat transfer through the bottom side of the aHB .The initial experiment analyzed the increment of lateral heat-flux losses as a function of the temperature gradient created on the sample. Different temperature gradients (from 20 °C to 60 °C) were used to measure the lateral losses. In the next experiments, the maximum temperature gradient was established between 30 °C and 50 °C due to its linearity behavior in this range of values and due to reduce the risk of injuries during the test avoiding exposure to high temperatures. In this sense, the maximum absolute temperature should be 70 °C. This maximum temperature avoids personal manipulation at higher temperature and damages due to HP contact with the aHB walls constructed with expanded polystyrene with polyurethane coating.Defining a temperature gradient of 30 °C, different materials were tested. Defining the same temperature gradient for all tests maintains stable the lateral losses and the efficiency of the electronic system for all materials.The results obtained using several materials are summarized in The materials analyzed with standard values maintain the error lower than 4.3% of the standard value. This error is enough for building applications.Some additional materials without standard equivalent values were analyzed. The results have been used in different works to explore the use of new natural mixed materials with different concentrations to improve thermal resistivity. An example of this aHB application is shown in The aHB instrument collects continuous sensor data which can be used to explore thermal features of sample under test at different test stages. The curves shown in All this information can be estimated, analyzed, and considered to better understand the relationship between materials and thermal behavior using the new aHB instrument.Nowadays there are numerous commercial thermal characterization methodologies able to obtain the thermal transmittance of different building elements in a highly reliable way, using standards. However, such characterization methodologies impose strong impediments and restrictions both in the type of sample, measurement process and mainly total analysis time of a sample until the transmittance value is obtained.The system proposed in this paper presents a hot-box system based on the ISO 8990:1994 standard that, although it does not meet the requirements set by the standard, is able to obtain a thermal transmittance value cheaper, because the aHB can be implemented using low-cost electronics and sensors, simpler, because the aHB instrument can be adapted to different sample sizes just by redesigning the insulating box, and faster, because it does not require a steady state to take the measurements and can obtain the U-value at lower thermal gradients, as reported in It can, therefore, meet the needs of developers, builders and owners who want to know in detail, but without laboratory precision, the thermal characteristics of different construction elements, which is especially useful when using materials not present in official catalogs or new nature- based materials.The proposed aHB can obtain results of thermal transmittance of a material in less than 18 h with adequate reliability, and without the need to keep the sample in quarantine to fix initial values, nor having to manipulate or substantially transform the geometry of the samples.Although the thermal gradient is defined and digitally controlled, the heat-flux losses through the box as well as the flanking losses increase substantially when there are large external thermal variations. For this reason, it is recommended to use the aHB in indoor environments to maximize the linearity of the measurement.


Ubiquitous sensor networks collecting real-time data have been adopted in many industrial settings. This paper describes the second stage of an end-to-end system integrating modern hardware and software tools for precise monitoring and control of soil conditions. In the proposed framework, the data are collected by the sensor network distributed in the soil of a commercial strawberry farm to infer the ultimate physicochemical characteristics of the fruit at the point of harvest around the sensor locations. Empirical and statistical models are jointly investigated in the form of neural networks and Gaussian process regression models to predict the most significant physicochemical qualities of strawberry. Color, for instance, either by itself or when combined with the soluble solids content (sweetness), can be predicted within as little as 9% and 14% of their expected range of values, respectively. This level of accuracy will ultimately enable the implementation of the next phase in controlling the soil conditions where data-driven quality and resource-use trade-offs can be realized for sustainable and high-quality strawberry production. In the world of big data sustained by ubiquitous applications of sensor networks, artificial intelligence (AI) and machine learning (ML) create significant opportunities in multidisciplinary fields, including healthcare, financial services, and smart agriculture. According to the U.S. Department of Agriculture (USDA), the agriculture field and surrounding industries contributed USD 1.109 trillion to the U.S. gross domestic product and provided 10.9% of the total employment in 2019 [Researchers have focused on the yield prediction sector to support the economy and develop a sustainable supply across many different crops. Strawberry fruit is an essential crop for the U.S. economy, as the U.S. is the second-largest strawberry producer worldwide, contributing to 26.2% of the world’s production with 231 tons in 2017–2018 ,5. StrawOver the past decade, most of the research (authors of this paper included) focused on evaluating the quality of strawberries postharvest with little attention to how to control the quality of the crop pre-harvest. This study proposes a holistic system, which is comprised of multiple components in the form of a wireless sensor network to collect real-time high-resolution data from the soil, machine learning algorithms to predict potential harvest quality from the measured data and a control system to adjust soil parameters, including water content (WC) and electrical conductivity (EC) to achieve desired physicochemical characteristics at the point and time of harvest. The high-resolution data which match the soil measurements with the postharvest quality analysis has been presented in . As the Previous studies have shown less than stellar results regarding strawberries’ overall sensory qualities, which do not always satisfy the customers . As was This study was conducted using data collected from an approximately 40 acre commercial strawberry farm in Plant City, Florida. The reader can learn more about the data collection process and the statistical analysis of the data in the first publication of this study . As showy season . The prey season  for thaty season ,24. Thery season ,19,25, by season ,24, the g for 20 min to obtain a clear juice, which was filtered through cheesecloth [The dataset includes data points for four harvests during the four months of the 2018–2019 strawberry season, where six different points in the field were harvested to yield a total of 24 multivariate data points after pre-processing the dataset, as shown in esecloth . The SSCesecloth . Ultimatesecloth ,30. Theresecloth ,32. Furtesecloth , so a 28The effectiveness of various machine learning algorithms has been proven in many agricultural applications ,33,34,35The dataset, even though it was collected over a 4-month period with thousands of data points for sensory recordings, still has a challenging size, in light of the limited harvesting capabilities, which allowed for 4 separate occasions for the harvest on the commercial farms. As a result, the dataset has 24 data points and a relatively large feature vector, so it is extremely important to apply the fail-safe measures to prevent the network from over-fitting, such as early stopping and proper cross-validation. Leave-one-out cross-validation was applied in training the algorithms, as described below.One of the recently introduced strategies used in training the empirical models is splitting training data into two partitions, where the first partition is used to train model parameters and the second partition is used to calculate model accuracy at each step. As illustrated in This study includes a thorough comparison between different machine learning topologies which fall under two main categories: empirical and statistical. The first step in this study compares the results of a neural network (NN) to avoid over-fitting on a small dataset to an ensemble of neural networks (ENN), which helps build a more stable algorithm at the expense of error rate.For each run, leave-one-out cross-validation was used with 23 samples for training and 1 sample for testing. The root mean square error (RMSE) and prediction error percentage (PEP) metrics were used to measure the models’ performance for both frameworks. The PEP is defined as the root mean square error of the network over the quality average (QA) for each feature to provide a general understanding of the relative accuracy with respect to quantifiable metrics for each output, as shown in Equation , which has gained immense popularity in recent years—to explore the value of a statistical approach. GPR is a powerful probabilistic model to deal with noisy and small datasets , gives uY given X, whileGaussian Process Regression: GPR is a non-parametric probabilistic model which uses the Bayesian approach to give a probabilistic output. It uses independent variables to determine the uncertainty in the model prediction and improve the model selection . GPR useWorking with GPR on a small dataset helps in saving resources, while computing the kernel matrix as the model complexity, imension ,38,39. Gimension ,41.The leave-one-out cross-validation technique was applied to improve the performance and avoid over-fitting, where 23 samples were used for training and one sample for testing. The input–output pairs followed the same pattern as before for each experiment, depending on whether univariate or multivariate scenarios were used, such as predicting color separately or color and SSC together. RMSE was used to measure the models’ performance for both the univariate and multivariate responses, whereas PEP was used to evaluate the network prediction error.The results overall suggest that the color of a strawberry can be best predicted from the water content (WC) of the soil averaged across the 4 weeks immediately preceding the harvest. Including the electrical conductivity (EC) in the input space for predicting both color and sugar content simultaneously generally resulted in higher RMSE values. The RMSE results on the testing set for all neural network topologies, including singular and ensemble frameworks as well as the GPR models, are shown in detail in The performances of the applied topologies for the univariate response, color, support the hypothesis that an empirical tune on an NN with a small dataset can overfit, particularly with sophisticated models, as shown in The GPR for the univariate response seems to have underperformed compared to the empirical methods. It is possible that the high variance in the case of the GPR could be due to the presence of some sample points, which are such outliers that they significantly impact the statistical fitting than the empirical back-propagation across the dataset . Figure Beyond its mathematical importance, combining the color and SSC features together can ultimately give us a more precise picture of how to adjust the color and sugar content for strawberries and improve the production based on available WC and EC averages for the 4 weeks prior to each harvest.As anticipated with small data, the RMSE/PEP increases as the number of hidden layers and the neurons in these layers increase. However, the population of the ensemble seems to help the variance of RMSE, as shown in The GPR performed better in predicting the color values using only the WC as the input compared to using both the WC and EC as input features. Not only is the PEP% lower, but also the variance in the root mean square error is smaller. Similarly, when predicting both color and SSC, using a univariate input (WC) had a better performance than using both WC and EC as inputs, both in terms of error% (PEP) and error variance. The reader can find detailed numerical values in 2 concentration) [Over the past decade, most of the research focused on evaluating the quality of specialty crops postharvest, whereas this study aims to develop a methodology to control the production quality of strawberries pre-harvest. Specifically, this paper discusses the algorithm development stage of a sensor-enabled real-time strawberry production monitoring system to improve both resource management and harvest quality. Recent studies tried to predict the crop yield ,19,20,34tration) , while Mtration)  tried totration)  developeThis paper presents a nondestructive method to predict strawberry quality based on appearance (color) and flavor (sweetness) from the soil properties (WC and EC) during the pre-harvest process. Compared to the previous studies, the novel contributions of this study are multi-fold. Specifically, it introduces both empirical and statistical models to find novel correlations between the soil sensory measurements and associated multivariate harvest quality. Furthermore, it demonstrates that a sufficient prediction error can be achieved to enable a future real-time implementation of a smart controller to exploit environmental and climate conditions to reduce resource use.Based on the structure of the data collected from a commercial farm throughout an entire Florida harvest season, several predictive models, statistical and empirical, were proposed to infer the color and sugar content of the harvested strawberries from the measured WC of the soil across a certain time period. To the best of our knowledge, both the collected data and the subsequently developed algorithms are unprecedented in the literature. This study demonstrates the performance of the algorithms through a series of use-case scenarios in predicting the univariate and multivariate responses in the form of color and sugar content of the produced strawberries as the most important physicochemical characteristics for marketability.The average color values in the collected data were around 36.4 (a quantitative measure for redness) and the average SSC values were 6.4 (a quantitative measure of sugar content). To accurately display the performance of each prediction model, these average values are used to create the PEP metric such that the RMSE values are contrasted against the average quality values for color and SSC to provide a general understanding of the relative accuracy with respect to quantifiable metrics for each output. In the end, the models were able to predict the color and color-sugar content within as little as 9% and 14% PEP of their expected range of values, respectively. Such accuracy values allow for us to implement the next phase of the project in controlling the WC based on predicted color values once the desired quality threshold is chosen.The authors also acknowledge the limitations of this study. Specifically, the data were collected across a single harvest season and the number of harvests for quality analysis was not enough to create a sufficiently generalizable input–output relationship for the prediction models. Even though widely accepted cross-validation methods have been deployed and validated, the study can greatly benefit from additional data points which are projected to be collected in the upcoming strawberry seasons.These findings suggest several courses of action to implement the proposed scheme of work shown in This paper presents the second stage of a system that uses sensor networks to collect real-time data for the precise monitoring and control of soil conditions in a commercial strawberry farm. The sensor network is distributed in the soil to gather data that can infer the ultimate physicochemical characteristics of the fruit at the point of harvest. Empirical and statistical models, such as neural networks and Gaussian process regression models, are used to predict the most significant physicochemical qualities of strawberry, such as color and sweetness. The level of accuracy achieved is as low as 9% and 14% of the expected range of values, respectively, which will enable the next and third phase of controlling soil conditions for sustainable and high-quality strawberry production.This paper introduces both empirical and statistical models to discover new relationships between soil sensor measurements and multivariate harvest quality. Furthermore, it shows that it is possible to achieve a sufficient level of prediction accuracy to implement a real-time smart controller in the future to optimize resource use based on environmental and climate conditions.The limitations of this study mainly include a lack of sufficient harvests to match the otherwise very-high-resolution multimodal data streaming from the soil sensors. This mismatch in data inputs and outputs limited the complexity of the model used for training. In future studies, more harvest points will be included and the effects of different cultivars, soil conditions, and temperatures across multiple climates will be studied through multi-climate and multiple field partnerships.


The depth completion task aims to generate a dense depth map from a sparse depth map and the corresponding RGB image. As a data preprocessing task, obtaining denser depth maps without affecting the real-time performance of downstream tasks is the challenge. In this paper, we propose a lightweight depth completion network based on secondary guidance and spatial fusion named SGSNet. We design the image feature extraction module to better extract features from different scales between and within layers in parallel and to generate guidance features. Then, SGSNet uses the secondary guidance to complete the depth completion. The first guidance uses the lightweight guidance module to quickly guide LiDAR feature extraction with the texture features of RGB images. The second guidance uses the depth information completion module for sparse depth map feature completion and inputs it into the DA-CSPN++ module to complete the dense depth map re-guidance. By using a lightweight bootstrap module, the overall network runs ten times faster than the baseline. The overall network is relatively lightweight, up to thirty frames, which is sufficient to meet the speed needs of large SLAM and three-dimensional reconstruction for sensor data extraction. At the time of submission, the accuracy of the algorithm in SGSNet ranked first in the KITTI ranking of lightweight depth completion methods. It was 37.5% faster than the top published algorithms in the rank and was second in the full ranking. With the continuous development of 3D computer vision research, the demands for dense depth maps have gradually increased. Therefore, the depth completion task as data preprocessing has received much attention in AR ,2, VR 3, and 3D Researchers have developed a variety of solutions, the most recent of which rely on Convolutional Neural Networks. The original and most commonly used depth completion network is the one-branch fusion network ,7,8 showHowever, joint representation alone will result in missing original features. Thus, some researchers have proposed the two-branch fusion network ,12,13,14In a complex environment, depth information is very sparse. Additionally, due to the large gradient of object edges, the depth information of object boundaries after depth completion is blurred. These two points make depth completion challenging. DynamicConv  reduces Researchers have also tried other guidance methods.To make better use of local affinities, spatial propagation networks (SPN)  have beeOn the basis of GuideNet, we designed a lightweight depth completion network based on secondary guidance and spatial fusion for fast and accurate depth completion, whose structure block diagram is shown in SGSNet proposes a lightweight depth completion network based on secondary guidance and spatial fusion borrowing from GuideNet and DA-CSPN++ networks, using the proposed image feature extraction module and the secondary guidance module to make full use of RGB image information and LiDAR information to obtain a more accurate depth map quickly. This network does not require additional datasets, and the KITTI dataset ,31 can bAn image feature extraction method, which contains a spatial feature extraction as well as a scale feature extraction, is used. Compared with the traditional image pyramid module, this module focuses more on mining richer multiscale information in the same domain.A secondary guidance module is used to guide the guidance features to the LiDAR features and the input DA-CSPN++ network. It is 10 times faster than that in the baseline GuideNet, allowing the overall network to meet the demand for real-time data preprocessing.The main contributions of SGSNet can be summarized as:We designed an end-to-end deep learning framework based on secondary guidance and spatial fusion for depth completion, whose network structure is shown in In the following subsection, we introduce the image feature extraction module based on image pyramids and the secondary guidance module.The feature map of these modules is shown in According to the image pyramid, the image has different image features at different scales. For feature extraction at different scales, the usual method is to first downsample the image, convolve it to obtain the features at that scale, and then upsample it to make the features at different scales the same size. Such a feature is partially complemented by upsampling, which results in some predicted data with great impact on edge information, and does not make full use of all the information at that scale. Therefore, based on the description of atrous convolution in Vip-DeepLab and the method of convolving images using different convolution kernel sizes in GoogleNet, SGSNet used the atrous heterokernel convolution kernel, which is shown schematically in For the same perceptual domain of a certain element, the feature extraction of the same perceptual domain at different scales is achieved by using different convolution kernel sizes and adjusting the interval of convolution kernel elements. The multiscale information of any domain can be extracted completely and efficiently using the atrous heterogeneous convolution kernel proposed in SGSNet compared with the traditional image pyramid convolution kernel.Spatial feature extraction only extracts the corresponding features at the level of a single feature map, while scale feature extraction extracts different features due to scale transformation at the overall network level, as shown in The lightweight guidance module was designed based on the guidance module proposed in GuideNet. Compared to the baseline, it can complete the guidance of image to depth map feature extraction more quickly with the same performance. Its main role is to guide the LiDAR features by depth gradient features. The formula for this module is: It is assumed that the size of the guidance features as well as the sparse depth features are Equation . The comAssuming the memory consumption of direct dynamic convolution, the guidance module mentioned in GuideNet and the lightweight guidance module proposed in SGSNet are From Equation , we can The depth map generated by the deep learning network may change the exact pixel depth value originally obtained from the LiDAR data. In order to make better use of this accurate data, DA-CSPN++ is used in SGSNet to second-guide the depth map generated by the first part. On the basis of DA-CSPN++, one modification was made. For the problem of the depth feature loss caused by cropping the depth map obtained from LiDAR by high-dimensional depth feature guidance depth map, SGSNet used a depth information completion module to complement the depth features, so that the accuracy obtained by DA-CSPN++ was higher when using high-latitude features.The module designed in SGSNet is shown in We used L2 loss for training, and the equation isHere, The ground truth represents different meanings in different branches. In the image guidance feature extraction branch, ground truth represents the depth scale map obtained by processing the dense depth map given by the dataset. In the other two branches, ground truth represents the dense depth map. In the LiDAR feature guidance branch, the train loss is different, and its expressions are: Our models were trained and evaluated on the KITTI dataset, which provides over 93,000 sparse depth maps converted from multiline LiDAR and their corresponding RGB images, with a resolution of 1216 × 352. A sparse depth map has about 5% valid pixels, and a ground truth dense depth map has around 16% valid pixels . The datWe adopted four metrics for performance evaluation, which were root mean squared error (RMSE [mm]), mean absolute error (MAE [mm]), root mean squared error of the inverse depth (iRMSE [1/km]), and mean absolute error of the inverse depth (iMAE [1/km]). Additionally, the runtime of inference is reported.The model in SGSNet was based on the Pytorch  frameworWe set up a series of ablation experiments to demonstrate the efficiency of our designed image feature extraction module and bidirectional guidance module, and the overall results are shown in GuideNet was our baseline. Compared with it, we see from the B1 and B2 results that our proposed method had a large improvement in RMSE and MAE and little change in iRMSE and iMAE.Based on B2, we evaluated the lightweight guidance module and the deep information completion module in the secondary guidance module.First, we evaluated the lightweight guidance module and compared the results of B2 and C. Our lightweight guidance module had less improvement in accuracy but had a ninefold improvement in run speed. This also showed the main reason for the network runtime was the guidance module.Next, we evaluated the depth information completion module. We trained the networks without the depth information completion module but with the addition of the DA-CSPN++ module at three different scales to be the baseline and trained the networks with the depth information completion module to compare with the baseline at the same scale. The results showed that when the depth information completion module was not included and the feature dimension was 4, the effect decreased compared to the feature dimension of 2. However, because of the completion of the depth features, when using the depth information completion module, the results improved. Particularly, at the feature dimension of 4, the improvement in RMSE and MAE was obvious, the RMSE was reduced from 748.93 to 744.04, and the MAE was reduced from 209.82 to 206.30.Our project was first in the KITTI online list for lightweight algorithms and second in the overall online list at the time of publication. We compared the published high-performance algorithms in the KITTI online list, and the results are shown in In this paper, we designed an efficient and parallel lightweight depth completion network based on secondary guidance and spatial fusion. It extracted the features of the image in parallel and efficiently through the spatial feature extraction and scale feature extraction. Then, it guided the sparse depth map through the lightweight module for fast LiDAR feature extraction and generated the dense depth map. Finally, the high-dimensional sparse depth map information was complemented by the depth information completion module and input into DA-CSPN++ for secondary guidance. The overall network was efficient and parallel and performed well on the KITTI list.


We present experimental and numerical studies demonstrating the influence of geometrical parameters on the fundamental spin-wave mode in planar 1D magnonic crystals. The investigated magnonic crystals consist of flat stripes separated by air gaps. The adjustment of geometrical parameters allows tailoring of the spin-wave frequencies. The width of stripes and the width of gaps between them affect spin-wave frequencies in two ways. First, directly by geometrical constraints confining the spin waves inside the stripes. Second, indirectly by spin-wave pinning, freeing the spin waves to a different extent on the edges of stripes. Experimentally, the fundamental spin-wave mode frequencies are measured using an all-optical pump-probe time-resolved magneto-optical Kerr-effect setup. Our studies address the problem of spin-wave confinement and spin-wave dipolar pinning in an array of coupled stripes. We show that the frequency of fundamental mode can be tuned to a large extent by adjusting the width of the stripes and the width of gaps between them. They can act as waveguides carrying the information encoded in spin waves6. Recently, many publications have focused on the spin waves in the sets of stripes, arranged in-plane periodically  or quasiperiodically . The stripe systems act not only as waveguides. By adjusting their dimensions, we can tailor the spin wave propagation and thus process magnonic signals17.Ferromagnetic stripes are one of the basic building blocks of magnonic structures18. However, this effect is partially mitigated by the reduction of precession amplitude close to the lateral faces for flat stripes, which is called dynamical pining of magnetization20. In other words, the system partially trades the demagnetizing energy related to the presence of surface charges on lateral faces (and related to the presence of dynamic stray field) for other contributions of demagnetizing energy, resulting from the volume magnetic charges induced by the non-homogeneous distribution of the spin-wave amplitude21. The pinning partially confines the fundamental mode within the stripes and causes a frequency up-shift when the stripe’s widths are narrowed. Another effect is the weakening of dipolar coupling between the stripes due to dynamic magnetization pinning because of the reduction of dynamic stray field.The collective magnetization dynamics in stripe arrays depend on the magnetic coupling between the stripes. Thus, the simplest possible structure of this type is a periodic sequence of flat stripes separated by air gaps, which can be carved in thin ferromagnetic films. In such a system, the coupling is provided by a dynamic stray field within the gaps. The strongest dynamic stray field is created by the fundamental mode, where the magnetization precesses in phase. The largest surface magnetic charges and, thus, the strongest dynamic stray field appears on the lateral faces between the stripes, which is also reflected in the ellipticity of precession20: The strength of the pinning is expressed by the pinning parameter22. Then, the pinning can be introduced by a different mechanism: the presence of surface magneto-crystalline anisotropy22. In the general case, the dipolar pinning can be combined with the influence of surface anisotropy20. However, for thin stripes , the dipolar interactions significantly impact pinning20.In the absence of the dipolar interaction, the spin wave is free on the surfaces  models with dipolar and exchange interactions taken into account31.When the dipolar interactions prevail over the exchange interactions, spin wave modes in confined geometry  can be calculated by solving the integral eigenvalue problem with the magnetostatic Green’s function as an integral kernel33, the time-resolved magneto-optical Kerr effect (TR-MOKE) spectroscopy37, to determine the fundamental mode frequency. Using the TR-MOKE technique, we measure the frequency of the fundamental spin-wave mode  on spin wave pinning and consequently on the frequency of the fundamental mode in such structures. Spin wave dynamics is calculated numerically by solving the linearized Landau-Lifshitz equations. We use an experimental technique complementary to Brillouin Light Spectrometry38), and theoretical approach  we used. We also provide the Supplementary Information, which describes: the details of post-processing for the TR-MOKE signal, the semi-analytical calculations of the demagnetizing factors for fundamental mode, and the determination of equilibrium orientation of static magnetization.The paper is organized in the following way. In “Results and discussion”, we present and describe the results of our measurements and computations. We show the dependence of frequency and mode profile of fundamental mode  on the structure’s geometry—stripes width and size of the air gap. “Results and discussion” is finalized with the conclusions. The following section (“Methods”) describes the experimental methods , numerical techniques (finite element method (FEM)The systems consist of CoFeB stripes of finite width mentclass2pt{minimIn our studies, we fixed the thickness mentclass2pt{minimThe numerically calculated FMR frequency for the CoFeB layer is equal to 13.6 GHz. The FMR frequencies obtained experimentally by TR-MOKE are in the range of 13.6 up to 13.95 GHz. Differences may be due to the quality of the samples measured, the quality of the laser in the pump-probe experiment, and other factors. It follows that measurement uncertainties of half a gigahertz are expected, even for simple structures. The value calculated for uniform CoFeB film is marked in Fig. After these preliminary studies, we performed (by TR-MOKE) the measurements of magnetization dynamics in all the fabricated periodic structures with stripes of the widths entclass1pt{minimaIt can be seen that we have achieved good agreement between experimental, computational, and semi-analytical results. Experimental results are subject to significant measurement error even for uniform CoFeB films due to the quality of the CoFeB material (homogeneity of composition), measurement uncertainty , which we have already described for the layers. In the case of periodic structures, the experimental measurement results are subject to even more significant uncertainty due to the difficulty of producing ideal thin magnetic stripes with sharp edges, separated by air gaps of the same width along the length of the stripe. Taking this into account, the presented experimental results are within the measurement uncertainty limit. It can be seen that the fundamental mode frequencies depend on the air gap separations between stripes. The change of fundamental mode frequency between uniform film and periodic structures is continuous. For very small separations, the fundamental mode frequency of periodic structure tends to be the FMR frequency of a uniform film, being the bottom limit. The bigger the separations, the higher the frequency of the fundamental mode of the structure. The fundamental mode frequency is the highest for completely separated stripes—i.e., single stripes—which is the upper limit. In our measurements, it is impossible to measure a signal from a single stripe since the signal would be too small, so the upper limit was only calculated numerically (dash-dotted line) and semi-analytically (dotted line). The fundamental mode frequency of a single stripe is presented as a dotted (dash-dotted) line for each subfigure in Fig. We can notice in Fig.  that theg, i.e., from For a better understanding and more explicit interpretation of the experimental results, we performed the simulations for the extended range of the widths of air gaps We have plotted the profiles of the fundamental mode for systems composed of stripes of one selected width (The profile marked with the label (s) is the profile of the mode of a single 500 nm wide stripe . It is worth noting that the wider stripes are more strongly coupled compared to the narrower stripes, at the same gaps, because the weaker pinning means the stronger stray field produced at the lateral faces of the steps, which is responsible for coupling. (ii) The dipolar interactions between the constituting nanoelements of magnonic planar nanostructure must be considered even if the distance between successive stripes is within a single micrometer. (iii) The TR-MOKE measurements allow for the investigation of the frequency of fundamental mode, i.e., the mode precessing uniformly in space (with wave vector We can summarize our research on the magnetization dynamics in the array of flat stripes arrays by highlighting the following conclusions. (i) The fundamental mode frequency increases with the stripes’ separation. It also depends on the width of the stripe due to the pinning. The frequency of the fundamental mode is lower for wider stripes. This decrease results not only from the extension of the space on which the mode is spanned  but also from the reduction of pinning  at a repetition rate of 40.Magnetization dynamics for precession frequency determination is measured in a time-resolved magneto-optical Kerr-effect setup (TR-MOKE) in an all-optical pump-probe scheme, depicted in Fig. mentclass2pt{minimThe dynamics is triggered via a broadband excitation by depositing energy from the pump beam laser pulses at fluences adjusted to 18:41. Both the magnetization of the ferromagnet 42:The magnetization dynamics in a magnetic system is described by the equation of motion of the magnetization, called the Landau–Lifshitz equationDipolar field y-coordinate. We consider monochromatic SWs in a fundamental mode (f is the frequency).To observe the TR-MOKE signal, we applied the external field mentclass2pt{minimLastly, coupling the Landau–Lifshitz equation with Gauss law for magnetism, we arrive at the following system of equations for the dynamic magnetization 38 to solve8 Eq.  for the flat stripes (Semi-analytical calculations supplemented the numerical results. The fundamental mode frequency was calculated using the Kittel formula for the planar system with the uniaxial shape anisotropy: Supplementary Information.


Giant thermal and solutal non-equilibrium fluctuations are observed in shadowgraphy experiments on liquid mixtures subjected to a temperature gradient. For large temperature differences, both the temperature and the composition dependence of the relevant thermophysical parameters and the nonlinear terms in the diffusion equation need to be taken into account, leading to a nonlinear concentration profile. For temperature differences exceeding the inverse of the Soret coefficient, in our example approximately 10 K, the usual data evaluation yields increasingly wrong diffusion and Soret coefficients that are off by almost a factor of two for a temperature difference of 50 K. A local model that treats the measured shadowgraph signal as a superposition of the contributions from every layer of the sample is able to capture the essential trend and yields a good agreement with experimental data. The results are important for the application of shadowgraphy as a tool for the measurement of Soret and diffusion coefficients, where large temperature gradients promise a good signal-to-noise ratio. Thermodynamic non-equilibrium fluctuations (NEFs) are observed in liquids under the influence of a temperature or a concentration gradient , 2. Theiple size , 4. Undeentation .q-dependence of the correlation time Shadowgraphy (SG) has become the method of choice for the investigation of NEFs, and the technique has been turned into an analytical tool for the measurement of thermal diffusivities and diffusion and Soret coefficients –15. Whenent}qroc . In partMeasurements of Soret and thermodiffusion coefficients require nonequilibrium conditions with a temperature gradient. As a rule, a larger temperature gradient translates to a better signal with less noise. But how much is too much? For most techniques, the temperature differences are relatively small: below one mK for thermal diffusion forced Rayleigh scattering (TDFRS) –19, \docon (OBD) –22 and 5on (OBD)  or durinon (OBD) , 25.Common to all experimental techniques is the usual assumption that the experiments are essentially performed at the mean sample temperature, that deviations from equilibrium are small, and that temperature and composition dependences of system parameters and transport coefficients are negligible. In this contribution, we will go beyond this linear model and investigate the consequences of various nonlinearities for the investigation of NEFs by means of the shadowgraphy technique with large temperature gradients. We will take both the temperature dependence of important physicochemical parameters and nonlinear concentration profiles that result from the nonlinear thermodiffusion equation into account. The results of this paper are particularly important for the application of shadowgraphy as a tool for the measurement of diffusion, thermodiffusion and Soret coefficients.The work presented here has been performed within the framework of the Giant Fluctuations (NEUF-DIX) project of ESA, which aims at the investigation of NEFs in complex multicomponent mixtures under microgravity conditions, and the associated CORA-MAP project ‘Technologies for Non-Equilibrium Systems’ (TechNES) for the development of NEFs into diagnostic tools. One major objective of these projects is the investigation of non-ideal systems, including the case of large gradients that give rise to nonlinearities and preclude the analytical modeling of the system by means of linearized hydrodynamics , 27.We have used the identical shadowgraphy setup as described in Ref. . It is bmentclass2pt{minimThe collimated beam of a superluminescent diode  is determined by the Soret coefficient The steady-state concentration distribution in a binary mixture of concentration mentclass2pt{minimAlthough it is widely used, the validity of this linearized approximation needs to be questioned for two reasons. First, the nonlinear concentration term in Eq.  can onlymentclass2pt{minimThe purpose of this section is to provide expressions for the temperature and concentration dependence of all relevant thermophysical parameters that will later be needed for the model calculations. Our goal is to keep it as simple as possible and to catch only the relevant dependencies, thereby ignoring the insignificant ones. Since we are dealing with dilute solutions, we will neglect the concentration dependence and consider only the temperature dependence of certain parameters of pure toluene. This is a reasonable approximation for coefficients that depend only weakly on concentration, such as the thermal diffusivity or the thermal conductivity.Soret coefficient In order to solve Eq.  can be obtained according to c stays below about ten percent [entclass1pt{minima percent . Its tementclass1pt{minimaD for all molar masses and for polymer concentrations up to at least D is limited to Also shown for comparison are the only available other temperature-dependent measurements from Ref.  for \docentclass1pt{minimawith Eq. , also foentclass1pt{minimaThermal diffusivity Figure Thermal conductivity The temperature dependence of the thermal conductivity i et al. :5\documeDensity and expansion coefficients Densities Viscosity An empirical formula for the molar mass, concentration and temperature dependence of the dynamic viscosity of PS/Tol is given in Ref. [rom Ref. , they le in Ref. ):7\docum in Ref. . It was, in Ref. . A bette in Ref.  for the M in g/mol. Equation  in the interval c and T and entclass1pt{minimafrom Eq. . The intIn the following treatment of the shadowgraphy experiment and the differential dynamic analysis (DDA) –42, we cZ from the center of the layer by the sensor of the camera. Starting point is the structure function of Fourier transformed difference images in q-space [B(q), the static structure factor of the fluctuations S(q) and the intermediate scattering function g) below the respective roll-off wavevectors [q-values.The light scattered by NEFs in a thin liquid layer is recorded at a distance  q-space :16\documfunction  \documenevectors 19\documegiven by 20\documeThe usual data evaluation is based on the assumption of a thin sample with constant concentration and temperature gradients throughout the liquid and with effectively constant values of all thermophysical parameters of the sample that correspond to the mean temperature in the center of the cell. In particular for systems with large Soret coefficients, such as polymer solutions or colloidal dispersions, and/or large temperature differences Since the amplitudes of the NEFs (Eq. ) are proors (Eq. ), they wIn order to understand how the experiments and the extracted data, e.g., diffusion and Soret coefficients, are affected, we will now simulate the expected multimodal measured signals. Then, we will apply the same standard data evaluation procedure as for real measurements, which is not aware of the nonlinearities, to these computed signals. The extracted coefficients can then be compared to the known input values and to shadowgraphy experiments.z as an additional variable for all quantities that depend on T and c and, thus, on the position within the cell. Equation (T(z) and concentration c(z) are given by Eqs.   22) holdging Eq.  over theEquation  now beco by Eqs.  and 14)\documentevectors . Besidesz-dependence of the concentration gradient shown in Fig. Figure g to Eq.    \documenons Fig. . They arAs predicted by Eq. , the plofrom Eq.  for \docThe solutal counterpart lows Eq.  only forentclass1pt{minimaFinally, the Soret coefficient is calculated from the roll-off wavevectors according to 24\documevevector . For theD, and Figure D results only from the temperature and concentration dependencies and not from the nonlinearity of the diffusion equation. The deviation of Also shown in Fig. We have investigated a problem that is inherent to many nonequilibrium experiments, which require finite temperature and/or concentration gradients in order to generate a measurable signal. The results are then typically assigned to a fixed temperature, which frequently corresponds to the mean sample temperature. Whether this approach is valid or not cannot easily be predicted. It depends on the temperature dependence of all relevant physicochemical parameters. For the polymer solution studied here, the most crucial question is, whether the underlying transport equations, the heat equation and the extended diffusion equation, can be linearized with respect to the temperature and concentration gradients. While this assumption is generally fulfilled for the temperature gradient, which is approximately constant even for large temperature differences of say mentclass2pt{minimWe have modeled the measured shadowgraphy signal as a superposition of the signals from parallel thin fluid layers, each of which characterized by its own temperature and concentration, and the respective gradients. Even though both the amplitudes of the concentration mode and the corresponding relaxation time constants vary over a broad range, as shown in Figs. We have compared our simulations to experimental shadowgraphy results for the diffusion and Soret coefficient as measured with different temperature gradients and found good agreement. It is difficult to generalize our findings, but it can be said that the signal anomaly mainly results from both the nonlinear concentration profile and from the temperature and concentration dependence of the system parameters. Thus, as a rule of thumb, the temperature difference should not exceed the inverse Soret coefficient: polymers , where tOur results are a contribution to the Giant Fluctuations and the TechNES projects of the European Space Agency ESA and the BTGIANT project of the German Aerospace Center DLR, which aim at the understanding of NEFs in non-ideal systems as encountered in the presence of large gradients both on ground and in microgravity.


So far, multiple approaches were described. Here, we investigated the impacts of different data fusion strategies on classification accuracy and feature selection stability, which allow the costs of diagnostic tests to be reduced. (2) Methods: We used molecular features (gene expression) combined with a feature extracted from the independent clinical data describing a patient’s sample. We considered the dependencies between selected features in two data fusion strategies (early fusion and late fusion) compared to classification models based on molecular features only. We compared the best accuracy classification models in terms of the number of features, which is connected to the potential cost reduction of the diagnostic classifier. (3) Results: We show that for thyroid cancer, the extracted clinical feature is correlated with (but not redundant to) the molecular data. The usage of data fusion allows a model to be obtained with similar or even higher classification quality (with a statistically significant accuracy improvement, a  In cancer diagnostics, many different methods and approaches are used independently. New diagnostic tools are implemented into common use if they are characterized by higher diagnostic abilities  and (possibly) lower costs. Construction of such tools typically begins with massive data obtained from radiology and medical imaging, or high-throughput molecular methods, including microarrays, next generation sequencing, and protein mass spectrometry. These technologies are good sources of data for machine learning (ML); supervised learning and sample type prediction are common techniques applied in diagnostics for a wide range of diseases . Since tDesigning a diagnostic test from molecular data involves many challenges due to high-dimensionality and  a limited number of samples. During the process of molecular test construction, the sample collection must be split into multiple subsets, such as test set and learning set. The latter must be split again for comparison of learning techniques using cross-validation methods, such as leave-one-out, bootstrap, or k-fold. Consequently, the number of samples available for training the model shrinks, which may influence the dimensionality reduction process if there are multiple intrinsic subgroups already present in the datasets. The molecular features obtained with high throughput techniques showed multiple dependencies. The relations between such a number of features measured with, e.g., correlation, mutual information, or distance measures, are hard to present/interpret in a readable form, and necessitate dimensionality reduction, which may remove clusters of differential features.One popular method in the context of data integration is feature extraction, which reduces the feature space by creation of new features basing on the existing ones. This is a useful tool to decrease the number of genomic features  . Some noIn order to improve the quality of classification models, data from multiple sources may be used. For the analysis and classification of data from multiple sources, such as -omic, clinical, and others, data integration is a useful practice. Data integration is a broad topic and is linked to data warehousing , data miData integration may be performed with multiple methods, as described in the literature. Data fusion could be considered a stage of data integration , and tecWe hypothesize that some clinical data representing the phenotype of a disease may contain complementary data to those of gene expression in terms of features for the classifier, and we investigated the impact of data fusion on the feature selection process. The proper selection of features has become a science of its own and has been widely described, for example in . Based oIn the present study, we investigated if a molecular classifier may benefit from data fusion resulting in a reduced number of features (lowering the cost of gene expression test) while keeping the accuracy comparable to a molecular test using only gene expression data. Here, we focused on the use of data fusion between high-dimensional gene expression data and low-dimensional clinical data, whose costs are already included in the basic diagnostics process. The inclusion of clinical data in the model may reduce the number of necessary molecular features, decreasing the cost of the whole test. The method we propose allows for assessing the usefulness of fused features and presents the most beneficial feature combination.We demonstrate the effectiveness of our method using data from thyroid cancer (in which overtreatment is a growing concern). A fine needle aspiration biopsy (FNAB) is the main tool for diagnosis of thyroid nodules . The samReferences ,22,23. GMolecular markers, as shown in the studies presented above, are promising for cancer diagnostics. A reduction in the number of molecular markers without any significant losses in accuracy will lower the costs of the test and make it more available for a wider group of patients. In this study, we compare the different integration strategies using sets of microarray gene expression profiles and sets of the most common clinical factors claimed to be risk indicators . We compare the results of data fusion for two popular feature selection methods in terms of classification accuracy and feature ranking stability. Because the aim of genomic feature selection is to find the optimal set of molecular markers, whose expressions may be measured with different methods, such as RT-qPCR , the presented study excludes the use of feature extraction techniques for molecular data.Instead of using the clinical data in raw form, we integrated all non-genomic data into one model to obtain one numeric value—the probability of a nodule’s malignancy. We used a Bayesian network; the dependent variable is represented by the node we called Risk. The graph for the created network is presented in The graph presents the connections that occur most frequently between variables. Malignancy risk is independent from sex and tumor size but we have found connections between malignancy risk and both age and Bethesda. The strength of the connection between Bethesda and malignancy is 10 times stronger than between age and malignancy. This should be interpreted as follows: the sex and size of the lesions show nothing special about the malignancy risk, but knowing the patient’s age, we can speculate about the probability of the malignant type of nodules. The risk of having a malignant nodule increases with age. The lack of connections between sex and age may be a result of a low number of samples and internal bootstrapping.We used two sets of molecular features previously published as markers for genomic classifiers, which we called Microarray_163 and Microarray_40. We estimated the similarity between features, because we considered that they may influence the stability of feature selection. We calculated Spearman’s correlation for each gene pair in genomic feature sets and for each gene and malignancy risk. For those pairs, we also estimated mutual information.We checked the relations between each feature pair in the given genomic feature sets. The dataset differences  are presented in Then, we compared the malignancy risk with each molecular feature for both molecular feature sets. For the Microarray_163 feature set and clinical risk, the correlation coefficients were in the range between moderate negative correlation and moderate positive correlation. For this feature set, most pairs had correlation coefficient close to 0. The smaller dataset showed bimodal distributions for molecular feature correlations and molecular features versus malignancy risk. Eventually, the number of moderate or highly correlated pairs of molecular featured and malignancy risks was comparable in both datasetsWe calculated the mutual information (MI) between the molecular features . Then we compared the reference models (molecular features only) and models with data fusion. We tested a wide range of selected features for each feature selection method. For the Microarray_163 feature set, we tested a whole range of features, but the accuracy decreased with the increasing number of predictors, so we analyzed only the range of 1–41 features. For each reference model, we observed a maximum accuracy for models with 15–16 features. For models with higher numbers of features, the accuracy slowly decreased. For both feature sets, the models with fusion had higher accuracies than the reference model for the small number of features. The results for models based on Microarray_163 are presented in The differences between feature selection algorithms are weak, but models with data fusions have higher accuracies than the best reference model with 15 features. Models with features form Microarray_40 are presented on For the Wilcoxon feature selection, the accuracy results were slightly higher for the late fusion strategy, but the confidence intervals overlapped.These results suggest that data fusion allows for increased accuracy with a reduction of the necessary features. In this case, late fusion seems to be more beneficial. We compared the best reference model with the best models of fusion and the p-values, presented in p-values and the differences between the model with fusion and the expression-only model for the nFeatures range of 1–15 are presented in the We checked if the similarity of the early fusion to the late fusion strategy meant that the malignancy risk was selected as often as in late fusion (in each model). For such a case, the model’s accuracy and feature selection stability would be similar for both data fusion strategies. The exact values of the While the performance of a model (in terms of classification accuracy) is crucial for its applicability, molecular markers can also provide valuable insight through pathway and functional analyses. Therefore, feature selection should also be evaluated for its consistency. We used the Kuncheva stability index , which aAs expected, slight differences were observed. The early fusion strategy seemed to have higher Kuncheva index scores than the reference model and the late fusion strategy. The unexpected result was that the early data fusion strategy and ReliefF feature selection helped increase the feature selection stability. We analyzed the feature rankings, and indeed, the selected feature lists were shorter for the early data fusion strategy.For the Microarray_163 feature set, the Kuncheva index is presented in The Kuncheva indexes for the Microarray_40 feature sets showed higher differences as the feature selections reached the maximum of the available features. The maximum values of each model reached the maximum stability  and are omitted in For a low number of features (where accuracy was highest), early fusion increased the stability of the feature selection for both ReliefF and Wilcoxon methods. The malignancy risk was selected, appeared on the top positions of the feature ranking, and enhanced the stability for the selection of molecular features. Higher stability is desired for feature selection, making the early fusion strategy a better solution for a given dataset, because this method produces a similar (or slightly lower) quality performance.Summarizing this study, we compared two data fusion strategies for the two types of feature sets: high-dimensional molecular data and clinical data represented by one extracted feature—malignancy risk. We used two popular ranking-based feature selection methods—ReliefF and the Wilcoxon test. We observed the influence on classification accuracy (using bootstrap) and the stability of feature selection.We added one continuous feature to the preselected subset of features and obtained a higher accuracy than the best subsets of the given molecular features and the malignancy risk itself.For the analyzed dataset, the accuracies of both methods were comparable, but they differed in the stability of feature selection. We should highlight that the comparison of data fusion strategies is far more informative than the analysis of feature dependencies. We observed some correlations between features but mutual information showed that the dependencies between malignancy risk and gene expression were rather weak. The analysis of dependencies between features may influence the feature selection method so a preliminary analysis of the data is still an important step in the process of feature selection. The dependencies between features are important to choose the classification method. Some models based on, e.g., logistic regression, may not work well when features are redundant. In this study, we used SVM with a linear kernel but the influence on classification accuracy may be different for other classification methods.The Kuncheva index is a very sensitive tool to investigate the differences between fusion strategies, especially for the number of features close to the minimum and maximum available features. According to , this inThe data fusion strategies presented here resulted in the increase in the maximum classification quality or kept it on a similar level as the best reference model, but with a considerable reduction in the number of predictors. However, the effect of data fusion was relevant to the interrelation between features. The stability index and comparison of the two data fusion strategies showed the influence of the added features. The effect of adding one feature in the fusion process was easy to detect in the feature rankings, but for multiple models and multiple features, it became a tedious task.The dependencies between features in the data fusion influenced the classification’s accuracy; however, a feature not correlated enough with the classifier outcome (or other features) may have a negative influence on the model’s quality. The data fusion of the other data types may improve the classification of the specimen, and cause the features collected for the lesions from different diagnostic procedures to set different points of view on the specimen. The features used for fusion may be related (such as in genotype—expression—phenotype relation); for example, the cytological picture of the lesion is caused by the changes in the molecular mechanisms in the cells. The data fusion may extend the list of significant features with new molecular markers of cancer.p-values are made from independent tests for each feature . For the other real data, use of the preselection algorithm may be necessary .In this study, the Wilcoxon test achieved slightly higher stability but the ReliefF method seemed to stabilize the selection after fusion of genomic features and malignancy risk. The steps to take following this research would be the comparison of more feature selection algorithms. We expected some differences; although they are both ranking methods, the ReliefF algorithm is more complex and uses internal shuffling of the sample and feature subsets in calculations of the feature weights while the ranking based on the Wilcoxon test In the present study, the data fusions were tested on one type of variable (continuous variables) and the simple combination of fusion and the feature selection, which showed a statistically significant accuracy improvement for models with few features in comparison to the homogenous feature set.The methods presented are not limited to thyroid cancer, but they need further investigations. We see a possibility of using the data fusion of molecular data with results in other diagnostic procedures, such as in the analysis of mutations, checking immunohistochemical markers, and imaging techniques, such as tomography, ultrasounds, magnetic resonance imaging, positron emission tomography, or others. Some of them may use advanced methods of feature extraction  but the methods are well described in the literature and the data fusion may be involved in studies after preprocessing of the features. The success of data fusion depends on the relationship between features. By the present study, the presence of a strong correlation and high mutual information with a few molecular features is beneficial to reduce the number of features. In the case of data fusion with the features represented , some other measures of similarities may be used, such as other implementations of mutual information  or the Kruskal–Wallis test for mixtures of continuous and discrete variables. The method of data fusion may have some limitations in the case of cancer heterogeneity; however, more excessive research should be performed in this field.The thyroid dataset consisted of 200 samples provided by Maria Sklodowska-Curie National Research Institute of Oncology Gliwice Branch. Biological materials for the microarray experiments were extracted from the biopsy of patients’ thyroid nodules. To each microarray, a label (acquired from histopathology studies) was assigned, indicating cancer (77 samples) or benign lesions (123 samples). The samples were assessed with a cytopathological test and fell into Bethesda categories II (benign) to VI , but the majority of samples were from III to V. Gene expression data was obtained using Gene Chip Affymetrix human transcriptome 2.0 arrays . GeneChip WT Pico Reagent Kit  were used for microarray preparation. All reactions including DNA target preparation, target hybridization, fluidics setup and array scanning were performed according to the user guide P/N 703262 rev 4. Skanning of the arrays were performed in GC30007G scanner.The preprocessing of the raw microarray dataset was conducted using the Aroma tool implemented in the R/Bioconductor environment . For bacTo avoid problems with continuous data resulting from unknown types of distributions of clinical features , we discThe correlations and mutual information were calculated using R. Mutual information was calculated using Kraskov’s method , using RIn this paper, we used the Bayesian framework as part of a supervised analysis. As described in , the netThe analysis was based on two gene sets (indicated as molecular markers for thyroid cancer). The first set published by Fujarewicz et al.  containeFrom each patient, the clinicians collected the data they deemed necessary to make decisions about the patient’s treatment, such as age, sex, tumor size, and the grade of disease progress assessed by the specialist. The summary of the used feature sets is presented in We compared the accuracies of the supervised learning models, varying in terms of parameters: (1) applied data fusion strategy, (2) feature selection method. As a reference, we used separate models for each feature subset .The clinical data were fused with genomic data by one of the following strategies: (1) data fusion performed after genomic feature selection (late fusion), (2) data fusion performed before feature selection (early fusion). Late fusion allowed simply adding all variables to the preselected genomic features and then we could measure the effect on classification accuracy in comparison to the one source of the data—the gene expression data only. Early fusion allowed combining information and selecting only the meaningful features from both data sources. In order to unify the data obtained by the classifier function for each strategy, the z-score normalization was performed as follows: (1) the whole dataset was normalized after fusion (and before classification) for late fusion; (2) the whole dataset was normalized before feature selection for early fusion. All fusion strategies are summarized in To validate the classification results, we used the bootstrap technique with 500 iterations. The stages of fusion, feature selection, normalization, and classification were inside the bootstrap loop to avoid an information leak. For each bootstrap iteration, we calculated accuracy based on a test set. Median values for the models based on all bootstrap iterations are presented in the tables and figures. Calculations were performed using SPICY project and the R environment .p-values (Benjamini–Hochberg procedure), and the first N features with the smallest values were selected for classification. For the ReliefF feature selection, we implemented the CORElearn package [The feature selection methods were implemented in the SPICY package. The Wilcoxon test features were ranked based on corrected  package .Classification accuracy is a common metric for the evaluation of the feature selection methods . In the S = {S1, S2, …, KS } containing sets of features, obtained by performing feature selection on K different samplings of a dataset, the Kuncheva stability index κ (S) is defined as:k is the number of selected features , n is the number of all features, and |.| denotes the set cardinality. The high stability of feature selection ensures that all markers are indeed relevant.The index is calculated as follows. For a sequence KS ). This approach allows comparing stability results for general purposes and use with any other combination of data fusion. Thus, the expected results of the comparisons of both fusion strategies were the higher accuracy for late fusion, because at least one feature appeared in each list of features before classification.We compared the stability between early and late fusion. For early data fusion method, the use of the stability index was intuitive, but for late data fusion, where the fusion came after the feature selection, we gathered all features involved in classification for each bootstrap model (as


Natural porous materials adjust their resulting mechanical properties by the optimal use of matter and space. When these are produced synthetically, they are known as mechanical metamaterials. This paper adds degrees of tailoring of mechanical properties by producing double levels of gradation in lattice structures via cross-section variation in struts in uniformly periodic lattice structures (UPLS) and layered lattice structures (LLS). These were then additively manufactured via material extrusion (ME) and vat photopolymerization (VP). Their effective mechanical properties under compressive loads were characterized, and their stiffness contrasted with finite element models (FEM). According to the simulation and experimental results, a better correlation was obtained in the structures manufactured via VP than by ME, denoting that printing defects affect the correlation results. The brittle natural behavior of the resin caused a lack of a plateau region in the stress–strain curves for the UPLS structures, as opposed to those fabricated with ME. The LLS increased energy absorption up to  Due to their characteristics, mechanical metamaterials are used as light materials with a well-known capacity to absorb energy, high mechanical strength, and stiffness with relatively low density ,2. They Lattice structures are built from unit cells uniformly distributed within a given volume, known as periodic lattice structures. On the other hand, some structures can also be found with gradual variations of topology  or paramLattice structures can also be classified depending on their deformation mechanism, i.e., stretch- or bending-dominated . The chaLiu et al.  created g et al.  analyzedg et al.  developei et al.  studied A common challenge to overcome in lattice structures with a geometric variation of the struts is how these are connected to adjacent struts with different cross-sections, which leads to reduced loading bearing capacity. To overcome this, Goel et al.  proposedFGLS have been explored to mimic the bone structure, density, and stiffness of trabecular or cancellous bone, often needed in prosthesis design to allow bone growth and to fix the implant naturally with human bone ,21. WangAdditive manufacturing (AM) is the most frequently used method to fabricate lattice structures since their designs demand complex geometries that are impossible or difficult to make using conventional manufacturing methods ,25,26. TThe review of related literature brings up several lines that still deserve further research. As seen, AM appears as the ideal fabrication technology for the fabrication of these structures; however, at relatively small dimensions, the numerous defects inherent to it demand attention. Additionally, intending to produce structures with tailor-made properties, different attempts use variations of the unit cell distribution or changes in the topology. Works that have attempted to vary the mechanical properties of the lattice structures at the strut level are scarce. Hence, the main objective of this research was to create new layered lattice structures using body-centered cubic-type unit cells (BBC) with different cross-section variations of the struts. The characterization of the mechanical properties is carried out via numerical simulations and laboratory experiments on additively manufactured samples. Specifically, fused filament fabrication (FFF) and liquid crystal display (LCD) methods were employed, which are classified as material extrusion and vat photopolymerization techniques according to , respectThe general methodology followed in this work is presented in ® , using unit cells with dimensions of 3. The lattice structures are comprised of unit cell arrangements of This work aims to tailor the mechanical properties of lattice structures at two different levels: (i) functionally graded modification of the strut cross-section and (ii) layered distribution of unit cells. The lattice structures are built with unit cells similar to the BCC. The angle of the inclined struts was modified from The first level, with the aim of tailoring the mechanical properties of lattice structures, is to grade varying strut cross-sections along their length. Six cross-section variations were considered: cosine (COS), cosine 2 (COS2), double slope (DS), double inverted slope (DIS), positive slope (PS), and negative slope (NS). This mathematical parameterization is proposed to vary the diameter of the struts in the unit cell achieving control of the accumulation of material in the center and at the ends of the strut’s length. These variations are plotted in The second level controls the unit cell distributions layer-by-layer, i.e., layered lattice structures (LLS). Six LLS were designed considering an initial finite element simulation of the structures under compressive loading shown in ®  software was used to perform the quasi-static and linear compression simulations. Fixed support was placed on the lower plate of the cell structure to simulate the conditions of the experimental tests, and a displacement in the Y-axis was applied to the upper plate  Ender 3D printer was used for FFF, and a Creality® LD002-R printer for LCD. Computational models (STL files) for the FFF method were processed in Ultimaker Cura® V4.8.0  software, and PLA material supplier (in the form of filament) was used as raw material. To determine the manufacturing parameters for the FFF process, tests were carried out with different sizes of unit cells, nozzles, and printing speed; in addition, a displacement in the Z-direction of 0.1 mm was set to the printing head, when it moved from one point to another. Finally, the minimum size of the unit cell that could be printed is shown in ®  V1.6.2 software; samples were made with Creality® photosensitive resin. The layer thickness was The lattice structures were additively manufactured using two printing technologies: FFF and LCD; a CrealityIn both manufacturing processes, the printing parameters were not optimized, i.e., standard parameters were used. The printing parameters were kept constant for all samples and printed without supports, and no special methods were required for adhesion to the print bed. All samples were fabricated-oriented, so the XZ-plane was parallel of the printing platform. The weight of the samples was measured with a RADWAG AS 220.RS balance to subsequently calculate the relative density.The UPLS fabricated by FFF and LCD were further inspected using a ZEIN microscope to contrast them with their computational model versions. The length of the spaces between unit cells were measured, i.e., horizontal (1) and vertical (2) directions, the length of the struts (3), and their diameter in three regions, i.e., at the end (4), at the center (5) and the beginning (6) of the strut were measured. ® Z-050 machine at room temperature; the test speed was 3 cube. The density of the materials obtained was 1.24 gr/cm3 and 3 for PLA and resin, respectively.The mechanical properties of the base materials used to fabricate the lattice structures were characterized by quasi-static tensile tests on solid dog bone specimens manufactured using the same two printing processes mentioned in ® Z-050 machine at room temperature. The test speed was ®  P7000 camera was used to capture the deformation of the lattice structure during the test.Quasi-static compression tests were carried out to evaluate the mechanical properties of the designed structures with a ZWICKThis section presents and discusses the manufacturing defects of the lattice structures, the properties characterized by the compression experiments, and the comparison of stiffness determined by simulations and experiments.The FFF fabrication took up to Two measurements were taken for each parameter, as shown in The samples manufactured by FFF had a more significant difference in the diameter measured at the midpoint of the strut length because the COS2 and DIS structures were thinner in this area. Also, unbonded material was observed at these zones; this can be seen in the third and fifth rows of the third column in The structures made with FFF presented defects such as threads between adjacent unit cells in the PS, NS, DIS, and COS2 structures, the latter resulting in the highest number of threads. These defects can be seen in the third column in The relative density The structures manufactured in LCD resulted in a relative density closer to that of the CAD model, as shown in As mentioned in  testing ; Young’sTriplicates of the LLS shown in Significant defects were observed in the zones between unit cells with struts with different cross-sections. These were due to sudden changes in the geometry of the struts, mainly encountered in the transitions between NS and COS. In this case, the connection between struts was lost entirely a. AnotheA comparison of the intended (CAD) relative densities and apparent porosities with those measured on LLS fabricated via FFF and LCD is presented in A total of The average load-displacement data of the UPLS structures manufactured with PLA is shown in In apse see , and theIn ells see ; the surLoad-displacement curve c for thermed see . The load-displacement curve for the DIS lattice structure, ells see . At the When the PS structure had reached its peak force see e, slightture see . At 30 mzone see .For the NS structure f, the peture see . Again, The cross-section variation in the unit cells influences the failure form of the structures, the magnitude of the maximum stress, and the plateau stress; the densification occurred approximately at According to ture see . Figure  45° see . After t 45° see b, a loadrred see . In the  45° see . 45° see . Figure ined see ; this faAlthough the structures were built with the same topology (BCC), the proposed cross-sectional variations influence the failure mode of the structure; this can be seen in The load capacity in most structures manufactured by LCD was more significant than the FFF. The most remarkable difference occurred in the COS2 and DIS structures with a difference of 2 (area of the top plate) were used to calculate the maximum and plateau stress. These are presented in The average force obtained from the three samples of each structure and its apparent area of Differences in the trends observed in The maximum stress for the COS and DS structures were similar in PLA and resin according to These structures were the weakest when made of PLA because the geometry of the strut was narrow in the center, coupled with the fact that these structures presented printing defects that compromised their structural performance.Results according to the stiffness obtained by FEA and experimental compression tests are shown in The COS2 and DIS structures manufactured via FFF were the weakest among the rest, which can be attributed to the defects present in the structure. However, they were among the structures that presented higher stiffness in both manufacturing processes; the common characteristic that these structures had is that the struts had a larger diameter in the center of the unit cell, which provides higher stiffness to the structure.As shown in The absorption energy was determined in the plastic zone because the elastic deformation provides recoverable energy absorption; in the densification zone, the structure has been completely compressed, and in this zone, there is no energy absorption . For UPLIn the load-displacement graphs of the LLS shown in In the structures manufactured with FFF and LCD, failure started in the area where COS was located because it had the lowest strength. The structures in form see . HM-IM-Lform see c and LM-form see d structuform see . The LM-ures see . The cenures see f, and atThe plateau of the structures had small steps due to the rupture of the zones of the structure at different magnitudes of displacement, and the densification of the structures occurred approximately at Deformation mechanisms were better appreciated for PLA structures. The COS unit cell layers deformed majorly, and the struts of the unit cell bent. These COS layers were also the ones that showed densification before any other strut cross-section variation. This was due to the low strength of COS compared to the other cells used in the structures. In the structures that combine the COS and DS cells, the fracture of the struts starts at the joining zone of these cells; later, the COS zone densifies, followed by DS. For the structures that combine the three-unit cells, it was observed that COS and DS densified entirely, and subsequently, NS started to deform; just like COS and DS, the struts of NS flexed, showing that the deformation mechanism was dominated by bending.ures see a. HoweveAs mentioned above, the plateau in the LLS presented staggering due to the fracture of the zones of the structure at different magnitudes of displacement. COS, DS, and NS structures presented plateau stress of The distribution of the unit cells in LLS was relevant to their stiffness; even though LLS were designed with the same relative density, the simulation results showed that placing layers of unit cells with lower stiffness in the center of the structure decreases the stiffness of the structure when compared to the rest of the models. The experimental stiffness results of the resin compression tests correlated with the simulation results are presented in 3. In the LLS, the energy absorption increased except in the LM-IM-LM and IM-LM-IM structures that absorbed the same energy as DS; LM-HM-LM is the structure that most increased the energy absorption up to The UPLS and LLS were printed via FFF and LCD without supports; the structures manufactured by FFF were those that presented defects such as accumulation of material in the nodes and the narrow areas of the struts. The most significant defects were presented in the LLS built with NS and COS unit cells because there was no connection between the struts of these structures. This defect could be corrected by smoothing the geometry change at the connection of these unit cells.The UPLS printed via LCD had a brittle behavior that did not allow the structure to present plateau or densification during its deformation, so it was not possible to measure the energy absorption. However, the lattice structures printed by this method presented a good correlation between the simulation and the experimental stiffness. The DS structure was the structure with the most significant discrepancy between the experimental and simulation stiffness with In the geometric characterization, it was observed that the struts of the unit cells manufactured by both processes were more significant than the CAD models; the manufactured structures had a higher relative density than the CAD models.The change of cross-section in the struts was the first level of gradation proposed, which allowed modifying the strength, stiffness, plateau stress, and energy absorption of the BCC structures. Lattice structures with thick struts in the center of the unit cell were stiffer and stronger. This trend was observed in structures made with resin and simulations; structures manufactured through FFF did not have this tendency due to manufacturing defects that compromised structural performance.The second level of gradation was implemented with LLS, and the experimental results showed an increase in the strength of the lattice structures in both fabrication processes. Furthermore, the plateau stress was higher for LLS than for UPLS. In resin, a comparison could not be made due to the absence of a plateau in the UPLS; however, the resin LLS presented a plateau during the deformation of the structure due to the rupture of the three zones of the structure at different levels of deformation. Although LLS had the same relative density, the stiffness of these structures depended on the arrangement of the unit cells. The lattice structures that had unit cells with low stiffness in their central zone were the least rigid. Energy absorption and plateau stress increased In general, the mechanical properties studied in this work depend on the geometry of the strut, being higher when the strut has a wider cross-section near the center of the unit cell. Additionally, it was demonstrated that with LLS structures, the right selection of unit cells in each layer could result in structural modifications, not only of the effective properties but also of the failure mechanisms. It is important to highlight that this was demonstrated here for the BCC structures, and the effect on lattices built from other topologies, or using different topologies within the same sample, is still an open issue.