N = 256 at all signal-to-noise ratios (SNRs), whereas it could detect the DSSS signals up to an SNR of −12 dB. The results obtained using the modulation stripping detector showed no significant phase distribution convergence for the GDSS signals, similar to the noise-only case, whereas the DSSS signals generated a phase distribution with a distinct shape, indicating the presence of a valid signal. Additionally, the spectral correlation detector applied to the GDSS signal at an SNR of −12 dB showed no identifiable peaks on the spectrum, providing further evidence of the effectiveness of the GDSS scheme and making it a favourable choice for covert communication applications. A semi-analytical calculation of the bit error rate is also presented for the uncoded system. The investigation results show that the GDSS scheme can generate a noise-like signal with reduced identifiable features, making it a superior solution for covert communication. However, achieving this comes at a cost of approximately 2 dB on the signal-to-noise ratio.Covert communication techniques play a crucial role in military and commercial applications to maintain the privacy and security of wireless transmissions from prying eyes. These techniques ensure that adversaries cannot detect or exploit the existence of such transmissions. Covert communications, also known as low probability of detection (LPD) communication, are instrumental in preventing attacks such as eavesdropping, jamming, or interference that could compromise the confidentiality, integrity, and availability of wireless communication. Direct-sequence spread-spectrum (DSSS) is a widely used covert communication scheme that expands the bandwidth to mitigate interference and hostile detection effects, reducing the signal power spectral density (PSD) to a low level. However, DSSS signals possess cyclostationary random properties that an adversary can exploit using cyclic spectral analysis to extract useful features from the transmitted signal. These features can then be used to detect and analyse the signal, making it more susceptible to electronic attacks such as jamming. To overcome this problem, a method to randomise the transmitted signal and reduce its cyclic features is proposed in this paper. This method produces a signal with a probability density function (PDF) similar to thermal noise, which masks the signal constellation to appear as thermal white noise to unintended receivers. This proposed scheme, called Gaussian distributed spread-spectrum (GDSS), is designed such that the receiver does not need to know any information about the thermal white noise used to mask the transmit signal to recover the message. The paper presents the details of the proposed scheme and investigates its performance in comparison to the standard DSSS system. This study used three detectors, namely, a high-order moments based detector, a modulation stripping detector, and a spectral correlation detector, to evaluate the detectability of the proposed scheme. The detectors were applied to noisy signals, and the results revealed that the moment-based detector failed to detect the GDSS signal with a spreading factor,  Secure communication schemes are essential for transmitting mission-critical information securely and privately, especially in hostile environments. Traditional methods to achieve secure communication can be broadly categorised into three main groups : cryptogn channel uses. This gives an information rate of n goes to infinity. Hence, recent studies have focused on developing LPD schemes to obtain a positive information rate [Research published in the field of LPD communications can be categorised into two main areas: (i) information-theoretic aspects of LPD communications and (ii) designing waveforms for LPD communications. Information-theoretic studies focus on determining the fundamental limits of LPD communication in terms of the amount of information that can be conveyed from a transmitter to a receiver subject to a constraint on adversary’s detection error probability ,12. The ion rate .This paper focuses on designing waveforms for LPD communication. For LPD communications, it is desirable to transmit with minimal PSD to hide the transmitted signal under the receiver’s noise floor  and haveExisting covert communication schemes use spread-spectrum, chaotic theory, or a combination of both to achieve covert communication. The proposed schemes vary: utilising machine learning , using nThe proposed scheme in this paper uses thermal white noise of the system to obscure signals generated by a DSSS transmitter and produce a spread-spectrum waveform that follows a Gaussian distribution (GDSS). The design of the GDSS scheme ensures that the receiver does not need any information about the sequences used to mask the signal to retrieve the message. To the best of our knowledge, this study represents the first investigation into utilising naturally occurring thermal noise for spread-spectrum communication. We conducted a performance evaluation of the proposed GDSS scheme and compared it to the widely used DSSS technique, which has several weaknesses that make it vulnerable to exploitation by adversaries. These vulnerabilities arise from the use of fixed modulation and repeatable spreading sequences.The paper is structured as follows. N determines the number of spreading bits that map to a message bit. After spreading, the symbols to be transmitted are commonly referred to as chips. When a DSSS system maintains the same bit rate and energy per bit as before spreading, the signal bandwidth will be spread by a factor of N, and the magnitude of the PSD of the signal will be reduced by a factor of N. This reduction in PSD helps to mitigate interference from other signals. To spread the signal, the data are multiplied by a pseudo-noise (PN) sequence. This PN spreading sequence is unique to each transmitter and receiver pair and helps to ensure secure communication. A binary phase shift keying (BPSK) DSSS spreading process is illustrated in DSSS, or direct-sequence spread-spectrum, is a method of modulation in which the message bits are modulated by a pseudorandom bit sequence known as a spreading sequence. This sequence has a much higher rate than the original information rate, and a spreading factor DSSS is an important technology for covert communications because it enables the system to operate under the thermal noise floor even at low SNR levels . This means that the communication signal can be hidden in the noise, making it difficult for adversaries to detect and intercept the signal. The spreading process in DSSS spreads the signal across a wide bandwidth, which reduces the PSD of the signal. As a result, the signal is less susceptible to noise and interference, making it easier to detect at low SNR levels. This is particularly important for covert communications, where it is essential to maintain a low profile and avoid unfriendly detection.The bit error rate (BER) performance of a DSSS system using quadrature phase shift keying (QPSK) spreading is given byExamples for various spreading factors are shown in The standard DSSS system has several vulnerabilities and may not be ideal for covert communication. This system normally uses repeating patterns and has deterministic features that could be used for detection/interception. For example, The block diagram of the proposed GDSS scheme is illustrated in S, a complex value The proposed scheme builds upon the standard QPSK DSSS-PN system by utilising the naturally occurring thermal white noise from the transmitter’s circuity. The independently obtained noise sequences are applied to the in-phase (I) and quadrature-phase (Q) components of the signal after spreading to perform the Gaussian masking. The Gaussian masking process for the scheme illustrated in A snapshot of the varying constellation points generated by masking the fixed QPSK points is shown in This section compares the distribution of the GDSS signals with the theoretical Gaussian distribution. The noise-free signal constellation of the GDSS scheme is shown in Z with Gaussian distribution is given byThe probability density function of a random variable Using Equation  its momeA closed-form expression of Equation  for evenThe transmitted noise free signal is compared against a standard Gaussian distribution (SGD) in A random white noise signal would have an ACF of zero at all lags except a value of unity at lag zero, to indicate that the signal is uncorrelated and does not exhibit repetitive time-domain features. The repetitive features of the GDSS signals were analysed using the ACF. The results obtained showed no identifiable features for either GDSS or DSSS noise-free signals provided each uses non-repeating spreading sequences. However, for the case when these systems use a fixed pair of spreading sequences, the ACF for DSSS shows several very strong identifiable components across multiple lags. Compared to this, for the GDSS, the correlation magnitudes are small and are overall at an insignificant level.This section investigates detectability of the GDSS waveform at low SNR using higher-order moments and modulation stripping and compares the performance with DSSS signals. Simulated noise is generated using a random number generator to create a sequence of values that mimic the behaviour of real-world noise. The noise power is adjusted based on the desired SNR value to create noisy signals at different SNR levels.Moments are statistical parameters that can be used to measure Gaussian distribution as discussed in the previous section. In this section, the 20th-order moment is used to assess the detectability of the GDSS and DSSS signals operating under the noise floor. The 20th-order moment of the zero-mean unit-variance Gaussian distribution is 654,729,075. The moments of the GDSS and DSSS signal components are estimated at various SNR and then compared with the theoretical moment value using the absolute deviation between the estimated and theoretical values. The results are generated by averaging results from five tests and expressing the average deviation as a percentage of the theoretical value. Each test result is conducted using a spreading factor of 256 on 1 × This figure shows that the average deviation of the DSSS signals are significantly large compared to GDSS values, indicating non-Gaussian features of the DSSS signal even in the presence of high noise levels. Unlike DSSS signals, the measures obtained for the GDSS signals show deviation values very close to zero across all SNR values.Assuming an average deviation threshold of 10% (to achieve detection with high confidence), the moment-based detector will fail to detect the presence of a GDSS signal, whereas the same detector can easily detect the DSSS signals for SNR > −12 dB. It should be noted that the standard DSSS signal can be Gaussian distributed if the system operates at a sufficiently low SNR. However, this would require an increase in the spreading factor, resulting in a reduction of data rate.In this section, a simple modulation stripping method is used to evaluate the detection performance of the GDSS signals. A non-linearity can be applied to the signal to produce discrete spectral spurs to aid detection. As an example, in the case of QPSK modulation, a fourth power produces a discrete spur at four times the carrier frequency offset. Energy detection is another commonly used method for detecting communication signals. The basic idea behind energy detection is to compare the energy of the received signal to a pre-defined threshold. If the energy of the received signal exceeds this threshold, the signal is assumed to be present. One of the advantages of the energy detection method is its simplicity and low computational complexity. However, energy detection can suffer from high false alarm rates in low SNR environments, where the noise can easily exceed the detection threshold. Therefore, energy detectors are generally not effective for detecting signals, such as DSSS and GDSS signals, operating under the noise floor. As the GDSS system requires more power than the DSSS system to achieve the same BER performance, it is expected that GDSS signals can be more likely detected compared to DSSS signals using an energy detector in high SNR conditions.Signal detectors based on cyclostationary analysis offer superior detection performance compared to energy detectors in low SNR environments. However, they may require more computational resources and expertise in signal properties. Cyclostationary analysis is a powerful technique used for detecting and analysing communication signals by leveraging their cyclostationary properties. These properties refer to repetitive characteristics of the signal, such as a constant modulation and coding scheme or a fixed synchronisation sequence embedded in the communication waveform. By exploiting these properties, cyclostationary analysis can provide more reliable detection and analysis of signals in challenging environments with low SNR.Cyclostationary analysis normally involves estimating the spectral correlation function (SCF) of a signal. The SCF is a measure of the correlation between different frequency components of the signal, as a function of frequency offset and time lag. In a cyclostationary signal, the SCF exhibits peaks at certain frequency offsets and time lags, known as cyclic frequencies and cycle periods, respectively. These peaks correspond to the cyclostationary properties of the signal and can be used to detect the presence of the signal operating under the noise floor. By exploiting these peaks, cyclostationary analysis can offer a more robust and reliable detection of weak signals.This section aims to validate the effectiveness of GDSS signals in hiding under the noise floor using the fast spectral correlation method proposed in . We presThe DSSS signal is generated using a repetitive spreading sequence, and the Gaussian masking process is applied to develop the GDSS signal. To ensure a fair comparison, we keep the observation period and spreading factor constant for both the DSSS and GDSS signals. By analysing the spectral correlation of the two signals, we demonstrate that the GDSS signal provides superior hiding capabilities compared to the DSSS signal under similar conditions. Our findings highlight the potential of GDSS signals for use in low-power and covert communication systems where signal detection and interception are critical concerns.The spectral correlation density plots shown in This section investigates the BER performance of the uncoded and coded GDSS systems and compares them with the corresponding DSSS systems.In this section we develop a semi-numerical calculation of the BER performance for the uncoded GDSS system and compare it with the simulated results. The BER performance can be analysed from the I or Q component. Assuming Gray coding is used, the two components are equivalent to two independent BPSK GDSS schemes . The BERz, which is the result of the de-spreading process using a binary spreading sequence (rather than a Gaussian sequence). Here, z is the sum of N noisy chips during a bit periodOur objective is to determine the probability density function (PDF) of the decision variable The BER is the probability the decision variable becoming negative due to noise disturbanceIn order to find ribution ,43(8)siThe corresponding noise Since It can be expressed as a function of SNR. For QPSK GDSS, the SNR in dB isFor BER calculations we can let Nth power of the characteristic function. Regrettably, we are unable to obtain an analytical expression for it. An alternative approach is to use self-convolution. As z is the sum of N independent N, we created a normalized functionx vector. For the sum of N received chips, the PDF is proportional to the If we can find the characteristic function of N. Instead, a faster algorithm can be implemented, as illustrated below.Performing We calculate N is an integer that is a power of two, our objective has been achieved. However, if N lies in the range m results from Equation  coding to improve the performance for the GDSS scheme. LDPC codes are a type of linear block error correction codes with parity-check matrices (H) that contain a very small number of non-zero entries. The sparseness of H guarantees the minimum Hamming distance and decoding complexity to increase linearly with the code length. Some of the published results show that these codes can perform close to 0.0045 dB away from the Shannon Limit, making it one of the most powerful error-correction codes known today . To reduN = 256 at all SNRs, whereas it could easily detect the DSSS signals as low as −12 dB. We applied the modulation stripping detector to both the GDSS and DSSS signals at an SNR of 0 dB and −5 dB, respectively. Our analysis revealed that the GDSS signals exhibited no significant phase distribution convergence, similar to the noise-only case . In contrast, the DSSS signals generated a phase distribution with a distinct shape, indicating the presence of a valid signal. Moreover, we applied the spectral correlation detector to the GDSS signal at an SNR of −12 dB. Our analysis showed no identifiable peaks on the spectral correlation spectrum, providing additional evidence of the effectiveness of the GDSS scheme and the lack of distinguishable peaks in the spectrum suggests that the GDSS signal is difficult to detect and intercept, making it an ideal choice for covert communication applications.In this paper, we propose a novel signalling scheme called GDSS for covert (LPD) communications, which aims to conceal the existence of wireless transmissions for enhanced security compared to cryptography and steganography-based schemes. We evaluate the performance of GDSS and compare it with the commonly used DSSS technique, which, despite its popularity, is susceptible to exploitation by adversaries due to various weaknesses. These vulnerabilities stem from the use of fixed modulation and repeatable spreading sequences. In contrast, the proposed GDSS scheme takes advantage of naturally occurring thermal noise at the transmitter to create non-repetitive, featureless signals for communication, which eliminates many of the shortcomings associated with DSSS. In this paper, the proposed GDSS scheme is compared with the DSSS system. The findings indicated that the signals produced by the GDSS approach have fewer distinctive characteristics compared to the DSSS signals, resulting in a reduced likelihood of detection for anyone attempting to intercept the transmission. The Gaussianity test demonstrated that the distribution of the noise-free GDSS signals closely resembled that of the naturally occurring noise in the receiver. To assess the detectability of the signals generated by the proposed scheme by an adversary, this study utilised three detectors: a high-order moments based detector, a modulation stripping detector, and a detector based on cyclostationary analysis. These detectors are applied to signals corrupted with noise. The results showed that the moment-based detector failed to detect the GDSS signal with A quasi-analytical expression is also used to derive the BER for the uncoded GDSS, and the results were consistent with the simulation. The comparison of BER between the uncoded GDSS and DSSS systems showed a penalty of 2 to 3 dB for GDSS. However, LDPC coding helped recover this loss and significantly improved the overall BER performance. As expected, the LDPC-coded GDSS performed about 2 dB worse than the corresponding LDPC-coded DSSS system.This paper did not investigate the effects of high power amplifiers on the generated GDSS signals. The GDSS scheme is capable of generating signals with a high peak-to-average power ratio (PAPR), which is a measure of the dynamic range of a signal. Consequently, amplifying GDSS signals can cause distortion or clipping, as the amplifier may not be able to handle the high instantaneous power levels , which can result in reduced signal quality and performance degradation.In future work, we plan to analyse the information-theoretic optimality of the proposed GDSS scheme and its variants. We would also like to investigate the impact of real-world factors such as radio impairments, channel effects, and receiver synchronisation on the performance of the GDSS system. These factors can significantly affect the quality and reliability of the communication channel, and thus it is crucial to study their effects on the proposed scheme. Additionally, we plan to explore ways to mitigate the high PAPR issue of the GDSS signals, which can lead to performance degradation.


Artificial intelligence (AI) is an emerging technology that is revolutionizing the discovery of new materials. One key application of AI is virtual screening of chemical libraries, which enables the accelerated discovery of materials with desired properties. In this study, we developed computational models to predict the dispersancy efficiency of oil and lubricant additives, a critical property in their design that can be estimated through a quantity named blotter spot. We propose a comprehensive approach that combines machine learning techniques with visual analytics strategies in an interactive tool that supports domain experts’ decision-making. We evaluated the proposed models quantitatively and illustrated their benefits through a case study. Specifically, we analyzed a series of virtual polyisobutylene succinimide (PIBSI) molecules derived from a known reference substrate. Our best-performing probabilistic model was Bayesian Additive Regression Trees (BART), which achieved a mean absolute error of  Formulated lubricants are essential components for countless industrial and mobility-related activities, and they represent an over $60 billion global chemical enterprise ,2,3. RegDispersant additives, which have been extensively used since the 1950s, are one of the main components of the total additive percentage of a formulated lubricant for modern internal combustion engines. Under the harsh operating conditions of an engine, soot is produced as a result of incomplete oxidation/combustion of the fuel. In an engine, soot aggregation increases lubricant viscosity, preventing regular flow, causing corrosion, deposit formation and mechanical wear. Dispersants are polymeric surfactant-like amphiphilic molecules characterized by at least one hydrophobic, oil soluble ‘tail’ polymer backbone component, often polyisobutylene (PIB), and at least one hydrophilic, polar ‘head’ unit that adsorbs onto the surface of ultrafine carbon deposit precursors (mainly sludge soot particles) stabilizing them by acid–base or electrostatic interactions, thereby reducing their aggregation ,8,9,10. The design of dispersants involves a deep understanding of which molecular architecture can best provide the functions required for the target application while considering the potential interactions of amine and imide functional groups with other additives. This task is typically carried out through trial and error, coupled with chemical intuition, but the process is expensive and time-consuming. In sharp contrast, artificial intelligence (AI) holds great potential to guide the design of next generation materials because of its capability for solving multiobjective optimization problems, thus allowing economic and time savings. In this sense, AI-based approaches are increasingly used in the design of complex materials ,3,15. InIn this context, the primary objective of our research is to aid the design of efficient dispersants through AI-based modeling and interactive visualizations, leading to reduced operational expenses and faster discovery of novel dispersants. Our hypothesis is that the polar head is mainly responsible for dispersant activity by absorbing onto the surface of soot particles. In this sense, a question that arises is whether a computational approach, based on machine learning and visual analytics, to determine the relationship between the chemical structure of the polar head and a given dispersancy measure is suitable to guide virtual screening in the design of new materials with an expected dispersancy profile. In particular, in this paper, we describe a machine learning based tool for dispersant design and optimization, which is focused on the prediction of a key performance property: dispersancy efficiency (measured using the blotter spot test) based on the molecular structure of the polar head of molecules. Complementary strategies were developed based on a combination of unsupervised and supervised learning, nonlinear dimensionality reduction methods and data visualization strategies. The resulting inol was statistically validated, and its application is illustrated by the evaluation of a series of virtual PIBSI molecules derived from a known reference substrate, by testing the potential of the proposed tool in virtual screening problems.In this section, we present all key issues related to the data curation, computational representation of molecules, proposed predictive modeling and design of the visual analytics tool. In this sense, two computational models were proposed as part of our tool in order to provide different perspectives for predicting the dispersancy efficiency of molecules: a structural similarity-based model and a Bayesian regression model. Thus, the best candidates for dispersants can be selected by the expert’s assessment of molecules with the highest prediction values from each model, taking into account predictive uncertainty.The first step of our work was to compile a dataset from the literature with 83 potential dispersants, mostly PIB-succinimide dispersants (PIBSIs), by conducting a manually curated data extraction process from an extensive collection of articles ,35,36,37R-Factor = soot reduction ratio × initial soot weight / concentration of dispersant). This allowed us to normalize the performance of dispersants as a common arbitrary unit from different experimental techniques. As a result of the incorporation of the R-factor calculation, the final dataset includes molecular structures with known blotter spot and/or R-factor values. However, as we explain below, the experiments presented in this work were focused on blotter spot values, since it is the most predominant property available for the chemical structures included in the dataset.Additionally, results from dispersancy evaluation methods based on thermal oxidative decomposition procedures were processed into a parameter known as reduction factor ,25,35,38The complete dataset of 83 molecular structures was used for the two-dimensional visualization based on structural similarity. For model validation purposes, we keep the 53 potential dispersants for which blotter spot values are available and paired them with the chemical structure of the polar head of the molecule. In view of the challenge presented by the sparse data found in the literature, we had to adapt our modeling approach to work in this regime. The scarcity of labeled data prevents us from using deep learning based approaches ,40. InstIn our dataset of potential dispersants extracted from the literature, each molecule is represented by the SMILES code  correspoEach molecule is thus represented by a vector of numerical values corresponding to different descriptors. This allows a tabular representation of the dataset.Additionally, SMILES-based molecular embeddings calculated from a pre-trained model based on recurrent neural networks (RNN) with long-short term memory cells  were alsOur first modeling strategy aims to predict the dispersancy efficiency of new molecules based on structural similarity with existing molecules with known dispersancy efficiency values. The hypothesis behind this strategy is underpinned by the QSAR modeling principle, which indicates that structurally similar compounds should exhibit similar properties . In our For this first model, we focused on classical molecular descriptors. These descriptors refer to specific molecular properties, thus facilitating their interpretation and enabling human experts’ intervention during the analysis and visual exploration of the results of the model. In particular, we focus on 2D molecular descriptors only. Then, descriptors with undefined values, constant values and those correlated with a value greater than 0.95 were discarded. A final set of 425 molecular descriptors was obtained. Then, the first step for designing the similarity-based model was to conduct a feature selection procedure to identify a reduced subset of molecular descriptors statistically related to the target property. This subset defines the underlying metric space used by the model.The relevance of the selected descriptors in the model was established through a two-stage process. The first stage aims at pre-selecting different subsets of molecular descriptors through fully automated strategies, using machine learning methods, and also through a selection made by experts in the chemical domain. The second stage aims to compare the pre-selected subsets of descriptors through an exploratory visual analysis of the relationships among them, following a human-in-the-loop methodology . The decIn the first stage, four pre-selected subsets of descriptors were obtained, three of them generated by applying descriptor selection methods based on machine learning techniques and the fourth one by using expert criteria. In this regard, the three subsets obtained through machine learning were the result of experimenting with Random Forests  and DeciFrom different runs with Random Forest and Decision Trees, we selected the three subsets of descriptors that obtained the lowest error values. In each experiment, we kept the top-8 performing descriptors. Regarding the subset obtained through expert criteria, this was defined by an organic chemist who participated in the project. They identified key features for the design of this type of chemical structures that are also highlighted elsewhere in the scientific literature, such as polarity, orbital electronegativity, basicity and percent nitrogen composition. Keeping these guidelines in mind, five molecular descriptors related to these characteristics were selected. The detailed list with the pre-selected subsets of descriptors is summarized in In the second stage, these subsets were used as input to make the final selection of descriptors using ViDeAn . Since sAATS5d is the Moreau–Broto descriptor that measures the autocorrelation in the topological structure, at topological distance 5, of the atomic property linked to the sigma electrons of the atoms. ATSC5v is the Moreau–Broto descriptor that measures the autocorrelation in the topological structure, also for topological distance 5, of the atomic property linked to the volume of van der Waals atoms. Finally, the PEOE_VSA9 descriptor is computed as the sum of the van der Waals surface areas of the atoms whose PEOE partial charge  is in the range of [0.05, 0.10). More information on how these descriptors are calculated is available in Todeschini and Consonni . The thrx from its neighbors:k is the number of neighbors to consider, i, and x and neighbor i. The weight i. The Weighted Mean  to seed the clustering process. Then, the molecules are assigned to one of those k groups taking into account a distance measure to the centroid. DBSCAN is one of the most widely used density-based clustering algorithm. DBSCAN does not require setting the number of clusters in advance, but rather the algorithm finds an optimal number of clusters based on an estimated density distribution of the data. The algorithm requires two important parameters: the distance threshold to consider two points as neighbors, and the minimum number of points for a region to be considered as a cluster. As per the sampling for each fold, a specific strategy was followed to ensure that structurally similar compounds are allocated evenly to different partitions. These clustering techniques were applied using the Python package sklearn.cluster: KMeans and DBSCAN [A cross-validation procedure was carried out for the model evaluation. For this, we use two clustering techniques for assigning each molecular structure to a given data fold: KMeans and Density Based Spatial Clustering of Applications with Noise (DBSCAN) . KMeans d DBSCAN ,56. For We opted for a Bayesian approach as a second predictive modeling technique, given their ability to produce uncertainty estimates for their predictions, a key aspect in small data regimes . In partf, between a p-dimensional covariate vector x (representing molecular descriptors in the present case) and the output of interest y . The probabilistic framework for this inference is expressed asIn the context of regression analysis, Bayesian Additive Regression Trees aim to infer the unknown, nonlinear functional relationship, denoted by j-th decision tree comprises a binary tree b terminal nodes with associated parameters x. The binary tree is designed such that each instance x is linked to a single terminal node through the sequential application of decision rules. The function x the corresponding BART approximates The BART model prevents overfitting by applying a regularization prior on the model parameters n et al. .N molecules with molecular descriptors Given a set z, samples from its posterior predictive blotter spot distribution can be easily obtained passing z through each of the generated posterior groups of m trees. The posterior predictive samples can be utilized to make point predictions and estimate the uncertainty of the blotter spot for the new molecule.Finally, given a new unseen molecule with associated molecular descriptors One of the notable advantages of the BART method is the capability to produce uncertainty estimates for the predictions, which is a significant departure from non-probabilistic methods such as Random Forest or Gradient Boosting. In our context, these uncertainty estimates are helpful to identify potential candidates for synthesis and are crucial in our small data regime. In particular, in an active learning setting, having estimates of uncertainty in the predictions made by the model allows for building a policy for synthesizing new targets that trades off between exploration and exploitation.For training this model, all the 2D molecular descriptors and molecular embeddings were used. Features that were constant over the dataset, and those correlated with a value greater than 0.95 were discarded. Finally, a set of 939 features, including both molecular descriptors and embeddings, was obtained. The accuracy of various supervised learning models, both Bayesian and non-Bayesian, was compared to ensure that the Bayesian Additive Regression Trees perform similarly to state-of-the-art models in terms of predictive accuracy. As the number of features is much higher than the number of observations, we opted for sparsity-inducing models. In particular, the BART model with and without variable selection was compared to Bayesian linear regression with a horseshoe prior , random The inclusion proportions of all variables in the model are calculated.The response vector is randomly permuted, thus breaking the relationship between the covariates and the response. The model is retrained with this new response vector, and the variable inclusion proportions are recalculated. These are considered as the existing inclusion proportions in case there is no association between the variables and the response. This step is repeated several times to create a distribution of inclusion proportions that we call the null distribution. This distribution will allow us to see whether the value of the proportion of inclusion of each observed variable is too high with respect to the expected distribution in the event that there is no association. If so, the variable in question would be considered important.In particular, Bleich et al.  describeWithin BART, variable selection was performed using the procedure described by Bleich et al. . This stx, the Bayesian model produces samples from the posterior predictive dispersancy, denoted as Mean predictive dispersancy: the expected value of the posterior predictive distribution defined as Predictive standard deviation: the standard deviation of the posterior predictive distribution defined as x is defined as The expected improvement: if we denote the best dispersancy value observed within the training set as rgued in , expectex has a dispersancy value higher than Probability of improvement: the probability that a candidate molecule with features Given a new candidate molecule described by features All of these metrics can be easily approximated through Monte Carlo using samples from the posterior predictive distribution provided by the BART model.Finally, to gain some interpretability, BART is used to compute partial dependence plots. These plots serve to illustrate how each of the descriptors affects dispersancy, on average. Additionally, to provide an interpretation of the features obtained from SMILES embeddings, molecular descriptors highly correlated with each of the embedding-based variables are highlighted.k neighboring molecules to the new candidate  than 1 means that the candidate compound is closer (farther apart) to the neighboring compounds than the rest of the compounds in the dataset. The equations are formalized as follows:x is the candidate molecule being screened, x and its neighbor i, and m molecules in the dataset.An important aspect of predictive modeling is determining the reliability of predictions ,63. In tThe two machine learning methods described in the previous sections need to be made accessible to the chemical expert. In this regard, a visual analytics strategy is proposed. Visual analytics  is a disWe designed two main interfaces that correspond to each of the modeling approaches. The first interface is the frontend for the similarity-based analysis method, and it is shown in t-distribution over pairs of samples in the reduced space. These last two steps are iterated until both spaces, the original and the reduced one, present similar distributions. On the other hand, UMAP is a dimensionality reduction algorithm that builds topological representations of the data both in the original dimension and in the reduced dimension. In the case of high-dimensional data, the topological structure seeks to approximate the manifold on which, it is assumed, the data are located. The topological representation of the low-dimensional data is initialized with random values. Once the topological representations of the data in high and low dimensions have been constructed, the position of the points in the low dimension is optimized to minimize the cross entropy between both topological representations. The projected spaces were obtained using Python’s sklearn.manifold and umap packages that provide implementation of the t-SNE and UMAP methods, respectively [The main difference between these methods is in the way that distances are computed. tSNE is an algorithm designed for the visualization of high-dimensional data. It first constructs a probability distribution (Gaussian) over the pairs of samples in the original space, in such a way that similar samples are assigned a high probability, while very different samples are assigned low probability. Similarly, the method projects the points from the high dimensional space to a low dimensional space and constructs a Student’s ectively ,69. For In the scatterplots generated by these projections, dots correspond to compounds and their size is proportional to the blotter spot value. The location of the dots depends on the dimensionality reduction method used for projecting from the original dimensional space defined by the molecular descriptor values onto a two-dimensional space. For this projection, the tool allows for using either t-SNE or UMAP. When a dot is hovered over, contextual information is shown such as name, dispersancy score (as Blotter spot or R factor), and a visualization of the chemical structure of the compound using SMILES Drawer .On the right-hand side of the interface B, the coFinally, it is also possible to add unseen compounds that are intended to be screened and evaluated in a visual manner D. Once aPredict button is clicked, the molecular descriptors and molecular embeddings described in SMILES of the compound for prediction;Mean value of the posterior predictive distribution as described in Median value of the posterior predictive distribution;95% prediction interval as described in Expected improvement of the predicted blotter spot value with regard to the highest blotter spot of the training dataset as described in Probability of improvement with respect to the highest blotter spot of the training dataset as described in Applicability domain measured as described in On a different tab, the interface enables the chemical expert to use the BART method described in Partial dependence plot (PDP), which shows for any chosen feature how the dispersancy value changes on average (black line) at different deciles of the feature value, marginalizing over the values of the rest of the features. Similarly, the plot also displays 95% percent intervals at different deciles (blue lines). For instance, for the molecular descriptor AATS5d  was calculated for each compound in the test set. The metric used to measure the distances between the molecular structures was the normalized Euclidean distances distance, and the number of neighbors was set to five . To help explaining the inner workings of the model, we can use partial dependence plots (PDPs), as the ones in In an attempt to further examine the predictive potential of our model and understand its inner workings, we proceeded to evaluate a series of virtual PIBSI molecules derived from a known reference substrate. In particular, PIBSI-TEPA was selected as a starting point for its simplicity and used to design similar derivatives which might reveal logical trends in the predictions. For that purpose, we computed the mean posterior predictive blotter spot of each derivative and compare it with that of PIBSI-TEPA (which was obtained experimentally and has value First, a cumulative replacement of the amino groups in the PIBSI-TEPA by oxygen caused the predicted blotter spot dispersancy to decrease down to a minimum when all the internal amines were removed , S1–S3. Along these lines, the groups of Mekewi and Abdel Azim ,29,38 stThe conformational flexibility of the polar head for maximizing the interaction with the randomly distributed acidic binding sites on the surface of soot particles has been proposed to be another decisive factor for a high particle-dispersant affinity . In pracFinally, encouraged by the consistency of the predictions with known experimental observations, we further explored subtle structural changes to obtain information towards designing an improved dispersant candidate. For instance, we probed the influence of each NH group from PIBSI-TEPA by simulating selective N-methylations. This revealed a higher sensitivity of NH groups towards the loss of dispersancy the closer they are to the succinimide linkage , S16–S19The use of AI is having a growing impact on the design of new molecular compounds. Although it does not replace some of the traditional wet-lab experimentation steps, it is playing a key role in accelerating discovery of new materials such as dispersants. In this work, we have illustrated how a structural similarity-based model and a Bayesian regression model can be successfully combined for the virtual screening of dispersants in the challenging context of a small data problem. We present a dataset of 53 potential dispersants constructed from the literature and design a variety of models to predict the dispersancy efficiency property. In addition, a visual analytics tool for exploring interactively the data and models has been presented. This tool aims to facilitate the involvement of chemical experts with the outputs produced by the machine learning models, contributing in this way to the interpretability of the results. Finally, a brief study was presented to illustrate the analysis that a chemical expert can follow with the tool to perform virtual screening of a molecular structure. In this sense, the performance of our models was evaluated with a virtual screening of representative polar head designs, which revealed a high consistency with well-known empirical trends in the blotter spot predictions. In summary, our AI methodology would provide useful insights to material designers beyond the limits of a classical Edisonian approach to materials discovery.


In practical wireless sensor networks (WSNs), cascading failures are closely related to network load distribution, which in turn strongly relies on the locations of multiple sink nodes. For such a network, understanding how the multisink placement affects its cascading robustness is essential but still largely missing in the field of complex networks. To this end, this paper puts forward an actual cascading model for WSNs based on the multisink-oriented load distribution characteristics, in which two load redistribution mechanisms  are designed to imitate the most commonly used routing schemes. On this basis, a number of topological parameters are considered to quantify the sinks’ locations, and then, the relationship between these quantities with network robustness is investigated on two typical WSN topologies. Moreover, by employing the simulated annealing approach, we find the optimal multisink placement for maximizing network robustness and compare the topological quantities before and after the optimization to validate our findings. The results indicate that for the sake of enhancing the cascading robustness of a WSN, it is better to place its sinks as hubs and decentralize these sinks, which is independent of network structure and routing scheme. As an essential part of the Internet of Things (IoT) system, wireless sensor networks (WSNs) are increasingly widely used in various fields, such as military, industry, transportation and environmental protection. In general, WSNs are composed of numerous low-cost sensors with data processing and wireless communication capabilities, which automatically collect environmental data in a self-organized manner and forward them to sinks through one-hop or multi-hop routing ,2,3. HowComplex network theory is now a powerful tool used in the research on the robustness of realistic network systems ,7. By abIn most of these existing studies, the cascading models for WSNs are developed based on general topological load metrics . The premise of those models is that the data transmission is conducted in a peer-to-peer mode, that is, data can be transferred between any pair of network nodes. However, in reality, all data in WSNs will be transmitted from general sensors to sinks, and the data transmission mode oriented to multiple sinks has obvious advantages in energy efficiency and reliability compared with only one sink ,21,22. TSpecifically, current studies on the multisink placement mainly focus on various optimization approaches that only aim to find the optimal locations of sinks to maximize network performance in terms of transmission latency, network lifetime, or other aspects ,24,25,26(1)We put forward a multisink-oriented cascading model for WSNs to characterize the actual cascading process of WSNs, which considers the multisink-oriented load distribution characteristics and the two most commonly used routing schemes.(2)We introduce five topological parameters to give quantitative measures of the sinks’ locations for WSNs.(3)We carry out an experimental analysis on the relationship between the topological location parameters of sinks and network robustness on the two typical network topologies imitating real-life WSN conditions.(4)We design a simulated annealing algorithm to maximize network robustness through optimizing the multisink placement and compare the topological quantities before and after optimization to validate the experimental results.In this paper, we develop a systematic study to fill this gap. We first construct an actual cascading model for multisink WSNs. Based on this model, a number of topological parameters are introduced to establish the connectivity between cascading failures and multisink placement. The new findings obtained here reveal the impact of varying topological location properties of sinks and its association with the network configuration considering network structure and routing scheme, providing insight into optimizing or designing WSNs to make them more robust against cascading failures. The main contributions of this paper are summarized as follows:The rest of the article is arranged as follows. In this section, we elaborate the constructed cascading model for WSNs in detail. First, we present the network description and introduce a load metric called multisink-oriented betweenness to capture the load distribution of WSNs. On this basis, we give the definition of the initial load and capacity of sensors. Then, to describe the process of multisink-oriented load redistribution in common routing schemes, we propose two load redistribution schemes. Finally, we discuss the cascading mechanism and robustness measure.i is connected with node j; otherwise, E does not contain the link created within the set of sinks.In this study, a WSN can be abstracted by an undirected graph j and j to its nearest sink m that run through sensor i. j to its nearest sink m. i, denoted by In an actual WSN, general sensors collect data or act as routers for transmitting data to sinks. Usually, the data flow from the sensors to their nearest sinks through the shortest path and maintain a balanced state owing to a long time evolving; thus, the initial load of a sensor relates to the number of shortest paths from all sensors to their nearest sinks that pass it in the network . To propt exceeds its capacity, it will malfunction at time In actual WSNs, the capacity of a sensor, which characterizes the maximum load this node can manipulate, is limited by its buffer size. The existing cascading models usually assume that the capacity is directly related to the initial load of the node ,13. HoweW=(1+β)∑iIf a sensor malfunctions, the load traffic should be rerouted to bypass it toward the destinations. This redistribution of load is a transient action and may be global or local, depending on the routing policies. In fact, global and local routing policies both exist . For thii fails at time t, it is removed from the network and the whole network topology is updated. A sensor’s load in the network is then renewed according to Equation i.The average degree of sinks ((2)i.The average betweenness of sinks (weenness  of node (3)i and j.The average efficiency of sinks ((4)The average closeness of sinks ((5)The average shortest path length of sinks  and scale-free network (SFN) to present an overall evaluation of how the above topological parameters for multisink placement affect network robustness. We apply the proposed cascading model considering different routing schemes  on these two typical networks. Network science tells us that the degree distribution of RN topology is homogeneous, while the degree distribution of SFN topology is heterogeneous. Note that “network topology” here defines how all nodes within a network are connected to each other no matter whether it is a sensor or a sink. Clearly, there exist four network scenarios for WSNs, which can be illustrated by the combinations of network structure and routing scheme, including RN-GR, SFN-GR, RN-LR and SFN-LR.Our simulations are based on Matlab. To imitate real-life network conditions, the RN and SFN we adopted are generated referencing the topology construction algorithms . IEEE 80For each network scenario, to discuss the impact of multisink placement on the cascading robustness of WSNs, the sinks’ locations are randomly assigned 1000 times. For each distribution in each network, we can obtain a set of values of topological parameters   to find (1)Randomly select (2)Randomly select a sink and modify its location randomly to obtain the new network (3)T denotes the temperature parameter and is a function of the time step t.(4)If the value of T should be progressively decreased from an initial value that is large enough. This enables the search of solutions to escape from the local optimum and ensures that the system can finally reach an equilibrium. In our study, the cooling schedule of the temperature T follows the exponential rule During the implementation of the algorithm, the temperature parameter er 15 of .The proposed SA algorithm is applied to the same network scenarios as the previous section. The results of topological parameters and robustness before and after optimization are shown in Moreover, for different network scenarios, when comparing the topological parameters before and after optimization, ADS, ABS and ASPLS should be larger, and the AES and ACS should be smaller, which means that its sinks should be arranged as hubs, and these sinks should be uniformly distributed in the network. These results are effective in different network structures and routing schemes studied, and they are also verified through our designed simulated annealing algorithm optimizing multisink placement. Moreover, both the network structure and routing scheme can affect the sensitivity of the robustness of the network to its sinks’ locations.In this paper, based on an actual cascading model, a WSN is investigated in terms of its multisink placement, and the association with the cascading robustness is established. The proposed cascading model takes into account the multisink-oriented load distribution characteristics and the two most commonly used routing schemes for WSNs. The statistical parameters considered for quantifying the sinks’ locations include Our study clearly illustrates the importance of considering multisink placement when optimizing the robustness of WSNs to resist cascading failures. In reality, how to engineer a large-scale WSN that has more cascading robustness is crucial in many applications. Our findings provide an efficient and easy way to do this: just manipulate the topological locations of a small number of its sinks in a reasonable manner. The self-organizing characteristic of WSNs which have a topology that can be flexibly tuned according to actual needs ,40 also In the present work, aiming to explore the impact of varying the topological location properties of sinks on network cascading robustness for WSNs, we mainly focus on the modeling of a multisink-oriented load-transfer process where the two routing schemes considered are topology-aware only. In the next step, we will extend the model by considering more practical routing factors . On this basis, we will figure out efficient ways to comprehensively analyze the influence of topological properties  of both the connectivity of the network and the distribution of sinks on the cascading process and launch a more robust network design for real-life multisink WSNs. The interesting challenge of this work is to make sure that the topology structure designed is robust to cascading failures and can also meet other network performance requirements, such as delivery latency and energy efficiency.


The palmaris longus frequently exhibits anatomical variations with palmaris longus agenesis and reversal being the most prevalent. These variations are relevant clinically, as the muscle is often used during plastic surgeries for grafting tendons. They are also relevant in pathology, as hypertrophy of the reversed muscle is related to median nerve compression. In this report, we describe an unusual case in which a male cadaver-donor exhibited a right-sided palmaris longus reversal and left-sided palmaris longus agenesis. Review of the literature documents no previous co-occurrence of these anomalies. Since the muscle has relevance in a variety of contexts within medicine and surgery, reporting on a variation like this carries significant educational and clinical value. The palmaris longus (PL) is a highly variable structure in the human body. This thin muscle is one of the superficial flexor muscles of the forearm, innervated by the median nerve and supplied by the ulnar artery. Anatomically, it is located medial to the flexor carpi radialis and lateral to the flexor carpi ulnaris (FCU), originating from the medial epicondyle of the humerus. It becomes tendinous in the middle third of the forearm and inserts at the palmar aponeurosis in the wrist. The function of PL is debated. When present, it acts as a weak flexor of the wrist and tenses the palmar aponeurosis. However, there is no dysfunction or pathology in humans associated with its absence . PresencThis case report describes the unique presence of PL agenesis in the left upper extremity (LUE) and reversal in the right upper extremity (RUE) of a white male cadaver-donor. We discuss relevant clinical and pathological implications related to PL and its variations. To our knowledge, this is the first case report to identify asymmetric co-occurrence of such PL variations. It is important that variations of the PL are recognized by medical professionals so as to improve patient outcomes during surgical procedures of the anterior forearm.This article was previously posted to the Research Square preprint server on June 30, 2023.Routine anatomical dissection of the bilateral anterior compartment of the forearm on a 79-year-old white male cadaver-donor was performed by first year medical students. The donor gifted his body to the Anatomical Gift Program at The Robert Larner, M.D. College of Medicine. A set of standard dissector instrumentation was used, including probes, scalpels, scissors, and forceps. The superficial flexor muscles of the right forearm were left intact to preserve the observed variation. On the left forearm, the superficial flexor muscles were further dissected in order to observe deeper muscles including the flexor digitorum superficialis and profundus, the flexor pollicis longus, and the pronator quadratus. The anatomical variations on both the left and right PL were photographed using the camera feature on an iPad . Figure Two variations of the PL were identified. On the right, reversal of the PL was observed. Here, the tendon of the right PL was attached at the anatomic origin  as opposed to the palmar aponeurosis in the wrist Figure . The musThis case documents the first presentation of an individual with two concurrent PL variations. In particular, the cadaver-donor demonstrated PL agenesis on the left and reversal on the right. These variations are well-documented in the literature which indicate PL reversal is more common in the LUE and agenesis incidence rates range from 1.5% to 63.9% -4. The PL and its associated variants may have evolved as a result of specialized movement such as bipedal locomotion or tool usage . In thisThere are many recorded variations in the PL muscle bellies including bifurcation, trifurcation, and fusion (defined as the merging of the PL and FCU tendons) . AdditioClinically, PL variations have been known to cause neuropathies as a result of neurovascular compression in the carpal tunnel or Guyon's canal. In particular, PL reversal has been shown to present with swelling, numbness, and pain that is exacerbated with wrist flexion . This exWhen identifying PL abnormalities, testing is required especially in the context of wrist pain syndromes and for procedure planning like in tendon transfer . InitialBy presenting a distinct case of asymmetrical variation, we aim to raise physician awareness of the diversity that can possibly be demonstrated in the PL. This awareness can increase clinical diagnostic accuracy and alleviate potential stress for the patient especially in the context of abnormal wrist pain or tendon grafting. Given the wide range of anatomical variations present in the PL, meticulous tests must be administered in order to recognize anatomical abnormalities. Our hope is that through ample case documentation, clinical science can improve currently utilized diagnostic tools to ensure the best possible outcomes for patients, even when considering uncommon anatomical variants.


During the Covid-19 pandemic, real-time social media data could in principle be used as an early predictor of a new epidemic wave. This possibility is examined here by employing a neural ordinary differential equation  trained to forecast viral outbreaks in a specific geographic region. It learns from multivariate time series of signals derived from a novel set of large online polls regarding COVID-19 symptoms. Once trained, the neural ODE can capture the dynamics of interconnected local signals and effectively estimate the number of new infections up to two months in advance. In addition, it may predict the future consequences of changes in the number of infected at a certain period, which might be related with the flow of individuals entering or exiting a region. This study provides persuasive evidence for the predictive ability of widely disseminated social media surveys for public health applications. However, the intrinsic parameters utilized by the prediction models to reflect the biological features of the virus cannot be determined until the pandemic has happened. While a pandemic is in progress, parameter estimation is fraught with uncertainty, which means that the first-principles models that rely on them inherit this uncertainty in their forecasts. According to one epidemiologist quoted in the New York Times3: “You tell me what numbers to put in my equations, and I’ll give you the answer ...But you can’t tell me the numbers, because nobody knows them...” , a statement that illustrates the difficulties that currently exist in predicting new infections during a pandemic.During a pandemic, the capacity to recognize and anticipate local viral outbreaks is critical for health experts to take proper action6. Multiple passive8 and active surveillance systems11 had been established across the globe12. In the last decade, new machine learning algorithms and vast data availability have enabled web-based surveillance as a supplement to conventional approaches15. Internet searches18, social media22, survey data24, contact tracking or monitoring using mobile devices26, and contact simulations27 are examples of information sources.A large amount of data is being created, either directly or indirectly, on the virus’ spread. Health Surveillance is a vital tool for forecasting, preventing, and eliminating infectious diseases and epidemics. Some of this information has been utilized for a long time in this field30. In addition, the use of predictive models based only on big data may be hampered by lack of reproducibility, overfitting, and the necessity to continuously update algorithms 31. In recent years, there has been widespread agreement on the need to mix old and new information sources to enhance health surveillance model forecasts33.While digital surveillance systems offer several benefits, such as low cost, fast deployment, and extensive area coverage, they also have numerous disadvantages. For example, content and demographic bias, incomplete information, difficulty segmenting by geographic area, and complexity in digital data structure are obstacles that must be overcome36. Large technology businesses have simultaneously made resources accessible to scholars and policymakers38. Using this information in conjunction with late indicators (such as virus positive case numbers) might be crucial to the development of more accurate outbreak prediction algorithms. The Delphi research group at Carnegie Mellon University created an API39 that gathers data from several sources and provides access to numerous COVID-specific and syndromic markers. This approach solves some of the aforementioned obstacles by providing simple access to geographic location and structured information. In addition, they presented a survey of symptoms developed in collaboration with universities and public health experts and presented via Facebook40. This social media-advertised survey reaches a wider audience and collects more information than comparable surveys. Despite the fact that the majority of web-based surveys are inexpensive and provide quick and easy access to the population, they are limited by sample bias41. In this case, bias was partially corrected by means of weight adjustment40.The development of the COVID-19 pandemic has rekindled the hunt for more accurate forecasting models45 as well as compartment modelling approaches49. In this article, we examine the predictive abilities of a state-of-the-art data-driven model to anticipate COVID-19 outbreaks using data-sets from the aforementioned symptoms survey40. In this case, time-dependent signals are retrieved from a particular geographic region. After processing several numerical indicators arising from the survey questions, each signal is generated. The acquired data pertains to the symptoms of individuals, infections within their social circle, hospital visits, number of internet searches for COVID-19, and average time away from home, among others. For example, a person’s input about the number of his contacts who tested positive for COVID will be linked to the number of new cases in his location.It is evident from the preceding that digital information paired with first principles models or data-driven models might be used to enhance health surveillance systems. Several models have been reported to date that use various machine learning techniques and information sources50, since they are not susceptible to delays caused by officially reported variables, local policies, or testing capacity.There is no obvious model based on fundamental principles that connects the survey components to the COVID-19 numbers. However, it is plausible to predict a correlation between the local variation in time of survey answers for an area and the emergence of new viral infections in that location. In addition, these signals have the potential to serve as early indicators51) was employed to parameterize the temporal rate of change of the signal. This object employs a parameterized universal approximator to represent all conceivable phase space dynamics with a limited set of parameters that can be learnt from the training data. In this study, the neural ODE is trained on these possible early indicators and is capable of predicting viral outbreaks two months in advance. In addition, once taught, these phase space methods allow the prediction of potential future scenarios or the measurement of the uncertainty associated with changes in the number of infected in the region.In order to discover this relationship, a neural ordinary differential equation .The second section provides further information regarding testing, symptoms, and medical-seeking behavior. The third portion collects information on contacts and risk factors, while the fourth component collects demographic information. There is a sample of the exact questions asked in the 52 and responses, after a bias correction via weight adjustment40, resulting in a set of time series (one for each indicator) at a specified location. The aggregated data is accessible to the public via the Delphi Group websites54.The survey has four sections and it contains 35 questions. The first section gathers information about a set of symptoms used to define a condition called COVID-like illness (CLI), defined as fever of at least 100 Data pertaining to the number of people who self-report CLI symptoms in a certain location may provide an early signal of COVID activity in that location. In addition, the information is not susceptible to reporting delays, unlike the formal testing metrics of confirmed daily COVID-19 cases, which are affected by testing policy and capacity.40 Blog, it is shown that the “CLI-in-community” signal increases concurrently with confirmed COVID-19 cases, providing evidence that survey-based CLI signals can serve as early indications of COVID activity. Indeed, more individuals report that others in their neighborhood are ill when COVID-19 tests reveal an increase in confirmed cases. In fact, when COVID-19 testing indicate an increase in cases, more people report that others in their community are ill. Intriguingly, the signal begins to rise dramatically days before COVID-19 cases begin a sharp increase . This study is a non-formal examination of the indicator’s recall that permits the use of noisy and indirect signals as early indicators of new cases. Although the survey cannot be used to draw definitive conclusions about the true prevalence of coronavirus disease in the studied region, changes in self-reported symptoms over time could still be a meaningful reflection of the changes in coronavirus infections over time and could therefore assist in forecasting changes in the number of newly infected patients in the coming days.In the Delphi Group’sThe use of these signals for the prediction of new cases could be done by means of a model that relates the rate of variation of the different indicators to the model’s state variables. However, unlike the case of common epidemiological models, the deduction of a quantitative expression that relates the new cases as a function of the different signals extracted from the surveys is far from obvious. Even if the relations were discovered and the model was characterized, for instance, as a system of ordinary differential equations, it would undoubtedly contain unknown parameters and be subject to uncertainty. Utilizing the quantity of data and indications gathered from the surveys, a data-driven method would be a reasonable alternative for obtaining a model for forecasting new infected cases in a geographical region.55, for instance, the vector components are the variables number of susceptible individuals (S), number of infected individuals (I), and number of recovered individuals (R), along with their temporal variation expressed with an ordinary differential equation based on intuition and qualitative knowledge of the dynamics of contagions. However, in the case of the vector produced with the survey indicators as components, we cannot simply build such a model as it is not clear how to characterize the link between them from first principles.Therefore, for a particular region, we establish a vector NN is used, it would match perfectly to the definition of a neural ordinary differential equation 51.Despite the absence of a known functional form that links the variables, we might examine their temporal rate of change for information. If they are represented by the vector 57 . In particular, we represent our dynamical system via:NN is a neural network given by weights t dependence since it is parameterized based on the time-dependent input signals from the data. The goal is to learn the underlying dynamics of change. The “forward pass” through a neural ODE is equivalent to solving an initial value problem where A Neural ODE is a neural network parametrization of an ordinary differential equation which allows for learning the dynamics of any possible dynamical system due to the universal approximation theorem58 or Long short-term memory (LSTMs)59, this model is continuous in time, allowing for incorporating non-uniform data and predictions. RNNs and LSTMs are designed for uniform time data and are equivalent to neural ODEs with uniform time steps (see61). In this sense, one could augment an RNN or LSTM with interpolations as part of the loss function; however, the accuracy of such a method for representing a continuous object is inferior to that of a differential equation solver with dense internal output (see Ref.62 for details). Given the constraints of the problem, it makes the most sense from a mathematical standpoint to represent the equations in this manner.Unlike other architectures used for time series like residual neural networks (RNNs)63. Thus in order to perform the minimization the gradient of the loss function with respect to all parameters 66, and thus we opted for stabilized techniques, which avoid reverse solving68.The parameters of the neural ODE are learned from the data as diagrammed in Fig. mentclass2pt{minimThe trained model could be applied to different initial conditions than those used during the learning procedure. With sufficient representative data, the neural ODE should be able to approximate the underlying dynamical system, particularly in the phase space region where the data was sampled. It is expected that this description will deteriorate as one moves further away. In particular, the trained neural network describes the vector field entclass1pt{minima52. A smoothing was performed via a cubic spline interpolation for all the signals/indicators69 time series. The 7-day averaged of reported new confirmed COVID-19 cases was used as the main indicator of interest70 for accounting for the new cases. We chose the following set of variables as components in order to build the state vector y(t) for each location: New daily cases (7 day averaged), (late indicator)Hospital Admission, (late indicator)COVID-Like Symptoms, (early indicator)COVID-Like Symptoms in Community, (early indicator)COVID-Related Doctor Visits (early indicator)The collection represents an assortment of early and late correlated indicators. The complete multivariate time series is thus represented by a five-component vector The raw signals for each USA State were downloaded using the Delphi Group API71 variant of multiple shooting74 direct training was conducted by calculating the loss between intervals of data points. The neural ODE was solved from the point 75 using the DifferentialEquations.jl implementation76 to obtain the prediction for the following point 77 were used to achieve backpropagation.The resulting multivariate time series were divided into a training set and a validation set. The training set was used to update the network’s weights entclass1pt{minima78. Once the neural net weights The neural networks used for parameterizing the ODE consisted of four interconnected layers with 64, 32, 16 and 8 neurons each and swish activation functions79 for part of the data pre processing69, matplotlib80 for plotting, and Inkspace for making figures81, The Julia library DiffEqFlux82 for training the neural ODEs, and the differential equation library DifferentialEquations.jl76 for solving the differential equations.The following open source software tools were used for this work: Pandas libraryFigure Once the model  has learned the dynamics of the local signals, it is capable of predicting new contagions and exploring potential future scenarios in the event of signal disruptions. For instance, the trained neural ODE model might estimate the influence of a sudden shift in the number of new cases at a specific time in the future. This is due to the fact that once the neural ODE learns the dynamics of the signals, it constructs parametrically a vector field parallel to the potential trayectories of the vector entclass1pt{minimaN individuals visit the region, People entering or leaving the modeled area will also cause a change in the trajectory of the state vector entclass1pt{minima83 provides a representative example of the calculation/estimation of the infected in the flow of persons leaving or entering cities. Models of the SEIR type depict the various geographical locations and the epidemiological dynamics of their respective populations. A flow matrix that connects the local models represents the transit of individuals. On the basis of the day flow, the number of infected I and exposed E individuals is estimated and variables are updated daily. The same flow-related reasoning can be applied to our situation by substituting the SEIR models of different locations with neural ODE models trained with data extracted from local surveys.The work by Mayorga et al.Using multivariate time series connected with a geographic region, gathered by quantifying indicators from large online surveys on COVID symptoms presented via Facebook, we describe how a neural ODE can learn the dynamics that connect these variables and detect viral outbreaks in the region. We demonstrate, by analyzing data from several U.S. states, that the neural ODE is capable of forecasting up to sixty days into the future in a variety of virus-spreading scenarios.We assert that once the neural ODE has learned the dynamics of the local signals/variables, it is capable of not only forecasting new infections in the region, but also analyzing possible future scenarios in the case of abrupt changes in the number of infected in a given day, for instance due to transit of people into or out of the analyzed region . This affords regions with strict closed borders the opportunity to predict the impact of the flow of people on the infection curve and, as a result, formulate policies in a controlled manner to optimize the transit of people and reduce economic stagnation during a pandemic.In addition to the considerations mentioned earlier, future works can explore the potential of incorporating compression analysis into our research. While our current study focused on training the neural ODE using data from a single location or state, it is likely that the dynamics connecting local signals in one region to those in another region exhibit similar properties. Therefore, it would be valuable to investigate alternative training schemes where the model learns from multiple locations.Furthermore, incorporating graphical models into the neural ODE framework, possibly through the utilization of graph neural networks, represents a promising avenue for future study. This approach would allow for a more comprehensive understanding of the interconnections and dependencies between different regions or entities within the system under consideration. By incorporating such graph-based techniques, we can potentially enhance the model’s predictive capabilities and capture more nuanced dynamics.68. By integrating the strengths of both data-driven and analytical modeling approaches, we can achieve a more comprehensive understanding of epidemic dynamics and improve the accuracy of the predictions.Our neural ODE model, trained on real-time social media data, extends the principles of first principles models like the SEIR model. While the SEIR model relies on assumptions about disease transmission and population dynamics, our neural ODE model directly learns from interconnected local signals extracted from social media surveys. This data-driven approach allows us to capture the underlying dynamics of disease transmission and population behavior with greater flexibility and adaptability. Moreover, our data-driven model can be combined with first principles models, such as the SEIR model, using a scientific machine learning approachproof of concept. It is essential to investigate various signals and combinations and evaluate their generalization capabilities. Accurate application of the uncertainty quantification requires a great deal more research before it can be utilized in public health situations. As Nobel laureate Niels Bohr remarked a century ago: “..prediction is very difficult, especially if it’s about the future...”. On the other hand, these findings provide some promising outcomes for future real-time forecasts that are based on predictive data from social media.This work ia a preliminary phase, a Supplementary Information 1.Supplementary Information 2.


Rotavirus vaccination was introduced in high-income countries starting in 2006, with no recommendation for optimal implementation. Economic evaluations were presented before launch projecting potential impacts. Few economic reassessments have been reported following reimbursement. This study compares the short- to long-term economic value of rotavirus vaccination between pre-launch predictions and real-world evidence collected over 15 years, proposing recommendations for optimal vaccine launch. A cost-impact analysis compared rotavirus hospitalisation data after the introduction of vaccination between pre-launch modelled projections and observed data collected in the RotaBIS study in Belgium. A best model fit of the observed data was used to simulate launch scenarios to identify the optimal strategy. Data from other countries in Europe were used to confirm the potential optimal launch assessment. The Belgian analysis in the short term (first 8 years) indicated a more favourable impact for the observed data than predicted pre-launch model results. The long-term assessment (15 years) showed bigger economic disparities in favour of the model-predicted scenario. A simulated optimal vaccine launch, initiating the vaccination at least 6 months prior the next seasonal disease peak with an immediate very high vaccine coverage, indicated important additional potential gains, which would make vaccination very cost impactful. Finland and the UK are on such a route leading to long-term vaccination success, whereas Spain and Belgium have difficulties in achieving optimum vaccine benefits. An optimal launch of rotavirus vaccination may generate substantial economic gains over time. For high-income countries that are considering implementing rotavirus vaccination, achieving an optimal launch is a critical factor for long-term economic success.  Economic evaluations of new vaccines coming onto the market are often developed and published prior to authorisation and launch, based on summary efficacy data from randomised controlled clinical trials conducted in places where the vaccine will be first administered ,2,3. SucHowever, effect monitoring of new vaccines in real-life settings is essential to obtain accurate economic value estimates in the short to long term . ResultsDifferent vaccines are available on the market against rotavirus infection, of which two are predominant in high-income countries: a two-dose human assorted live-attenuated vaccine called Rotarix (GSK), and a three-dose live-attenuated human–bovine assorted vaccine called RotaTeq (Merck) ,13. It iThe objective of the present analysis is to evaluate the economic value of an optimal vaccine launch, compared with a non-optimal situation such as the one observed in Belgium. The analysis uses an evaluation technique that allows the simulation of different vaccine launch scenarios, with different long-term accumulated outcome results for the economic assessment. It may identify threshold conditions that determine whether an initial vaccination strategy moves to optimal or less optimal long-term cost-impact results.Assessing the economic value of rotavirus vaccination in the short to long term, simulating different scenarios, rests on two pillars: the data source and the model.Understanding the real-world long-term economic effects of rotavirus vaccination requires the systematic collection of observed data on items causing the high cost of managing the disease and on which the vaccination is known to have a positive impact. Such data were collected in the RotaBIS study, which was initiated in 2007, a year after the vaccine was introduced and partially reimbursed by the Belgian authorities in November 2006 ,20,25. DThe model needs to replicate the observed data and must include those variables that affect the shape of the observed curve using direct and indirect vaccine effects . The modThe first period is the vaccine uptake period that can last 5 to 8 years until a new infection equilibrium has been reached in the target group of children aged ≤5 years. For this period, the model uses a regression equation to characterise the shape of the curve, in which different forces influence the regression line simulating the number of disease-specific hospitalisations observed per year. There are two main forces in the regression equation, each of which combines several components. The first force defines the direct vaccine effects . The second force represents the indirect effects of the vaccine (herd effect and secondary sources of infection).The vaccine uptake period is followed by a post-uptake period, in which the dynamic spread of the infection is simulated using a time differential equation with compartments of susceptible, infectious, and recovered (SIR) groups linked by time-dependent rates of transitions, starting at the hospitalisation level and the time required to replicate the observed biennial disease peaks. The frequency and height of these peaks depend on the entry conditions for the post-uptake period after the vaccine uptake period. These entry conditions include the remaining infection rate in the population, the maintained vaccine coverage rate with its net effect, the susceptible group (new-borns) entering at any given time point, and the contact matrix for the at-risk population see . It is ipv) [uv) group and the vaccinated group (v):C = cost; E = health effect often expressed in quality-adjusted life-years (QALYs); pv = pre-vaccination; uv = unvaccinated; v = vaccinatedA cost-impact analysis (CIA) was used for this analysis instead of a cost-effectiveness analysis (CEA), because impact evaluation covers the whole vaccinated and unvaccinated at-risk population in which the vaccine has direct and indirect effects, and which is compared with a situation prior to the initiation of the vaccination programme (pv) . The calThis contrasts with CEA, which evaluates the initially intended vaccinated population, considering the effectiveness of the direct and indirect positive effect of the vaccine such as the herd effect in the control group from within the vaccinated population (the test-negative controls) . Here, tTwo comparative CIAs were reported for the Belgian data: one compared the economic results projected prior to market launch with those obtained from the observation of the vaccine uptake period in the RotaBIS study ,21; the This model mimics the hospitalisation rates during the vaccine uptake period and the post-vaccine uptake period of the RotaBIS study. It was used to simulate selecting a better time to start the vaccination programme  and immediately reaching a very high vaccine coverage rate (90% instead of 66%). This scenario leads to a higher herd effect during the first year of the vaccine introduction, making it more difficult for the virus to activate secondary infections that produce the small disease peaks later. This is the optimal vaccination introduction scenario  that should produce substantially improved results compared with the initial launch in Belgium. An intermediate launch scenario was considered with a launch in October and an initial vaccine coverage rate of 67% to evaluate intermediate effects (intermediate) in contrast to the optimum launch strategy  or the borderline cost-impact results (Belgium). Launch data from other countries in Europe, Finland, the UK, and Spain, ,31,32 coThe input data used to estimate the cost and QALY-loss impact of hospitalisation are presented in The output obtained is the incremental cost–impact ratio (ICIR) achieved using different modelling approaches with different scenarios for vaccine launch, listed in The pre-launch predicted hospitalisation reduction, observed hospitalisation reduction data, and predicted hospitalisations with no vaccination are presented for the vaccine uptake period (first 8 years) in The cost-impact results are shown in There is a difference in the ICIR results in favour of the observed data because of a lower use of the vaccine, compared with the pre-launch model. The predicted results reach a similar plateau level in hospitalisations as the observed data, mainly because of the imposed reduction in vaccine effect over time, whereas the plateau level in the observed data is explained by the initial small herd effect, the vaccine coverage rate, and the appearance of secondary sources of infection, while the vaccine effect is maintained at the same level over the period. The observed results therefore broadly achieved the predicted effect on hospitalisations, but at a lower vaccine coverage rate with consequently lower vaccine costs, resulting in a more favourable ICIR than predicted.The next analysis compares the whole period of the observed data with the results from the extension of the pre-launch prediction model, assuming the effect observed after 8 years in the vaccine uptake period is maintained. The observed data differ from the pre-launch prediction by the appearance of small hospitalisation peaks at 9- and 11-years post-vaccine introduction that negatively impact the vaccine effect over time, as shown in These results now show that the ICIR is more favourable in the predicted data, in contrast with the results for the vaccine uptake period. This difference is explained by the appearance of the hospitalisation peaks in the observed data, causing a marginal gain in the ICIR results for the predicted model. Extrapolation of the observation period beyond 13 years of vaccination with the inclusion of modelled regular biennial peaks over time results in larger changes in the cost-impact results in favour of the extended prediction model. At 18-years post-vaccine introduction, the ICIR results are, respectively, €57,080 for the modelled pre-launch prediction and €65,797 for the observed simulated data, undiscounted (data not shown). The discounted results significantly reduce the difference in the ICIR results .Using the model constructed from the observed data, the vaccination introduction was adjusted by starting vaccination in August instead of November with an immediate coverage rate of 90% instead of 65% . These adjustments result in a much higher herd effect during the first years of the vaccination programme, which in turn hinders the development of new primary sources of infection in an older age group causing the later disease peaks. Depending on the level of increased herd effect simulated at the start, this scenario produces smaller and less frequent (every 4 years) disease peaks that begin earlier (after 5 years) than those in the observed data . The earThe simulation is further used to identify thresholds for vaccination launch parameters that determine when the vaccination produces better cost-impact results overall compared with the observed data. This is illustrated in The accumulated reduction in hospitalisations after 13 years of vaccination differs between the categories, reaching at least 65% to 74% ; 75–84% ; and >85% . The ICIR is considerably more favourable for the optimal introduction scenario  compared with the intermediate introduction scenario  and the Belgian situation  .Countries across Europe have launched rotavirus vaccination programmes that differ from the Belgian launch in their initial vaccine coverage rates and date of initiating the vaccination programme. Countries that started vaccination early in the year and with a very high coverage rate from the start (Finland and UK) saw a greater fall in hospitalisations than countries with a less stringent vaccination policy (Belgium and Spain). Finland and the UK appear to be on track to reach the region of the Category C scenario in the model. Long-term vaccination impact is now more difficult to assess because of the effect of preventative measures introduced in response to the COVID-19 pandemic, such as lockdowns, which caused an important additional impact on rotavirus hospitalisations, as observed in Belgium . HoweverRotavirus vaccination is an interesting case study to illustrate that there may be potentially important differences in economic value between pre-launch model predictions compared with real-world observational data over time. At the beginning, performing a cost-effectiveness analysis for rotavirus vaccination was considered a straightforward exercise, even with the use of dynamic models, to estimate the potential health gain and price-setting ,41. The Modelling these elements has helped to clarify the indirect effects of the vaccine that increase or reduce the herd effect, influencing the net vaccine effect and explaining the appearance of new disease peaks over time with a shift to older children as the primary source of infection . The datA few additional questions could be asked in relation to this economic evaluation. One is about the economic value this vaccine should have pre-launch that defines its price of reimbursement at launch, with a better understanding of the importance of how the vaccine programme is introduced. Analyses relying on simpler models, without taking into account the new knowledge of the optimal method of introducing the vaccination programme, as was carried out in Belgium, may produce a range of cost-effectiveness results in the sensitivity analysis that includes the optimal result. However, such an analysis would not be able to indicate how to achieve the optimal result if not all the necessary details were included in the model construct. In this case, the absence of information on an optimal vaccine introduction to define the price-setting at launch is a risk for both the producer and the paying party. Either may find that they are paying or being paid too much or too little for a vaccine, and it is difficult to readjust the vaccination programme after a non-optimal introduction because of the limitations of readjustment interventions, such as increasing the vaccine coverage rate. Therefore, it is very important to refine the vaccination programme at its introduction to maximise the efficiency of the programme in the long term. Thus, the recommendation is that an economic submission for reimbursement should evaluate different scenarios of vaccine introduction that consider the differences in cost-effectiveness and cost-impact analyses related to the vaccine coverage rate, and the time selected for vaccine introduction, in relation to the expected seasonal disease peak. This approach, with an emphasis on obtaining initial high coverage ahead of the next expected seasonal peak, could be applicable to other diseases with marked seasonality and high contagion. If COVID-19 becomes an endemic disease in infants with seasonal peaks, these findings may be relevant to future research on the design of a potential COVID-19 vaccination programme in this age group. Could this have been foreseen in the Belgium submission file for the rotavirus vaccine? This would have been difficult if the full infection spread was not well understood at the beginning, having identified the importance of an optimal introduction of the vaccination and having discovered the age shift in the primary source of infection after a sub-optimal introduction. In this respect, one should remember that the European randomised controlled trial (RCT) conducted for Rotarix in 2004–2006 had a randomisation process of two vaccinated children for one placebo child [Finally, is this economic model also applicable to other settings such as non-high-income countries? Some critical points that are essential for the optimal functioning of the vaccine in high-income countries but that could be absent in other countries include the seasonality of infection spread, easy contact patterns among very young children (such as day-care centres) that facilitate virus transmission, and the hospitalisation of severe cases leading to a high healthcare cost. It would be a challenge to apply the current model if any of those conditions were not fulfilled. Nevertheless, this analysis indicates that rapidly achieving high coverage at the start of a rotavirus vaccination programme is essential for maximising the health benefit of the vaccine, as this minimises the development of secondary sources of infection that persist over time and are very difficult to correct at a later stage.The analysis presented here has some limitations. Some cost items, such as first-line support and indirect costs, were not considered, and not all the QALY losses at different disease stages were included in this evaluation. However, the focus of the analysis was to demonstrate that quite different economic value results could be obtained for a vaccine from a predicted pre-launch value assessment and real-life data observations. Vaccination needs data monitoring on its effect over time once approved and implemented, in order to capture deviations from what could be considered an optimal launch. The economic analysis is an additional tool to help in the selection of a vaccine strategy. For instance, some countries like to produce price–volume contracts when introducing new vaccines. These results suggest that such a policy would be a disaster for rotavirus vaccination if the volume is fixed at 40% or 50% for the first year of implementation followed by progressive increases in vaccine coverage over time. With a start at 40–50% vaccine coverage across a country, the present model suggests that it is likely that a limited effect will be seen on hospitalisation reduction, limiting the total value of the vaccine in the short to long term. Conversely, this model suggests that obtaining immediate very high vaccine coverage ahead of the next expected seasonal disease peak would maximise both the health benefit of rotavirus vaccination and its cost impact over the long term.Pre-launch economic assessments of new vaccines against rotavirus in high-income countries should be considered very carefully, as modelling based on observational data from Belgium indicates that the long-term vaccine benefit strongly depends on the details of the vaccination introduction. Issues such as changes in the infection spread and the consequent effects on vaccine impact make rotavirus vaccination assessment much more complex than initially thought, with quite disparate economic results depending on whether the initial vaccine introduction was optimal or sub-optimal.