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Simultaneous Localization and Mapping (SLAM) is a fundamental problem in the field of robotics, enabling autonomous robots to navigate and create maps of unknown environments. Nevertheless, the SLAM methods that use cameras face problems in maintaining accurate localization over extended periods across various challenging conditions and scenarios. Following advances in neuroscience, we propose NeoSLAM, a novel long-term visual SLAM, which uses computational models of the brain to deal with this problem. Inspired by the human neocortex, NeoSLAM is based on a hierarchical temporal memory model that has the potential to identify temporal sequences of spatial patterns using sparse distributed representations. Being known to have a high representational capacity and high tolerance to noise, sparse distributed representations have several properties, enabling the development of a novel neuroscience-based loop-closure detector that allows for real-time performance, especially in resource-constrained robotic systems. The proposed method has been thoroughly evaluated in terms of environmental complexity by using a wheeled robot deployed in the field and demonstrated that the accuracy of loop-closure detection was improved compared with the traditional RatSLAM system.

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The widespread adoption of massively parallel processors over the past decade has fundamentally transformed the landscape of high-performance computing hardware. This revolution has recently driven the advancement of FPGAs, which are emerging as an attractive alternative to power-hungry many-core devices in a world increasingly concerned with energy consumption. Consequently, numerous recent studies have focused on implementing efficient dense and sparse numerical linear algebra (NLA) kernels on FPGAs. To maximize the efficiency of these kernels, a key aspect is the exploration of analytical tools to comprehend the performance of the developments and guide the optimization process. In this regard, the roofline model (RLM) is a well-known graphical tool that facilitates the analysis of computational performance and identifies the primary bottlenecks of a specific software when executed on a particular hardware platform. Our previous efforts advanced in developing efficient implementations of the sparse matrix-vector multiplication (SpMV) for FPGAs, considering both speed and energy consumption. In this work, we propose an extension of the RLM that enables optimizing runtime and energy consumption for NLA kernels based on sparse blocked storage formats on FPGAs. To test the power of this tool, we use it to extend our previous SpMV kernels by leveraging a block-sparse storage format that enables more efficient data access.

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While sparse testing methods have been proposed by researchers to improve the efficiency of genomic selection (GS) in breeding programs, there are several factors that can hinder this. In this research, we evaluated four methods (M1-M4) for sparse testing allocation of lines to environments under multi-environmental trails for genomic prediction of unobserved lines. The sparse testing methods described in this study are applied in a two-stage analysis to build the genomic training and testing sets in a strategy that allows each location or environment to evaluate only a subset of all genotypes rather than all of them. To ensure a valid implementation, the sparse testing methods presented here require BLUEs (or BLUPs) of the lines to be computed at the first stage using an appropriate experimental design and statistical analyses in each location (or environment). The evaluation of the four cultivar allocation methods to environments of the second stage was done with four data sets (two large and two small) under a multi-trait and uni-trait framework. We found that the multi-trait model produced better genomic prediction (GP) accuracy than the uni-trait model and that methods M3 and M4 were slightly better than methods M1 and M2 for the allocation of lines to environments. Some of the most important findings, however, were that even under a scenario where we used a training-testing relation of 15-85%, the prediction accuracy of the four methods barely decreased. This indicates that genomic sparse testing methods for data sets under these scenarios can save considerable operational and financial resources with only a small loss in precision, which can be shown in our cost-benefit analysis.

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Gamma oscillations are believed to underlie cognitive processes by shaping the formation of transient neuronal partnerships on a millisecond scale. These oscillations are coupled to the phase of breathing cycles in several brain areas, possibly reflecting local computations driven by sensory inputs sampled at each breath. Here, we investigated the mechanisms and functions of gamma oscillations in the piriform (olfactory) cortex of awake mice to understand their dependence on breathing and how they relate to local spiking activity. Mechanistically, we find that respiration drives gamma oscillations in the piriform cortex, which correlate with local feedback inhibition and result from recurrent connections between local excitatory and inhibitory neuronal populations. Moreover, respiration-driven gamma oscillations are triggered by the activation of mitral/tufted cells in the olfactory bulb and are abolished during ketamine/xylazine anesthesia. Functionally, we demonstrate that they locally segregate neuronal assemblies through a winner-take-all computation leading to sparse odor coding during each breathing cycle. Our results shed new light on the mechanisms of gamma oscillations, bridging computation, cognition, and physiology.

The cerebral cortex is the most recently evolved region of the mammalian brain. There, millions of neurons can synchronize their activity to create brain waves, a series of electric rhythms associated with various cognitive functions. Gamma waves, for example, are thought to be linked to brain processes which require distributed networks of neurons to communicate and integrate information. These waves were first discovered in the 1940s by researchers investigating brain areas involved in olfaction, and they are thought to be important for detecting and recognizing smells. Yet, scientists still do not understand how these waves are generated or what role they play in sensing odors. To investigate these questions, González et al. used a battery of computational approaches to analyze a large dataset of brain activity from awake mice. This revealed that, in the cortical region dedicated to olfaction, gamma waves arose each time the animals completed a breathing cycle ­ that is, after they had sampled the air by breathing in. Each breath was followed by certain neurons relaying olfactory information to the cortex to activate complex cell networks; this included circuits of cells known as feedback interneurons, which can switch off weakly activated neurons, including ones that participated in activating them in the first place. The respiration-driven gamma waves derived from this 'feedback inhibition' mechanism. Further work then examined the role of the waves in olfaction. Smell identification relies on each odor activating a unique set of cortical neurons. The analyses showed that gamma waves acted to select and amplify the best set of neurons for representing the odor sensed during a sniff, and to quieten less relevant neurons. Loss of smell is associated with many conditions which affect the brain, such as Alzheimer's disease or COVID-19. By shedding light on the neuronal mechanisms that underpin olfaction, the work by González et al. could help to better understand how these impairments emerge, and how the brain processes other types of complex information.

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Since December 2019, the world has been intensely affected by the COVID-19 pandemic, caused by the SARS-CoV-2. In the case of a novel virus identification, the early elucidation of taxonomic classification and origin of the virus genomic sequence is essential for strategic planning, containment, and treatments. Deep learning techniques have been successfully used in many viral classification problems associated with viral infection diagnosis, metagenomics, phylogenetics, and analysis. Considering that motivation, the authors proposed an efficient viral genome classifier for the SARS-CoV-2 using the deep neural network based on the stacked sparse autoencoder (SSAE). For the best performance of the model, we explored the utilization of image representations of the complete genome sequences as the SSAE input to provide a classification of the SARS-CoV-2. For that, a dataset based on k-mers image representation was applied. We performed four experiments to provide different levels of taxonomic classification of the SARS-CoV-2. The SSAE technique provided great performance results in all experiments, achieving classification accuracy between 92% and 100% for the validation set and between 98.9% and 100% when the SARS-CoV-2 samples were applied for the test set. In this work, samples of the SARS-CoV-2 were not used during the training process, only during subsequent tests, in which the model was able to infer the correct classification of the samples in the vast majority of cases. This indicates that our model can be adapted to classify other emerging viruses. Finally, the results indicated the applicability of this deep learning technique in genome classification problems.

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The present work proposes to locate harmonic frequencies that distort the fundamental voltage and current waves in electrical systems using the compressed sensing (CS) technique. With the compressed sensing algorithm, data compression is revolutionized, a few samples are taken randomly, a measurement matrix is formed, and according to a linear transformation, the signal is taken from the time domain to the frequency domain in a compressed form. Then, the inverse linear transformation is used to reconstruct the signal with a few sensed samples of an electrical signal. Therefore, to demonstrate the benefits of CS in the detection of harmonics in the electrical network of this work, power quality analyzer equipment (commercial) is used. It measures the current of a nonlinear load and issues its results of harmonic current distortion (THD-I) on its screen and the number of harmonics detected in the network; this equipment acquires the data based on the Shannon-Nyquist theorem taken as a standard of measurement. At the same time, an electronic prototype senses the current signal of the nonlinear load. The prototype takes data from the current signal of the nonlinear load randomly and incoherently, so it takes fewer samples than the power quality analyzer equipment used as a measurement standard. The data taken by the prototype are entered into the Matlab software via USB, and the CS algorithm run and delivers, as a result, the harmonic distortions of the current signal THD-I and the number of harmonics. The results obtained with the compressed sensing algorithm versus the standard measurement equipment are analyzed, the error is calculated, and the number of samples taken by the standard equipment and the prototype, the machine time, and the maximum sampling frequency are analyzed.

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This paper presents a method to solve a linear regression problem subject to grouplassoand ridge penalisation when the model has a Kronecker structure. This model was developed to solve the inverse problem of electrocardiography using sparse signal representation over a redundant dictionary or frame. The optimisation algorithm was performed using the block coordinate descent and proximal gradient descent methods. The explicit computation of the underlying Kronecker structure in the regression was avoided, reducing space and temporal complexity. We developed an algorithm that supports the use of arbitrary dictionaries to obtain solutions and allows a flexible group distribution.

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The adoption of machine learning frameworks in areas beyond computer science have been facilitated by the development of user-friendly software tools that do not require an advanced understanding of computer programming. In this paper, we present a new package (sparse kernel methods, SKM) software developed in R language for implementing six (generalized boosted machines, generalized linear models, support vector machines, random forest, Bayesian regression models and deep neural networks) of the most popular supervised machine learning algorithms with the optional use of sparse kernels. The SKM focuses on user simplicity, as it does not try to include all the available machine learning algorithms, but rather the most important aspects of these six algorithms in an easy-to-understand format. Another relevant contribution of this package is a function for the computation of seven different kernels. These are Linear, Polynomial, Sigmoid, Gaussian, Exponential, Arc-Cosine 1 and Arc-Cosine L (with L = 2, 3, … ) and their sparse versions, which allow users to create kernel machines without modifying the statistical machine learning algorithm. It is important to point out that the main contribution of our package resides in the functionality for the computation of the sparse version of seven basic kernels, which is indispensable for reducing computational resources to implement kernel machine learning methods without a significant loss in prediction performance. Performance of the SKM is evaluated in a genome-based prediction framework using both a maize and wheat data set. As such, the use of this package is not restricted to genome prediction problems, and can be used in many different applications.

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Efficient computing techniques allow the estimation of variance components for virtually any traditional dataset. When genomic information is available, variance components can be estimated using genomic REML (GREML). If only a portion of the animals have genotypes, single-step GREML (ssGREML) is the method of choice. The genomic relationship matrix (G) used in both cases is dense, limiting computations depending on the number of genotyped animals. The algorithm for proven and young (APY) can be used to create a sparse inverse of G (GAPY~-1) with close to linear memory and computing requirements. In ssGREML, the inverse of the realized relationship matrix (H-1) also includes the inverse of the pedigree relationship matrix, which can be dense with a long pedigree, but sparser with short. The main purpose of this study was to investigate whether costs of ssGREML can be reduced using APY with truncated pedigree and phenotypes. We also investigated the impact of truncation on variance components estimation when different numbers of core animals are used in APY. Simulations included 150K animals from 10 generations, with selection. Phenotypes (h2 = 0.3) were available for all animals in generations 1-9. A total of 30K animals in generations 8 and 9, and 15K validation animals in generation 10 were genotyped for 52,890 SNP. Average information REML and ssGREML with G-1 and GAPY~-1 using 1K, 5K, 9K, and 14K core animals were compared. Variance components are impacted when the core group in APY represents the number of eigenvalues explaining a small fraction of the total variation in G. The most time-consuming operation was the inversion of G, with more than 50% of the total time. Next, numerical factorization consumed nearly 30% of the total computing time. On average, a 7% decrease in the computing time for ordering was observed by removing each generation of data. APY can be successfully applied to create the inverse of the genomic relationship matrix used in ssGREML for estimating variance components. To ensure reliable variance component estimation, it is important to use a core size that corresponds to the number of largest eigenvalues explaining around 98% of total variation in G. When APY is used, pedigrees can be truncated to increase the sparsity of H and slightly reduce computing time for ordering and symbolic factorization, with no impact on the estimates.

The estimation of variance components is computationally expensive under large-scale genetic evaluations due to several inversions of the coefficient matrix. Variance components are used as parameters for estimating breeding values in mixed model equations (MME). However, resulting breeding values are not Best Linear Unbiased Predictions (BLUP) unless the variance components approach the true parameters. The increasing availability of genomic data requires the development of new methods for improving the efficiency of variance component estimations. Therefore, this study aimed to reduce the costs of single-step genomic REML (ssGREML) with the Algorithm for Proven and Young (APY) for estimating variance components with truncated pedigree and phenotypes using simulated data. In addition, we investigated the influence of truncation on variance components and genetic parameter estimates. Under APY, the size of the core group influences the similarity of breeding values and their reliability compared to the full genomic matrix. In this study, we found that to ensure reliable variance component estimation, it is required to consider a core size that corresponds to the number of largest eigenvalues explaining around 98% of the total variation in G to avoid biased parameters. In terms of costs, the use of APY slightly decreased the time for ordering and symbolic factorization with no impact on estimations.

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Background: Huanglongbing (HLB, yellow shoot disease) is a highly destructive citrus disease associated with a nonculturable bacterium, "Candidatus Liberibacter asiaticus" (CLas), which is transmitted by Asian citrus psyllid (ACP, Diaphorina citri). In Mexico, HLB was first reported in Tizimin, Yucatán, in 2009 and is now endemic in 351 municipalities of 25 states. Understanding the population diversity of CLas is critical for HLB management. Current CLas diversity research is exclusively based on analysis of the bacterial genome, which composed two regions, chromosome (> 1,000 genes) and prophage (about 40 genes). Methods and results: In this study, 40 CLas-infected ACP samples from 20 states in Mexico were collected. CLas was detected and confirmed by PCR assays. A prophage gene(terL)-based typing system (TTS) divided the Mexican CLas strains into two groups: Term-G including four strains from Yucatán and Chiapas, as well as strain psy62 from Florida, USA, and Term-A included all other 36 Mexican strains, as well as strain AHCA1 from California, USA. CLas diversity was further evaluated to include all chromosomal and prophage genes assisted by using machine learning (ML) tools to resolve multidimensional data handling issues. A Term-G strain (YTMX) and a Term-A strain (BCSMX) were sequenced and analyzed. The two Mexican genome sequences along with the CLas genome sequences available in GenBank were studied. An unsupervised ML was implemented through principal component analysis (PCA) on average nucleotide identities (ANIs) of CLas whole genome sequences; And a supervised ML was implemented through sparse partial least squares discriminant analysis (sPLS-DA) on single nucleotide polymorphisms (SNPs) of coding genes of CLas guided by the TTS. Two CLas Geno-groups, Geno-group 1 that extended Term-A and Geno-group 2 that extended Term-G, were established. Conclusions: This study concluded that: 1) there were at least two different introductions of CLas into Mexico; 2) CLas strains between Mexico and USA are closely related; and 3) The two Geno-groups provide the basis for future CLas subspecies research.

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This work provides a guide to design ultrasonic synthetic aperture systems for non-grid two-dimensional sparse arrays such as spirals or annular segmented arrays. It presents an algorithm that identifies which elements have a more significant impact on the beampattern characteristics and uses this information to reduce the number of signals, the number of emitters and the number of parallel receiver channels involved in the beamforming process. Consequently, we can optimise the 3D synthetic aperture ultrasonic imaging system for a specific sparse array, reducing the computational cost, the hardware requirements and the system complexity. Simulations using a Fermat spiral array and experimental data based on an annular segmented array with 64 elements are used to assess this algorithm.

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Sudden Cardiac Death (SCD) is an unexpected sudden death due to a loss of heart function and represents more than 50% of the deaths from cardiovascular diseases. Since cardiovascular problems change the features in the electrical signal of the heart, if significant changes are found with respect to a reference signal (healthy), then it is possible to indicate in advance a possible SCD occurrence. This work proposes SCD identification using Electrocardiogram (ECG) signals and a sparse representation technique. Moreover, the use of fixed feature ranking is avoided by considering a dictionary as a flexible set of features where each sparse representation could be seen as a dynamic feature extraction process. In this way, the involved features may differ within the dictionary's margin of similarity, which is better-suited to the large number of variations that an ECG signal contains. The experiments were carried out using the ECG signals from the MIT/BIH-SCDH and the MIT/BIH-NSR databases. The results show that it is possible to achieve a detection 30 min before the SCD event occurs, reaching an an accuracy of 95.3% under the common scheme, and 80.5% under the proposed multi-class scheme, thus being suitable for detecting a SCD episode in advance.

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High-resolution 3D scanning devices produce high-density point clouds, which require a large capacity of storage and time-consuming processing algorithms. In order to reduce both needs, it is common to apply surface simplification algorithms as a preprocessing stage. The goal of point cloud simplification algorithms is to reduce the volume of data while preserving the most relevant features of the original point cloud. In this paper, we present a new point cloud feature-preserving simplification algorithm. We use a global approach to detect saliencies on a given point cloud. Our method estimates a feature vector for each point in the cloud. The components of the feature vector are the normal vector coordinates, the point coordinates, and the surface curvature at each point. Feature vectors are used as basis signals to carry out a dictionary learning process, producing a trained dictionary. We perform the corresponding sparse coding process to produce a sparse matrix. To detect the saliencies, the proposed method uses two measures, the first of which takes into account the quantity of nonzero elements in each column vector of the sparse matrix and the second the reconstruction error of each signal. These measures are then combined to produce the final saliency value for each point in the cloud. Next, we proceed with the simplification of the point cloud, guided by the detected saliency and using the saliency values of each point as a dynamic clusterization radius. We validate the proposed method by comparing it with a set of state-of-the-art methods, demonstrating the effectiveness of the simplification method.

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The applicability of the path planning strategy to robotic manipulators has been an exciting topic for researchers in the last few decades due to the large demand in the industrial sector and its enormous potential development for space, surgical, and pharmaceutical applications. The automation of high-degree-of-freedom (DOF) manipulator robots is a challenging task due to the high redundancy in the end-effector position. Additionally, in the presence of obstacles in the workspace, the task becomes even more complicated. Therefore, for decades, the most common method of integrating a manipulator in an industrial automated process has been the demonstration technique through human operator intervention. Although it is a simple strategy, some drawbacks must be considered: first, the path's success, length, and execution time depend on operator experience; second, for a structured environment with few objects, the planning task is easy. However, for most typical industrial applications, the environments contain many obstacles, which poses challenges for planning a collision-free trajectory. In this paper, a multiple-query method capable of obtaining collision-free paths for high DOF manipulators with multiple surrounding obstacles is presented. The proposed method is inspired by the resistive grid-based planner method (RGBPM). Furthermore, several improvements are implemented to solve complex planning problems that cannot be handled by the original formulation. The most important features of the proposed planner are as follows: (1) the easy implementation of robotic manipulators with multiple degrees of freedom, (2) the ability to handle dozens of obstacles in the environment, (3) compatibility with various obstacle representations using mathematical models, (4) a new recycling of a previous simulation strategy to convert the RGBPM into a multiple-query planner, and (5) the capacity to handle large sparse matrices representing the configuration space. A numerical simulation was carried out to validate the proposed planning method's effectiveness for manipulators with three, five, and six DOFs on environments with dozens of surrounding obstacles. The case study results show the applicability of the proposed novel strategy in quickly computing new collision-free paths using the first execution data. Each new query requires less than 0.2 s for a 3 DOF manipulator in a configuration space free-modeled by a 7291 × 7291 sparse matrix and less than 30 s for five and six DOF manipulators in a configuration space free-modeled by 313,958 × 313,958 and 204,087 × 204,087 sparse matrices, respectively. Finally, a simulation was conducted to validate the proposed multiple-query RGBPM planner's efficacy in finding feasible paths without collision using a six-DOF manipulator (KUKA LBR iiwa 14R820) in a complex environment with dozens of surrounding obstacles.

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Skin burns in color images must be accurately detected and classified according to burn degree in order to assist clinicians during diagnosis and early treatment. Especially in emergency cases in which clinical experience might not be available to conduct a thorough examination with high accuracy, an automated assessment may benefit patient outcomes. In this work, detection and classification of burnt areas are performed by using the sparse representation of feature vectors by over-redundant dictionaries. Feature vectors are extracted from image patches so that each patch is assigned to a class representing a burn degree. Using color and texture information as features, detection and classification achieved 95.65% sensitivity and 94.02% precision. Experiments used two methods to build dictionaries for burn severity classes to apply to observed skin regions: (1) direct collection of feature vectors from patches in various images and locations and (2) collection of feature vectors followed by dictionary learning accompanied by K-singular value decomposition.

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Purification of the density matrix methods should be employed when dealing with complex chemical systems containing many atoms. The running times for these methods scale linearly with the number of atoms if we consider the sparsity from the density matrix. Since the efficiency expected from those methods is closely tied to the underlying parallel implementations of the linear algebra operations (e.g., P2 = P × P), we proposed a central processing unit (CPU) and graphics processing unit (GPU) parallel matrix-matrix multiplication in SVBR (symmetrical variable block row) format for energy calculations through the SP2 algorithm. This algorithm was inserted in MOPAC's MOZYME method, using the original LMO Fock matrix assembly, and the atomic integral calculation implemented on it. Correctness and performance tests show that the implemented SP2 is accurate and fast, as the GPU is able to achieve speedups up to 40 times for a water cluster system with 42,312 orbitals running in one NVIDIA K40 GPU card compared to the single-threaded version. The GPU-accelerated SP2 algorithm using the MOZYME LMO framework enables the calculations of semiempirical wavefunction with stricter SCF criteria for localized charged molecular systems, as well as the single-point energies of molecules with more than 100.000 LMO orbitals in less than 1 h. Graphical abstract Parallel CPU and GPU purification algorithms for electronic structure calculations were implemented in MOPAC's MOZYME method. Some matrices in these calculations, e.g., electron density P, are compressed, and the developed linear algebra operations deal with non-zero entries only. We employed the NVIDIA/CUDA platform to develop GPU algorithms, and accelerations up to 40 times for larger systems were achieved.

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Denoising the point cloud is fundamental for reconstructing high quality surfaces with details in order to eliminate noise and outliers in the 3D scanning process. The challenges for a denoising algorithm are noise reduction and sharp features preservation. In this paper, we present a new model to reconstruct and smooth point clouds that combine L1-median filtering with sparse L1 regularization for both denoising the normal vectors and updating the position of the points to preserve sharp features in the point cloud. The L1-median filter is robust to outliers and noise compared to the mean. The L1 norm is a way to measure the sparsity of a solution, and applying an L1 optimization to the point cloud can measure the sparsity of sharp features, producing clean point set surfaces with sharp features. We optimize the L1 minimization problem by using the proximal gradient descent algorithm. Experimental results show that our approach is comparable to the state-of-the-art methods, as it filters out 3D models with a high level of noise, but keeps their geometric features.

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The training procedure of the minimal learning machine (MLM) requires the selection of two sets of patterns from the training dataset. These sets are called input reference points (IRP) and output reference points (ORP), which are used to build a mapping between the input geometric configurations and their corresponding outputs. In the original MLM, the number of input reference points is the hyper-parameter and the patterns are chosen at random. Therefore, the conventional proposal does not consider which patterns will belong to each reference point group, since the model does not implement an appropriate way of selecting the most suitable patterns as reference points. Such an approach can impact on the decision function in terms of smoothness, resulting in high complexity models. This paper introduces a new approach to select IRP for MLM applied to classification tasks. The optimally selected minimal learning machine (OS-MLM) relies on the multiresponse sparse regression (MRSR) ranking method and the leave-one-out (LOO) criterion to sort the patterns in terms of relevance and select an appropriate number of input reference points, respectively. The experimental assessment conducted on UCI datasets reports the proposal was able to produce sparser models and achieve competitive performance when compared to the regular strategy of selecting MLM input RPs.

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Remote identification of illegal plantations of Cannabis sativa Linnaeus is an important task for the Brazilian Federal Police. The current analytical methodology is expensive and strongly dependent on the expertise of the forensic investigator. A faster and cheaper methodology based on automatic methods can be useful for the detection and identification of Cannabis sativa L. in a reliable and objective manner. In this work, the high potential of Near Infrared Hyperspectral Imaging (HSI-NIR) combined with machine learning is demonstrated for supervised detection and classification of Cannabis sativa L. This plant, together with other plants commonly found in the surroundings of illegal plantations and soil, were directly collected from an illegal plantation. Due to the high correlation of the NIR spectra, sparse Principal Component Analysis (sPCA) was implemented to select the most important wavelengths for identifying Cannabis sativa L. One class Soft Independent Class Analogy model (SIMCA) was built, considering just the spectral variables selected by sPCA. Sensitivity and specificity values of 89.45% and 97.60% were, respectively, obtained for an external validation set subjected to the s-SIMCA. The results proved the reliability of a methodology based on NIR hyperspectral cameras to detect and identify Cannabis sativa L., with only four spectral bands, showing the potential of this methodology to be implemented in low-cost airborne devices.

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Magnetic Resonance (MR) Imaging is a diagnostic technique that produces noisy images, which must be filtered before processing to prevent diagnostic errors. However, filtering the noise while keeping fine details is a difficult task. This paper presents a method, based on sparse representations and singular value decomposition (SVD), for non-locally denoising MR images. The proposed method prevents blurring, artifacts, and residual noise. Our method is composed of three stages. The first stage divides the image into sub-volumes, to obtain its sparse representation, by using the KSVD algorithm. Then, the global influence of the dictionary atoms is computed to upgrade the dictionary and obtain a better reconstruction of the sub-volumes. In the second stage, based on the sparse representation, the noise-free sub-volume is estimated using a non-local approach and SVD. The noise-free voxel is reconstructed by aggregating the overlapped voxels according to the rarity of the sub-volumes it belongs, which is computed from the global influence of the atoms. The third stage repeats the process using a different sub-volume size for producing a new filtered image, which is averaged with the previously filtered images. The results provided show that our method outperforms several state-of-the-art methods in both simulated and real data.

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