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Fractals are ubiquitous in the natural world, and their connection with phase transitions has been widely observed. This study investigates mechanisms of fractal formation from the perspective of phase transitions. A novel set of probability calculation methods is introduced to establish a direct link between fractals and phase transitions. Notably, in the Ising model, a specific category of boundary lattice points undergoes a phase transition when the associated weight reaches ∼0.4. The identified correlation between phase transitions and fractals suggests the emergence of fractal structures at this critical weight. This paper offers supporting evidence for this conclusion through the deliberate manipulation of the proposed probability-based method. This research contributes to a deeper understanding of the interplay between fractals and phase transitions, providing valuable insights for further exploration in diverse scientific domains. [ABSTRACT FROM AUTHOR]

Wafer inspection is crucial for semiconductor manufacturing, as it identifies defects in wafers before manufacturing. Wafer defect detection avoids wasting time and production capacity, boosts productivity, and assures production quality. In this paper, we propose an ensemble learning-based method for wafer defect detection that fuses the classification results of four models, namely, ResNet, ResNeSt, ResNeSt + CBAM, and ResNeSt + Self-attention. During the integration phase, we employ a hybrid strategy that combines weighted averaging and voting to determine weight coefficients. Our analysis shows that the model's performance surpasses that of the arithmetic mean model within an interval of 0.8–1, according to our mathematical derivations. Furthermore, results demonstrate and substantiate that optimal performance is attained by setting the weighting value to 1. We experimentally validated the effectiveness of the proposed method on the WM-811k industrial dataset. In the experiments, the ensemble learning based method achieves an accuracy of 99.70%, which outperforms the individual model. Our approach outperforms the traditional arithmetic mean model by combining the strengths of all prediction models to improve prediction accuracy. Experimental results demonstrate that the proposed method has the potential to be an ideal option for wafer defect detection. [ABSTRACT FROM AUTHOR]

The present study delves into the examination of the stereoscopic cells and wavefront structures characterizing the propagation of three-dimensional detonation waves within square ducts. Leveraging numerical solutions derived from three-dimensional reactive Euler equations, incorporating an induction-exothermic reaction kinetic model, this work reveals the distinct classification of three modes of detonation waves based on the direction of propagation and the phase characteristics of transverse shock waves on the wavefront. This paper delineates the presence of two different types of phenomena: duct wall slapping waves due to shock–wall collisions and internal slapping waves resulting from shock interactions. Furthermore, this investigation exposes the existence of two distinct types of triple-wave lines on the wavefront: the first comprising a strong Mach disk, a weak Mach disk, and a transverse shock wave; the second characterized by a weak Mach disk, an incident shock wave, and a transverse shock wave. Notably, the pressure behind the first type of triple-wave line is observed to be the highest. It elucidates the transition from two- to three-dimensional detonation waves, revealing that the prevalence of transverse shock waves on the wavefront in the rectangular and diagonal modes is twofold and quadruple, respectively, when compared to their two-dimensional counterparts within identical ducts/channels. [ABSTRACT FROM AUTHOR]

Elementary cellular automata are the simplest form of cellular automata, studied extensively by Wolfram in the 1980s. He discovered complex behavior in some of these automata and developed a classification for all cellular automata based on their phenomenology. In this paper, we present an algorithm to classify them more effectively by measuring difference patterns using the Hamming distance. Our classification aligns with Wolfram's and further categorizes them into additional subclasses. Finally, we have found a heuristic reasoning providing and explanation about why some rules evolve into fractal patterns. [ABSTRACT FROM AUTHOR]

Hypernetwork is a useful way to depict multiple connections between nodes, making it an ideal tool for representing complex relationships in network science. In recent years, there has been a marked increase in studies on hypernetworks; however, the comparison of the difference between two hypernetworks has received less attention. This paper proposes a hyper-distance (HD)-based method for comparing hypernetworks. The method is based on higher-order information, i.e, the higher-order distance between nodes and Jensen–Shannon divergence. Experiments carried out on synthetic hypernetworks have shown that HD is capable of distinguishing between hypernetworks generated with different parameters, and it is successful in the classification of hypernetworks. Furthermore, HD outperforms current state-of-the-art baselines to distinguish empirical hypernetworks when hyperedges are randomly perturbed. [ABSTRACT FROM AUTHOR]

In this paper, we classify the orbits of the group SL(3,F)3 on the space F3 ⊗ F3 ⊗ F3 for F = C and F = R. This is known as the classification of complex and real three-qutrit states. We also give an overview of physical theories where these classifications are relevant. [ABSTRACT FROM AUTHOR]

We respond to the comment on 'Classification of Lie point symmetries for quadratic Liénard type equation ẍ + f(x)ẋ2 + g(x) = 0' [J. Math. Phys. 61, 044101 (2013)] by Iacono regarding linearizability and isochronicity. We assert here that the condition for linearization of the equation ẍ + f(x)ẋ2 + g(x) = 0 given by us in our paper is correct with the condition g 1 = ω 0 2 > 0. We present the explicit form of local and nonlocal transformations that transform the quadratic Liénard equation x ̈ + F + 1 1 − x x ̇ 2 + x (1 − x) (1 + D x) = 0 into the harmonic oscillator equation for the four cases mentioned in the comment and confirm the statements given in our paper are all valid. [ABSTRACT FROM AUTHOR]

In this paper, a class of non-weight modules over the topological N = 2 super-BMS3 algebra g are completely constructed. Assume that h ̄ = C L 0 ⊕ C P 0 ⊕ C G 0 ⊕ C Q 0 is the Cartan subalgebra of g and h = C L 0 ⊕ C P 0 is a two-dimensional subalgebra of h ̄ . These modules over g are free of rank 2 as modules of the subalgebra h. In fact, these modules are reducible. Moreover, we give a complete classification of free U (h) -modules of rank 2 over g. [ABSTRACT FROM AUTHOR]

The Lyapunov exponent method is generally used for classifying hyperchaotic, chaotic, and regular dynamics based on the equations modeling the system. However, several systems do not benefit from appropriate modeling underlying their dynamic behaviors. Therefore, having methods for classifying hyperchaotic, chaotic, and regular dynamics using only the observational data generated either by the theoretical or the experimental systems is crucial. In this paper, we use single nonlinear node delay-based reservoir computers to separate hyperchaotic, chaotic, and regular dynamics. We show that their classification capabilities are robust with an accuracy of up to 99.61% and 99.03% using the Mackey–Glass and the optoelectronic oscillator delay-based reservoir computers, respectively. Moreover, we demonstrate that the reservoir computers trained with the two-dimensional Hénon-logistic map can classify the dynamical state of another system (for instance, the two-dimensional sine-logistic modulation map). Our solution extends the state-of-the-art machine learning and deep learning approaches for chaos detection by introducing the detection of hyperchaotic signals. [ABSTRACT FROM AUTHOR]

Recently, a system of spintronic vortex oscillators has been experimentally trained to classify vowel sounds. In this paper, we have carried out a combination of device-level and system-level simulations to train a system of spin Hall nano oscillators (SHNOs) of smaller size (25X lower in area compared to those vortex oscillators) for such data classification tasks. Magnetic moments precess in an uniform mode as opposed to the vortex mode in our oscillators. We have trained our system to classify inputs in various popular machine learning data sets like Fisher's Iris data set of flowers, Wisconsin Breast Cancer (WBC) data set, and MNIST data set of handwritten digits. We have employed a new technique for input dimensionality reduction here so that the clustering/target synchronization pattern changes based on the nature of the data in the different data sets. Our demonstration of learning in a system of such small SHNOs for a wide range of data sets is promising for scaling up the oscillator-based neuromorphic system for complex data classification tasks. [ABSTRACT FROM AUTHOR]

Motivated by the string diagrammatic approach to undirected tracial quantum graphs by Musto et al. [J. Math. Phys. 59(8), 081706 (2018)], in the former part of this paper, we diagrammatically formulate directed nontracial quantum graphs by Brannan et al. [Commun. Math. Phys. 375(3), 1777 (2019)]. In the latter part, we supply a concrete classification of undirected reflexive quantum graphs on M2 and their quantum automorphism groups in both tracial and nontracial settings. We also obtain quantum isomorphisms between tracial quantum graphs on M2 and certain classical graphs, which reproves the monoidal equivalences between SO(3) and S 4 + and O(2) and H 2 + . [ABSTRACT FROM AUTHOR]

Adversarial attacks have been alerting the artificial intelligence community recently since many machine learning algorithms were found vulnerable to malicious attacks. This paper studies adversarial attacks on Broido and Clauset classification for scale-free networks to test its robustness in terms of statistical measures. In addition to the well-known random link rewiring (RLR) attack, two heuristic attacks are formulated and simulated: degree-addition-based link rewiring (DALR) and degree-interval-based link rewiring (DILR). These three strategies are applied to attack a number of strong scale-free networks of various sizes generated from the Barabási–Albert model and the uncorrelated configuration model. It is found that both DALR and DILR are more effective than RLR in the sense that rewiring a smaller number of links can succeed in the same attack. However, DILR is as concealed as RLR in the sense that they both are introducing a relatively small change on several typical structural properties, such as the average shortest path-length, the average clustering coefficient, the average diagonal distance, and the Kolmogorov–Smirnov test of the degree distribution. The results of this paper suggest that to classify a network to be scale-free, one has to be very careful from the viewpoint of adversarial attack effects. [ABSTRACT FROM AUTHOR]

When processing instrumental data by using classification approaches, the imbalanced dataset problem is usually challenging. As the minority class instances could be overwhelmed by the majority class instances, training a typical classifier with such a dataset directly might get poor results in classifying the minority class. We propose a cluster-based hybrid sampling approach CUSS (Cluster-based Under-sampling and SMOTE) for imbalanced dataset classification, which belongs to the type of data-level methods and is different from previously proposed hybrid methods. A new cluster-based under-sampling method is designed for CUSS, and a new strategy to set the expected instance number according to data distribution in the original training dataset is also proposed in this paper. The proposed method is compared with five other popular resampling methods on 15 datasets with different instance numbers and different imbalance ratios. The experimental results show that the CUSS method has good performance and outperforms other state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Non-intrusive load monitoring (NILM) is a technique that efficiently monitors appliances' operational status and energy consumption by utilizing voltage and current data, without intrusive measurements. In NILM, designing efficient classification models and building distinctive load features are crucial. However, due to its continuously variable load characteristics, multi-state load identification remains the most challenging problem in NILM. In this paper, we improve the encoding of the color V–I trajectory by incorporating instantaneous power, thereby enhancing the uniqueness of V–I trajectory features. Furthermore, we investigate a NILM method based on deep learning methods and propose a densely connected convolutional network with squeeze-and-excitation network (SE-DenseNet) architecture to solve the multi-state load identification problem. Initially, the architecture leverages DenseNet's dense connectivity property to generate a multitude of feature maps from the V–I trajectory. Then, SENet's channel attention mechanism is employed to enhance the utilization of effective features, which is more effective for multi-state load identification. Experimental results on the NILM public datasets PLAID and WHITED show that the recognition accuracy of the proposed method reaches 98.60% and 98.88%, respectively, which outperforms most existing methods. [ABSTRACT FROM AUTHOR]

The multiple signal classification (MUSIC) type method has been widely used to detect point-like scatterers embedded in a homogeneous background medium. This paper extends the MUSIC-type method to the detection of point-like scatterers that are embedded in an inhomogeneous background. Although the background Green’s function at each test point is not directly available in inhomogeneous background scenario, this paper proposes an approach, based on the finite element method, to simultaneously obtain the Green’s function at all test points. Numerical simulations illustrate the efficacy of the proposed theory and algorithm presented in this paper, and some interesting observations, which are absent in homogeneous background scenario, are highlighted and discussed. [ABSTRACT FROM AUTHOR]

This paper mainly focuses on the I/O cache of the server layer device of the network block device in the embedded background. It proposes a method focusing on different read/write loading features, configuring the cache capacity ratio utilized for isolated processing reading data and writing data, and an algorithm for automatically analyzing sequential addressing writing and random addressing writing data streams. The effectiveness of the algorithm for automatically analyzing sequential addressing writing and random addressing writing data streams is verified by experiments. The experimental results show that according to the different interleaving conditions of the data stream, the proportion of the data stream can be written in sequential addressing, which can be different in all input data streams. After separating sequential data streams interleaved by three inputs, the percentage of data streams written in sequential addressing is significantly increased by 50%. [ABSTRACT FROM AUTHOR]

In this paper, we introduce an extension of the image method for generating room impulse responses in a structure with more than a single confined space, namely, the structure image method (StIM). The proposed method, StIM, can efficiently generate a large number of environmental examples for a structure impulse response, which is required by current deep-learning methods for many tasks, while maintaining low computational complexity. We address the integration of the environment representation, produced by StIM, into the training process, and present a framework for training deep models. We demonstrate the usage of StIM when training an audio classification model and testing with real recordings acquired by accessible day-to-day devices. StIM shows promising results for indoors audio classification, where the target sound source is not located in the same room as the microphones. StIM enables large scale simulations of multi-room acoustics with low computational complexity which is mostly beneficial for training of deep learning networks. [ABSTRACT FROM AUTHOR]

The Hindmarsh–Rose neural model is widely accepted as an important prototype for fold/hom and fold/Hopf burstings. In this paper, we are interested in the mechanisms for the production of extra spikes in a burst, and we show the whole parametric panorama in an unified way. In the fold/hom case, two types are distinguished: a continuous one, where the bursting periodic orbit goes through bifurcations but persists along the whole process and a discontinuous one, where the transition is abrupt and happens after a sequence of chaotic events. In the former case, we speak about canard-induced spike-adding and in the second one, about chaos-induced spike-adding. For fold/Hopf bursting, a single (and continuous) mechanism is distinguished. Separately, all these mechanisms are presented, to some extent, in the literature. However, our full perspective allows us to construct a spike-adding map and, more significantly, to understand the dynamics exhibited when borders are crossed, that is, transitions between types of processes, a crucial point not previously studied. [ABSTRACT FROM AUTHOR]

In order to study a large number of generalized Bell states (GBSs) efficiently, it is important to classify them by local unitary (LU) equivalence. For example, there are C 25 4 (= 12 650) sets of four GBSs in C 5 ⊗ C 5 , which greatly exceed the C 16 4 (= 1820) sets of four GBSs in C 4 ⊗ C 4 , and it is inconceivable to explore these sets directly without prior classification. In this paper, we consider the classification of GBS sets in C 5 ⊗ C 5 . First, two simple and useful characterizations of LU-equivalence of GBS sets are given. Then, one characterization is used to divide all 12 650 sets of four GBSs into eight equivalence classes including six locally distinguishable classes and two classes that cannot be discriminated by one-way local operations and classical communication. The second characterization is powerful and can be used to write a program, by using which all C 25 5 (= 53 130) sets of five GBSs in C 5 ⊗ C 5 are divided into 21 equivalence classes including 9 locally distinguishable classes and 12 locally indistinguishable classes. [ABSTRACT FROM AUTHOR]

In this paper, we consider the nonlinear equation arising from the Chern–Simons theory of planar matter fields interacting with the Chern–Simons gauge field in a CP(1) invariant fashion. Then, we establish the sharp region of flux for non-topological solutions and prove the classification of solutions of all types in the case of one vortex point. Moreover, we also give the complete result of Theorem 1.3 in the work by Choe et al. [J. Differ. Equations, 255, 2136 (2013)] from Theorem 1.4(ii) as follows. [ABSTRACT FROM AUTHOR]

Classifying foliage targets using echolocation is important for recognizing landmarks by bats using ultrasonic emissions and blind human echolocators (BEs) using palatal clicks. Previous attempts to classify foliage used ultrasonic frequencies and single sensor (monaural) detection. Motivated by the echolocation capabilities of BEs, a biomimetic sonar emitting audible clicks acquired 5600 binaural echoes from five sequential emissions that probed two foliage targets at aspect angles separated by 18·. Echo spectrograms formed feature vector inputs to artificial neural networks (ANNs) for classifying two targets, Ficus benjamina and Schefflera arboricola, with leaf areas that differ by a factor of four. Classification performances of ANNs without and with hidden layers were analyzed using tenfold cross-validation. Performance improved with input feature size, with binaural echo classification outperforming that using monaural echoes for the same number of emissions and for the same number of echoes. Linear classification accuracy was comparable to that using nonlinear classification with both achieving fewer than 1% errors with binaural spectrogram features from five sequential emissions. This result was better by a factor of 20 compared to previous classification of these targets using only the time envelopes of the same echoes. [ABSTRACT FROM AUTHOR]

In this paper, we use machine learning strategies aiming to predict chaotic time series obtained from the Lorenz system. Such strategies prove to be successful in predicting the evolution of dynamical variables over a short period of time. Transitions between the regimes and their duration can be predicted with great accuracy by means of counting and classification strategies, for which we train multi-layer perceptron ensembles. Even for the longest regimes the occurrences and duration can be predicted. We also show the use of an echo state network to generate data of the time series with an accuracy of up to a few hundreds time steps. The ability of the classification technique to predict the regime duration of more than 11 oscillations corresponds to around 10 Lyapunov times. [ABSTRACT FROM AUTHOR]

Accurate and explainable artificial-intelligence (AI) models are promising tools for accelerating the discovery of new materials. Recently, symbolic regression has become an increasingly popular tool for explainable AI because it yields models that are relatively simple analytical descriptions of target properties. Due to its deterministic nature, the sure-independence screening and sparsifying operator (SISSO) method is a particularly promising approach for this application. Here, we describe the new advancements of the SISSO algorithm, as implemented into SISSO++, a C++ code with Python bindings. We introduce a new representation of the mathematical expressions found by SISSO. This is a first step toward introducing "grammar" rules into the feature creation step. Importantly, by introducing a controlled nonlinear optimization to the feature creation step, we expand the range of possible descriptors found by the methodology. Finally, we introduce refinements to the solver algorithms for both regression and classification, which drastically increase the reliability and efficiency of SISSO. For all these improvements to the basic SISSO algorithm, we not only illustrate their potential impact but also fully detail how they operate both mathematically and computationally. [ABSTRACT FROM AUTHOR]

Feature learning for music applications has recently received considerable attention from many researchers. This paper reports on the sparse feature learning algorithm for musical instrument identification, and in particular, focuses on the effects of the frame sampling techniques for dictionary learning and the pooling methods for feature aggregation. To this end, two frame sampling techniques are examined that are fixed and proportional random sampling. Furthermore, the effect of using onset frame was analyzed for both of proposed sampling methods. Regarding summarization of the feature activation, a standard deviation pooling method is used and compared with the commonly used max- and average-pooling techniques. Using more than 47 000 recordings of 24 instruments from various performers, playing styles, and dynamics, a number of tuning parameters are experimented including the analysis frame size, the dictionary size, and the type of frequency scaling as well as the different sampling and pooling methods. The results show that the combination of proportional sampling and standard deviation pooling achieve the best overall performance of 95.62% while the optimal parameter set varies among the instrument classes. [ABSTRACT FROM AUTHOR]

This paper aims to present an improved bicoherence spectrum (IBS) combined with cyclic modulation spectrum (CMS) and cross-correlation that is suitable for classification of hydrophone signals involving deep learning (DL). First, the proposed feature utilizes the all-phase fast Fourier transform to modify the spectrum leakage caused by CMS; this can be used to detect line spectra with low signal-to-noise ratios (SNRs). Second, the cross-correlation and bispectrum are both exploited to suppress non-periodic line spectra interference from CMS. Based on numerous numerical simulations and experimental verification, compared with CMS and conventional bispectrum, the prominent characteristics of IBS include: detecting higher-precision periodic harmonics without single-line interference, superior robustness under low SNR, and greatly reducing the data redundancy. In addition, to test the performance of IBS for DL application, three deep belief network (DBN)-based classifiers—DBN-softmax, DBN-support vector machine, and DBN-random forest—are introduced and employed for five experimental scenarios (including ships and underwater source). The results indicate that benefiting from DBN pre-training, the IBS classification accuracy of DBN-based models is generally higher than 80%. [ABSTRACT FROM AUTHOR]

Major hysteresis loops of the F/NM/F/AF structure are classified according to the magnetization process, with the assumption of coherent rotation for each F component and antiferromagnetic coupling between the two F layers. Magnetic stable states of the system as well as specific reversal modes of magnetization during each stage of the major hysteresis cycle are studied in detail based on energetics analysis, in the whole range of exchange bias field and interlayer antiferromagnetic coupling strength. The analysis shows 12 different types of major hysteresis loops for this system and is confirmed by simulation. Strategies to determine key material parameters for the F/NM/F/AF structure from major hysteresis loops are proposed and illustrated by numerical simulation. The research shows a subtle tuning of the magnetization process in the F/NM/F/AF structure, collectively by exchange biasing and interlayer antiferromagnetic coupling. Practically, this serves as a theoretical grounding for the identification of root causes of failure in the product analysis of GMR (giant magnetoresistance) sensors. [ABSTRACT FROM AUTHOR]

Classifying reliably active and inactive molecular conformations of wildtype (WT) and mutated oncogenic proteins is a key, ongoing challenge in molecular cancer studies. Here, we probe the GTP-bound K-Ras4B conformational dynamics using long-time atomistic molecular dynamics (MD) simulations. We extract and analyze the detailed underlying free energy landscape of WT K-Ras4B. We use two key reaction coordinates, labeled d1 and d2 (i.e., distances coordinating the Pβ atom of the GTP ligand with two key residues, T35 and G60), shown to correlate closely with activities of WT and mutated K-Ras4B. However, our new K-Ras4B conformational kinetics study reveals a more complex network of equilibrium Markovian states. We show that a new reaction coordinate is required to account for the orientation of acidic K-Ras4B sidechains such as D38 with respect to the interface with binding effector RAF1 and rationalize the activation/inactivation propensities and the corresponding molecular binding mechanisms. We use this understanding to unveil how a relatively conservative mutation (i.e., D33E, in the switch I region) can lead to significantly different activation propensities compared with WT K-Ras4B. Our study sheds new light on the ability of residues near the K-Ras4B—RAF1 interface to modulate the network of salt bridges at the binding interface with the RAF1 downstream effector and, thus, to influence the underlying GTP-dependent activation/inactivation mechanism. Altogether, our hybrid MD-docking modeling approach enables the development of new in silico methods for quantitative assessment of activation propensity changes (e.g., due to mutations or local binding environment). It also unveils the underlying molecular mechanisms and facilitates the rational design of new cancer drugs. [ABSTRACT FROM AUTHOR]

This contribution presents sediment classification results derived from different sources of data collected at the Dordtse Kil river, the Netherlands. The first source is a multi-beam echo-sounder (MBES). The second source is measurements taken with a gamma-ray scintillation detector, i.e., the Multi-Element Detection System for Underwater Sediment Activity (Medusa), towed over the sediments and measuring sediment natural radioactivity. Two analysis methods are employed for sediment classification based on the MBES data. The first is a Bayesian estimation method that uses the average backscatter data per beam and, therefore, is independent of the quality of the MBES calibration. The second is a model-based method that matches the measured backscatter curves to theoretical curves, predicted by a physics-based model. Medusa provides estimates for the concentrations of potassium, uranium, thorium, and cesium, known to be indicative for sediment properties, viz. mean grain size, silt content, and the presence of organic matter. In addition, a hydrophone attached to the Medusa system provides information regarding the sediment roughness. This paper presents an inter-comparison between the sediment classification results using the above-mentioned methods. It is shown that although originating from completely different sources, the MBES and Medusa provide similar information, revealing the same sediment distribution. [ABSTRACT FROM AUTHOR]

Preliminary group classification became a prominent tool in the symmetry analysis of differential equations due to the paper by Ibragimov, Torrisi, and Valenti [J. Math. Phys. 32, 2988-2995 (1991)]. In this paper the partial preliminary group classification of a class of nonlinear wave equations was carried out via the classification of one-dimensional Lie symmetry extensions related to a fixed finite-dimensional subalgebra of the infinite-dimensional equivalence algebra of the class under consideration. In the present paper we implement the complete group classification of the same class up to both usual and general point equivalence using the algebraic method of group classification. This includes the complete preliminary group classification of the class and finding those Lie symmetry extensions which are not associated with subalgebras of the equivalence algebra. The complete preliminary group classification is based on listing all inequivalent subalgebras of the whole infinite-dimensional equivalence algebra whose projections are qualified as maximal extensions of the kernel algebra. The set of admissible point transformations of the class is exhaustively described in terms of the partition of the class into normalized subclasses. [ABSTRACT FROM AUTHOR]

Linear and nonlinear waves in anisotropic media are useful in investigating complex materials in physics, biomechanics, biomedical acoustics, etc. The present paper is devoted to investigation of symmetries and conservation laws for nonlinear anisotropic wave equations with specific external sources when the equations in question are nonlinearly self-adjoint. These equations involve two arbitrary functions. Construction of conservation laws associated with symmetries is based on the generalized conservation theorem for nonlinearly self-adjoint partial differential equations. First we calculate the conservation laws for the basic equation without any restrictions on the arbitrary functions. Then we make the group classification of the basic equation in order to specify all possible values of the arbitrary functions when the equation has additional symmetries and construct the additional conservation laws. [ABSTRACT FROM AUTHOR]

In this paper, the Lie group method is developed to study a class of time fractional evolution systems. As an application, the complete group classification of a system of two component fractional evolution equations with an arbitrary function is performed. The admitted symmetries of all inequivalent systems belonging to the class under study are determined. What is more, all reduced fractional systems of ordinary differential equations and even explicit exact solutions are presented. [ABSTRACT FROM AUTHOR]

In this paper, we focus on (n+3)-dimensional metric n-Lie algebras. To begin with, we give some properties on (n+3)-dimensional n-Lie algebras. Then based on the properties, we obtain the classification of (n+3)-dimensional metric n-Lie algebras. [ABSTRACT FROM AUTHOR]

In dispersive propagation, waves from the same source will generally differ depending on how far they have traveled. Accordingly, it is desirable for classification in such environments to either account for propagation effects, or to obtain features that are invariant to such effects. The latter approach is taken in this paper, and features are derived that are unaffected by channel dispersion, per mode. A “local” view of pulse propagation in time-frequency phase space is considered. It is shown that the local duration of a wave, obtained from its time-frequency Wigner distribution, is invariant to dispersion. While higher moments of the Wigner distribution are not invariant to dispersion, the phase space considerations suggest an approach for defining “dispersion-invariant moments” (DIMs) of any order. This approach is also used to define a dispersion-invariant correlation coefficient that can be used for classification. The classification utility of the DIMs, and of the dispersion-invariant correlation coefficient, is evaluated via simulations of acoustic scattering from steel shells in a dispersive channel model (Pekeris waveguide). Receiver operating characteristic curves quantify the improved discriminability of the DIMs versus ordinary temporal moments, and of the dispersion-invariant correlation coefficient versus the ordinary correlation coefficient. [ABSTRACT FROM AUTHOR]

In the five-decade search for efficient photocatalysts to convert natural sunlight into hydrogen via photoelectrochemical (PEC) dissociation of water, the underlying physics and chemistry of PEC processes taking place at metal-oxide photocatalysts remains relatively poorly understood and is an active area of research by both theorists and experimentalists. This is surely the case for water structuring at metal-oxide surfaces, including their "self-ordering." In this work, we apply classical molecular-dynamics techniques to investigate and classify the structure and ordering of water layers at two TiO2 surfaces—anatase ⟨101⟩ and rutile ⟨110⟩. We are interested in identifying and classifying layers using local order parameters to distinguish the layered-water superstructure from bulk-like water configurations as observed in liquid water and common ice polymorphs. In particular, we look for the formation of regions with reduced molecular mobility and assess whether they are "ice-like," as has been proposed in recent interpretations in the literature, or, instead, how these interfacial-water structures might be otherwise described. We leverage quantitative and order-parameter analysis techniques to categorize the structural properties of layers of water molecules formed and compare them to both cubic and hexagonal polytypes of bulk ice I, as well as bulk liquid water. In doing so, we propose a general structural recognition/classification framework suitable for identifying and describing molecules at any condensed-state-water interface. [ABSTRACT FROM AUTHOR]

To improve the qualitative accuracy of foreign protein adulteration in milk powder, a novel method named multidimensional spectral information laser-induced breakdown spectroscopy (MSI-LIBS) was proposed, which fully mined the effective information in the spectra by integrating the absolute intensity, the first derivative spectra, and the ratio spectra. Compared with traditional LIBS, the performance of the models based on MSI-LIBS was significantly improved. The accuracy of the cross-validation set of support vector machine, k-nearest neighbor, and random subspace method-linear discriminant analysis models increased from 80.98%, 75.61%, and 79.25% to 85.17%, 79.32%, and 81.18%, respectively. The accuracy of the prediction set increased from 81.50%, 76.03%, and 79.07% to 85.82%, 79.74%, and 81.28%, respectively. Furthermore, the visualization results of t-distributed stochastic neighbor embedding also showed that there was a more obvious boundary between the spectra of different samples based on MSI-LIBS. Therefore, these results fully prove the effectiveness of MSI-LIBS in improving the performance of LIBS classification. [ABSTRACT FROM AUTHOR]

We investigate non-homogeneous Hamiltonian operators composed of a first order Dubrovin–Novikov operator and an ultralocal one. The study of such operators turns out to be fundamental for the inverted system of equations associated with a class of Hamiltonian scalar equations. Often, the involved operators are degenerate in the first order term. For this reason, a complete classification of the operators with a degenerate leading coefficient in systems with two and three components is presented. [ABSTRACT FROM AUTHOR]

We classify finite irreducible modules over the conformal superalgebra K 4 ′ by their correspondence with finite conformal modules over the associated annihilation superalgebra A ( K 4 ′ ). This is achieved by a complete classification of singular vectors in generalized Verma modules for A ( K 4 ′ ). We also show that morphisms between generalized Verma modules can be arranged in infinitely many bilateral complexes. [ABSTRACT FROM AUTHOR]

Deep learning is one established tool for carrying out classification tasks on complex, multi-dimensional data. Since audio recordings contain a frequency and temporal component, long-term monitoring of bioacoustics recordings is made more feasible with these computational frameworks. Unfortunately, these neural networks are rarely designed for the task of open set classification in which examples belonging to the training classes must not only be correctly classified but also crucially separated from any spurious or unknown classes. To combat this reliance on closed set classifiers which are singularly inappropriate for monitoring applications in which many non-relevant sounds are likely to be encountered, the performance of several open set classification frameworks is compared on environmental audio datasets recorded and published within this work, containing both biological and anthropogenic sounds. The inference-based open set classification techniques include prediction score thresholding, distance-based thresholding, and OpenMax. Each open set classification technique is evaluated under multi-, single-, and cross-corpus scenarios for two different types of unknown data, configured to highlight common challenges inherent to real-world classification tasks. The performance of each method is highly dependent upon the degree of similarity between the training, testing, and unknown domain. [ABSTRACT FROM AUTHOR]

This study investigates the characteristics of flow-field patterns generated by burst-mode actuation of a dielectric-barrier-discharge plasma actuator in quiescent air. Particle-image velocimetry and background-oriented schlieren measurements conducted over a wide range of burst-signal parameters show that there are three types of flow-field patterns. Type 1 is the wall-surface jet seen in continuous mode actuation; type 2 features periodical independent vortices traveling along the wall surface; type 3 features such vortices moving away from the surface. The vortex sizes in types 2 and 3 are proportional to the energy consumed in generating one vortex. When the time-averaged jet velocity estimated by the power consumption is used as the characteristic velocity in the nondimensional scaling law, the time profiles of the vortex location in the type 3 flow-field pattern collapse into a single line, independently of the burst frequency and ratio. However, in the initial phase, the nondimensional vortex-core motion is better described using the jet velocity in continuous-mode actuation as the characteristic velocity. The transitions of the flow-field pattern from type 1 to type 3 result from interference between cyclically generated vortices and depend on the inter-vortex distances and the energy consumed in generating one vortex. [ABSTRACT FROM AUTHOR]

In the framework of general relativistic classical mechanics on a spacetime with absolute time, we classify the infinitesimal symmetries of the classical structure by means of distinguished Lie subalgebras of the Lie algebra of “special phase function.” These subalgebras are crucial also for the classification of infinitesimal quantum symmetries, which will be analyzed in a forthcoming paper. [ABSTRACT FROM AUTHOR]

The “chick-a-dee” call of the black-capped chickadee (Poecile atricapillus) contains four note types, A, B, C, and D that have important functional roles. This provides strong motivation for studying the classification of acoustic components of the call into different note types. In this paper, the spectrograms from a sample of A, B, and C notes (370 in total) were each described as a set of 9 summary features. An artificial neural network was trained to identify note type on the basis of these features, and was able to obtain better than 98% accuracy. An internal analysis of this network revealed a distributed code in which different hidden units generated high activities to different subsets of notes. By combining these different sensitivities, the network could discriminate all three types of notes. The performance of this network was compared to a discriminant analysis of the same data. This analysis also achieved a high level of performance (95%). A comparison between the two approaches revealed some striking similarities, but also some intriguing differences. These results are discussed in terms of two related issues: developing a research tool for note classification, and developing a theory of how birds themselves might classify notes. [ABSTRACT FROM AUTHOR]

We study solutions to Nahm's equations with continuous symmetries, and under certain (mild) hypotheses, we classify the corresponding Ansätze. Using our classification, we construct novel Nahm data and prescribe methods for generating further solutions. Finally, we use these results to construct new BPS monopoles with spherical symmetry. [ABSTRACT FROM AUTHOR]

The millimeterwave radar has made possible high resolution tracking, activity classification, and vital signs detection, at higher precisions than is possible with most other wireless approaches. However, detecting multiple moving targets is a challenge, as dynamic scene with a lot of motion leads to clutter and noise, which interfere with the responses of targets of interest. We present a digital beamforming approach using the MIMO radar, with a range resolution of 6.4 cm and a Doppler resolution of 0.18 m/s, which reduces interference between closely neighboring targets. Thus, measurements of individual target micro-Doppler signatures are possible, even in the presence of multiple other moving targets, and the signatures are, thereby, used to train a Deep Neural Network (DNN) for activity classification. The DNN has been applied to recognize six exercise-based classes, correctly predicting with over 95% classification accuracy for all classes, but that is extendable to fall detection and other activities. [ABSTRACT FROM AUTHOR]

We study invertible states of 1D bosonic quantum lattice systems. We show that every invertible 1D state is in a trivial phase: after tensoring with some unentangled ancillas, it can be disentangled by a fuzzy analog of a finite-depth quantum circuit. If an invertible state has symmetries, it may be impossible to disentangle it in a way that preserves the symmetries, even after adding unentagled ancillas. We show that in the case of a finite unitary symmetry G, the only obstruction is an index valued in degree-2 cohomology of G. We show that two invertible G-invariant states are in the same phase if and only if their indices coincide. [ABSTRACT FROM AUTHOR]

We investigate representations of the Z 2 2 -graded extension of osp(1|2), which is the spectrum generating algebra of the recently introduced Z 2 2 -graded version of superconformal mechanics. The main result is a classification of irreducible lowest weight modules of the Z 2 2 -graded extension of osp(1|2). This is done via the introduction of Verma modules and its maximal invariant submodule generated by singular vectors. Explicit formulas of all singular vectors are also presented. [ABSTRACT FROM AUTHOR]

This study proposes a sound classification model for natural disasters. Deep learning techniques, a convolutional neural network (CNN) and long short-term memory (LSTM), were used to train two individual classifiers. The study was conducted using a dataset acquired online1 and truncated at 0.1 s to obtain a total of 12 937 sound segments. The result indicated that acoustic signals are effective for classifying natural disasters using machine learning techniques. The classifiers serve as an alternative effective approach to disaster classification. The CNN model obtained a classification accuracy of 99.96%, whereas the LSTM obtained an accuracy of 99.90%. The misclassification rates obtained in this study for the CNN and LSTM classifiers (i.e., 0.4% and 0.1%, respectively) suggest less classification errors when compared to existing studies. Future studies may investigate how to implement such classifiers for the early detection of natural disasters in real time. [ABSTRACT FROM AUTHOR]

Passive acoustic monitoring (PAM) is a useful technique for monitoring marine mammals. However, the quantity of data collected through PAM systems makes automated algorithms for detecting and classifying sounds essential. Deep learning algorithms have shown great promise in recent years, but their performance is limited by the lack of sufficient amounts of annotated data for training the algorithms. This work investigates the benefit of augmenting training datasets with synthetically generated samples when training a deep neural network for the classification of North Atlantic right whale (Eubalaena glacialis) upcalls. We apply two recently proposed augmentation techniques, SpecAugment and Mixup, and show that they improve the performance of our model considerably. The precision is increased from 86% to 90%, while the recall is increased from 88% to 93%. Finally, we demonstrate that these two methods yield a significant improvement in performance in a scenario of data scarcity, where few training samples are available. This demonstrates that data augmentation can reduce the annotation effort required to achieve a desirable performance threshold. [ABSTRACT FROM AUTHOR]

We prove that on any two-dimensional lattice of qudits of a prime dimension, every translation invariant Pauli stabilizer group with local generators and with the code distance being the linear system size is decomposed by a local Clifford circuit of constant depth into a finite number of copies of the toric code stabilizer group (Abelian discrete gauge theory). This means that under local Clifford circuits, the number of toric code copies is the complete invariant of topological Pauli stabilizer codes. Previously, the same conclusion was obtained under the assumption of nonchirality for qubit codes or the Calderbank–Shor–Steane structure for prime qudit codes; we do not assume any of these. [ABSTRACT FROM AUTHOR]

The symmetry classifications of two fractional higher dimensional nonlinear systems, namely, (3 + 1)-dimensional incompressible non-hydrostatic Boussinesq equations and (3 + 1)-dimensional Boussinesq equations with viscosity, are discussed. Both the fractional Boussinesq equations are considered to have derivatives with respect to all variables of fractional type, and some exact solutions are reported along with graphical illustrations. [ABSTRACT FROM AUTHOR]

The magnetization evolution of the free layer in an orthogonal spin torque device is studied based on a macrospin model. The trajectory of the magnetization vector under various conditions has shown rich nonlinear properties. The phase diagram is obtained in the parameter spaces of current density and the polarization distribution (the ratio of polarization of in-plane to out-of-plane layers), where two critical currents and three phases are found. These dynamic phases can be classified according to their nonlinear behaviors, which are different in terms of limit cycles and limit points. The classification is meaningful to design ultra-fast spin torque devices under different dynamic conditions toward various applications, such as in memory and oscillators. [ABSTRACT FROM AUTHOR]