Characterization of Quantum and Classical Critical Points for an Integrable Two-Qubit Spin–Boson Model

Communications in Nonlinear Science and Numerical Simulation

Noisy and ac forcing can cooperatively lead to the emergence of sine-Gordon breathers robust to dissipation. This phenomenon is studied, for both Neumann and periodic boundary conditions, at different values of the main system parameters, such as the noise intensity and the ac frequency-amplitude pair. In all the considered cases, nonmonotonicities of the probability of generating only breathers versus the noise strength are observed, implying that optimal noise ranges for the breather formation process exist. Within the latter scenarios, the statistics of the breathers’ number, position, and amplitude are analyzed. The number of breathers is found to grow, on average, with the noise amplitude. The breathers’ spatial distribution is sharply peaked at the system’s edges for Neumann boundary conditions, whereas it is essentially uniform for periodic boundary conditions. The average breather amplitude is dictated by …

arXiv preprint arXiv:2404.04275

In the recent work "Non-reciprocal topological solitons in active metamaterials" (see arXiv:2312.03544v1), for an analytical understanding of the system under consideration, the authors derive an ordinary differential equation for the sine-Gordon (anti)soliton velocity, with the perturbation theory in the adiabatic approximation, via the inverse scattering transform formalism, see Eq. (3) in their work. Here we note that the latter equation for the (anti)soliton velocity also follows from an energy balance approach.

arXiv preprint arXiv:2402.10275

We present a general framework to tackle quantum optics problems with giant atoms, i.e. quantum emitters each coupled {\it non-locally} to a structured photonic bath (typically a lattice) of any dimension. The theory encompasses the calculation and general properties of Green's functions, atom-photon bound states (BSs), collective master equations and decoherence-free Hamiltonians (DFHs), and is underpinned by a formalism where a giant atom is formally viewed as a normal atom lying at a fictitious location. As a major application, we provide for the first time a general criterion to predict/engineer DFHs of giant atoms, which can be applied both in and out of the photonic continuum and regardless of the structure or dimensionality of the photonic bath. This is used to show novel DFHs in 2D baths such as a square lattice and photonic graphene.

arXiv preprint arXiv:2302.10132

Measurement-induced phase transition arises from the competition between a deterministic quantum evolution and a repeated measurement process. We explore the measurement-induced phase transition through the Quantum Fisher Information in two different metrological scenarios. We demonstrate through the scaling behavior of the quantum Fisher information the transition of the multi-partite entanglement across the phases. In analogy with standard quantum phase transition, we reveal signature of a measurement-induced phase transition in the non-analytic behaviour of the quantum Fisher information as the measurement strength approaches the critical value. Our results offer novel insights into the features of a quantum systems undergoing measurement-induced phase transition and indicate potential avenues for further exploration in the field of quantum physics.

Nature

In the version of this article initially published, CMS Collaboration author names, affiliations and acknowledgements were omitted and have now been included in the HTML and PDF versions of the article.

Chaos, Solitons & Fractals

Despite the observation of cyclic and chaotic dynamics in nature, it is still not clear whether this behaviour is inherent to ecological systems or caused by external forcings. Here we explored a set of approximately 210,000 simulations to assess how often a model of realistic complexity exhibits non-stationary dynamics when external perturbations are excluded. Remarkably, less than one third of the population shown non-stationary dynamics and, even when present, fluctuations were rather small. The inherent stability of plankton communities showed to be related to the presence of multiple feedbacks in the food web structure, omnivory, low centre of gravity, and supports the conclusion that food webs of realistic complexity rarely exhibit significant endogenous non-stationary dynamics. Finally, we computed Lyapunov exponents for the non-stationary trajectories, in order to assess in which proportion they were …

Entropy

The study of the human psyche has elucidated a bipartite structure of logic reflecting the quantum–classical nature of the world. Accordingly, we posited an approach toward studying the brain by means of the quantum–classical dynamics of a mixed Weyl symbol. The mixed Weyl symbol can be used to describe brain processes at the microscopic level and, when averaged over an appropriate ensemble, can provide a link to the results of measurements made at the meso and macro scale. Within this approach, quantum variables (such as, for example, nuclear and electron spins, dipole momenta of particles or molecules, tunneling degrees of freedom, and so on) can be represented by spinors, whereas the electromagnetic fields and phonon modes can be treated either classically or semi-classically in phase space by also considering quantum zero-point fluctuations. Quantum zero-point effects can be incorporated into numerical simulations by controlling the temperature of each field mode via coupling to a dedicated Nosé–Hoover chain thermostat. The temperature of each thermostat was chosen in order to reproduce quantum statistics in the canonical ensemble. In this first paper, we introduce a general quantum–classical Hamiltonian model that can be tailored to study physical processes at the interface between the quantum and the classical world in the brain. While the approach is discussed in detail, numerical calculations are not reported in the present paper, but they are planned for future work. Our theory of brain dynamics subsumes some compatible aspects of three well-known quantum approaches to brain dynamics, namely the …

Chaos, Solitons & Fractals

The dynamics of sine-Gordon breathers is studied in the presence of dissipative and stochastic perturbations. Taking a stationary breather with a random phase value as the initial state, the simulations demonstrate that a spatially-homogeneous noisy source can make the oscillatory excitation more stable, i.e., it enables the latter to last significantly longer than it would in a noise-free scenario. Both the frequency domain and the localization of energy are examined to illustrate the effectiveness of the noise-enhanced stability phenomenon, which manifests itself as a nonmonotonic behavior of the mean first-passage time for the breather as a function of the noise intensity. The influence of the mode’s initial frequency on the results and their robustness against an additional thermal background are also addressed. Overall, the analysis highlights a counter-intuitive, positive role of noise in the breather’s persistence.

European Physical Journal C

In Fig. 3, the y axis titles were mistakenly written showing a single-differential cross section in either dimuon pT or rapidity, when in fact the cross section is normalized by both the pT and rapidity ranges used for a given measurement point. The corrected version is shown in the new Fig. 3 provided below.

Nature physics

Protons consist of three valence quarks, two up-quarks and one down-quark, held together by gluons and a sea of quark-antiquark pairs. Collectively, quarks and gluons are referred to as partons. In a proton-proton collision, typically only one parton of each proton undergoes a hard scattering – referred to as single-parton scattering – leaving the remainder of each proton only slightly disturbed. Here, we report the study of double- and triple-parton scatterings through the simultaneous production of three J/ψ mesons, which consist of a charm quark-antiquark pair, in proton-proton collisions recorded with the CMS experiment at the Large Hadron Collider. We observed this process – reconstructed through the decays of J/ψ mesons into pairs of oppositely charged muons – with a statistical significance above five standard deviations. We measured the inclusive fiducial cross-section to be , and …

Journal of High Energy Physics

A search for supersymmetry is presented in events with a single charged lepton, electron or muon, and multiple hadronic jets. The data correspond to an integrated luminosity of 138 fb− 1 of proton-proton collisions at a center-of-mass energy of 13 TeV, recorded by the CMS experiment at the CERN LHC. The search targets gluino pair production, where the gluinos decay into final states with the lightest supersymmetric particle (LSP) and either a top quark-antiquark () pair, or a light-flavor quark-antiquark () pair and a virtual or on-shell W boson. The main backgrounds, pair and W+ jets production, are suppressed by requirements on the azimuthal angle between the momenta of the lepton and of its reconstructed parent W boson candidate, and by top quark and W boson identification based on a machine-learning technique. The number of observed events is consistent with the expectations from standard model …

Chaos, Solitons & Fractals

The model of two coupled quantum pendula is studied and its suitability to describe Josephson junctions interacting with axions is analysed. It is shown that some physical features of one pendulum, not directly accessible, can be deduced by local measures on the other one, which is experimentally available. Such an effect can be exploited for the axion (the invisible pendulum) detection based on Josephson junctions (the accessible pendulum). The interaction between axion and Josephson junction can be enhanced at the resonance, if the axion and the junction frequencies match, and if the accessible system is prepared in the most convenient initial quantum state.

The second-order () and third-order () Fourier coefficients describing the azimuthal anisotropy of prompt and nonprompt (from b-hadron decays) J/, as well as prompt (2S) mesons are measured in lead-lead collisions at a center-of-mass energy per nucleon pair of = 5.02 TeV. The analysis uses a data set corresponding to an integrated luminosity of 1.61 nb recorded with the CMS detector. The J/ and (2S) mesons are reconstructed using their dimuon decay channel. The and coefficients are extracted using the scalar product method and studied as functions of meson transverse momentum and collision centrality. The measured values for prompt J/ mesons are found to be larger than those for nonprompt J/ mesons. The prompt J/ values at high are found to be underpredicted by a model incorporating only parton energy loss effects in a quark-gluon plasma medium. Prompt and nonprompt J/ meson and prompt (2S) and values are also reported for the first time, providing new information about heavy quark interactions in the hot and dense medium created in heavy ion collisions.

Recent measurements in the top quark sector at the CERN Large Hadron Collider are discussed. This review discusses the most recent measurements of inclusive and differential top quark cross-sections in strong and electroweak production of top quarks and related measurements, such as top quark properties, as well as searches, including EFT approaches.

Materials

The direct effect of an axion field on Josephson junctions is analyzed through the consequences on the effective potential barrier that prevents the junction from switching from the superconducting to the finite-voltage state. We describe a method to reliably compute the quasipotential with stochastic simulations, which allows for the spanning of the coupling parameter from weakly interacting axion to tight interactions. As a result, we obtain an axion field that induces a change in the potential barrier, therefore determining a significant detectable effect for such a kind of elusive particle.

The European Physical Journal C

Measurements of Higgs boson production, where the Higgs boson decays into a pair of τ leptons, are presented, using a sample of proton-proton collisions collected with the CMS experiment at a center-of-mass energy of, corresponding to an integrated luminosity of 138 fb-1. Three analyses are presented. Two are targeting Higgs boson production via gluon fusion and vector boson fusion: a neural network based analysis and an analysis based on an event categorization optimized on the ratio of signal over background events. These are complemented by an analysis targeting vector boson associated Higgs boson production. Results are presented in the form of signal strengths relative to the standard model predictions and products of cross sections and branching fraction to τ leptons, in up to 16 different kinematic regions. For the simultaneous measurements of the neural network based analysis and the …

arXiv preprint arXiv:2309.15393

Statistical physics and dynamical systems theory are key tools to study high-impact geophysical events such as temperature extremes, cyclones, thunderstorms, geomagnetic storms and many more. Despite the intrinsic differences between these events, they all originate as temporary deviations from the typical trajectories of a geophysical system, resulting in well-organised, coherent structures at characteristic spatial and temporal scales. While statistical extreme value analysis techniques are capable to provide return times and probabilities of occurrence of certain geophysical events, they are not apt to account for their underlying physics. Their focus is to compute the probability of occurrence of events that are large or small with respect to some specific observable (e.g. temperature, precipitation, solar wind), rather than to relate rare or extreme phenomena to the underlying anomalous geophysical regimes. This paper delineates this knowledge gap, presenting some related challenges and new formalisms which arise in the study of geophysical extreme events and may help better understand them.

Entropy

A spin-boson-like model with two interacting qubits is analysed. The model turns out to be exactly solvable since it is characterized by the exchange symmetry between the two spins. The explicit expressions of eigenstates and eigenenergies make it possible to analytically unveil the occurrence of first-order quantum phase transitions. The latter are physically relevant since they are characterized by abrupt changes in the two-spin subsystem concurrence, in the net spin magnetization and in the mean photon number.

Entropy

A spin-boson-like model with two interacting qubits is analysed. The model turns out to be exactly solvable since it is characterized by the exchange symmetry between the two spins. The explicit expressions of eigenstates and eigenenergies make it possible to analytically unveil the occurrence of first-order quantum phase transitions. The latter are physically relevant since they are characterized by abrupt changes in the two-spin subsystem concurrence, in the net spin magnetization and in the mean photon number.

Symmetry

The dynamical systems of trigonometric functions are explored, with a focus on sz=sin(z) and the fractal image created by iterating the Newton map, Fs(z), of s(z). The basins of attraction created from iterating Fs(z) are analyzed, and some bounds are determined for the primary basins of attraction. We further prove x and y-axis symmetry of the Newton map as well as some interesting results on periodic points on the real axis.

Symmetry

A new subclass TXq[λ,A,B] of analytic functions is introduced by making use of the q-derivative operator associated with the Pascal distribution. Certain properties of analytic functions in the subclass TXq[λ,A,B] are derived. Some known results are generalized.

Symmetry

Presently, active detectors are widely used to detect mines, providing high accuracy. However, the principle of the operation of active detectors can lead to the explosion of hidden mines. The novelty of this work is the development of the morphology of a neural network for the classification of mines made of different materials (metallic, semi-metallic, plastic) with high accuracy (99.23%), based on a vector of input features with the following components: the value of the output voltage of the FLC-100 magnetic field sensor, which measures magnetic field anomalies in the vicinity of mines with an accuracy of 10−10–10−4 Tesla; six different soil types, depending on the humidity; and the height at which the magnetic field sensor is located above the mine. Due to the fact that mines, when made of different materials (metallic, semi-metallic, plastic), have different magnetic properties, the neural network method of mine classification, based on the sensor data regarding anomalies of the magnetic field in the vicinity of mines, allows the classification of mines made of different materials. The accuracy of mine classification was assessed with two-layer and three-layer neural networks on various metrics (confusion matrix, ROC curves, accuracy–loss curves), using ADAM, RMSprop, and SGD optimisers, and analyses and comparisons were then carried out. The impact of asymmetry in the neuron number and the types of activation functions in the first and second hidden layers on the values of the accuracy and loss metrics was studied. In particular, it was established that the asymmetry of the number of neurons in the first and second hidden layers relative to the …

Symmetry

Shape memory alloys (SMAs) represent an exceptional class of smart materials as they are able to recover their shape after mechanical deformation, making them suitable for use in actuators, sensors and smart devices. These unique properties are due to the thermoelastic martensitic transformation that can occur during both thermal and mechanical deformation. Cu-based SMAs, especially those incorporating Al and Ag, are attracting much attention due to their facile production and cost-effectiveness. Among them, Cu-Al-Ag SMAs stand out due to their notably high temperature range for martensitic transformation. In this study, a Cu-based SMA with a new ternary composition of Cu-10Al-7Ag wt.% was prepared by arc melting and the samples cut from this casting alloy were quenched in water. Subsequently, the phase composition and the development of the microstructure were investigated. In addition, the morphology of the martensite was studied using advanced techniques such as electron backscatter diffraction (EBSD) and transmission electron microscopy (TEM). The analyzes confirmed the presence of martensitic structures in both samples; mainly 18R (β1′) martensite was present but a small volume fraction of (γ1′) martensite also was noticed in the as-quenched sample. The observation of fine, twinned martensite plates in the SMA alloy with symmetrically occurring basal plane traces between the twin variants underlines the inherent correlation between microstructural symmetry and the properties of the material and provides valuable insights into its behavior. The hardness of the quenched sample was found to be lower than the as …

Symmetry

The reliability of circuit systems is primarily affected by cascading failures due to their complex structural and functional coupling. Causes of cascading failure during circuit operation include the continuous degradation process of components and external random shocks. Circuit systems can exhibit asymmetric structural changes and functional loss during cascading failure propagation due to the coupling of degradation and shock and their uncertainty effects. To tackle this issue, this paper abstracts the circuit into an impedance network and constructs a component failure behavior model that considers the correlation between degradation and shock. The interactions between soft and hard failure processes among different components are discussed. Two types of cascading failure propagation processes are described: slow propagation associated with continuous degradation and damage shock, and fast propagation due to fatal shock. Based on this, a cascading failure simulation algorithm is developed. This article presents a case study to demonstrate the proposed models and to analyze the reliability of a typical circuit system.

Symmetry

As industrial processes grow increasingly complex, fault identification becomes challenging, and even minor errors can significantly impact both productivity and system safety. Fault detection and diagnosis (FDD) has emerged as a crucial strategy for maintaining system reliability and safety through condition monitoring and abnormality recovery to manage this challenge. Statistical-based FDD methods that rely on large-scale process data and their features have been developed for detecting faults. This paper overviews recent investigations and developments in statistical-based FDD methods, focusing on probabilistic models. The theoretical background of these models is presented, including Bayesian learning and maximum likelihood. We then discuss various techniques and methodologies, e.g., probabilistic principal component analysis (PPCA), probabilistic partial least squares (PPLS), probabilistic independent component analysis (PICA), probabilistic canonical correlation analysis (PCCA), and probabilistic Fisher discriminant analysis (PFDA). Several test statistics are analyzed to evaluate the discussed methods. In industrial processes, these methods require complex matrix operation and cost computational load. Finally, we discuss the current challenges and future trends in FDD.

Symmetry

The application of contemporary artificial intelligence techniques to address geometric problems and automated deductive proofs has always been a grand challenge to the interdisciplinary field of mathematics and artificial intelligence. This is the fourth article in a series of our works, in our previous work, we established a geometric formalized system known as FormalGeo. Moreover, we annotated approximately 7000 geometric problems, forming the FormalGeo7k dataset. Despite the fact that FGPS (Formal Geometry Problem Solver) can achieve interpretable algebraic equation solving and human-like deductive reasoning, it often experiences timeouts due to the complexity of the search strategy. In this paper, we introduced FGeo-TP (theorem predictor), which utilizes the language model to predict the theorem sequences for solving geometry problems. The encoder and decoder components in the transformer architecture naturally establish a mapping between the sequences and embedding vectors, exhibiting inherent symmetry. We compare the effectiveness of various transformer architectures, such as BART or T5, in theorem prediction, and implement pruning in the search process of FGPS, thereby improving its performance when solving geometry problems. Our results demonstrate a significant increase in the problem-solving rate of the language model-enhanced FGeo-TP on the FormalGeo7k dataset, rising from 39.7% to 80.86%. Furthermore, FGeo-TP exhibits notable reductions in solution times and search steps across problems of varying difficulty levels.

Symmetry

We first briefly summarize several well-known properties of regular tessellations of the three two-dimensional maximally symmetric manifolds, E2, S2, and H2, by bounded regular tiles. For instance, there exist infinitely many regular tessellations of the hyperbolic plane H2 by curved hyperbolic equilateral triangles whose vertex angles are 2π/d for d=7,8,9,… On the other hand, we prove that there is no curved hyperbolic regular tetrahedron which tessellates the three-dimensional hyperbolic space H3. We also show that a regular tessellation of H3 can only consist of the hyperbolic cubes, hyperbolic regular icosahedra, or two types of hyperbolic regular dodecahedra. There exist only two regular hyperbolic space-fillers of H4. If n>4, then there exists no regular tessellation of Hn.

Symmetry

Poisson structures related to affine Courant-type algebroids are analyzed, including those related with cotangent bundles on Lie-group manifolds. Special attention is paid to Courant-type algebroids and their related R structures generated by suitably defined tensor mappings. Lie–Poisson brackets that are invariant with respect to the coadjoint action of the loop diffeomorphism group are created, and the related Courant-type algebroids are described. The corresponding integrable Hamiltonian flows generated by Casimir functionals and generalizing so-called heavenly-type differential systems describing diverse geometric structures of conformal type in finite dimensional Riemannian manifolds are described.

Symmetry

This research explores an improved operation of a recently studied converter, the so-called two-phase sixth-order boost converter (2P6OBC). The converter consists of a symmetric design of power stations followed by an LC filter; its improved operation incorporates an asymmetric pulse width modulation (PWM) scheme for transistor switching, sometimes known as an interleaved PWM approach. The new operation leads to improved performance for the 2P6OBC. Along with studying the 2P6OBC, one of the contributions of this research is providing design equations for the converter and comparing it versus the interleaved (or multiphase) boost converter, known for its competitiveness and advantages; the single-phase boost topology was also included in the comparison. The comparison consisted of a design scenario where all converters must achieve the same power conversion with an established maximum switching ripple, and then the stored energy in passive components is compared. Although the 2P6OBC requires a greater number of components, the total amount of stored energy is smaller. It is known that the stored energy is related to the size of the passive components. Still, the article includes a discussion of this topic. The new operation of the converter offers more streamlined, cost-effective, and efficient alternatives for a range of applications within power electronics. The final design of the 2P6OBC required only 68% of the stored energy in inductors compared to the multiphase boost converter, and 60% of the stored energy in capacitors. This result is outstanding, considering that the multiphase boost converter is a very competitive …

Symmetry

In this study, the idea of using a fully symmetric U-Net deep learning model for forecasting a segmented image of high global aerosol concentrations is implemented. As the forecast relies on historical data, the model used a sequence of the last eight segmented images to make the prediction. For this, the classic U-Net model was modified to use ConvLSTM2D layers with MaxPooling3D and UpSampling3D layers. In order to achieve complete symmetry, the output data are given in the form of a series of eight segmented images shifted by one image in the time sequence so that the last image actually represents the forecast of the next image of high aerosol concentrations. The proposed model structure was tuned by the new FOX metaheuristic algorithm. Based on our analysis, we found that this algorithm is suitable for tuning deep learning models considering their stochastic nature. It was also found that this algorithm spends the most time in areas close to the optimal value where there is a weaker linear correlation with the required metric and vice versa. Taking into account the characteristics of the used database, we concluded that the model is capable of generating adequate data and finding patterns in the time domain based on the ddc and dtc criteria. By comparing the achieved results of this model using the AUC-PR metric with the previous results of the ResNet3D-101 model with transfer learning, we concluded that the proposed symmetric U-Net model generates data better and is more capable of finding patterns in the time domain.

Symmetry

Accurate and fast traffic prediction is the data-based foundation for achieving traffic control and management, and the accuracy of prediction results will directly affect the effectiveness of traffic control and management. This paper proposes a new spatiotemporal periodic polynomial model for road traffic, which integrates the temporal, spatial, and periodic features of speed time series and can effectively handle the nonlinear mapping relationship from input to output. In terms of the model, we establish a road traffic speed prediction model based on polynomial regression. In terms of spatial feature extraction methods, we introduce a maximum mutual information coefficient spatial feature extraction method. In terms of periodic feature extraction methods, we introduce a periodic trend modeling method into the prediction of speed time series, and effective fusion is carried out. Four strategies are evaluated based on the Guangzhou road speed dataset: a univariate polynomial model, a spatiotemporal polynomial model, a periodic polynomial model, and a spatiotemporal periodic polynomial model. The test results show that the three methods proposed in this article can effectively improve prediction accuracy. Comparing the spatiotemporal periodic polynomial model with multiple machine learning models and deep learning models, the prediction accuracy is improved by 5.94% compared to the best feedforward neural network. The research in this article can effectively deal with the temporal, spatial, periodic, and nonlinear characteristics of speed prediction, and to a certain extent, improve the accuracy of speed prediction.

Symmetry

Peyssonnoside A is an unusual natural product consisting of a diterpene unit and a sulfonated monosaccharide. The experimental and theoretical comparison of Optical Rotatory Dispersion (ORD) and quantitative Nuclear Magnetic Resonance (NMR) data provided strong evidence for the stereochemistry of the diterpene unit. However, predicted Vibrational Circular Dichroism (VCD) spectra of Peyssonnoside A at the B3LYP/6-311++G(2d,2p) level showed poor correlation to the corresponding experimental spectra, preventing independent absolute configuration (AC) determination from VCD analysis. New calculations using the B3PW91 functional and the 6-311G(3df,2pd) basis set suggest that we can now independently and confidently assign the AC of Peyssonnoside A through VCD analyses. The use of f-polarization functions is responsible for the current successful assignment, compared to previously failed VCD analysis. This study highlights two important points: (a) the importance of using multiple levels of theories for satisfactorily reproducing the experimental spectra and (b) for quantitative comparisons using similarity indices, it is important to consider not only the VCD spectra but also the corresponding absorption spectra.

Symmetry

Hellwig’s method is a multi-criteria decision-making technique designed to facilitate the ranking of alternatives based on their proximity to the ideal solution. Typically, this approach calculates distances using the Euclidean norm, assuming implicitly that the considered criteria are independent. However, in real-world situations, the assumption of criteria independence is rarely met. The paper aims to propose an extension of Hellwig’s method by incorporating the Mahalanobis distance. Substituting the Euclidean distance with the Mahalanobis distance has proven to be effective in handling correlations among criteria, especially in the context of asymmetrical relationships between criteria. Subsequently, we investigate the impact of the Euclidean and Mahalanobis distance measures on the several variants of Hellwig procedures, analyzing examples based on various illustrative data with 10 alternatives and 4 criteria. Additionally, we examine the influence of three normalization formulas in Hellwig’s aggregation procedures. The investigation results indicate that both the distance measure and normalization formulas have some impact on the final rankings. The evaluation and ranking of alternatives using the Euclidean distance measure are influenced by the normalization formula, albeit to a limited extent. In contrast, the Mahalanobis distance-based Hellwig’s method remains unaffected by the choice of normalization formulas. The study concludes that the ranking of alternatives is strongly dependent on the distance measure employed, whether it is Euclidean or Mahalanobis. The Mahalanobis distance-based Hellwig method is deemed a valuable …

Symmetry

Canoe modality in flatwater canoeing has a clear asymmetrical nature. This study aimed (1) to determine the magnitude and direction of neuromuscular properties, range of motion (ROM) and lower-limb strength asymmetries in female and male canoeists; (2) to establish sex-individualized asymmetry thresholds for canoeists’ neuromuscular properties, ROM and lower-limb strength; and (3) to determine the relationship of canoeists’ neuromuscular properties, ROM and lower-limb strength asymmetries with a specific canoe–dynamometer performance test. Twenty-one international canoeists were assessed through tensiomyography (TMG), ROM, lower-limb explosive strength, and a specific canoe incremental dynamometric test. The magnitude of asymmetry assessed through TMG and ROM was not modulated either by sex or performance level (international medal vs. non-medal). Females showed greater asymmetry than males on muscle tone of the erector spinae towards non-stroke side (22.75% vs. 9.72%) and the tibialis anterior (30.97% vs. 16.29%), and Fmax in explosive leg press (2.41% vs. 0.63%) towards the stroke side. International medalists showed greater asymmetry in semitendinosus contraction time towards non-stroke side (20.51% vs. 9.43%) and reached Vmax earlier in explosive leg press towards stroke side leg (19.20% vs. 9.40%). A greater asymmetry in Fmax and in Vm, and a smaller asymmetry in Tvmax and in leg press showed a small predictive capacity for canoeists’ performance on a specific canoe incremental dynamometry test. Reporting reference data from world-class canoeists’ asymmetries can be of great …

Symmetry

The canonical decomposition of a bipartite graph is a new decomposition method that involves three operators: parallel, series, and K⨁ S. The class of weak-bisplit graphs is the class of totally decomposable graphs with respect to these operators, and the class of bicographs is the class of totally decomposable graphs with respect to parallel and series operators. We prove in this paper that the class of bipartite (P6,C6)-free graphs is the class of bipartite graphs that are totally decomposable with respect to parallel and K⨁S operators. We present a linear time recognition algorithm for (P6,C6)-free graphs that is symmetrical to the linear recognition algorithms of weak-bisplit graphs and star1,2,3-free bipartite graphs. As a result of this algorithm, we present efficient solutions in this class of graphs for two optimization graph problems: the maximum balanced biclique problem and the maximum independent set problem.

Symmetry

Multilevel inverters play a key role in improving the power quality for industrial, domestic, and renewable energy sectors due to sinusoidal output voltage through small voltage steps, lesser THD (total harmonic distortion), and EMI (electromagnetic interference). There are several variants in MLI structures to generate a stepped voltage with their own operating characteristics, which flaws in switching devices with gate drivers, current conducting switches varied with varied voltage levels, and switches with different abilities in blocking voltagesto overcome increases in implementation costs and restrict its usage in high-power applications. Therefore, this article paves a solution for the above problem, which orients a new structure for asymmetric operation to propel large voltage levels with small values of switches in parallel with conventional topologies. The subtlety of the proposed topology is governed by a multicarrier pulse width modulation scheme, and ten different voltage magnitude algorithms are developed and compared foreffectiveness.Hitherto, many existing MLI topologies with reduced power switches have beendeveloped; among these, the H6 structure attempts to curtail the reduced conduction path. The operation of the suggested topology is confirmed in a Matlab/Simulink environment, and real-time performance is investigated using a laboratory prototype to accord the simulated results.

Symmetry

This research explores an improved operation of a recently studied converter, the so-called two-phase sixth-order boost converter (2P6OBC). The converter consists of a symmetric design of power stations followed by an LC filter; its improved operation incorporates an asymmetric pulse width modulation (PWM) scheme for transistor switching, sometimes known as an interleaved PWM approach. The new operation leads to improved performance for the 2P6OBC. Along with studying the 2P6OBC, one of the contributions of this research is providing design equations for the converter and comparing it versus the interleaved (or multiphase) boost converter, known for its competitiveness and advantages; the single-phase boost topology was also included in the comparison. The comparison consisted of a design scenario where all converters must achieve the same power conversion with an established maximum switching ripple, and then the stored energy in passive components is compared. Although the 2P6OBC requires a greater number of components, the total amount of stored energy is smaller. It is known that the stored energy is related to the size of the passive components. Still, the article includes a discussion of this topic. The new operation of the converter offers more streamlined, cost-effective, and efficient alternatives for a range of applications within power electronics. The final design of the 2P6OBC required only 68% of the stored energy in inductors compared to the multiphase boost converter, and 60% of the stored energy in capacitors. This result is outstanding, considering that the multiphase boost converter is a very competitive …

Symmetry

Complex network theory involves network structure and dynamics; dynamics on networks and interactions between networks; and dynamics developed over a network. As a typical application of complex networks, the dynamics of disease spreading and control strategies on networks have attracted widespread attention from researchers. We investigate the dynamics and optimal control for an epidemic model with demographics and heterogeneous asymmetric control strategies (immunization and quarantine) on complex networks. We derive the epidemic threshold and study the global stability of disease-free and endemic equilibria based on different methods. The results show that the disease-free equilibrium cannot undergo a Hopf bifurcation. We further study the optimal control strategy for the complex system and obtain its existence and uniqueness. Numerical simulations are conducted on scale-free networks to validate and supplement the theoretical results. The numerical results indicate that the asymmetric control strategies regarding time and degree of node for populations are superior to symmetric control strategies when considering control cost and the effectiveness of controlling infectious diseases. Meanwhile, the advantages of the optimal control strategy through comparisons with various baseline immunization and quarantine schemes are also shown.

Symmetry

We investigate the Noether symmetries of the Klein–Gordon Lagrangian for Bianchi I spacetime. This is accomplished using a set of new Noether symmetry relations for the Klein–Gordon Lagrangian of Bianchi I spacetime, which reduces to the wave equation in a special case. A detailed Noether symmetry analysis of the Klein–Gordon and the wave equations for Bianchi I spacetime is presented, and the corresponding conservation laws are derived.