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Chimera states, or coherence-incoherence patterns in systems of symmetrically coupled identical oscillators, have been the subject of intensive study for the last two decades. In particular it is now known that the continuum limit of phase-coupled oscillators allows an elegant mathematical description of these states based on a nonlinear integro-differential equation known as the Ott-Antonsen equation. However, a systematic study of this equation usually requires a substantial computational effort. In this paper, we consider a special class of nonlocally coupled phase oscillator models where the above analytical approach simplifies significantly, leading to a semi-analytical description of both chimera states and of their linear stability properties. We apply this approach to phase oscillators on a one-dimensional lattice, on a two-dimensional square lattice and on a three-dimensional cubic lattice, all three with periodic boundary conditions. For each of these systems we identify multiple symmetric coherence-incoherence patterns and compute their linear stability properties. In addition, we describe how chimera states in higher-dimensional models are inherited from lower-dimensional models and explain how they can be grouped according to their symmetry properties and global order parameter.

This paper presents a study of participants interacting with and using GaMaDHaNi, a novel hierarchical generative model for Hindustani vocal contours. To explore possible use cases in human-AI interaction, we conducted a user study with three participants, each engaging with the model through three predefined interaction modes. Although this study was conducted \"in the wild\"- with the model unadapted for the shift from the training data to real-world interaction - we use it as a pilot to better understand the expectations, reactions, and preferences of practicing musicians when engaging with such a model. We note their challenges as (1) the lack of restrictions in model output, and (2) the incoherence of model output. We situate these challenges in the context of Hindustani music and aim to suggest future directions for the model design to address these gaps.

We show that Cohen's Kappa and Matthews Correlation Coefficient (MCC), both extended and contrasted measures of performance in multi-class classification, are correlated in most situations, albeit can differ in others. Indeed, although in the symmetric case both match, we consider different unbalanced situations in which Kappa exhibits an undesired behaviour, i.e. a worse classifier gets higher Kappa score, differing qualitatively from that of MCC. The debate about the incoherence in the behaviour of Kappa revolves around the convenience, or not, of using a relative metric, which makes the interpretation of its values difficult. We extend these concerns by showing that its pitfalls can go even further. Through experimentation, we present a novel approach to this topic. We carry on a comprehensive study that identifies an scenario in which the contradictory behaviour among MCC and Kappa emerges. Specifically, we find out that when there is a decrease to zero of the entropy of the elements out of the diagonal of the confusion matrix associated to a classifier, the discrepancy between Kappa and MCC rise, pointing to an anomalous performance of the former. We believe that this finding disables Kappa to be used in general as a performance measure to compare classifiers.

This article describes conceptual advances of the Grading of Recommendations Assessment, Development, and Evaluation (GRADE) working group guidance to evaluate the certainty of evidence (confidence in evidence, quality of evidence) from network meta-analysis (NMA). Application of the original GRADE guidance, published in 2014, in a number of NMAs has resulted in advances that strengthen its conceptual basis and make the process more efficient. This guidance will be useful for systematic review authors who aim to assess the certainty of all pairwise comparisons from an NMA and who are familiar with the basic concepts of NMA and the traditional GRADE approach for pairwise meta-analysis. Two principles of the original GRADE NMA guidance are that we need to rate the certainty of the evidence for each pairwise comparison within a network separately and that in doing so we need to consider both the direct and indirect evidence. We present, discuss, and illustrate four conceptual advances: (1) consideration of imprecision is not necessary when rating the direct and indirect estimates to inform the rating of NMA estimates, (2) there is no need to rate the indirect evidence when the certainty of the direct evidence is high and the contribution of the direct evidence to the network estimate is at least as great as that of the indirect evidence, (3) we should not trust a statistical test of global incoherence of the network to assess incoherence at the pairwise comparison level, and (4) in the presence of incoherence between direct and indirect evidence, the certainty of the evidence of each estimate can help decide which estimate to believe. •The application of the Grading of Recommendations Assessments, Development, and Evaluation approach to a number of network meta-analyses in the 3 years since the original guidance publication has led to advances that have strengthened the conceptual basis.•We present, discuss, and illustrate four conceptual advances. These are based on two principles: we need to rate the certainty of the evidence of each pairwise comparison within a network separately and that we need to consider both the direct and indirect evidence contributing to each network estimate.•Although maximizing the efficiency of the process is desirable, as illustrated in the conceptual advances, use of these strategies requires careful judgment.

Synchronization processes play critical roles in the functionality of a wide range of both natural and man-made systems. Recent work in physics and neuroscience highlights the importance of higher-order interactions between dynamical units, i.e., three- and four-way interactions in addition to pairwise interactions, and their role in shaping collective behavior. Here we show that higher-order interactions between coupled phase oscillators, encoded microscopically in a simplicial complex, give rise to added nonlinearity in the macroscopic system dynamics that induces abrupt synchronization transitions via hysteresis and bistability of synchronized and incoherent states. Moreover, these higher-order interactions can stabilize strongly synchronized states even when the pairwise coupling is repulsive. These findings reveal a self-organized phenomenon that may be responsible for the rapid switching to synchronization in many biological and other systems that exhibit synchronization without the need of particular correlation mechanisms between the oscillators and the topological structure. While first order phase transitions between incoherence and synchronization are critical for collective behavior in various oscillator system application, e.g., the brain and power grids, such transitions typically require finely tuned properties. In this work the authors show that first order phase transitions and bistability can emerge naturally as a consequence of the presence of higher-order interactions between oscillators.

We develop a new primal-dual witness proof framework that may be used to establish variable selection consistency and ℓ∞-bounds for sparse regression problems, even when the loss function and regularizer are nonconvex. We use this method to prove two theorems concerning support recovery and ℓ∞-guarantees for a regression estimator in a general setting. Notably, our theory applies to all potential stationary points of the objective and certifies that the stationary point is unique under mild conditions. Our results provide a strong theoretical justification for the use of nonconvex regularization: For certain nonconvex regularizers with vanishing derivative away from the origin, any stationary point can be used to recover the support without requiring the typical incoherence conditions present in ℓ1-based methods. We also derive corollaries illustrating the implications of our theorems for composite objective functions involving losses such as least squares, nonconvex modified least squares for errors-in-variables linear regression, the negative log likelihood for generalized linear models and the graphical Lasso. We conclude with empirical studies that corroborate our theoretical predictions.

Jet formation is the decisive factor of penetrating power of shaped charge, coherence and stability contribute to penetration. In the same condition, multiple penetrating tests of the shaped charge with depleted uranium(DU) liner did not get the expected results. In order to study the jet forming characteristics of DU liner under static explosion condition, an X-ray photography experiment was designed, which turned out to show the jet being badly incoherent. To research the incoherence of DU shaped charge jet from principles of jet incoherence, supersonic collision worked out to be the reasons for incoherence of the shaped charge jet. This paper provides a method for structural optimization of DU shaped charge and DU liner processing, which has guiding significance for application of DU liner in high explosive antitank projectile.

Large collections of time series often have aggregation constraints due to product or geographical groupings. The forecasts for the most disaggregated series are usually required to add-up exactly to the forecasts of the aggregated series, a constraint we refer to as \"coherence.\" Forecast reconciliation is the process of adjusting forecasts to make them coherent. The reconciliation algorithm proposed by Hyndman et al. ( 2011 ) is based on a generalized least squares estimator that requires an estimate of the covariance matrix of the coherency errors (i.e., the errors that arise due to incoherence). We show that this matrix is impossible to estimate in practice due to identifiability conditions. We propose a new forecast reconciliation approach that incorporates the information from a full covariance matrix of forecast errors in obtaining a set of coherent forecasts. Our approach minimizes the mean squared error of the coherent forecasts across the entire collection of time series under the assumption of unbiasedness. The minimization problem has a closed-form solution. We make this solution scalable by providing a computationally efficient representation. We evaluate the performance of the proposed method compared to alternative methods using a series of simulation designs which take into account various features of the collected time series. This is followed by an empirical application using Australian domestic tourism data. The results indicate that the proposed method works well with artificial and real data. Supplementary materials for this article are available online.

The morphological component analysis (MCA) method can be used to suppress the clutter in a synthetic aperture radar (SAR) image when the dictionaries of clutter and target components are mutually incoherent. However, the effectiveness of the conventional MCA method may be reduced since the mutual incoherence assumption is difficult to fulfill in practice. To overcome the problem, a modified MCA method is proposed in this paper. The proposed method formulates clutter suppression as a constraint optimization problem that combines MCA with incoherence constraint and L0 gradient minimization, and it presents an effective solution to the optimization problem. Specifically, the incoherence constraint of image components is designed to decorrelate different components and better separate targets from clutter. Meanwhile, the L0 gradient minimization constraint is applied to further reduce the artifacts and preserve edges. Then, the optimization problem of the modified MCA is split into solvable subproblems to obtain the target image. Finally, experimental results from real images are carried out to demonstrate the effectiveness of the proposed clutter suppression method.

About two decades ago it was discovered that systems of nonlocally coupled oscillators can exhibit unusual symmetry-breaking patterns composed of coherent and incoherent regions. Since then such patterns, called chimera states, have been the subject of intensive study but mostly in the stationary case when the coarse-grained system dynamics remains unchanged over time. Nonstationary coherence–incoherence patterns, in particular periodically breathing chimera states, were also reported, however not investigated systematically because of their complexity. In this paper we suggest a semi-analytic solution to the above problem providing a mathematical framework for the analysis of breathing chimera states in a ring of nonlocally coupled phase oscillators. Our approach relies on the consideration of an integro-differential equation describing the long-term coarse-grained dynamics of the oscillator system. For this equation we specify a class of solutions relevant to breathing chimera states. We derive a self-consistency equation for these solutions and carry out their stability analysis. We show that our approach correctly predicts macroscopic features of breathing chimera states. Moreover, we point out its potential application to other models which can be studied using the Ott–Antonsen reduction technique.