Unknown Distribution Research Articles

Power flow distribution identification via machine learning algorithm and distributed resource clearing method

Abstract Under the background of dual carbon, a large number of distributed new energy sources are connected to the demand side, which leads to great risks in the operation of the power system. As an effective solution, distributed power transaction still has problems, such as high clearing time, unknown low-voltage distribution network structure, and resource scheduling ignoring user needs. Therefore, this paper proposes an optimal regulation method of demand-side resources based on distributed transactions. Based on the historical operation data of the distribution network, the eXtreme Gradient Boosting (XGBoost) algorithm is used to study the relationship between node injection power, node voltage, and node-side line power flow. It is also used to check the results of distributed transactions and design a market mechanism for rapid clearing and settlement of distributed transactions. The results of an example show that the identification of power flow distribution in a distribution network based on reinforcement learning can meet the security check requirements of distributed transaction results.

Instance-optimal information-based voting

The classical Condorcet Jury Theorem considers a voting scenario in which there exists a candidate whose election would be ideal for each voter; each voter, though, has only a limited understanding of the world and is thus unable to determine exactly who this candidate is. The main question in this scenario is whether the voters, acting individually, can cast their ballots so that the unknown optimal candidate wins the election, and the welfare of the group of voters is maximized.In this setting, each candidate is represented by a known probability distribution over signals about the world that the voters can perceive, that is, over bits. One of these candidates is chosen (secretively, by an adversary) to be the ideal candidate. Afterwards, each voter samples this unknown candidate's distribution once and casts a ballot with the hope that the unknown ideal candidate wins the election.In this paper, we consider the famous Condorcet voting system, as well as some of its variants. First, we give a positive answer to an open question of Chierichetti and Kleinberg [8], and show that, with Condorcet voting, there exists a uniform voting strategy that makes the group of voters succeed with probability 1−δ provided that Θ(ϵtv−2⋅ln⁡δ−1) voters take part in the election — here, ϵtv is the minimum total variation distance between the distributions of two candidates.We also give a uniform voting strategy for the Copeland voting system (a variant of Condorcet) that makes the group succeed with probability 1−δ with Θ(ϵH−2⋅ln⁡δ−1) voters, where ϵH is the minimum Hellinger distance between the distributions. Our uniform Copeland strategy, then, is an instance-optimal hypothesis testing algorithm: constants aside, the strategy is as efficient as the optimal omniscient algorithm which determines the unknown candidate after having directly observed each of the signals perceived by the voters. Then, we “derandomize” our uniform Copeland strategy, and obtain a Condorcet strategy that achieves instance-optimality at the cost of losing uniformity; finally, we prove that this loss of uniformity is necessary: no uniform Condorcet strategy can achieve instance-optimality, in general.Thus, the right voting strategies let these classical combinatorial voting systems attain the same efficiency of centralized, optimal, hypothesis testers.

Solving an internal problem for finite regular two-dimensional lattice spiral elements, excitable plate electromagnetic wave

Background. The work is aimed at developing and researching rigorous methods for solving internal problem of electrodynamics for multi-element structures (metastructures) consisting from the final number of elements, as well as to study the physical processes occurring in them. A special case of such structures are two-dimensional lattices with a fixed interelement distance, consisting of identical elements having the same spatial orientation (regular lattices). Aim. In this work, based on an iterative approach, the internal solution is solved. problems of electrodynamics for a finite regular two-dimensional lattice of spiral elements. In order to obtain a priori information about the electrodynamic characteristics of elements lattice and justification for the choice of projection function systems are analyzed spectral characteristics of the integral operator of the internal problem for a single spiral element. Then the currents on the structure elements are calculated, their spectral characteristics are determined. The results of spectral analysis allow increase the efficiency of solving an internal problem. Methods. The research is based on a strict electrodynamic approach, within the framework of which, for the specified structure in the thin-wire approximation, an integral representation of the electromagnetic field is formed, which, when considered on the surface of conductors together with boundary conditions, is reduced to a system of Fredholm integral equations of the second kind, written relative to unknown current distributions on conductors (internal task). The solution of the internal problem within the framework of the method of moments is reduced to solving a SLAE with a block matrix. Results. A mathematical model of a finite two-dimensional lattice of spiral elements is proposed radiating structure. For the specified structure, in the case of its excitation by a flat electromagnetic wave, based on the iterative approach, the internal problem of electrodynamics was solved. The following were carried out in a wide frequency range: analysis of the convergence of the iterative process, spectral analysis of the integral operator of the internal problem for a single spiral element, as well as spectral analysis of external field and current functions functions on lattice elements. Conclusion. The feasibility of determining the spectral characteristics of integral operators is shown internal task for the elements forming the metastructure. A relationship has been identified between the frequency dependence eigenvalues of the integral operator of the internal problem of single elements, forming a metastructure, with resonance phenomena arising in the metastructure, the influence of resonances on the convergence of the iterative process was confirmed. The feasibility of considering averaged amplitude current spectra is shown. It was revealed that the averaged spectrum of current functions is close to degenerate, especially near resonant frequencies. This allows for use as projection functions a compact set of eigenfunctions that have significant amplitudes in the vicinity of the frequency under study, which significantly simplifies the solution of the internal problem.

Electrodynamic analysis of a sinusoidal antenna for small wave sizes

Background. The work is aimed at developing and researching rigorous methods for calculating thin-wire structures with a complex generatrix shape, having small wave sizes, as well as studying the physical processes occurring in them. A special case of such structures is a sinusoidal antenna operating in a standing current wave mode. Aim. In progress the solution of internal and external problems of electrodynamics is carried out for a sinusoidal antenna of small wave sizes located above an infinitely extended ideal reflector. The currents on the elements of the structure are calculated, its input resistance and radiation characteristics are determined. Methods. The research is based on a strict electrodynamic approach, within the framework of which, for the specified structure in the thin-wire approximation, an integral representation of the electromagnetic field is formed, which, when considered on the surface of conductors together with boundary conditions, is reduced to a system of Fredholm integral equations of the second kind, written relative to unknown current distributions on conductors (internal task). Results. A mathematical model of the radiating structure is proposed, determined: the input resistance of the structure and the basic characteristics of its radiation. It is shown that the operating range of a sinusoidal antenna in the standing wave mode is determined by the quality factor of the input impedance resonances; An increase in the width of the sinusoidal conductor leads to a decrease in the resonant frequencies of the input resistance with a simultaneous increase in the quality factor of the resonances. Conclusion. From a practical point of view, the use of the considered structure allows significantly reduce the dimensions in comparison with a thin electric vibrator, however in this case, the operating range will be correspondingly narrowed, which is determined, due to the weak dependence of the radiation characteristics on frequency, by the quality factor of the resonances. The current distribution on the generatrix of the structure can be considered as a «projection» standing surface wave localized in the plane of a sinusoidal conductor, and resulting from the superposition of forward and backward surface (slow) waves propagating at a speed significantly lower than the speed of light. To further clarify the physics of the processes occurring in the structure, one should use spectral analysis of current functions and study the distributions of the electromagnetic field in the near zone of the structure.

Characterisation of the stellar wind in Cyg X-1 via modelling of colour-colour diagrams

Context. Cygnus X-1 (Cyg X-1) is a high-mass X-ray binary where accretion onto the black hole (BH) is mediated by the stellar wind from the blue supergiant companion star HDE 226868. Due to its inclination, the system is a perfect laboratory to study the not yet well-understood stellar wind structure. In fact, depending on the position of the BH along the orbit, X-ray observations can probe different layers of the stellar wind. Deeper wind layers can be investigated at superior conjunction (i.e. null orbital phases). Aims. We aim to characterise the stellar wind in the Cyg X-1/HDE 226868 system, analysing one passage at superior conjunction covered by XMM-Newton during the ‘Cyg X-1 Hard state Observations of a Complete Binary Orbit in X-rays’ (CHOCBOX) campaign. Methods. To analyse the properties of the stellar wind, we computed colour-colour diagrams. Since X-ray absorption is energy-dependent, colour indices provide information on the parameters of the stellar wind, such as the column density, NH, w, and the covering factor, fc. We fitted colour-colour diagrams with models that include both a continuum and a stellar wind component. We used the kernel density estimation method to infer the unknown probability distribution of the data points in the colour-colour diagram, and selected the model corresponding to the highest likelihood. In order to study the temporal evolution of the wind around superior conjunction, we extracted and fitted time-resolved colour-colour diagrams. Results. We found that the model that best describes the shape of the colour-colour diagram of Cyg X-1 at superior conjunction requires the wind to be partially ionised. The shape of the colour-colour diagram strongly varies during the analysed observation, due to concurrent changes of the mean NH, w and the fc of the wind. Our results suggest the existence of a linear scaling between the rapid variability amplitude of NH, w (on timescales between 10 s and 11 ks) and its long-term variations (on timescales > 11 ks). Using the inferred best-fit values, we estimated the stellar mass loss rate to be ∼7 × 10−6 M⊙ yr−1 and the clumps to have a characteristic mass of ∼1017 g.

A data-driven prediction for concrete crack propagation path based on deep learning method

Accurate and efficient prediction of concrete crack propagation path facilitates timely maintenance. To avoid errors arising from assumptions in physical models and parameter measurements, a data-driven prediction method for concrete crack propagation path is proposed. The spatio-temporal prediction approach is presented by unifying the conditional Generative Adversarial Network and Long Short-Term Memory Network (UcGLS-Net). The UcGLS-Net has the advantage of enabling temporal (by Long Short-Term Memory Network, LSTM) and spatial information (by the conditional Generative Adversarial Network, cGAN) in the concrete crack propagation process to be treated simultaneously and distinctly thus improving prediction accuracy. Notably, results demonstrate that UcGLS-Net still works in crack propagation path prediction even with unknown aggregate distribution. Moreover, the effects of historical input quantity and prediction intervals on prediction accuracy of the UcGLS-Net are studied and the network framework is optimized. Due to high efficiency, this study provides a new adaptable and real-time prediction method for concrete crack propagation path, offering support for the design, damage prediction, assessment, and maintenance of concrete structures.

A Wasserstein perspective of Vanilla GANs

The empirical success of Generative Adversarial Networks (GANs) caused an increasing interest in theoretical research. The statistical literature is mainly focused on Wasserstein GANs and generalizations thereof, which especially allow for good dimension reduction properties. Statistical results for Vanilla GANs, the original optimization problem, are still rather limited and require assumptions such as smooth activation functions and equal dimensions of the latent space and the ambient space. To bridge this gap, we draw a connection from Vanilla GANs to the Wasserstein distance. By doing so, existing results for Wasserstein GANs can be extended to Vanilla GANs. In particular, we obtain an oracle inequality for Vanilla GANs in Wasserstein distance. The assumptions of this oracle inequality are designed to be satisfied by network architectures commonly used in practice, such as feedforward ReLU networks. By providing a quantitative result for the approximation of a Lipschitz function by a feedforward ReLU network with bounded Hölder norm, we conclude a rate of convergence for Vanilla GANs as well as Wasserstein GANs as estimators of the unknown probability distribution.

Wasserstein regression with empirical measures and density estimation for sparse data.

The problem of modeling the relationship between univariate distributions and one or more explanatory variables lately has found increasing interest. Existing approaches proceed by substituting proxy estimated distributions for the typically unknown response distributions. These estimates are obtained from available data but are problematic when for some of the distributions only few data are available. Such situations are common in practice and cannot be addressed with currently available approaches, especially when one aims at density estimates. We show how this and other problems associated with density estimation such as tuning parameter selection and bias issues can be side-stepped when covariates are available. We also introduce a novel version of distribution-response regression that is based on empirical measures. By avoiding the preprocessing step of recovering complete individual response distributions, the proposed approach is applicable when the sample size available for each distribution varies and especially when it is small for some of the distributions but large for others. In this case, one can still obtain consistent distribution estimates even for distributions with only few data by gaining strength across the entire sample of distributions, while traditional approaches where distributions or densities are estimated individually fail, since sparsely sampled densities cannot be consistently estimated. The proposed model is demonstrated to outperform existing approaches through simulations and Environmental Influences on Child Health Outcomes data.

An image-based nonparametric multivariate EWMA control chart for metal additive manufacturing process monitoring

Additive manufacturing offers considerable promise in terms of manufacturing flexibility, but print quality remains a major obstacle to its widespread adoption. Consequently, timely and accurate detection of process variations or anomalies is critical for implementing corrective actions. Melt pool characteristics are crucial to final product quality, and current state-of-the-art studies on melt pool image flow have primarily focused on in-situ sensing, feature extraction, and their relationship with process settings and material properties. This study aims to develop a statistical process control approach to detect process variations immediately using a predefined distribution of monitoring statistics. Two main challenges are addressed: 1) the unknown distribution of melt pool image features, rendering traditional parametric control charts unreliable and 2) the autocorrelation of melt pool image flow features, violating the traditional control chart assumption of independent and identically distributed monitoring data. To overcome these challenges, we propose a multivariate nonparametric Exponential Weighted Moving Average (EWMA) control chart that can appropriately accommodate stationary serial data correlation to monitor process stability by tracking physical features extracted from the original images. Key features of the proposed control chart include its ability to eliminate serial correlation effects and its distribution-free nature, requiring no prior information about the data distribution. Comparative analysis of simulated and real data demonstrates that the proposed approach outperforms baseline methods in anomaly detection accuracy. An actual case study in laser metal deposition (LMD) further validates the effectiveness of the proposed method.

Learning on manifolds without manifold learning

Function approximation based on data drawn randomly from an unknown distribution is an important problem in machine learning. The manifold hypothesis assumes that the data is sampled from an unknown submanifold of a high dimensional Euclidean space. A great deal of research deals with obtaining information about this manifold, such as the eigendecomposition of the Laplace–Beltrami operator or coordinate charts, and using this information for function approximation. This two-step approach implies some extra errors in the approximation stemming from estimating the basic quantities of the data manifold in addition to the errors inherent in function approximation. In this paper, we project the unknown manifold as a submanifold of an ambient hypersphere and study the question of constructing a one-shot approximation using a specially designed sequence of localized spherical polynomial kernels on the hypersphere. Our approach does not require preprocessing of the data to obtain information about the manifold other than its dimension. We give optimal rates of approximation for relatively “rough” functions.

Multi-reference source aircraft classification network based on unknown class prototype estimation

Abstract Gathering complete aircraft types for close-set tasks is challenging and costly in fine-grained aircraft classification, resulting in encountering unknown class aircraft images in real-world models. To address this problem, we propose a network called a multi-reference source fine-grained aircraft classification network (MRSN) to explicitly and implicitly distinguish known class boundaries and embed unknown classes into the sample space. Specifically, we propose an embedding module (UCPE) to synthesize an unknown class prototype to facilitate the modeling of unknown class data distribution. Besides, we introduce a concatenated multi-reference source module (CMS) that combines distance measurement and probability estimation to classify whether testing images are of unknown class or not. Our proposed MRSN innovatively extends the open-set learning paradigm to the fine-grained classification of geospatial objects rather than simple scene classification. Besides, it shows excellent performance in our constructed dataset, which demonstrates the effectiveness and progressiveness of our method.

PDE-regularised spatial quantile regression

We consider the problem of estimating the conditional quantiles of an unknown distribution from data gathered on a spatial domain. We propose a spatial quantile regression model with differential regularisation. The penalisation involves a partial differential equation defined over the considered spatial domain, that can display a complex geometry. Such regularisation permits, on one hand, to model complex anisotropy and non-stationarity patterns, possibly on the basis of problem-specific knowledge, and, on the other hand, to comply with the complex conformation of the spatial domain. We define an innovative functional Expectation-Maximisation algorithm, to estimate the unknown quantile surface. We moreover describe a suitable discretisation of the estimation problem, and investigate the theoretical properties of the resulting estimator. The performance of the proposed method is assessed by simulation studies, comparing with state-of-the-art techniques for spatial quantile regression. Finally, the considered model is applied to two real data analyses, the first concerning rainfall measurements in Switzerland and the second concerning sea surface conductivity data in the Gulf of Mexico.

Distribution reconstruction and reliability assessment of complex LSFs via an adaptive Non-parametric Density Estimation Method

Complex limit state functions (LSFs), often characterized by strong nonlinearity, non-smoothness, or discontinuity, pose challenges for structural reliability analysis in engineering practices. Conventional methods for uncertainty propagation and reliability assessment may struggle to handle these issues effectively. This paper introduces a novel approach to adaptively reconstruct the unknown distributions of complex LSFs. The Non-parametric Density Estimation Method based on Harmonic Transform (NDEM-HT) is employed as the tool for this purpose. An adaptive strategy is then proposed to determine the number of harmonic moments required in NDEM-HT for achieving high accuracy. Specifically, the Adaptive Kernel Density Estimation (AKDE) method is also adopted to provide an initial estimation of the rough distribution. Subsequently, the optimal number of harmonic moments is determined by minimizing the relative entropy between the distributions obtained by AKDE and NDEM-HT. The efficacy of the proposed method is demonstrated through five numerical examples, considering various types of complex LSFs. Comparative results are also provided employing MCS along with both conventional and state-of-the-art methods.

Crowd Counting Using Meta-Test-Time Adaptation.

Machine learning algorithms are commonly used for quickly and efficiently counting people from a crowd. Test-time adaptation methods for crowd counting adjust model parameters and employ additional data augmentation to better adapt the model to the specific conditions encountered during testing. The majority of current studies concentrate on unsupervised domain adaptation. These approaches commonly perform hundreds of epochs of training iterations, requiring a sizable number of unannotated data of every new target domain apart from annotated data of the source domain. Unlike these methods, we propose a meta-test-time adaptive crowd counting approach called CrowdTTA, which integrates the concept of test-time adaptation into the meta-learning framework and makes it easier for the counting model to adapt to the unknown test distributions. To facilitate the reliable supervision signal at the pixel level, we introduce uncertainty by inserting the dropout layer into the counting model. The uncertainty is then used to generate valuable pseudo labels, serving as effective supervisory signals for adapting the model. In the context of meta-learning, one image can be regarded as one task for crowd counting. In each iteration, our approach is a dual-level optimization process. In the inner update, we employ a self-supervised consistency loss function to optimize the model so as to simulate the parameters update process that occurs during the test phase. In the outer update, we authentically update the parameters based on the image with ground truth, improving the model's performance and making the pseudo labels more accurate in the next iteration. At test time, the input image is used for adapting the model before testing the image. In comparison to various supervised learning and domain adaptation methods, our results via extensive experiments on diverse datasets showcase the general adaptive capability of our approach across datasets with varying crowd densities and scales.

Conformal cylindrical microstrip loop radiator input impedance calculation

Problem statement. Antennas that fully or partially repeat the shape of the object on which they are placed are called conformal. The main areas of application of conformal antennas are aviation, rocketry, and vehicles. Despite the presence of a large number of publications devoted to conformal antennas in our country and abroad, issues related to the formation of the radiation characteristics of conformal microstrip antennas, as well as the influence of the overall dimensions and geometry of the emitter on the radiation characteristics, have still not been sufficiently studied. Goal. The purpose of this work was to obtain an approximate formula for calculating the input impedance of a conformal cylindrical microstrip loop radiator. Results. In this article, an integral equation is obtained for the unknown current density distribution function on the surface of a conformal cylindrical microstrip loop radiator; as a result of its solution, an approximate formula for this function is obtained. An approximate formula for calculating the input impedance is obtained. The dependences of the input impedance of a conformal cylindrical microstrip loop radiator on its length normalized to the wavelength are calculated. Practical significance. The proposed method for calculating the input impedance of a conformal cylindrical microstrip loop radiator makes it possible to effectively calculate and study the dependence of the input impedance on the geometric dimensions of the emitter, as well as the dimensions and electrodynamic parameters of the substrate. This technique can be generalized to emitters located on substrates made of other materials, for example, chiral metamaterials.

Input-to-State Stability of Switched Network Control Systems Under Unknown Deception Attacks.

This article focuses on the stability issue of switched network control systems (SNCSs) under deception attacks described by a Bernoulli process with unknown probability distribution. The false information in deception attacks is unknown but bounded and may be state dependent or state independent. By means of the input-to-state stability (ISS) tool and the convex combination method, an improved lemma is first developed for SNCSs, which facilitates the derivations of our results. After that, some attack-independent sufficient conditions for the ISS of SNCSs are obtained for mode-dependent average dwell time switching and stochastic switching, respectively. Different from existing results, the concerned switching contributes to the stability of SNCSs, which benefits the ISS performance of SNCSs even though the unknown deception attacks cause all subsystems to be non-ISS. The proposed results provide an effective solution with strong robustness to deal with unknown deception attacks or denial-of-service attacks.

Treatment of epistemic uncertainty in conjunction analysis with Dempster-Shafer theory

The paper presents an approach to the modelling of epistemic uncertainty in Conjunction Data Messages (CDM) and the classification of conjunction events according to the confidence in the probability of collision. The approach proposed in this paper is based on Dempster-Shafer Theory (DSt) of evidence and starts from the assumption that the observed CDMs are drawn from a family of unknown distributions. The Dvoretzky–Kiefer–Wolfowitz (DKW) inequality is used to construct robust bounds on such a family of unknown distributions starting from a time series of CDMs. A DSt structure is then derived from the probability boxes constructed with DKW inequality. The DSt structure encapsulates the uncertainty in the CDMs at every point along the time series and allows the computation of the belief and plausibility in the realisation of a given probability of collision. The methodology proposed in this paper is tested on a number of real events and compared against existing practices in the European and French Space Agencies. We will show that the classification system proposed in this paper is more conservative than the approach taken by the European Space Agency but provides an added quantification of uncertainty in the probability of collision.

Information bounds for Gaussian copula parameter in stationary semiparametric Markov models

Let {Vt}t=1n be any univariate stationary first-order semiparametric Markov process generated from an unknown invariant marginal distribution and a bivariate Gaussian copula with unknown correlation coefficient α0∈(−1,1). We prove that 1−α02 is the semiparametric efficient variance bound for estimating the correlation parameter α0 in any Gaussian copula generated first-order stationary Markov models. Surprisingly, this variance bound is strictly larger than 1−α022 (when α0≠0), which is the semiparametric efficient variance bound derived by Klaassen and Wellner (1997) for estimating the correlation parameter using any i.i.d. data {(Xi,Yi)}i=1n generated from a bivariate Gaussian copula with two unknown marginal distributions.

Weighing Milky Way and Andromeda in an expanding ΛCDM Universe

The dynamics of the Local Group (LG), especially the contribution of the Milky Way (MW) and Andromeda (M 31) galaxies, is sensitive to the presence of dark energy. This work analyzes the evolution of the LG by considering it as a two-body problem in a homogeneous and isotropic expanding spacetime in a full Λcold dark matter (ΛCDM) background. Using the timing argument (TA), which links LG dynamics to LG mass, we find that the full ΛCDM background predicts a ∼10% lower mass for the LG; whereas Λ alone predicts a ∼10% higher mass. The TA mass is modified by (i) simulations and (ii) the effect of the Large Magellanic Cloud (LMC) to alleviate the poorly constrained internal mass distributions of M 31 and the MW, their time evolution, and the unknown distribution of dark matter between them. First, using IllustrisTNG simulations, we accounted for the effects of two extended halos and their environment (rather than point particles) and predicted their mass (3.89 ± 0.62)×1012 M⊙. Second, the LMC effectively changes the separation and velocities of M 31 towards the MW and reduces the predicted mass to (2.33 ± 0.72)×1012 M⊙. Despite the uncertainties around dark matter between these galaxies, the overall estimated mass is compatible with the mere sum of the MW and M 31 masses. The total mass of the TA is compatible with other estimates, such as the Hubble flow and the Virial Theorem with other dwarf galaxies. The combined result shows, for the first time, that a lower mass estimate can be obtained from the TA, with a consistent embedding and other systematic effects, and without an additional dark matter halo around the galaxies.

Learning subjective time-series data via Utopia Label Distribution Approximation

Subjective time-series regression (STR) tasks have gained increasing attention recently. However, most existing methods overlook the label distribution bias in STR data, which results in biased models. Emerging studies on imbalanced regression tasks, such as age and depth estimations, hypothesize the label distribution is uniform and known. But in reality, the label distribution of test set in STR tasks is usually non-uniform and unknown. Moreover, the time-series data exhibits continuity in both temporal context and label spaces, which has not been addressed by existing methods. To tackle these issues, we propose a Utopia Label Distribution Approximation (ULDA) method, which approximates the training label distribution to the real-world but unknown (utopia) label distribution for calibrating the training and test sets. The utopia label distribution is generated by convolving the original one using a Gaussian kernel. ULDA also has two new devised modules (Time-slice Normal Sampling (TNS) generating required new samples and Convolution Weighted Loss (CWL) lowering learning weights for redundant samples), which not only assist the model training, but also maintain the sample continuity in temporal context space. Extensive experiments demonstrate that ULDA lifts the state-of-the-art performance on STR tasks and shows a considerable generalization ability to other time-series tasks.