Sparse Ones Research Articles

On the Approximation of Nash Equilibria in Sparse Win-Lose Multi-player Games

A polymatrix game is a multi-player game over n players, where each player chooses a pure strategy from a list of its own pure strategies. The utility of each player is a sum of payoffs it gains from the two player's game from all its neighbors, under its chosen strategy and that of its neighbor. As a natural extension to two-player games (a.k.a. bimatrix games), polymatrix games are widely used for multi-agent games in real world scenarios. In this paper we show that the problem of approximating a Nash equilibrium in a polymatrix game within the polynomial precision is PPAD-hard, even in sparse and win-lose ones. This result further challenges the predictability of Nash equilibria as a solution concept in the multi-agent setting. We also propose a simple and efficient algorithm, when the game is further restricted. Together, we establish a new dichotomy theorem for this class of games. It is also of independent interest for exploring the computational and structural properties in Nash equilibria.

Stability of cluster formations in adaptive Kuramoto networks

This paper studies stability properties of multi-cluster formations in Kuramoto networks with adaptive coupling. Sufficient conditions for the local asymptotic stability of the corresponding synchronization invariant toroidal manifold are derived and formulated in terms of the intra-cluster interconnection topology and plasticity parameters of the adaptive couplings. The proposed sufficient stability conditions qualitatively mimic certain counterpart results for Kuramoto networks with static coupling which require sufficiently strong and dense intra-cluster connections and sufficiently weak and sparse inter-cluster ones. Remarkably, the existence of cluster formations depends on the interconnection structure between nodes belonging to different clusters and does not require any coupling links between nodes that form a cluster. On the other hand, the stability properties of clusters depend on the interconnection structure inside the clusters. This dependence constitutes the main contribution of the paper. Also, a numerical example is provided to validate the proposed theoretical findings.

The greedy strategy for optimizing the Perron eigenvalue

We address the problems of minimizing and of maximizing the spectral radius over a compact family of non-negative matrices. Those problems being hard in general can be efficiently solved for some special families. We consider the so-called product families, where each matrix is composed of rows chosen independently from given sets. A recently introduced greedy method works very fast. However, it is applicable mostly for strictly positive matrices. For sparse matrices, it often diverges and gives a wrong answer. We present the “selective greedy method” that works equally well for all non-negative product families, including sparse ones. For this method, we prove a quadratic rate of convergence and demonstrate its efficiency in numerical examples. The numerical examples are realised for two cases: finite uncertainty sets and polyhedral uncertainty sets given by systems of linear inequalities. In dimensions up to 2000, the matrices with minimal/maximal spectral radii in product families are found within a few iterations. Applications to dynamical systems and to the graph theory are considered.

Transforming Lindblad Equations into Systems of Real-Valued Linear Equations: Performance Optimization and Parallelization of an Algorithm.

With their constantly increasing peak performance and memory capacity, modern supercomputers offer new perspectives on numerical studies of open many-body quantum systems. These systems are often modeled by using Markovian quantum master equations describing the evolution of the system density operators. In this paper, we address master equations of the Lindblad form, which are a popular theoretical tools in quantum optics, cavity quantum electrodynamics, and optomechanics. By using the generalized Gell–Mann matrices as a basis, any Lindblad equation can be transformed into a system of ordinary differential equations with real coefficients. Recently, we presented an implementation of the transformation with the computational complexity, scaling as for dense Lindbaldians and for sparse ones. However, infeasible memory costs remains a serious obstacle on the way to large models. Here, we present a parallel cluster-based implementation of the algorithm and demonstrate that it allows us to integrate a sparse Lindbladian model of the dimension and a dense random Lindbladian model of the dimension by using 25 nodes with 64 GB RAM per node.

Block Sparse Bayesian Learning over Local Dictionary for Robust SAR Target Recognition

This paper applied block sparse Bayesian learning (BSBL) to synthetic aperture radar (SAR) target recognition. The traditional sparse representation-based classification (SRC) operates on the global dictionary collaborated by different classes. Afterwards, the similarities between the test sample and various classes are evaluated by the reconstruction errors. This paper reconstructs the test sample based on local dictionaries formed by individual classes. Considering the azimuthal sensitivity of SAR images, the linear coefficients on the local dictionary are sparse ones with block structure. Therefore, to solve the sparse coefficients, the BSBL is employed. The proposed method can better exploit the representation capability of each class, thus benefiting the recognition performance. Based on the experimental results on the moving and stationary target acquisition and recognition (MSTAR) dataset, the effectiveness and robustness of the proposed method is confirmed.

Влияние различных элементов технологии возделывания на содержание хлорофилла в растениях озимой пшеницы и ее урожайность

Abstract. The chlorophyll content is the most important factor that determines the intensity of photosynthesis and the overall biological productivity of plants. Therefore, the search for mechanisms that allow you to manage the production process is an important task, the solution of which will allow you to improve the technological methods of growing crops to obtain high yields. The purpose of the study is to determine the influence of various elements of cultivation technology on the chlorophyll content in plants and the yield of winter wheat. Methods. The objects of research were winter wheat crops of various varieties. The chlorophyll content was determined by the method of Ya. I. Milaeva and N. P. Primak. Crop accounting was performed using the combine method. Results. The relative chlorophyll content in winter wheat plants: lea predecessor on average 9,4 % higher than for cereals; the use of mineral fertilizers in a few increased this figure by 38,0 %, wheat ‒ 14,0 %; in the later sowing time the amount of green pigments in plants on average more than early and optimum of 10,5 and 4,0 %, respectively; in more thickened crops, the chlorophyll content in plants is lower than in sparse ones (by 13,0 %). The absolute chlorophyll content (g/m2) in winter wheat plants: in a few in an average of 45,0 % higher than for cereals; the use of mineral fertilizers in a few increased this figure at 73,4 %, for winter wheat ‒ 76,8 %; number of green pigments in plants at the optimum sowing time is on average higher than in the early (29,6 %) and late (15,2 %); at the optimal seeding rate accumulates more chlorophyll than the minimum (by 33,4 %) and the maximum (24,2 %). On average, for all cultivation technologies, the variety Stat' contains the largest amount of chlorophyll in plants, and Zustrich – the smallest. The yield of winter wheat for the lea precursor was 4,9 t/ha, for winter wheat – 3,3 t/ha. Use of mineral fertilizers on couple increased this indicator on average by 44,1 %, and on the cereal predecessor ‒ by 55,3 %. At the optimal time of sowing, the highest yield was formed, and on average it was 5,1 t/ha for varieties. seeding Rates did not have provable differences on the yield of winter wheat. The highest yield was obtained in the Rate variety on the predecessor of pairs on a fertilized background – 7,5 t/ha. Scientific novelty. The features of the influence of various precursors, the level of mineral nutrition, timing and seeding rates on the content of chlorophyll in plants and the yield of winter wheat crops of new varieties of selection of the North Caucasian FSAC were revealed. The correlation between the relative and absolute content of chlorophyll in winter wheat plants and its yield for these varieties in the zone of unstable moisture in the Stavropol territory was determined.

Estimation of error variance via ridge regression

Summary We propose a novel estimator of error variance and establish its asymptotic properties based on ridge regression and random matrix theory. The proposed estimator is valid under both low- and high-dimensional models, and performs well not only in nonsparse cases, but also in sparse ones. The finite-sample performance of the proposed method is assessed through an intensive numerical study, which indicates that the method is promising compared with its competitors in many interesting scenarios.

Multiple Change Points Detection in Low Rank and Sparse High Dimensional Vector Autoregressive Models

Identifying change/break points in multivariate time series represents a canonical problem in signal processing, due to numerous applications related to anomaly detection problems. The underlying detection methodology heavily depends on the nature of the mechanism determining the temporal dynamics of the data. Vector auto-regressive models (VAR) constitute a widely used model in diverse areas, including surveillance applications, economics/finance and neuroscience. In this work, we consider piece-wise stationary VAR models exhibiting break points between the corresponding stationary segments, wherein the transition matrices that govern the model's temporal evolution are decomposed into a common low-rank component and time evolving sparse ones. Further, we assume that the number of available time points are smaller than the number of model parameters and hence we are operating in a high-dimensional regime . We develop a three-step strategy that accurately detects the number of change points together with their location and subsequently estimates the model parameters in each stationary segment. The effectiveness of the proposed procedure is illustrated on both synthetic and real data sets.

ChannelNets: Compact and Efficient Convolutional Neural Networks via Channel-Wise Convolutions.

Convolutional neural networks (CNNs) have shown great capability of solving various artificial intelligence tasks. However, the increasing model size has raised challenges in employing them in resource-limited applications. In this work, we propose to compress deep models by using channel-wise convolutions, which replace dense connections among feature maps with sparse ones in CNNs. Based on this novel operation, we build light-weight CNNs known as ChannelNets. ChannelNets use three instances of channel-wise convolutions; namely group channel-wise convolutions, depth-wise separable channel-wise convolutions, and the convolutional classification layer. Compared to prior CNNs designed for mobile devices, ChannelNets achieve a significant reduction in terms of the number of parameters and computational cost without loss in accuracy. Notably, our work represents an attempt to compress the fully-connected classification layer, which usually accounts for about 25 percent of total parameters in compact CNNs. Along this new direction, we investigate the behavior of our proposed convolutional classification layer and conduct detailed analysis. Based on our in-depth analysis, we further propose convolutional classification layers without weight-sharing. This new classification layer achieves a good trade-off between fully-connected classification layers and the convolutional classification layer. Experimental results on the ImageNet dataset demonstrate that ChannelNets achieve consistently better performance compared to prior methods.

Compressing Deep Neural Networks With Sparse Matrix Factorization.

Modern deep neural networks (DNNs) are usually overparameterized and composed of a large number of learnable parameters. One of a few effective solutions attempts to compress DNN models via learning sparse weights and connections. In this article, we follow this line of research and present an alternative framework of learning sparse DNNs, with the assistance of matrix factorization. We provide an underlying principle for substituting the original parameter matrices with the multiplications of highly sparse ones, which constitutes the theoretical basis of our method. Experimental results demonstrate that our method substantially outperforms previous states of the arts for compressing various DNNs, giving rich empirical evidence in support of its effectiveness. It is also worth mentioning that, unlike many other works that focus on feedforward networks like multi-layer perceptrons and convolutional neural networks only, we also evaluate our method on a series of recurrent networks in practice.

On a Sparse Approximation of Compressible Signals

Many physical phenomena can be modeled by compressible signals, i.e., the signals with rapidly declining sample amplitudes. Although all the samples are usually nonzero, due to practical reasons such signals are attempted to be approximated as sparse ones. Because sparsity of compressible signals cannot be unambiguously determined, a decision about a particular sparse representation is often a result of comparison between a residual error energy of a reconstruction algorithm and some quality measure. The paper explores a relation between mean square error (MSE) of the recovered signal and the residual error. A novel, practical solution that controls the sparse approximation quality using a target MSE value is the result of these considerations. The solution was tested in numerical experiments using orthogonal matching pursuit (OMP) algorithm as the signal reconstruction procedure. The obtained results show that the proposed quality metric provides fine control over the approximation process of the compressible signals in the mean sense even though it has not been directly designed for use in compressed sensing methods such as OMP.

Appearance Flow Completion for Novel View Synthesis

AbstractNovel view synthesis from sparse and unstructured input views faces challenges like the difficulty with dense 3D reconstruction and large occlusion. This paper addresses these problems by estimating proper appearance flows from the target to input views to warp and blend the input views. Our method first estimates a sparse set 3D scene points using an off‐the‐shelf 3D reconstruction method and calculates sparse flows from the target to input views. Our method then performs appearance flow completion to estimate the dense flows from the corresponding sparse ones. Specifically, we design a deep fully convolutional neural network that takes sparse flows and input views as input and outputs the dense flows. Furthermore, we estimate the optical flows between input views as references to guide the estimation of dense flows between the target view and input views. Besides the dense flows, our network also estimates the masks to blend multiple warped inputs to render the target view. Experiments on the KITTI benchmark show that our method can generate high quality novel views from sparse and unstructured input views.

Frobenius linear translators giving rise to new infinite classes of permutations and bent functions

We show the existence of many infinite classes of permutations over finite fields and bent functions by extending the notion of linear translators, introduced by Kyureghyan (J. Combin. Theory Ser. A 118(3), 1052–1061, 2011). We call these translators Frobenius translators since the derivatives of $f:{\mathbb F}_{p^{n}} \rightarrow {\mathbb F}_{p^{k}}$, where n = rk, are of the form $f(x+u\gamma )-f(x)=u^{p^{i}}b$, for a fixed $b \in {\mathbb F}_{p^{k}}$ and all $u \in {\mathbb F}_{p^{k}}$, rather than considering the standard case corresponding to i = 0. It turns out that Frobenius translators correspond to standard linear translators of an exponentiated version of f, namely to $f^{p^{k-i}}$ with respect to $b^{p^{k-i}}$. Nevertheless, this concept turns out to be useful for providing further explicit specification of a rather rare family {f} of quadratic polynomials (especially sparse ones) admitting linear translators. In this direction, we solve a few open problems in the recent article (Cepak et al., Finite Fields Appl. 45, 19–42, 2017) concerning the existence and an exact specification of f admitting classical linear translators. In addition, an open problem introduced in Hodžic et al. (2018), of finding a triple of bent functions f1,f2,f3 such that their sum f4 is bent and that the sum of their duals satisfies $f_{1}^{*}+f_{2}^{*}+f_{3}^{*}+f_{4}^{*}=1$, is also resolved. We also specify two huge families of permutations over ${\mathbb F}_{p^{n}}$ related to the condition that $G(y)=-L(y)+(y+\delta )^{s}-(y+\delta )^{p^{k}s}$ permutes the set ${\mathcal S}=\{\beta \in {\mathbb F}_{p^{n}}: T{r_{k}^{n}}(\beta )=0\}$, where n = 2k and p > 2. Finally, we give some generalizations of constructions of bent functions in Mesnager et al. (2017) and describe some new bent families using the permutations found in Cepak et al. (Finite Fields Appl. 45, 19–42, 2017).

Universal hypotrochoidic law for random matrices with cyclic correlations.

The celebrated elliptic law describes the distribution of eigenvalues of random matrices with correlations between off-diagonal pairs of elements, having applications to a wide range of physical and biological systems. Here, we investigate the generalization of this law to random matrices exhibiting higher-order cyclic correlations between k tuples of matrix entries. We show that the eigenvalue spectrum in this ensemble is bounded by a hypotrochoid curve with k-fold rotational symmetry. This hypotrochoid law applies to full matrices as well as sparse ones, and thereby holds with remarkable universality. We further extend our analysis to matrices and graphs with competing cycle motifs, which are described more generally by polytrochoid spectral boundaries.

The Regression Learning of the Imbalanced and Big Data by the Online Mixture Model for the Mach Number Forecasting

Extracting valuable information to enhance the performance of forecasting models from the imbalanced and big data requires the scalable implementation of advanced statistical learning methods. This paper proposes the online mixture model (OMM) and applies it to the Mach number forecasting. Treating the key variable (e.g., Mach number) forecasting under all working conditions as an entire task, and viewing that of each individual working condition as a subtask, the OMM separates the dense samples from the sparse ones on the basis of subtasks. The subtask models are independently learnt on the samples with reduced volume, and updated for the new working conditions without retaining samples from the old working conditions. Moreover, the tree-structure ensemble (TSE)-feature subsets ensembles (FSEs) algorithm is presented to fit the nonlinear function of a subtask model, where the FSE local models with low-dimensional input features are established on the non-overlapping sample subsets constructed by the TSE method. The TSE-FSEs not only reduce the volume of data but also perform distributed computing with parallel structure, and thus has the advantage of the learning of big data. Experiments carried out on the measurement data of wind tunnel indicate that the OMM with the TSE-FSEs outperforms other learning algorithms for the Mach number forecasting, and meets the precision and forecasting speed requirements in engineering.

Random Matching Pursuit for Image Watermarking

The classical solution to an underdetermined system of linear equations mainly has two opposite directions, which lead to either a large $\ell _{2}$ -norm sparse solution or a non-sparse minimum $\ell _{2}$ -norm solution. In this paper, we systematically show that by modifying the well-known basic matching pursuit algorithm originally proposed to identify the sparse solution, an alternative solution between the two classical ones could be obtained. The modified algorithm, termed as random matching pursuit (RMP), is then used to create a novel image watermarking framework. Compared to conventional systems, the security is substantially improved by the use of random over-complete dictionaries and the order parameter of RMP. Capacity can also be increased thanks to the transform with over-complete dictionaries that could expand signal dimension. Meanwhile, imperceptibility and robustness properties of the proposed design framework are not compromised. The classical spread spectrum and improved spread spectrum techniques are applied to the proposed framework for practical implementations. The novelty and effectiveness of the proposed systems are supported by rigorous performance analysis and experimental results using an image data set. This paper reveals the potential of using over-complete dictionaries in multimedia watermarking systems, which theoretically leads to the exploration of alternative candidates among the infinite solutions to underdetermined linear systems other than minimum $\ell _{2}$ -norm and sparse ones.

A transformation approach that makes SPAI, PSAI and RSAI procedures efficient for large double irregular nonsymmetric sparse linear systems

A sparse matrix is called double irregular sparse if it has at least one relatively dense column and row, and it is double regular sparse if all the columns and rows of it are sparse. The sparse approximate inverse preconditioning procedures SPAI, PSAI( t o l ) and RSAI( t o l ) are costly and even impractical to construct preconditioners for a large sparse nonsymmetric linear system with the coefficient matrix being double irregular sparse, but they are efficient for double regular sparse problems. Double irregular sparse linear systems have a wide range of applications, and 24.4% of the nonsymmetric matrices in the Florida University collection are double irregular sparse. For this class of problems, we propose a transformation approach, which consists of four steps: (i) transform a given double irregular sparse problem into a small number of double regular sparse ones with the same coefficient matrix A ˆ , (ii) use SPAI, PSAI( t o l ) and RSAI( t o l ) to construct sparse approximate inverses M of A ˆ , (iii) solve the preconditioned double regular sparse linear systems by Krylov solvers, and (iv) recover an approximate solution of the original problem with a prescribed accuracy from those of the double regular sparse ones. A number of theoretical and practical issues are considered on the transformation approach. Numerical experiments on a number of real-world problems confirm the very sharp superiority of the transformation approach to the standard approach that preconditions the original double irregular sparse problem by SPAI, PSAI( t o l ) or RSAI( t o l ) and solves the resulting preconditioned system by Krylov solvers.

Scalable training of artificial neural networks with adaptive sparse connectivity inspired by network science

Through the success of deep learning in various domains, artificial neural networks are currently among the most used artificial intelligence methods. Taking inspiration from the network properties of biological neural networks (e.g. sparsity, scale-freeness), we argue that (contrary to general practice) artificial neural networks, too, should not have fully-connected layers. Here we propose sparse evolutionary training of artificial neural networks, an algorithm which evolves an initial sparse topology (Erdős–Rényi random graph) of two consecutive layers of neurons into a scale-free topology, during learning. Our method replaces artificial neural networks fully-connected layers with sparse ones before training, reducing quadratically the number of parameters, with no decrease in accuracy. We demonstrate our claims on restricted Boltzmann machines, multi-layer perceptrons, and convolutional neural networks for unsupervised and supervised learning on 15 datasets. Our approach has the potential to enable artificial neural networks to scale up beyond what is currently possible.

Soil seed bank under variegated thistle does not explain thistle dominance

Variegated thistle (Silybum marianum) is a large, spiny annual that often forms dense monospecific communities on dry ridges and sunny hillslopes. The owner of a typical Poverty Bay hill-country farm with persistent variegated-thistle infestations reported that winter applications of herbicide were ineffectual in the long term as more variegated thistles simply recolonised the sprayed sites. An absence of preferred species, particularly perennial ryegrass (Lolium perenne) and legumes (Lotus and Trifolium spp.), in the soil seed bank under dense thistle populations may explain the persistence of these monospecific populations. To test this hypothesis, soil samples were collected from a dense and sparse variegated-thistle population in each of seven paddocks and incubated in a glasshouse. Emerged seedlings were identified and counted. The incubation was repeated three times. Total soil seed numbers were similar under both the dense and sparse populations with similar numbers of preferred legumes under both. However, there were significantly more perennial ryegrass seeds under the dense variegated-thistle populations compared with the sparse ones. Domination of thistles in densely infested patches was not due to lack of preferred species, or indeed other weed species, in the soil seed bank.

Sparsity constraint nearest subspace classifier for target recognition of SAR images

This paper proposes a sparsity constraint nearest subspace classifier (SNSC) for target recognition of synthetic aperture radar (SAR) images. Unlike optical images, SAR images are highly sensitive to target azimuth. Therefore, the global dictionary collaborated by samples from different classes has high between-class correlation, which will impair the performance of sparse representation-based classification (SRC). Furthermore, even on the subspace spanned by a single class, only a small number of samples with similar azimuths to the test image are highly correlated with the test image. Thus, the linear coefficients over the subspace are actually sparse ones. Therefore, in this paper we impose sparsity constraint on nearest subspace classifier (NSC) classifier and apply it to SAR target recognition. The target label of the test sample is decided to be the class with the minimum reconstruction error. The proposed method is tested on moving and stationary target acquisition and recognition (MSTAR) dataset and compared with several state-of-the-art methods and the experimental results verify the validity and robustness of the proposed method.