相关论文: On algebraic and combinatorial properties of weigh…

Weakly Supervised Object Localization (WSOL) methods only require image level labels as opposed to expensive bounding box annotations required by fully supervised algorithms. We study the problem of learning localization model on target…

This paper theoretically proposes a multichannel functional metasurface computer characterized by Generalized Sheet Transition Conditions (GSTCs) and surface susceptibility tensors. The study explores a polarization- and angle-multiplexed…

The development of external evaluation criteria for soft clustering (SC) has received limited attention: existing methods do not provide a general approach to extend comparison measures to SC, and are unable to account for the uncertainty…

We define vertex cover algebras for weighted simplicial multicomplexes and prove basics properties of them. Also, we describe these algebras for multicomplexes which have only one maximal facet and we prove that they are finitely generated.

We revisit the feasibility approach to the construction of compactly supported smooth orthogonal wavelets on the line. We highlight its flexibility and illustrate how symmetry and cardinality properties are easily embedded in the design…

Polar codes are a class of {\bf structured} channel codes proposed by Ar{\i}kan based on the principle of {\bf channel polarization}, and can {\bf achieve} the symmetric capacity of any Binary-input Discrete Memoryless Channel (B-DMC). The…

A generalization of the semisimplicity concept for polyadic algebraic structures is proposed. If semisimple structures can be presented in block diagonal matrix form (resulting in the Wedderburn decomposition), a general form of polyadic…

Clustering is a fundamental task for analyzing unlabeled data based solely on its underlying distribution. Spectral clustering is a clustering method that represents a dataset as a graph and uses the relationships between data points.…

A method is proposed, called channel polarization, to construct code sequences that achieve the symmetric capacity $I(W)$ of any given binary-input discrete memoryless channel (B-DMC) $W$. The symmetric capacity is the highest rate…

Most multi-view clustering methods are limited by shallow models without sound nonlinear information perception capability, or fail to effectively exploit complementary information hidden in different views. To tackle these issues, we…

Polar codes are usually constructed by ranking synthetic bit-channels according to reliability, which guarantees capacity-achieving behavior but can yield poor low-weight spectra at short and moderate lengths. Recent algebraic results…

Clustering the nodes of a graph allows the analysis of the topology of a network. The stochastic block model is a clustering method based on a probabilistic model. Initially developed for binary networks it has recently been extended to…

Context: The huge and still rapidly growing amount of galaxies in modern sky surveys raises the need of an automated and objective classification method. Unsupervised learning algorithms are of particular interest, since they discover…

For large-scale point cloud processing, resampling takes the important role of controlling the point number and density while keeping the geometric consistency. % in related tasks. However, current methods cannot balance such different…

Abstract separation systems provide a simple general framework in which both tree-shape and high cohesion of many combinatorial structures can be expressed, and their duality proved. Applications range from tangle-type duality and tree…

Higher-order networks are able to capture the many-body interactions present in complex systems and to unveil new fundamental phenomena revealing the rich interplay between topology, geometry, and dynamics. Simplicial complexes are…

One emerging approach for the fabrication of complex architectures on the nanoscale is to utilize particles customized to intrinsically self-assemble into a desired structure. Inverse methods of statistical mechanics have proven…

A study of correlations in tractable multiparticle cascade models in terms of wavelets reveals many promising features. The selfsimilar construction of the wavelet basis functions and their multiscale localization properties provide a new…

Clustering techniques create hierarchal network structures, called clusters, on an otherwise flat network. In a dynamic environment-in terms of node mobility as well as in terms of steadily changing device parameters-the clusterhead…

We study a number of topics in the theory of Boolean Representable Simplicial Complexes (BRSC). These include various operators on BRSC. We look at shellability in higher dimensions and propose a number of new conjectures.