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Granular convergence is a property of a granular pack as it is repeatedly sheared in a cyclic, quasistatic fashion, as the packing configuration changes via discrete events. Under suitable conditions the set of microscopic configurations…
In this paper, we introduce and develop the circle embedding method. This method hinges essentially on a combinatorial-geometric structure which we choose to call circles of partition. We provide applications in the context of problems that…
We present a finite-order system of recurrence relations for a permanent of circulant matrices containing a band of k any-value diagonals on top of a uniform matrix (for k = 1, 2, and 3) as well as the method for deriving such recurrence…
An agglomerative clustering of random variables is proposed, where clusters of random variables sharing the maximum amount of multivariate mutual information are merged successively to form larger clusters. Compared to the previous…
The analysis of continously larger datasets is a task of major importance in a wide variety of scientific fields. In this sense, cluster analysis algorithms are a key element of exploratory data analysis, due to their easiness in the…
The Planck Collaboration has shown that the number of clusters as a function of their mass and redshift is an extremely powerful tool for cosmological analyses. However, the true cluster mass is not directly measurable. Among the possible…
One of the fundamental problems in network analysis is detecting community structure in multi-layer networks, of which each layer represents one type of edge information among the nodes. We propose integrative spectral clustering approaches…
The concept of QCD sum rules is extended to bound states composed of particles with finite mass such as scalar quarks or strange quarks. It turns out that mass corrections become important in this context. The number of relevant corrections…
Clustering of data points is a fundamental tool in data analysis. We consider points $X$ in a relaxed metric space, where the triangle inequality holds within a constant factor. The {\em cost} of clustering $X$ by $Q$ is $V(Q)=\sum_{x\in X}…
A scaling theory is developed for diffusion-limited cluster aggregation in a porous medium, where the primary particles and clusters stick irreversibly to the walls of the pore space as well as to each other. Three scaling regimes are…
This article is devoted to the study of existence of a mass conserving global solution for the collision-induced nonlinear fragmentation model which arises in particulate processes, with the singular type of collision kernel. The above…
The randomized $k$-number partitioning problem is the task to distribute $N$ i.i.d. random variables into $k$ groups in such a way that the sums of the variables in each group are as similar as possible. The restricted $k$-partitioning…
In many applications of X-ray computed tomography, an unsupervised segmentation of the reconstructed 3D volumes forms an important step in the image processing chain for further investigation of the digitized object. Therefore, the goal is…
Clustering is a widely used unsupervised learning method for finding structure in the data. However, the resulting clusters are typically presented without any guarantees on their robustness; slightly changing the used data sample or…
Existing clustering methods are based on a single granularity of information, such as the distance and density of each data. This most fine-grained based approach is usually inefficient and susceptible to noise. Inspired by adaptive process…
We suggest efficient and provable methods to compute an approximation for imbalanced point clustering, that is, fitting $k$-centers to a set of points in $\mathbb{R}^d$, for any $d,k\geq 1$. To this end, we utilize \emph{coresets}, which,…
Clustering serves as a vital tool for uncovering latent data structures, and achieving both high accuracy and interpretability is essential. To this end, existing methods typically construct binary decision trees by solving mixed-integer…
Clustering is a fundamental problem in unsupervised machine learning with many applications in data analysis. Popular clustering algorithms such as Lloyd's algorithm and $k$-means++ can take $\Omega(ndk)$ time when clustering $n$ points in…
For any infinite zero-density integer set M, we found a rigid measure-preserving transformation mixing along M by answering Bergelson's question. Gaussian and Poisson suspensions over infinite constructions are suggested as suitable…
A one-dimensional cluster model with next-nearest-neighbor interactions and two additional composite interactions is solved; the free energy is obtained and a correlation function is derived exactly. The model is diagonalized by a…