相关论文: Discrete fragmentation systems in weighted $\ell^1…

We calculate the time-evolution of a discrete-time fragmentation process in which clusters of particles break up and reassemble and move stochastically with size-dependent rates. In the continuous-time limit the process turns into the…

We consider the Cauchy problem of massless Dirac-Maxwell equations on an asymptotically flat background and give a global existence and uniqueness theorem for initial values small in an appropriate weighted Sobolev space. The result can be…

Utilizing a partitioning method based on equal (or unequal) probabilities -- without incorporating the alpha-cluster ($\alpha$-cluster) model -- allows for the derivation of diverse topological configurations of nuclear fragments resulting…

We consider the natural time-dependent fractional $p$-Laplacian equation posed in the whole Euclidean space, with parameter $1<p<2$ and fractional exponent $s\in (0,1)$. Rather standard theory shows that the Cauchy Problem for data in the…

We use SPH simulations to investigate the gravitational fragmentation of expanding shells through the linear and non--linear regimes. The results are analysed using spherical harmonic decomposition to capture the initiation of structure…

We employ the perturbative field-theoretic renormalization group method to investigate the universal critical behavior near the continuous non-equilibrium phase transition in the complex Ginzburg-Landau equation with additive white noise.…

We study the convergence of semilinear parabolic stochastic evolution equations, posed on a sequence of Banach spaces approximating a limiting space and driven by additive white noise projected onto the former spaces. Under appropriate…

We consider the Cauchy problem for a second-order nonlinear evolution equation in a Hilbert space. This equation represents the abstract generalization of the Ball integro-differential equation. The general nonlinear case with respect to…

Semi-supervised clustering is a basic problem in various applications. Most existing methods require knowledge of the ideal cluster number, which is often difficult to obtain in practice. Besides, satisfying the must-link constraints is…

In reaction-diffusion models of annihilation reactions in low dimensions, single-particle dynamics provides a bottleneck for reactions, leading to an anomalously slow approach to the empty state. Here, we construct a reaction model with a…

Let $X,X_1,X_2,\ldots$ be i.i.d. mean zero random vectors with values in a separable Banach space $B$, $S_n=X_1+\cdots+X_n$ for $n\ge1$, and assume $\{c_n:n\ge1\}$ is a suitably regular sequence of constants. Furthermore, let…

As a model problem for clustering, we consider the densest k-disjoint-clique problem of partitioning a weighted complete graph into k disjoint subgraphs such that the sum of the densities of these subgraphs is maximized. We establish that…

Accurate approximations of the change of system's output and its statistics with respect to the input are highly desired in computational dynamics. Ruelle's linear response theory provides breakthrough mathematical machinery for computing…

Due to the seminal works of Hochbruck and Ostermann exponential splittings are well established numerical methods utilizing operator semigroup theory for the treatment of semilinear evolution equations whose principal linear part involves a…

Partitioning is a fundamental challenge for non-centralized control of large-scale systems, such as hierarchical, decentralized, distributed, and coalitional strategies. The problem consists of finding a decomposition of a network of…

The problem of clustering is considered, for the case when each data point is a sample generated by a stationary ergodic process. We propose a very natural asymptotic notion of consistency, and show that simple consistent algorithms exist,…

The problem of clustering is considered, for the case when each data point is a sample generated by a stationary ergodic process. We propose a very natural asymptotic notion of consistency, and show that simple consistent algorithms exist,…

We propose a theoretical framework that generalizes simple and fast algorithms for hierarchical agglomerative clustering to weighted graphs with both attractive and repulsive interactions between the nodes. This framework defines GASP, a…

We study the propagation properties of the solutions of the finite-difference space semi-discrete wave equation on an uniform grid of the whole Euclidean space. We provide a construction of high frequency wave packets that propagate along…

We study anomaly clustering, grouping data into coherent clusters of anomaly types. This is different from anomaly detection that aims to divide anomalies from normal data. Unlike object-centered image clustering, anomaly clustering is…