Related papers: Combinatorial solutions to generalized electrorheo…
We consider a system of particles confined in a box $\La\subset\R^d$ interacting via a tempered and stable pair potential. We prove the validity of the cluster expansion for the canonical partition function in the high temperature - low…
We present a comprehensive study of the commute time kernel method via the effective resistance framework analyzing the quantum complexity of the originally classical approach. Our study reveals that while there is a trade-off between…
We consider the problem of gelation in the cluster coagulation model introduced by Norris [\textit{Comm. Math. Phys.}, 209(2):407-435 (2000)], where pairs of clusters of types $(x,y)$ taking values in a measure space $E$, merge to form a…
We generalize the compact group approach to conducting systems to give a self-consistent analytical solution to the problem of the effective quasistatic electrical conductivity of macroscopically homogeneous and isotropic dispersions of…
We present a novel way of modeling common envelope evolution in binary and few-body systems. We consider the common envelope inspiral as driven by a drag force with a power-law dependence in relative distance and velocity. The orbital…
In this paper, we consider the task of clustering a set of individual time series while modeling each cluster, that is, model-based time series clustering. The task requires a parametric model with sufficient flexibility to describe the…
The empirical observation of aggregation of dielectric particles under the influence of electrostatic forces lies at the origin of the theory of electricity. The growth of clusters formed of small grains underpins a range of phenomena from…
Molecular dynamics (MD) simulation has been employed to study the nonequilibrium structure formation of two types of particles in a colloidal suspension, driven by type-dependent forces. We examined the time evolution of structure formation…
Kernel-based methods offer a powerful and flexible mathematical framework for addressing histopolation problems. In histopolation, the available input data does not consist of pointwise function samples but of averages taken over intervals…
Kernel $k$-means clustering is a powerful tool for unsupervised learning of non-linearly separable data. Since the earliest attempts, researchers have noted that such algorithms often become trapped by local minima arising from…
Group equivariant convolutional networks (GCNNs) endow classical convolutional networks with additional symmetry priors, which can lead to a considerably improved performance. Recent advances in the theoretical description of GCNNs revealed…
We propose a kernel compression method for solving Distributed-Order (DO) Fractional Partial Differential Equations (DOFPDEs) at the cost of solving corresponding local-in-time PDEs. The key concepts are (1) discretization of the integral…
Despite their wide presence in various models in the study of collective behaviors, explicit swarming patterns are difficult to obtain. In this paper, special stationary solutions of the aggregation equation with power-law kernels are…
When a strong electric field is applied to a colloidal suspension, it may cause an aggregation of the suspended particles in response to the field. In the case of a rotating field, the electrorotation (ER) spectrum can be modified further…
We elaborate on a general method that we recently introduced for characterizing the "natural" structures in complex physical systems via a multiscale network based approach for the data mining of such structures. The approach is based on…
We describe early success in the evolution of binary black hole spacetimes with a numerical code based on a generalization of harmonic coordinates. Indications are that with sufficient resolution this scheme is capable of evolving binary…
An efficient simulation framework is proposed to model collective emission in disordered ensembles of quantum emitters. Using a cumulant expansion approach, the computational complexity scales polynomially as opposed to exponentially with…
The continuous generalized exchange-driven growth model (CGEDG) is a coagulation-fragmentation equation that describes the evolution of the macroscopic cluster size distribution induced by a microscopic dynamic of binary exchanges of masses…
Simulating energy systems is vital for energy planning to understand the effects of fluctuating renewable energy sources and integration of multiple energy sectors. Capacity expansion is a powerful tool for energy analysts and consists of…
We derive diffusive macroscopic equations for the particle and energy density of a system whose time evolution is described by a kinetic equation for the one particle position and velocity function f(r,v,t) that consists of a part that…