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A computational theory for clustering and a semi-supervised clustering algorithm is presented. Clustering is defined to be the obtainment of groupings of data such that each group contains no anomalies with respect to a chosen grouping…
Accurate pipe roughness estimation in large-scale water distribution networks is often hindered by the high cost of traditional field methods. This study investigates whether network partitioning, by utilizing hydraulic and graph-derived…
A parallel lightlike vector field on a Lorentzian manifold $X$ naturally defines a foliation $\mathcal{F}$ of codimension one. If either all leaves of $\mathcal{F}$ are compact or $X$ itself is compact admitting a compact leaf and the…
Using linearized elasticity as a convenient mechanical framework, we show that volumetric growth can be formulated as an optimization-driven process in which the growth tensor is determined implicitly by constrained optimization rather than…
This paper proposes an improved lattice Boltzmann scheme for incompressible axisymmetric flows. The scheme has the following features. First, it is still within the framework of the standard lattice Boltzmann method using the…
We describe an algorithm based on a logarithmic barrier function, Newton's method, and linear conjugate gradients that obtains an approximate minimizer of a smooth function over the nonnegative orthant. We develop a bound on the complexity…
Several issues in machine learning and inverse problems require to generate discrete data, as if sampled from a model probability distribution. A common way to do so relies on the construction of a uniform probability distribution over a…
A database of minima and transition states corresponds to a network where the minima represent nodes and the transition states correspond to edges between the pairs of minima they connect via steepest-descent paths. Here we construct…
We revisit the one-dimensional model of the symmetric simple exclusion process slowly coupled with two unequal reservoirs at the boundaries. In its non-equilibrium stationary state, the large deviations functions of density and current have…
In arXiv:1801.01238 a variation of Bowen's topological entropy that can be applied to the study of discontinuous semiflows on compact metric spaces was introduced. The main novetly is the use of certain family of pseudosemimetrics…
We introduce a new metric to assess the quality of generated images that is more reliable, data-efficient, compute-efficient, and adaptable to new domains than the previous metrics, such as Fr\'echet Inception Distance (FID). The proposed…
The logarithmic minimal models are not rational but, in the W-extended picture, they resemble rational conformal field theories. We argue that the W-projective representations are fundamental building blocks in both the boundary and bulk…
We propose two new evaluation metrics to assess realness of generated images based on normalizing flows: a simpler and efficient flow-based likelihood distance (FLD) and a more exact dual-flow based likelihood distance (D-FLD). Because…
Exponential random graph theory is the complex network analog of the canonical ensemble theory from statistical physics. While it has been particularly successful in modeling networks with specified degree distributions, a naive model of a…
This paper looks to apply the mathematical framework of the Theory of Functional Connections to the solution of boundary-value problems arising from hybrid systems. The Theory of Functional Connections is a technique to derive constrained…
We develop efficient algorithms for a fundamental network design problem arising in potential-based flow models, which are central to many energy transport networks (e.g., hydrogen and electricity). In contrast to classical network flow…
An existence and uniqueness result, up to fattening, for crystalline mean curvature flows with forcing and arbitrary (convex) mobilities, is proven. This is achieved by introducing a new notion of solution to the corresponding level set…
The embedding of finite metrics in $\ell_1$ has become a fundamental tool for both combinatorial optimization and large-scale data analysis. One important application is to network flow problems in which there is close relation between…
The lattice Boltzmann method has been successfully applied for the simulation of flow through porous media in the creeping regime. Its technical properties, namely discretization, straightforward implementation and parallelization, are…
We give a deterministic algorithm for finding the minimum (weight) cut of an undirected graph on $n$ vertices and $m$ edges using $\text{polylog}(n)$ calls to any maximum flow subroutine. Using the current best deterministic maximum flow…