Related papers: Potent and Max-Flow Algorithms
This paper presents a methodology and numerical algorithms for constructing accelerated gradient flows on the space of probability distributions. In particular, we extend the recent variational formulation of accelerated gradient methods in…
Retrieving the phase of a complex-valued field from the measurements of its amplitude is a crucial problem with a wide range of applications in microscopy and ultracold atomic physics. In particular, obtaining an accurate and efficient…
The vortex method is a common numerical and theoretical approach used to implement the motion of an ideal flow, in which the vorticity is approximated by a sum of point vortices, so that the Euler equations read as a system of ordinary…
In this paper, we propose a new method for path planning to a point for robot in environment with obstacles. The resulting algorithm is implemented as a simple variation of Dijkstra's algorithm. By adding a constraint to the shortest-path,…
This paper presents a new gradient flow dissipation geometry over non-negative and probability measures. This is motivated by a principled construction that combines the unbalanced optimal transport and interaction forces modeled by…
We propose a method for optimal Bayesian filtering with deterministic particles. In order to avoid particle degeneration, the filter step is not performed at once. Instead, the particles progressively flow from prior to posterior. This is…
In this article we give an account of a method of smoothing spatial inhomogeneous data sets by using wavelet reconstruction on a regular grid in an auxilliary space onto which the original data is mapped. In a previous paper by the present…
We present an algorithm for computing $s$-$t$ maximum flows in directed graphs in $\widetilde{O}(m^{4/3+o(1)}U^{1/3})$ time. Our algorithm is inspired by potential reduction interior point methods for linear programming. Instead of using…
Stellar kinematics provide a window into the gravitational field, and therefore into the distribution of all mass, including dark matter. Deep Potential is a method for determining the gravitational potential from a snapshot of stellar…
Given a multidimensional free-energy or potential-energy landscape, finding reaction paths that connect an initial (or reactant) state and a final (or product) state is important for biophysics and materials science. The likelihood of a…
We develop new algorithmic techniques for VLSI detailed routing. First, we improve the goal-oriented version of Dijkstra's algorithm to find shortest paths in huge incomplete grid graphs with edge costs depending on the direction and the…
The vortex method is a common numerical and theoretical approach used to implement the motion of an ideal flow, in which the vorticity is approximated by a sum of point vortices, so that the Euler equations read as a system of ordinary…
Line integration of stream-, streak-, and pathlines is widely used and popular for visualizing single-phase flow. In multiphase flow, i.e., where the fluid consists, e.g., of a liquid and a gaseous phase, these techniques could also provide…
A passive scalar is advected by a velocity field, with a nonuniform spatial source that maintains concentration inhomogeneities. For example, the scalar could be temperature with a source consisting of hot and cold spots, such that the mean…
The generation of 3D molecules requires simultaneously deciding the categorical features~(atom types) and continuous features~(atom coordinates). Deep generative models, especially Diffusion Models (DMs), have demonstrated effectiveness in…
We give an algorithm for computing exact maximum flows on graphs with $m$ edges and integer capacities in the range $[1, U]$ in $\widetilde{O}(m^{\frac{3}{2} - \frac{1}{328}} \log U)$ time. For sparse graphs with polynomially bounded…
Two path integral representations for the $T$-matrix in nonrelativistic potential scattering are derived and proved to produce the complete Born series when expanded to all orders. They are obtained with the help of "phantom" degrees of…
The advent of datasets of stars in the Milky Way with six-dimensional phase-space information makes it possible to construct empirically the distribution function (DF). Here, we show that the accelerations can be uniquely determined from…
Transmission system operators need to adapt their decision-making tools to the technological evolutions of the twenty first century. A computation inherent to most tools seeks to find alternating-current power flows that minimize power loss…
We give an $O(k^3 n \log n \min(k,\log^2 n) \log^2(nC))$-time algorithm for computing maximum integer flows in planar graphs with integer arc {\em and vertex} capacities bounded by $C$, and $k$ sources and sinks. This improves by a factor…