Sharp sphere packings

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Increasing the scanning speed in Atomic Force Microscopy (AFM) relies on improving the tracking performance in the vertical direction of motion. The lightly damped resonances of piezo-actuators utilized in AFM nano-positioning stages hinder the maximum ach ...

We prove that the Cohn-Elkies linear programming bound for sphere packing is not sharp in dimension 6. The proof uses duality and optimization over a space of modular forms, generalizing a construction of Cohn- Triantafillou [Math. Comp. 91 (2021), pp. 491 ...

We develop new tools to study landscapes in nonconvex optimization. Given one optimization problem, we pair it with another by smoothly parametrizing the domain. This is either for practical purposes (e.g., to use smooth optimization algorithms with good g ...

We provide new explicit examples of lattice sphere packings in dimensions 54, 55, 162, 163, 486 and 487 that are the densest known so far, using Kummer families of elliptic curves over global function fields. In some cases, these families of elliptic curve ...

Orthogonal group synchronization is the problem of estimating n elements Z(1),& mldr;,Z(n) from the rxr orthogonal group given some relative measurements R-ij approximate to Z(i)Z(j)(-1). The least-squares formulation is nonconvex. To avoid its local minim ...

Cutting plane methods are a fundamental approach for solving integer linear programs (ILPs). In each iteration of such methods, additional linear constraints (cuts) are introduced to the constraint set with the aim of excluding the previous fractional opti ...

This paper develops a fast algorithm for computing the equilibrium assignment with the perturbed utility route choice (PURC) model. Without compromise, this allows the significant advantages of the PURC model to be used in large-scale applications. We form ...

This paper offers a new algorithm to efficiently optimize scheduling decisions for dial-a-ride problems (DARPs), including problem variants considering electric and autonomous vehicles (e-ADARPs). The scheduling heuristic, based on linear programming theor ...

Established techniques that enable robots to learn from demonstrations are based on learning a stable dynamical system (DS). To increase the robots' resilience to perturbations during tasks that involve static obstacle avoidance, we propose incorporating b ...

In light of the challenges posed by climate change and the goals of the Paris Agreement, electricity generation is shifting to a more renewable and decentralized pattern, while the operation of systems like buildings is increasingly electrified. This calls ...

We introduce and derive the Fourier -enhanced 3D electrostatic field solver of the gyrokinetic full -f PIC code PICLS. The solver makes use of a Fourier representation in one periodic direction of the domain to make the solving of the system easily paralle ...

We develop a very general version of the hyperbola method which extends the known method by Blomer and Brudern for products of projective spaces to complete smooth split toric varieties. We use it to count Campana points of bounded log-anticanonical height ...

Distributed learning is the key for enabling training of modern large-scale machine learning models, through parallelising the learning process. Collaborative learning is essential for learning from privacy-sensitive data that is distributed across various ...

We prove a sharp quantitative version of the Faber–Krahn inequality for the short-time Fourier transform (STFT). To do so, we consider a deficit which measures by how much the STFT of a function fails to be optimally concentrated on an arbitrary set of pos ...

Modern power distribution systems are experiencing a large-scale integration of Converter-Interfaced Distributed Energy Resources (CIDERs). Their presence complicates the analysis and mitigation of harmonics, whose creation and propagation may be amplified ...

The increasing reliance on numerical methods for controlling dynamical systems and training machine learning models underscores the need to devise algorithms that dependably and efficiently navigate complex optimization landscapes. Classical gradient desce ...

In this paper, we present a new parameterization and optimization procedure for minimizing the weight of ribbed plates. The primary goal is to reduce embodied CO2 in concrete floors as part of the effort to diminish the carbon footprint of the construction ...

The Schottky monitors of the Large Hadron Collider (LHC) can be used for non-invasive beam diagnostics to estimate various bunch characteristics, such as tune, chromaticity, bunch profile or synchrotron frequency distribution. However, collective effects, ...

Modern optimization is tasked with handling applications of increasingly large scale, chiefly due to the massive amounts of widely available data and the ever-growing reach of Machine Learning. Consequently, this area of research is under steady pressure t ...

Quantum support vector machines employ quantum circuits to define the kernel function. It has been shown that this approach offers a provable exponential speedup compared to any known classical algorithm for certain data sets. The training of such models c ...

Sharp sphere packings

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Data-driven control in atomic force microscopy using a genetic algorithm

Six-dimensional sphere packing and linear programming

The effect of smooth parametrizations on nonconvex optimization landscapes

Some Mordell-Weil lattices and applications to sphere packings

BENIGN LANDSCAPES OF LOW-DIMENSIONAL RELAXATIONS FOR ORTHOGONAL SYNCHRONIZATION ON GENERAL GRAPHS

Learning to Remove Cuts in Integer Linear Programming

Perturbed Utility Stochastic Traffic Assignment

A ride time-oriented scheduling algorithm for dial-a-ride problems

Learning Barrier-Certified Polynomial Dynamical Systems for Obstacle Avoidance with Robots

Quantifying the Unknown: Data-Driven Approaches and Applications in Energy Systems

Verification of the Fourier-enhanced 3D finite element Poisson solver of the gyrokinetic full-f code PICLS

HYPERBOLA METHOD ON TORIC VARIETIES

Optimization Algorithms for Decentralized, Distributed and Collaborative Machine Learning

Stability of the Faber-Krahn inequality for the short-time Fourier transform

Unified Harmonic Power-Flow and Stability Analysis of Power Grids with Converter-Interfaced Distributed Energy Resources

Learning to Optimize with Convergence Guarantees Using Nonlinear System Theory

Mesh-based topology, shape and sizing optimization of ribbed plates

Impact of beam-coupling impedance on the Schottky spectrum of bunched beam

Scalable constrained optimization

The complexity of quantum support vector machines