13 citations · 19 across the 17 of their papers we have counts for
22 papers
Algebraic Distance Optimization in Polyhedral Norms
Eliana Duarte, Nidhi Kaihnsa, Julia Lindberg +2
We consider the distance minimization problem to a real algebraic variety $X \subseteq \RR^n$ when the metric is induced by a polyhedral norm. Each point in the variety has a Voron…
Reinforcement Learning for Power-Flow Network Analysis
Alperen Ergur, Julia Lindberg, Vinny Miller
The power flow equations are non-linear multivariate equations that describe the relationship between power injections and bus voltages of electric power networks. Given a network…
Efficient Tensor Decomposition via Moment Matrix Extension
Bobby Shi, Julia Lindberg, Joe Kileel
Motivated by a flurry of recent work on efficient tensor decomposition algorithms, we show that the celebrated moment matrix extension algorithm of Brachat, Comon, Mourrain, and Ts…
Tropical Bisectors and Carlini-Wagner Attacks
Gillian Grindstaff, Julia Lindberg, Daniela Schkoda +2
Pasque et al. showed that using a tropical symmetric metric as an activation function in the last layer can improve the robustness of convolutional neural networks (CNNs) against s…
Method of moments for Gaussian mixtures: Implementation and benchmarks
Haley Colgate Kottler, Julia Lindberg, Jose Israel Rodriguez
Gaussian mixture models are universal approximators in the sense that any smooth density can be approximated arbitrarily well with a Gaussian mixture model with enough components.…
Symmetric Hyperbolic Polynomials
Grigoriy Blekherman, Julia Lindberg, Kevin Shu
Hyperbolic polynomials have been of recent interest due to applications in a wide variety of fields. We seek to better understand these polynomials in the case when they are symmet…
The algebraic degree of sparse polynomial optimization
Julia Lindberg, Leonid Monin, Kemal Rose
We study a broad class of polynomial optimization problems whose constraints and objective functions exhibit sparsity patterns. We give two characterizations of the number of criti…
The symmetric geometric rank of symmetric tensors
Julia Lindberg, Pierpaola Santarsiero
Inspired by recent work of Kopparty-Moshkovitz-Zuiddam and motivated by problems in combinatorics and hypergraphs, we introduce the notion of the symmetric geometric rank of a symm…
A polyhedral homotopy algorithm for computing critical points of polynomial programs
Julia Lindberg, Leonid Monin, Kemal Rose
In this paper we propose a method that uses Lagrange multipliers and numerical algebraic geometry to find all critical points, and therefore globally solve, polynomial optimization…
Real circles tangent to 3 conics
Paul Breiding, Julia Lindberg, Wern Juin Gabriel Ong +1
In this paper we study circles tangent to conics. We show there are generically complex circles tangent to three conics in the plane and we characterize the real discriminant…
Invariants of SDP exactness in quadratic programming
Julia Lindberg, Jose Rodriguez
In this paper we study the Shor relaxation of quadratic programs by fixing a feasible set and considering the space of objective functions for which the Shor relaxation is exact. W…
On the typical and atypical solutions to the Kuramoto equations
Tianran Chen, Evgeniia Korchevskaia, Julia Lindberg
The Kuramoto model is a dynamical system that models the interaction of coupled oscillators. There has been much work to effectively bound the number of equilibria to the Kuramoto…
Deploying Enhanced Speech Feature Decreased Audio Complaints at SVT Play VOD Service
Annika Bidner, Julia Lindberg, Olof Lindman +1
At Public Service Broadcaster SVT in Sweden, background music and sounds in programs have for many years been one of the most common complaints from the viewers. The most sensitive…
Implementing real polyhedral homotopy
Kisun Lee, Julia Lindberg, Jose Israel Rodriguez
We implement a real polyhedral homotopy method using three functions. The first function provides a certificate that our real polyhedral homotopy is applicable to a given system; t…
Using Geographic Load Shifting to Reduce Carbon Emissions
Julia Lindberg, Bernard C. Lesieutre, Line A. Roald
An increasing focus on the electricity use and carbon emissions associated with computing has lead to pledges by major cloud computing companies to lower their carbon footprint. Da…
Estimating Gaussian mixtures using sparse polynomial moment systems
Julia Lindberg, Carlos Améndola, Jose Israel Rodriguez
The method of moments is a classical statistical technique for density estimation that solves a system of moment equations to estimate the parameters of an unknown distribution. A…
A Guide to Reducing Carbon Emissions through Data Center Geographical Load Shifting
Julia Lindberg, Yasmine Abdennadher, Jiaqi Chen +2
Recent computing needs have lead technology companies to develop large scale, highly optimized data centers. These data centers represent large loads on electric power networks whi…
The maximum likelihood degree of sparse polynomial systems
Julia Lindberg, Nathan Nicholson, Jose Israel Rodriguez +1
We consider statistical models arising from the common set of solutions to a sparse polynomial system with general coefficients. The maximum likelihood degree counts the number of…
Exploiting Symmetry in the Power Flow Equations Using Monodromy
Julia Lindberg, Nigel Boston, Bernard C. Lesieutre
We propose solving the power flow equations using monodromy. We prove the variety under consideration decomposes into trivial and nontrivial subvarieties and that the nontrivial su…
The Environmental Potential of Hyper-Scale Data Centers: Using Locational Marginal CO Emissions to Guide Geographical Load Shifting
Julia Lindberg, Bernard C. Lesieutre, Line Roald
Increasing demand for computing has lead to the development of large-scale, highly optimized data centers, which represent large loads in the electric power network. Many major com…
The Distribution of the Number of Real Solutions to the Power Flow Equations
Julia Lindberg, Alisha Zachariah, Nigel Boston +1
In this paper we study the distributions of the number of real solutions to the power flow equations over varying electrical parameters. We introduce a new monodromy and parameter…
Solving Parameterized Polynomial Systems with Decomposable Projections
Carlos Améndola, Julia Lindberg, Jose Israel Rodriguez
The Galois group of a parameterized polynomial system of equations encodes the structure of the solutions. This monodromy group acts on the set of solutions for a general set of pa…