Andrea L. Bertozzi

Andrea L. Bertozzi
University of California, Los Angeles | UCLA · Department of Mathematics

PhD

About

406
Publications
59,156
Reads
How we measure 'reads'
A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more
16,964
Citations
Citations since 2017
139 Research Items
8431 Citations
201720182019202020212022202305001,0001,500
201720182019202020212022202305001,0001,500
201720182019202020212022202305001,0001,500
201720182019202020212022202305001,0001,500
Additional affiliations
December 2012 - present
University of California, Los Angeles
Position
  • Chair
July 2005 - present
University of California, Los Angeles
Position
  • Managing Director
July 2003 - present
University of California, Los Angeles
Position
  • Professor
Education
July 1987 - June 1991
Princeton University
Field of study
  • Mathematics
September 1983 - June 1987
Princeton University
Field of study
  • Mathematics

Publications

Publications (406)
Preprint
Full-text available
Symmetry plays a major role in subgraph matching both in the description of the graphs in question and in how it confounds the search process. This work addresses how to quantify these effects and how to use symmetries to increase the efficiency of subgraph isomorphism algorithms. We introduce rigorous definitions of structural equivalence and esta...
Article
Symmetry plays a major role in subgraph matching both in the description of the graphs in question and in how it confounds the search process. This work addresses how to quantify these effects and how to use symmetries to increase the efficiency of subgraph isomorphism algorithms. We introduce rigorous definitions of structural equivalence and esta...
Article
Purpose The impact of the COVID-19 pandemic on crime has been highly variable. One possible source of variation runs indirectly through the impact that the pandemic had on groups tasked with preventing and responding to crime. Here, this paper aims to examine the impact of the pandemic on the activities undertaken by front-line workers in the City...
Preprint
Full-text available
Pretraining neural networks with massive unlabeled datasets have become popular as it equips the deep models with a better prior to solve downstream tasks. However, this approach generally assumes that for downstream tasks, we have access to annotated data of sufficient size. In this work, we propose ALOE, a novel system for improving the data- and...
Article
In this paper, we use modified versions of the SIAR model for epidemics to propose two ways of understanding and quantifying the effect of non-compliance to non-pharmaceutical intervention measures on the spread of an infectious disease. The SIAR model distinguishes between symptomatic infected (I) and asymptomatic infected (A) populations. One mod...
Article
Full-text available
An important area of microfluidics is the creation and manipulation of small droplets. This is commonly done using microchannels or electrowetting. Recently a new method is proposed to create templated droplets using amphiphilic microparticles. These particles are observed to hold nearly equal volumes of aqueous liquid when dispersed in an oil–wate...
Preprint
Full-text available
Learning neural ODEs often requires solving very stiff ODE systems, primarily using explicit adaptive step size ODE solvers. These solvers are computationally expensive, requiring the use of tiny step sizes for numerical stability and accuracy guarantees. This paper considers learning neural ODEs using implicit ODE solvers of different orders lever...
Preprint
We present a novel method for classification of Synthetic Aperture Radar (SAR) data by combining ideas from graph-based learning and neural network methods within an active learning framework. Graph-based methods in machine learning are based on a similarity graph constructed from the data. When the data consists of raw images composed of scenes, e...
Chapter
This chapter presents a novel point process model for COVID-19 transmission—the multivariate recursive Hawkes process, which is an extension of the recursive Hawkes model to the multivariate case. Equivalently the model can be viewed as an extension of the multivariate Hawkes model to allow for varying productivity as in the recursive model. Severa...
Preprint
Full-text available
Microchannels are well-known in microfluidic applications for the control and separation of microdroplets and cells. Often the objects in the flow experience inertial effects, resulting in dynamics that is a departure from the underlying channel flow dynamics. This paper considers small neutrally buoyant spherical particles suspended in flow throug...
Article
Deterministic compartmental models for infectious diseases give the mean behaviour of stochastic agent-based models. These models work well for counterfactual studies in which a fully mixed large-scale population is relevant. However, with finite size populations, chance variations may lead to significant departures from the mean. In real-life appl...
Article
During the COVID-19 pandemic, conflicting opinions on physical distancing swept across social media, affecting both human behavior and the spread of COVID-19. Inspired by such phenomena, we construct a two-layer multiplex network for the coupled spread of a disease and conflicting opinions. We model each process as a contagion. On one layer, we con...
Article
Full-text available
Analyzing and understanding the movement of the mitral valve is of vital importance in cardiology, as the treatment and prevention of several serious heart diseases depend on it. Unfortunately, large amounts of noise as well as a highly varying image quality make the automatic tracking and segmentation of the mitral valve in two-dimensional echocar...
Preprint
Full-text available
Active learning in semi-supervised classification involves introducing additional labels for unlabelled data to improve the accuracy of the underlying classifier. A challenge is to identify which points to label to best improve performance while limiting the number of new labels. "Model-change" active learning quantifies the resulting change incurr...
Preprint
The construction and application of knowledge graphs have seen a rapid increase across many disciplines in recent years. Additionally, the problem of uncovering relationships between developments in the COVID-19 pandemic and social media behavior is of great interest to researchers hoping to curb the spread of the disease. In this paper we present...
Preprint
Full-text available
We propose heavy ball neural ordinary differential equations (HBNODEs), leveraging the continuous limit of the classical momentum accelerated gradient descent, to improve neural ODEs (NODEs) training and inference. HBNODEs have two properties that imply practical advantages over NODEs: (i) The adjoint state of an HBNODE also satisfies an HBNODE, ac...
Article
Drop-carrier particles (DCPs) are solid microparticles designed to capture uniform microscale drops of a target solution without using costly microfluidic equipment and techniques. DCPs are useful for automated and high-throughput biological assays and reactions, as well as single-cell analyses. Surface energy minimization provides a theoretical pr...
Preprint
During the COVID-19 pandemic, conflicting opinions on physical distancing swept across social media, affecting both human behavior and the spread of COVID-19. Inspired by such phenomena, we construct a two-layer multiplex network for the coupled spread of a disease and conflicting opinions. We model each process as a contagion. On one layer, we con...
Article
Full-text available
Deforestation is a major threat to global environmental wellness, with illegal logging as one of the major causes. Recently, there has been increased effort to model environmental crime, with the goal of assisting law enforcement agencies in deterring these activities. We present a continuous model for illegal logging applicable to arbitrary domain...
Preprint
Full-text available
This paper develops a method of biologically guided deep learning for post-radiation FDG-PET image outcome prediction based on pre-radiation images and radiotherapy dose information. Based on the classic reaction-diffusion mechanism, a novel biological model was proposed using a partial differential equation that incorporates spatial radiation dose...
Article
Reported gang-related violent crimes in Los Angeles, California, from 1/1/14 to 12/31/17 are modeled using spatial-temporal marked Hawkes point processes with covariates. We propose an algorithm to estimate the spatial-temporally varying background rate non-parametrically as a function of demographic covariates. Kernel smoothing and generalized add...
Article
An active area of research in computational science is the design of algorithms for solving the subgraph matching problem to find copies of a given template graph in a larger world graph. Prior works have largely addressed single-channel networks using a variety of approaches. We present a suite of filtering methods for subgraph isomorphisms for mu...
Article
Wet electrostatic precipitators (WESP) have been widely studied for collecting fine and ultrafine particles, such as diesel particulate matter (DPM), which have deleterious effects on human health. Here, we report an experimental and numerical simulation study on a novel string-based two-stage WESP. Our new design incorporates grounded vertically a...
Article
Full-text available
The ability to create uniform subnanoliter compartments using microfluidic control has enabled new approaches for analysis of single cells and molecules. However, specialized instruments or expertise has been required, slowing the adoption of these cutting-edge applications. Here, we show that three dimensional–structured microparticles with sculpt...
Article
Modelling film flows down a fibre influenced by nozzle geometry - Volume 901 - H. Ji, A. Sadeghpour, Y. S. Ju, A. L. Bertozzi
Article
Full-text available
Networks, which represent agents and interactions between them, arise in myriad applications throughout the sciences, engineering, and even the humanities. To understand large-scale structure in a network, a common task is to cluster a network’s nodes into sets called “communities,” such that there are dense connections within communities but spars...
Article
In the past few years, graph-based methods have proven to be a useful tool in a wide variety of energy minimization problems. In this article, we propose a graph-based algorithm for feature extraction and segmentation of multimodal images. By defining a notion of similarity that integrates information from each modality, we create a fused graph tha...
Article
Full-text available
Remote sensing data from hyperspectral cameras suffer from limited spatial resolution, in which a single pixel of a hyperspectral image may contain information from several materials in the field of view. Blind hyperspectral image unmixing is the process of identifying the pure spectra of individual materials (i.e., endmembers) and their proportion...
Article
In this paper, we develop a continuum model for the movement of agents on a lattice, taking into account location desirability, local and far-range migration, and localized entry and exit rates. Specifically, our motivation is to qualitatively describe the homeless population in Los Angeles. The model takes the form of a fully nonlinear, nonlocal,...
Article
Graph-based semi-supervised regression (SSR) is the problem of estimating the value of a function on a weighted graph from its values (labels) on a small subset of the vertices. This paper is concerned with the consistency of SSR in the context of classification, in the setting where the labels have small noise and the underlying graph weighting is...
Preprint
Graph-based semi-supervised regression (SSR) is the problem of estimating the value of a function on a weighted graph from its values (labels) on a small subset of the vertices. This paper is concerned with the consistency of SSR in the context of classification, in the setting where the labels have small noise and the underlying graph weighting is...
Preprint
We present a novel adaptation of active learning to graph-based semi-supervised learning (SSL) under non-Gaussian Bayesian models. We present an approximation of non-Gaussian distributions to adapt previously Gaussian-based acquisition functions to these more general cases. We develop an efficient rank-one update for applying "look-ahead" based met...
Preprint
Full-text available
We study the effects of nozzle geometry on the dynamics of thin fluid films flowing down a vertical cylindrical fibre. Recent experiments show that varying the nozzle diameter can lead to different flow regimes and droplet characteristics in the film. Using a weighted residual modeling approach, we develop a system of coupled equations that account...
Article
Full-text available
Significance The coronavirus disease 2019 (COVID-19) pandemic has placed epidemic modeling at the forefront of worldwide public policy making. Nonetheless, modeling and forecasting the spread of COVID-19 remain a challenge. Here, we present and detail three regional-scale models for forecasting and assessing the course of the pandemic. This work is...
Preprint
Designing deep neural networks is an art that often involves an expensive search over candidate architectures. To overcome this for recurrent neural nets (RNNs), we establish a connection between the hidden state dynamics in an RNN and gradient descent (GD). We then integrate momentum into this framework and propose a new family of RNNs, called {\e...
Preprint
We present a method for optimal path planning of human walking paths in mountainous terrain, using a control theoretic formulation and a Hamilton-Jacobi-Bellman equation. Previous models for human navigation were entirely deterministic, assuming perfect knowledge of the ambient elevation data and human walking velocity as a function of local slope...
Preprint
We address the problem of optimal path planning for a simple nonholonomic vehicle in the presence of obstacles. Most current approaches are either split hierarchically into global path planning and local collision avoidance, or neglect some of the ambient geometry by assuming the car is a point mass. We present a Hamilton-Jacobi formulation of the...
Article
Full-text available
Governments have implemented social distancing measures to address the ongoing COVID-19 pandemic. The measures include instructions that individuals maintain social distance when in public, school closures, limitations on gatherings and business operations, and instructions to remain at home. Social distancing may have an impact on the volume and d...
Preprint
Full-text available
We present three data driven model-types for COVID-19 with a minimal number of parameters to provide insights into the spread of the disease that may be used for developing policy responses. The first is exponential growth, widely studied in analysis of early-time data. The second is a self-exciting branching process model which includes a delay in...
Preprint
Full-text available
Governments have implemented social distancing measures to address the ongoing COVID-19 pandemic. The measures include instructions that individuals maintain a distance from one another when in public, limitations on gatherings and the operation of businesses, and instructions to remain at home. Social distancing may have a critical impact on the v...
Article
We introduce the isoperimetric loss as a regularization criterion for learning the map from a visual representation to a semantic embedding, to be used to transfer knowledge to unknown classes in a zero-shot learning setting. We use a pre-trained deep neural network model as a visual representation of image data, a Word2Vec embedding of class label...
Chapter
Full-text available
Opioid addictions and overdoses have increased across the U.S. and internationally over the past decade. In urban environments, overdoses cluster in space and time, with 50% of overdoses occurring in less than 5% of the city and dozens of calls for emergency medical services being made within a 48-hour period. In this work, we introduce a system fo...
Preprint
Full-text available
The ability to create uniform sub-nanoliter compartments using microfluidic control has enabled new approaches for analysis of single cells and molecules. However, specialized instruments or expertise have been required, slowing the adoption of these cutting-edge applications. Here, we show that 3D-structured microparticles with sculpted surface ch...
Article
Full-text available
We revisit the tears of wine problem for thin films in water-ethanol mixtures and present a model for the climbing dynamics. The formulation includes a Marangoni stress balanced by both the normal and tangential components of gravity as well as surface tension which lead to distinctly different behavior. The prior literature did not address the win...
Preprint
Full-text available
Deep neural nets (DNNs) compression is crucial for adaptation to mobile devices. Though many successful algorithms exist to compress naturally trained DNNs, developing efficient and stable compression algorithms for robustly trained DNNs remains widely open. In this paper, we focus on a co-design of efficient DNN compression algorithms and sparse n...
Preprint
Full-text available
Stochastic gradient descent (SGD) with constant momentum and its variants such as Adam are the optimization algorithms of choice for training deep neural networks (DNNs). Since DNN training is incredibly computationally expensive, there is great interest in speeding up convergence. Nesterov accelerated gradient (NAG) improves the convergence rate o...
Article
Full-text available
Residential burglary is a social problem in every major urban area. As such, progress has been to develop quantitative, informative and applicable models for this type of crime: (1) the Deterministic-time-step (DTS) model [Short, D’Orsogna, Pasour, Tita, Brantingham, Bertozzi & Chayes (2008) Math. Models Methods Appl. Sci.18 , 1249–1267], a pioneer...
Chapter
We study epidemic forecasting on real-world health data by a graph-structured recurrent neural network (GSRNN). We achieve state-of-the-art forecasting accuracy on the benchmark CDC dataset. To improve model efficiency, we sparsify the network weights via a transformed-\(\ell _1\) penalty without losing prediction accuracy in numerical experiments.
Chapter
In the field of swarm robotics, the design and implementation of spatial density control laws has received much attention, with less emphasis being placed on performance evaluation. This work fills that gap by introducing an error metric that provides a quantitative measure of coverage for use with any control scheme. The proposed error metric is c...
Chapter
Deep neural nets (DNNs) compression is crucial for adaptation to mobile devices. Though many successful algorithms exist to compress naturally trained DNNs, developing efficient and stable compression algorithms for robustly trained DNNs remains widely open. In this paper, we focus on a co-design of efficient DNN compression algorithms and sparse n...
Article
Full-text available
Particle-laden slurries are pervasive in both natural and industrial settings, whenever particles are suspended or transported in a fluid. Previous literature has investigated the case of a single species of negatively buoyant particles suspended in a viscous fluid. On an incline, three distinct regimes emerge depending on the particle concentratio...
Conference Paper
Stress is a common problem in modern life that can bring both psychological and physical disorder. Wearable sensors are commonly used to study the relationship between physical records and mental status. Although sensor data generated by wearable devices provides an opportunity to identify stress in people for predictive medicine, in practice, the...
Article
A viscous suspension of negatively buoyant particles released into a wide, open channel on an incline will stratify in the normal direction as it flows. We model the early dynamics of this stratification under the effects of sedimentation and shear-induced migration. Prior work focuses on the behaviour after equilibration where the bulk suspension...