Algebraic Methods for the Study of Logics on Trees
Prof. Howard Straubing
The automaton-logic connection is a basic theme in Computer Science that arises in many different contexts (e.g., hardware verification, XML document processing, to name a couple of the more practical examples). My work in Theory of Computation, at the intersection of mathematical logic (particularly finite model theory), automata theory, and abstract algebra, explores fundamental questions about this connection. I am interested in the following kind of problem: We have some formal language, usually a variant of first-order logic, for expressing properties of strings of symbols, or of labeled trees. How can we tell if a given property is expressible in the language? The property might be 'given' by an expression in a different logical formalism, or by a finite automaton that tests for the property. Ideally we would like an effective and reasonably efficient algorithm for answering the expressibility question.
Beginning in the late 1960's, questions of this sort for strings were fruitfully investigated by algebraic means, and parallelled the development of a rich algebraic theory of the structure of finite semigroups. My current research is devoted to generalizing and applying these methods to investigate logics for trees. Here, even some of the basic questions, such as determining whether a given property is definable in first-order logic, remain unanswered. To address these questions, my research collaborators and I have been investigating properties of a new kind of algebraic structure, called forest algebras, with promising results. This work is supported by a grant from the National Science Foundation.
Earlier work of mine concerned the complexity of small-depth circuits, and I have been particularly intrigued by the power of modular counting gates in such circuits, especially the long-standing and seemingly unapproachable problem of separating the circuit complexity class ACC^0from NC1 which I still sometimes dream of solving.
Algorithms in Vertex-Centric Computations
Prof. Hsin-Hao Su
In a distributed network, vertices (nodes) operate autonomously without a centralized coordinator or global knowledge. Each vertex only has a local view and it can only communicate with its neighbors. Prof. Su's research focuses on developing algorithms for fundamental problems such as routing, symmetry breaking, and matching in such a vertex-centric setting. Understanding how to solve the problem efficiently in the vertex-centric setting not only facilitates the shifting of computing paradigm to the distributed setting but it also allows us to:
- Process large-scale graph data by using Pregel-like tools such as Apache GraphX because vertex-centric algorithms can be easily parallelized to run on multiple machines.
- Get a better glimpse of how Nature works. Many biological systems (such as insect colonies) operate in a distributed manner where individuals operate autonomously without a centralized coordinator.
Computational Homotopy Theory
Prof. Carl McTague
I study the connection between exotic geometries and chromatic homotopy theory, and what this connection reveals about the surprising relationship between topology and the arithmetic of algebraic curves. Specifically, I am working to uncover higher genus generalizations of elliptic cohomology suggested by the exceptional geometry of the Cayley plane (and categorifying moduli spaces of theta characteristics). I am also working to compute the homotopy type of the string bordism spectrum MO<8> at the prime 3, based on computer-assisted computations of its BP-homology, considered as a Hopf ring. I have also investigated novel uses of curvature in data analysis, pattern formation in cellular automata, as well as computational and geometric aspects of bookbinding and music composition.
Computer Vision and Biomedical Image Analysis
Prof. Donglai Wei
Computer vision (CV) is the branch of artificial intelligence that enables computers to reconstruct, recognize, and re-organize the rich information from input images. Especially automating biomedical image analysis with CV methods has dramatically accelerated both scientific discoveries and healthcare innovations.
Prof. Wei's research focuses on the interplay between natural and artificial intelligence. On the one hand, he has been developing novel computer vision methods to reconstruct a detailed wiring diagram of neurons from large-scale microscopy images, revealing the brain's workings and accelerating drug discovery for brain diseases. On the other hand, he has been advancing neuroscience-inspired designs to enhance computer vision methods for video understanding applications. In addition, he has been contributing to open-source biomedical image analysis solutions to assist collaborators in biology, psychology, radiology, and pathology.
Prof. Lewis Tseng
As more and more industries are adopting varieties of distributed systems for their critical business applications (e.g., clouds for social applications or a fleet of autonomous trucks for transportation), it is important to design and develop reliable distributed systems. The ultimate goal of Prof. Tseng's research is to identify a science of reliable distributed systems that can be applied by individuals and industries designing, implementing and using distributed systems for various purposes. His research touches both the practical and theoretical aspects.
The first aspect is to identify a body of “laws” that serve as the foundation of reliable systems. For example, he and collaborators have identified fundamental properties for achieving fault-tolerant consensus.
The second direction considers how the “laws” can be applied to practical systems and applications. For example, he and collaborators have adapted and designed algorithms for Cassandra, a popular distributed NoSQL system.
Human-Computer Interaction and Visualization
Prof. Nam Wook Kim
Data is all around us in our daily lives, ranging from everyday human activity to environmental and socio-economic indicators. Making sense of data is becoming an important skill for everyone to understand ourselves better and make our society better.
Prof. Kim's research vision lies in the democratization of data, lowering barriers for everyone to understand and communicate complex data. He tackles this challenge by using visualizations as external cognition aids to help people see the unseen. Within the broad context of human-computer interaction, his research investigates innovative approaches to interact with data, going beyond traditional expert systems and addressing the needs of a broader audience.
Machine Learning for Human Health and Behavior
Prof. Sergio Alvarez
Prof. Alvarez's research focuses on the application of machine learning techniques to health-related data science. He and his research group have developed new algorithms and approaches for predictive modeling in sleep medicine, surgical oncology, stroke, and autism spectrum disorder (ASD). He has also made contributions to foundational issues in data science, including results on the measurement of similarity between data representations that emerge within deep neural network models, among others.
Models and Algorithms Over Networks
Prof. José Bento
Prof. Bento's research involves understanding how to solve problems over networks. These networks can represent either communication constraints on a set of nodes that need to collaborate to solve a problem, or mathematical constraints among the variables of a mathematical model. In particular, he has devoted much attention to networks in the context of graphical models and distributed optimization algorithms. His work finds application in robot path planning, combinatorial optimization, video stylization, computer vision tracking, and, more recently, systems biology. Prof. Bento is currently one of five PIs on a large interdisciplinary collaboration that aims to understand the mechanisms of antibiotic resistance. This collaboration involves the van Opijnen Lab in the Department of Biology at Boston College, and a team of researchers at Tufts University, St. Jude Children's Hospital, and the University of Pittsburgh. Their joint research is supported by a $10 million U01 grant from NIH/NIAID.
Natural Language Processing
Prof. Emily Prud'hommeaux
Natural language processing (NLP) is the branch of artificial intelligence that explores how computers model, analyze, and generate human language. In our daily lives, it is NLP that enables us to interact with our digital devices using written or spoken language — from web search and autocorrect to Siri and Alexa to the algorithms that guide our experience when using social media.
Prof. Prud’hommeaux’s research focuses on the development of NLP methods for addressing challenges in health and accessibility, with a focus on the automated discovery of linguistic features of neurological disorders like autism and dementia. In addition, she works with endangered language communities to create technologies that support language instruction, preservation, and revitalization.
Probabilistic Machine Learning
Prof. Jean-Baptiste Tristan
Machine learning is the study of computer algorithms that can improve automatically through experience and by the use of data. The probabilistic approach to machine learning uses probabilistic models and inference to design such algorithms. Prof. Tristan's research covers the theory, tools, and applications of probabilistic machine learning.
Parallelization, distribution, streaming, and approximation of probabilistic inference algorithms.
Design and implementation of probabilistic programming languages. Using probabilistic programming, a model is specified in a formal language and an inference algorithm is derived automatically
Use of Gaussian processes in theoretical chemistry to model the potential energy surface of molecules and geometry optimization.