Gaining timely insights on real-world emergency events, such as infectious disease outbreaks, is critical for developing appropriate response strategies. In this work, we propose a data-driven approach to study the spreading dynamics of the global Covid-19 pandemic. Specifically, we aim to identify a set of most “similar” geographic regions as proxies for making predictions on a targeted location. Example predictions include the number of new cases, number of hospitalizations, and number of deaths. Such predictions can be made at different levels of regional granularities, including city, county, and state levels. Our approach starts by transforming regional time series into graph representations using the natural visibility graph (NVG) model in order to capture their intrinsic trends and properties. These graphs are then projected onto a common embedding space using graph-level network embedding techniques. Essentially, each time series is converted as a data point in a feature embedding space, where spatial proximity indicates similarity among time series. Given a targeted region, our approach can identify the most “relevant” geographic regions by finding its k-nearest neighbors in the embedding space. Subsequently, appropriate response strategies and policies (e.g., school shutdown, indoor dining restriction) can be adapted based on the success or failure experiences from relevant regions. Our approach will potentially provide valuable insights in mitigating the spreading of infectious disease.

Subgraph Matching is one of the fundamental problems in network analysis, with a wide range of applications ranging from drug repurposing and discovery to programming language analysis. Due to the increasing prevalence of knowledge graphs (KGs), there has been growing interests in extending existing subgraph matching algorithms to the KG domain. One of the main challenges here lies on the structural gap, which refers to the difference between the query pattern and the corresponding subgraph instance due to variations in semantic expression. To address this challenge, we propose a semantic guided subgraph matching method for knowledge graphs, which extends our prior filtering-based method. Specifically, our approach leverages an external semantic ontology to estimate the overall fitness/quality of subgraph candidates with respect to the query template. In addition, our approach incorporates effective query decomposition strategies to reduce the overall query cost. Furthermore, we develop a distributed implementation of the algorithm such that it can be scaled up to handle knowledge graphs with a large number of entities and relations. We demonstrate the effectiveness of the proposed approach on a variety of semantic networks provided in the DARPA Modeling Adversarial Activity (MAA) program.

Networks are natural representations in modeling adversarial activities, such as smuggling, human trafficking, and illegal arms dealing. However, such activities are often covert and embedded across multiple domains and sources. They are generally not detectable and recognizable from the perspective of an isolated network, and only become apparent when multiple networks are analyzed in a unified m anner. T o t his e nd, we propose Complex Analytics of Network of Networks (CANON), a mathematical and computational framework for modeling adversarial activities from large-scale, multi-sourced data inputs. Central to our framework is a network-of-networks model, where nodes and edges can be defined across different domains and at multiple resolutions. Based on this model, we address the key challenges in modeling adversarial activities via four technical components, including optimization-based network alignment, network embedding and conditioning, approximate subgraph matching, and investigative subgraph discovery.In this paper, we describe the design and implementation of the individual components as well as integrating these components into a unified system using a modular microservice architecture. Extensive experiments have been conducted in both synthetics and real-world datasets to demonstrate the effectiveness of our proposed system under the DARPA Modeling Adversarial Activity (MAA) program.

We study the problem of detecting matching subgraphs in a large multiplex background network based on predefined subgraph templates. Our approach extends existing filtering-based subgraph matching algorithms and proposes a new set of filters leveraging the monotone function properties in the multiplex setting. This enables effective pruning of irrelevant subgraph regions and expedites the overall matching process. In addition, our approach proposes a new strategy based on maximum likelihood estimate to identify “closely matched” subgraphs that are not isomorphic to the given templates from a noisy background network. This allows us to generalize this approach to real-world networks, which are often noisy, incomplete and ambiguous. We demonstrate the effectiveness of the proposed method on a real-world multiplex network provided by the DARPA Modeling Adversarial Activity (MAA) program. Our approach obtains highly accurate subgraph matching results for both the clean and noisy versions of the network, which significantly outperforms the baseline filtering methods. Furthermore, our proposed approach is parallelizable such that it can scale up to handle large input networks.

We investigate the development of a general-purpose framework for mechanized reasoning about the meta-theory of programming languages. In order to provide a standard, uniform account of a programming language, we propose to define it as a logic in a logical framework, using the same mechanisms for definition, reasoning, and automation that are available to other logics. Then, in order to reason about the language's meta-theory, we use reflection to inject the programming language into (usually richer and more expressive) meta-theory.One of the key features of our approach is that structure of the language is preserved when it is reflected, including variables, meta-variables, and binding structure. This allows the structure of proofs to be preserved as well, and there is a one-to-one map from proof steps in the original programming logic to proof steps in the reflected logic. The act of reflecting a language is automated; all definitions, theorems, and proofs are preserved by the transformation and all the key lemmas (such as proof and structural induction) are automatically derived.The principal representation used by the reflected logic is higher-order abstract syntax (HOAS). However, reasoning about terms in HOAS can be awkward in some cases, especially for variables. For this reason, we define a computationally equivalent variable-free de Bruijn representation that is interchangeable with the HOAS in all contexts. The de Bruijn representation inherits the properties of substitution and alpha-equality from the logical framework, and it is not complicated by administrative issues like variable renumbering.We further develop the concepts and principles of proofs, provability, and structural and proof induction. This work is fully implemented in the MetaPRL theorem prover. We illustrate with an application to F<: as defined in the POPLmark challenge.

Records and dependent records are a powerful tool for programming, representing mathematical concepts, and program verification. In this last decade several type systems with records as primitive types were proposed. The question is arisen whether it is possible to define record type in existent type theories using standard types without introducing new primitives. It was known that independent records can be defined in type theories with dependent functions or intersection. On the other hand dependent records cannot be formed using standard types. Hickey introduced a complex notion of very dependent functions to represent dependent records. In the current paper we extend Martin-Lof's type theory with a simpler type constructor dependent intersection, i.e., the intersection of two types, where the second type may depend on elements of the first one (not to be confused with the intersection of a family of types). This new type constructor allows us to define dependent records in a very simple way. It also allows us to define the set type constructor.