Research Areas
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Computational Group Theory and Applications to Cryptography
Computational group theory is the study of computational aspects of groups. It is concerned 
with designing and analysing algorithms and data structures to compute information about groups. Specific groups that I am interested in include: free groups, the automorphism group of free groups, one relator groups, permutation groups, and fully residually free groups.
Equations over free groups. We are developing software which, given a system of equations S over a free group, computes a complete description of the set of all solutions of S, and provides a formal mathematical proof that this description is complete and correct. Such computational software represents a realization of the Makinin-Razborov process, and will significantly impact the development of the general theory of algebraic geometry over free groups, leading to the discovery of new hypotheses, the confirmation and exploration of existing conjectures, and the construction of databases of equations with interesting properties. The software will be instrumental in bringing us closer to the resolution of several open problems in combinatorial group theory that can be formulated in terms of such equations. Examples include questions regarding the faithfulness of the Gassner representation for Braid groups, the cardinality of the Burnside group of exponent 5, and Hanna Neumann's conjecture bounding the rank of the intersections of subgroups of free groups.
Graph Algorithms and Applications to Networking
We explore fundamental problems in graph theory, with an emphasis on metric and algebraic 
structures on the set of all graphs. We consider graph embedding problems which arise naturally from the context of multi-agent systems, distributed computing, wireless networks, and optical networks.
Students/Grants/Collaborations: Birendro Roy (B.Sc).
NRL Center for Computational Sciences
Prof. Kiran Bhutani, Catholic University of America
Network and Computer Security
Transparent security for memory. We have developed software that permits us to transparently add memory encryption to existing software, without requiring complicated software redesign or additional costly hardware.
Wifi Security. We have developed a system for spatial isolation of wifi attackers using a single directional antennae.
DoS/DDoS Reconstruction and Countermeasures. We are developing mechanisms for reconstructing essential flows during denial of service attacks, and using this information to dynamically instrument throttling countermeasures.
Interposition detection in the LAN and WAN. We are developing a system that uses a secure permutational cover channel, superimposed over TCP/IP, to detect interposition and man-in-the-middle attacks in local and wide-area networks.
Students/Grants/Collaborators
- Jamie Levy, M.Sc. in Forensic Computing 2007, Retrofitting Legacy Applications with: Memory Encryption and Transparent Aegis Library.
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Juseop Lim, M.Sc. in Forensic Computing 2008, A Feasibility Study on Wireless Device Location using a Single Directional Antenna
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Jaroslaw Paduch, M.Sc. in Forensic Computing 2008, Using a Secure Covert Channel to Detect Interposition Attacks.
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Omer Demirkos, PhD. Candidate
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Jeremy Seideman, PhD Candidate
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Costas Nicolopoulos, PhD Candidate
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New York State Graduate Teaching & Research Initiatives (GTRI) Grant 2008,
Laboratory for Computer Malware Detection, Immunization, and Taxonomy -
City University of New York, PSC Research Grant, Fall 2006-Spring 2007.
Scalable Worm Outbreak Detection and Immunization in Untrusted Environments.
Wireless Mobile Ad-hoc Networks and Applications to Battlespaces and Disaster Recovery
A Mobile Ad Hoc Network (MANET) consists of mobile router/host platforms connected by wireless communications channels. Important examples of MANETs include communication networks for emergency rescue operations, and military networks. In dynamic settings such as these, centralised coordination of connectivity is not feasible, and MANET nodes must execute distributed topology discovery and message delivery.
Cooperative Networks. Traditional wireless MANETs assume complete autonomy of all nodes with regards to mobility. While this popular model is appropriate for consumer cellular networks, it does not adequately capture the environmental parameters of military and battlespace networks. In battlespace settings, it is unnecessarily restrictive to require constant and complete autonomy for all nodes--indeed, it is feasible and realistic to have a subset of nodes which are subordinate and/or cooperative (e.g. unmanned vehicles). Indeed, Comms Infrastructure optimization is a necessary function of command and control. This research task begins with the premise that future battlespace networks will not be homogenous in terms of node autonomy. We will consider a setting where wireless nodes exhibit a full range of cooperativeness with regards to mobility: i.e. different nodes exhibit a different level of “willingness to move when asked". We develop an integrated solution to complementary online problems of routing and network design, in a model where some of the wireless MANET nodes can be moved by the network layer itself (at a per-node specified cost). Our goal is to devise scalable distributed schemes in which cooperative nodes can be leveraged to improve the performance of existing network connections.
Students/Grants/Collaborations
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Ghassen Ben Brahim, Ph.D in Computer Science 2007, Cooperative Networking and Mobility in MANETs.
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Zeki Bilgin, Ph.D candidate in Computer Science
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IBM-ITA Research Grant from the DoD/MoD (Fall 2007-Spring 2008)
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City University of New York, PSC Research Grant, Fall 2007-Spring 2008.
Mobility and Power Planning in Disaster Recovery Mobile Ad-hoc Networks -
National Security Agency, Research Grant, Fall 2007-Spring 2008.
Information Acquisition and Delivery for Disaster Recovery Teams.
Optical Networks: Signalling, Routing, and Management
Physical topology design. We are developing effective methods for design of optimal physical topologies for large-scale Dense Wavelength Division Multiplexing (DWDM) networks that support multi-granular switching. This requires new analytic formulations and planning heuristics that consider factors such as: placement of wavelength/band switching resources, traffic grooming resources, optical signal strengths/dispersions, and equipment costs. By quantifying tradeoffs between wavelength, band, and multi-granular switching techniques we seek to develop models that enable network designers to optimally leverage wavelength and band switching resources, while minimizing total network cost and maximizing network performance.
Survivability and QoS path protection. We are developing an alarm correlation expert system to perform root cause analysis of network alarms, and to determine when the QoS of a given path is degraded and protection paths should be enabled. This alarm management system will also be used to construct dynamic failure-condition models for individual network elements, and the lightpath route selection process uses these models to proactively route around network elements that are nearing dysfunctional states.
QoS routing, signalling and management protocols for ATM virtual-circuit switched networks.
Students/Grants/Collaborations:
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Ghassen Ben Brahim, M.Sc. in Computer Science 2000, A Toolkit for Routing in Optical Networks
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As part of the NRL summer program for undergraduates: Nicolai Zeldovich (B.Sc), Ron Shacham (B.Sc), Jennifer Trotta (B.Sc), Rudy Kellner (B.Sc), Max Berman (B.Sc), Chris Westmoreland (B.Sc), Rodney Walker (B.Sc), Daniel Russakoff (B.Sc), Tolentino Correia (B.Sc), Lionel Pagador (B.Sc), Sean Mountcastle (B.Sc).
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NRL Center for Computational Sciences
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Ala Al Fuqaha (University of Western Michigan). .
Data Management in Peer-to-Peer Networks with Applications to Scalable Spatiotemporal Information Retrieval
The successful transition of current centralized geographic information systems to the next-generation of scalable open distributed systems for universal situational awareness. Besides issues in decentralized data management and search, this requires a transition from data that is geospatially indexed to data that is spatiotemporally indexed. We consider the following central problems:
Time Lens. How can the user be guided through time in order to efficiently discover temporal regions of interest? This entails the development of a framework for temporal aggregation schemes, multi-resolution representations of time-sequence data, and mechanisms for iterative refinement of temporal queries.
WorldLine. How can the user be dynamically informed about the data that is presently available within their declared spatiotemporal region of interest, at the appropriate level of detail? This requires the development of a distributed geospatial/temporal directory service that serves as a dynamic matchmaker between users and relevant publishers of data.
Students/Grants/Collaborations
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James Johnson (B.Sc)
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Petrit Duraku (B.Sc. 2006)
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NRL Center for Computational Sciences
Applications of Mathematics and Computer Science
Dynamics of retail methamphetamine markets in New York City. Develop new techniques to study completions of respondent driven sampling trees, in order to evaluate the possible structure of methamphetime use networks in New York City.
Students/Grants/Collaborations:(NDRI Grant: Travis Wendel, Ric Curtis, Kirk Dombrowski).
Stochastic Modeling of IDU Network Factors for HIV Stabilization Dynamics. Statistical modelling to assess the dynamics of HIV propagation in IDU networks.
Students/Grants/Collaborations: (NSF Cultural Anthropology Scholars Award: Kirk Dombrowski).
The Nature and Scope of Child Prostitution in New York City . Statistical modelling and inference for a study undertaken by John Jay College of Criminal Justice, using respondent driven sampling to assess the extent and structure of child prostitution networks in New York City.
Students/Grants/Collaborations:(Ric Curtis, Karen Terry)
Report on the Nature and Scope of Sexual Abuse of Minors by Catholic Priests and Deacons in the United States. Statistical modelling and inference for a study undertaken by John Jay College of Criminal Justice in 2003, sponsored by the United States Conference of Catholic Bishops, initiated by
the National Review Board and the Office of Child and Youth Protection.
Students/Grants/Collaborations:(Karen Terry, Margaret L.Smith)
National Incident Based Reporting System. We are developing guided navigation tools for NIBRS, an incident-based reporting system for crimes known to the police. For each crime incident, a variety of data are collected about the incident, including the nature and types of specific offenses in the incident, characteristics of the victim(s) and offender(s), types and value of property stolen and recovered, and characteristics of persons arrested in connection with a crime incident.
Students/Grants/Collaborations: Petrit Duraku (B.Sc candidate), Aljona Necaj (B.Sc candidate).