Institute for Systems Research Technical Reports
Permanent URI for this collectionhttp://hdl.handle.net/1903/4376
This archive contains a collection of reports generated by the faculty and students of the Institute for Systems Research (ISR), a permanent, interdisciplinary research unit in the A. James Clark School of Engineering at the University of Maryland. ISR-based projects are conducted through partnerships with industry and government, bringing together faculty and students from multiple academic departments and colleges across the university.
Browse
Search Results
Item On the Converse to Pompeiu's Problem(1997) Berenstein, Carlos A.; ISRThis is a reprint of a 1976 paper that appears in an inaccessible Brazilian journal and has become very looked after. It deals with the problem of determining a convex plane domain from the existence of infinitely many over determined Neumann eigenvalues. Recent related work in magneto hydrodynamics of Vogelius and other applications are closely related to this result. The more general result appears in J. Analyse Math 1980 and Crelle l987. See Zalcmain's bibliographic survey of pompeiu problem for other references.Item Network Tomography(2005) Gavilanez, Franklin; Berenstein, Carlos A.; Baras, John S.; ISRWhile conventional tomography is associated to the Radon transform in Euclidean spaces, electrical impedance tomography or EIT is associated to the Radon transform in the hyperbolic plane. We discuss some recent work on network tomography that can be associated to a problem similar to EIT on graphs and indicate how in some sense it may be also associated to the Radon transform on trees.Item Continuous and Discrete Inverse Conductivity Problems(2004) Gavilanez, Franklin; Baras, John S.; Berenstein, Carlos A.; ISRTomography using CT scans and MRI scans is now well-known as a medical diagnostic tool which allows for detection of tumors and other abnormalities in a noninvasive way, providing very detailed images of the inside of the body using low dosage X-rays and magnetic fields. They have both also been used for determination of material defects in moderate size objects. In medical and other applications they complement conventional tomography. There are many situations where one wants to monitor the electrical conductivity of different portions of an object, for instance, to find out whether a metal object, possibly large, has invisible cracks. This kind of tomography, usually called Electrical Impedance Tomography or EIT, has also medical applications like monitoring of blood flow. While CT and MRI are related to Euclidean geometry, EIT is closely related to hyperbolic geometry. A question that has arisen in the recent past is whether there is similar omographicmethod to monitor the ealthof networks. Our objective is to explain how EIT ideas can in fact effectively be used in this context.Item Harmonic Functions and Inverse Conductivity Problems on Networks(2003) Berenstein, Carlos A.; Chung, Soon-Yeong; ISRIn this paper, we discuss the inverse problem of identifying the connectivity and the conductivity of the links between adjacent pair of nodes in a network, in terms of an input-output map. To do this we introduce an elliptic operator Dw and an w-harmonic function on thegraph, with its physical interpretation been the diffusion equation on the graph, which models an electric network. After deriving the basic properties of w-harmonic functions, we prove the solvability of (direct) problems such as the Dirichlet and Neumann boundary value problems.Our main result is the global uniqueness of the inverse conductivity problem for a network under a suitable monotonicity condition.Item Local Monitoring of the Internet Network(2003) Gavilanez, Franklin; Baras, John S.; Berenstein, Carlos A.; ISRThe internet, as well as other freely evolving networks, has a topology that changes dynamically; therefore the topology is very complicated. Presently, there is an increase in dependency on the internet for several things such as communication, information traffic and many more, hence it is imperative that we prevent attackers from disrupting this network. To do this, it is essential to count on a mathematical model that can allow early detection (then ring the bell) of attacks to the network. The mathematical tool that we are looking for to accomplish that early detection is based on the use of Tomography ideas.The last statement is based on the April 28-29, 2000 workshop on the inter-face between the mathematical sciences and three areas of computer science:network traffic modeling, computer vision, and data mining and search. Thisworkshop was cosponsored by the Board on Mathematical Sciences andthe Computer Science and Telecommunications Board of the National ResearchCouncil.
Item Quotient Signal Decomposition and Order Estimation(2002) Napoletani, D.; Berenstein, Carlos A.; Krishnaprasad, Perinkulam S.; ISRIn this paper we propose a method for blind signal decomposition that does not require the independence or stationarity of the sources. This method, that we consider a simple instance of non-linear projection pursuit, is based on the possibility of recovering the areas in the time-frequency where the original signals are isolated or almost isolated with the use of suitable quotients of linear combinations of the spectrograms of the mixtures.We then threshold such quotients according to the value of their imaginary part to prove that the method is theoretically sound under mild assumptions on the mixing matrix and the sources. We study one basic algorithm based on this method. Moreover we propose a practical measure of separation for the sources in a given time frequency representation.
The algorithm has the important feature of estimating the number of sources with two measurements, it then requires n-2 additional measurements to provide a reconstruction of n sources. Experimental results show that the method works even when severalshifted version of the same source are mixed.
Item Implementation and Application of Principal Component Analysis on Functional Neuroimaging Data(2001) Gwadry, Fuad; Berenstein, Carlos A.; Horn, John Van; Braun, Allen; ISRRecent interest has arisen regarding the application of principal component analysis (PCA)-style methods for the analysis of large neuroimaging data sets. However, variation between different implementation of these techniques has resulted in some confusion regarding the uniqueness of these approaches.In the present article, we attempt to provide a more unified insight into the use of PCA as a useful method of analyzing brain image data contrasted between experimental conditions. We expand on the general approach by evaluating the use of permutation tests as a means of assessing whether a given solution, as a whole, exposes significant effects of the task difference. This approach may have advantages over more simplistic methods for evaluating PCA results and does not require extensive or unrealistic statistical assumptions made by conventional procedures.
Furthermore, we also evaluate the use of axes rotation on the interpretability of patterns of PCA results. Finally, we comment on the variety of PCA-style techniques in the neuroimaging literature that are motivated largely by the kind of research question being asked and note how these seemingly disparate approaches differ in how the data is preprocessed not in the fundamentals of the underlying mathematical model.
Item Radon Transform, Wavelets, and Applications(1996) Berenstein, Carlos A.; ISRNotes of a graduate course given in Venice, Italy, during June 1996 organized by CIME, directed to graduate students to show the interplay of different kinds of Radon transforms and medical and material science problemsItem Residue Calculus and Effective Nullstellensatz(1996) Berenstein, Carlos A.; Yger, A.; ISRWe provide new tools to compute multidimensional residues for rational functions, even over fields of positive characteristic. As a corollary one obtains solutions of the Betout equation for polynomials over a ring with a site that have almost optimal estimates for degree and size.Item Approximation by Spherical Waves in Lp-Space(1996) Agranovsky, Mark; Berenstein, Carlos A.; Kuchment, Peter; ISRWe prove that functions of the form f(1x-a1), a in a closed surface, are dense in the space of all functions in Lp, for zn/(n+1). This property fails for 1zn/(n+1). By letting f be a Gsussian, we obtain a result about approximation by wavelets generated by the Gaussian.