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ISR develops, applies and teaches advanced methodologies of design and analysis toAbstract Tomography 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 "tomographic" method to monitor the "health" of networks. Our objective is to explain how EIT ideas can in fact effectively be used in this context.

Tomography 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 "topographic" method to monitor the "health" of networks. Our objective is to explain how EIT ideas can in fact effectively be used in this context. IntroducciónProblemas tomográficos aparecen en varios contextos, desde el monitoreo de redes hasta el procesamiento de señales, así como situaciones relacionadas a biología y medicina, consecuentemente, hay diferentes tipos de aplicaciones de tomografía y tópi-cos misceláneos en análisis harmóni-co y complejo que se relacionan. Estos problemas son vistos como problemas inversos y entre estos aquellos de índole discreto sobre conductividad en redes, lo cual se basa en ideas y métodos tomográficos ya existentes para el caso continuo. Mi investigación se enmarca en este tipo de problemas que realizo con la colaboración de Carlos Berenstein, quien 129

ISR develops, applies and teaches advanced methodologies of design and analysis to solve complex, hierarchical, heterogeneous and dynamic problems of engineering technology and systems for industry and government. ISR is a permanent institute of the University of Maryland AbstractWhile 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.