Subspace Arrangement Codes and Cryptosystems
Errors often occur when data is transferred from point to point electronically. Encoding information with an error-correcting code can often alleviate the problem of corrupt or lost data. In order to not overburden computing systems with the additional overhead of error-correcting codes, an efficient code must be used that will quickly encode and decode data while detecting and correcting a large number of errors. The goal of this project is to construct and develop efficient codes using recent advances in algebraic geometry, combinatorics, and commutative algebra.
In particular, mathematical subspace arrangements and simplicial complexes lend themselves well for applications to coding theory. A subspace arrangement is a finite collection of subspaces in a vector space. A simplicial complex is an abstract generalization of a polygon or Euclidean solid. Fortunately, both simplicial complexes and subspaces arrangements can be described algebraically by a collection of polynomials, which can be used to construct a code. Then the combinatorial and geometric properties of subspace arrangements and simplicial complexes can be used to enumerate these efficient codes.
Scripts and algorithms were written in the computer algebra systems Sage and Macaulay2 to compute properties of the codes. For polygon and skeletal simplicial complex evaluation codes the data suggested the existence of formulas, which efficiently calculate the length, dimension, and minimum distance. Then new scripts were written that aided in the construction of proofs for these formulas. The formulas give favorable lengths (short to minimize computation), dimensions (large to allow for more codewords), and minimum distances (to allow more errors to be corrected and identified) of these polygon and skeletal simplicial complex evaluation codes.
The last part of the project involved extensions to a cryptosystem based on these codes. A cryptosystem deals with enciphering a message, which is an algorithmic process designed to make a sent message unreadable to an interloper, but, after another algorithmic deciphering process, is readable to the intended receiver (who, unlike the interloper, knows the deciphering key). Work was done on extensions to the code-based McEliece Cryptosystem, which has been demonstrated to withstand theoretical quantum computing attacks that would render common modern ciphers useless.
Electrodynamic Tethers (EDT’s) offer a real option for zero-propellant orbital maneuvers in the near future. By controlling the electrical current through a long conductive cable aligned with the local vertical and in the presence of a magnetic field, an electrodynamic thrust can be generated. The local ionosphere provides the necessary electrons for the generation of an electrical current. Control systems for EDT’s are still in an infant stage due to the complex, highly nonlinear nature of continuous low thrust systems in earth orbit and the lack of high precision environmental models. Previous investigation has been focused on feed-forward or open-loop control schemes. Open-loop control methods are very susceptible to model error. The relevant models for an EDT system are the atmospheric density model and the magnetic field model. This work is concerned with compensating for normally distributed errors in the atmospheric density model. Applying feedback control principles to the nonlinear feed-forward scenario is a necessary step for reliable performance in spite of model errors. The problem consists of two parts: solving the feed forward non-linear optimal control problem and solving the associated linear feedback system to generate an LQR control law.
To solve the first part we assume the orbit remains nearly circular, that is, the eccentricity remains very small. As we are focused on long duration maneuvers, we apply the method of averaging to the state dynamics, expressed in the equinoctial coordinates. The short period motion of the spacecraft drives the shape of the control. We control the coefficients on a 5 term modified Fourier series describing the tether’s alternating electrical control current. The series is modified by using square waves rather than sine and cosine waves. The control solution from this part is then used as reference in the feedback problem.
Solving the associated linear feedback system involves linearizing state dynamics. Standard linearization yields a classic state-space structured system using state error to generate control corrections. We assume complete state feedback to simplify the solution. Treating the system as linear time invariant, we determine a new LQR control law and update the gain matrix once per orbit.
Preliminary results indicate this strategy significantly improves performance and reliability of a system in the presence of model errors and unmodeled disturbances.
CDR Robert E. Stevens, USN
Aerospace Engineering Department
Started initially as an alternative means to extend credit to the poorest of people without the need for collateral, Microfinance (MF) has experienced exponential growth and has spread throughout the globe in the last 10 years. The creation of microfinance technologies such as group lending has unexpectedly allowed a business model based on small loan sizes and no collateral to flourish and succeed. High repayment rates of up to 96% have drawn immense interest from both for-profit and non-profit institutions. As more lenders join the rush to gain a slice of the microfinance market, various allegations have surfaced that the entry of these for-profit only lenders distort the market by providing easy credit at exorbitant interest rates. Existing literature focuses primarily on the effects of microfinance on welfare and the sustainability of such an industry. However, as competition in the market intensifies, there exists a need for research to focus on formalization of the current market structure and how interactions between for –profit and non-profit microfinance institutions will shape the market; research that is currently found in abundance on traditional banking but far lacking in the field of MF. Our initial stylized facts on the microfinance industry highlight the various differences that exist between for-profit and non-profit microfinance institutions (MFI) and motivate the study of both the theoretical and empirical models of the industry.
We used a Bertrand differentiated product model to formalize the theoretical aspect and to model both the price setting and demand function of the firms and market. Attributes that differentiate the products each MFI produces are often unobservable, but will instead include proxies such as the profit status and women to active borrower ratio of each firm. With the theoretical demand and Nash equilibrium equations we then proceeded to structurally estimate the parameters within the equations and subsequently derive a welfare analysis. The data used in this work was obtained from www mixmarket.org, a free public domain that provides information on MFIs around the world. We find from both the theoretical and empirical models that MFIs posses market power and in some instances even result in crowding others out. Further studies on the model will include spatial analysis, which allows us to understand the influence of geographically factors affecting key variables such as interest rates, loan sizes and number of borrowers.
Directed Energy Beam Jitter Mitigation Using the Line-of-Sight Reference Frame
Directed energy weapons will dramatically increase naval capability by offering extreme precision, scalable power, speed-of-light engagement, and a nearly limitless magazine. Precise beam control is essential for maximizing the energy on target and damaging the target structure. Directed energy weapon systems operating in a maritime combat environment, however, will be mounted on dynamic platforms that are subject to jitter inducing mechanical vibrations. Jitter is any deviation of the beam from its intended path due to platform induced vibrations or atmospheric effects. Jitter dramatically decreases the energy on target by displacing the beam from the aim-point. The Office of Naval Research (ONR) Directed Energy Weapon Program has tasked researchers at the United States Naval Academy (USNA) to address this issue. Trident Scholar Ensign Matt Roberts developed a feedforward jitter compensation beam control system with the USNA Directed Energy Research Center that calculates and mitigates beam jitter due to platform vibrations. The purpose of this research is to increase the technology readiness level of this beam control system. Outside of the laboratory environment, off-platform orientation references are unavailable. In order to isolate the platform, on-platform angular rate sensors and linear accelerometers are used to determine platform orientation. Once platform orientation is determined, the first fast steering mirror (FSM) in the optical train can be controlled by the jitter compensation system to mitigate jitter. In maritime combat environments, targets are also rarely stationary. The line-of-sight reference frame is established to allow the second FSM to direct the beam at targets moving relative to the source platform. This research demonstrates the necessary subsystems for isolated-platform, feedforward beam control in the line-of-sight and has the potential to minimize source laser power and engagement time requirements in practical directed energy weapon systems.
CDR R. Joseph Watkins, USN
Visiting Professor Craig E. Steidle
Aerospace Engineering Department
Search for the Exotic Wobbling Mode in 171Re
It is often assumed that the nucleus of an atom is spherical; however, this is not always the case. At excited or high-spin states, where the nucleus is rotating very rapidly, it can either stretch or compress along a body-fixed principal axis, giving it the shape of an American football or a doorknob. Very rarely a nucleus can assume an asymmetric shape where it does not rotate around a principal axis, but instead wobbles. This wobbling motion is analogous to the spinning motion of an asymmetric top. The wobbling mode has been found in isotopes of Lutetium (Lu). Surprisingly, this mode was not observed in neighboring Hafnium (Hf) and Thulium (Tm) isotopes and was only recently found in an isotope of Tantalum (Ta).
The observation of a wobbling band is a strong indication that a nucleus possesses asymmetric deformation. In order to determine the role of the atomic number on the observation of asymmetric deformation, an experiment was conducted to search for the wobbling mode in Rhenium (171Re). High-spin states in 171Re were produced in a collision reaction with a metal ion beam at Argonne National Laboratory. Off-center collisions between the beam and target nuclei resulted in large amounts of angular momentum (spin) in the new compound nucleus. To dispel this angular momentum, gamma rays were emitted by the nucleus; these gamma rays were then detected using germanium detectors in the Gammasphere spectrometer at Argonne National Laboratory.
Gamma ray data were subsequently analyzed at the Naval Academy. Gamma rays that were emitted in coincidence, or nearly simultaneously, came from one unpaired nucleon in its decay to the ground state. Seven decay sequences in 171Re were established, but the focus of this project was based on sequences feeding into the previously determined wobbling band. Two bands were found to feed into the i13/2 (wobbling band) structure. Their characteristics have been assessed to determine if these sequences are associated with wobbling. Implications of this result on the region of triaxiality will be discussed.
System Size and Energy Dependence of Strangeness Production in 22 GeV Cu+Cu Collisions at RHIC
The Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory collides different ions at a wide variety of energies in order to study the properties of nuclear matter in extreme conditions. Beams of ions are sent around an accelerator ring at relativistic speeds approaching the speed of light before they meet in an extremely high temperature collision. The Solenoidal Tracker at RHIC (STAR) experiment exists to examine and identify the particles produced in these collisions in order to gather information about the behavior of quarks and gluons, the smallest known building blocks of matter. The strange quark is of particular interest since no strange quarks are sent into the collision. Consequently, the existence of particles with strange quarks, such as K0-shorts, lambdas, and anti-lambda baryons, shows that strange quarks were produced from the energy of the collision. Particles carrying strange quarks (“strangeness”), therefore, carry information about the matter produced in the collision. This matter is believed to be quark-gluon plasma, a state in which quarks and gluons become deconfined in a space of extremely high energy and temperature.
This project determines the yield of strange quarks through measurements of K0-shorts, lambdas, and anti-lambda particles in collision of cooper nuclei conducted at 22 GeV, one of RHIC’s lowest collision energies. The measurement of strangeness production for varying ranges of beam energy contributes to the overall understanding of the phase diagram for nuclear matter. The relatively low collision energy aids in the search for a critical point in nuclear matter phase transition. This project compares strangeness yields and spectra with current results from collisions at other beam energies and system sizes to allow better understanding of the properties of nuclear matter in extreme conditions.
Assistant Professor Richard Witt
A wireless sensor network, or WSN, is an emerging commercial technology that may have many practical applications on the modern battlefield. In a surveillance role, a WSN could be deployed across a geographic area of interest, allowing military commanders to monitor enemy troop positions and movements. Wireless sensor networks have enormous potential as an information gathering tool, but they also present many unique challenges to security engineers. An adversary can easily capture and tamper with one of the many unguarded sensor nodes so as to disrupt or significantly degrade the quality of surveillance that the WSN provides. This project examined potential attacks against WSNs and worked to develop a modified routing protocol that would increase the overall data integrity and reliability of wireless sensor networks.
Due to the battery limitations of individual sensor nodes, many WSN protocols seek to conserve battery power by simplifying computations and reducing the number of radio transmissions required for communication. Despite allowing the WSN to have a longer life expectancy, such protocols become easy targets for enemy exploitation. In what is known as a ‘sinkhole’ attack, a comprised sensor node is maliciously used to alter the wireless mesh of a sensor network for the purpose of disrupting the logical flow of information across the network. In the interest of minimizing the disruption from such an attack, this project has modified a tree based routing protocol that utilizes suboptimal routes in the network. The modified protocol attempts to avoid sinkholes and increase the overall data throughput of the network by sacrificing some of the network’s transmission efficiency. The efficacy of the project’s modified routing protocol was evaluated using an open source wireless network simulator. Using the simulator, the effectiveness of the modified protocol was tested against a sinkhole attack. Results from the tests of the modified protocol were compared to simulated sinkhole attacks run against the standard, unmodified protocol as a control.
Visiting Professor Eric J. Harder
CDR Patrick J. Vincent, USN
Computer Science Department
Can Interest-Free Finance Mitigate the Frequency and Amplitude of the Business Cycle and Crises?
This project examines the effects of debt prohibition on business cycles and financial crises. Researchers of Islamic Finance (which prohibits interest), based upon the works of Minsky (1992) and Khan (1986), argue that interest-bearing debt exacerbates and promotes economic shocks. On the other hand, the Financial Accelerator theory promulgated by Bernanke, Gertler, and Gilchrist (1994) claims that restrictions on capital structure exacerbate shocks.
The first part of the project will be the development of an econometric model relating the volatility of economic output and severity of recessions to a country’s capital structure. This model will incorporate data from various countries around the world.
The second part of the project will be an attempt to explain the results of the econometric model with a stylistic model. We will modify a model with financial accelerators in order to propose a mechanism for how a constraint on interest-bearing debt would affect shocks. We will then calibrate the model using real-world data.
Associate Professor Katherine Smith
Assistant Professor Leah Jager
Microstrip patch antennas are desirable in modern microwave communications systems due to their ease of production, ruggedness, and conformability. However, such resonant antennas suffer from small bandwidths and fixed operating frequencies. Due to their small size, low loss characteristics, and compatibility with integrated circuits, microelectromechanical systems (MEMS) have been the focus of recent efforts at developing frequency reconfigurable patch antennas able to operate at a number of different user-selected frequencies. Although variable reactive loading with MEMS variable capacitors is a well-documented method in reconfigurable antenna design, MEMS variable inductors have not received the same attention in that role.
This research presents designs for frequency tunable patch antennas using MEMS variable inductors and capacitors. Variations on previous thermally actuated MEMS variable inductor designs and electrostatically actuated MEMS variable capacitors were manufactured and integrated with various patch antenna designs and networks. The inductors feature pre-bent beams that are buckled due to lateral forces from a thermal actuator. As a result of the resulting deflection, the mutual inductance of the device is changed. The capacitors utilize electrostatic control to raise and lower a ground plane that is suspended beneath the signal line.
Associate Professor Deborah M. Mechtel
Associate Professor Samara L. Firebaugh
Harry K. Charles, Office of Naval Research, Distinguished Chair
Electrical Engineering Department