We present a post-processing technique that selectively reduces the salience of distracting regions in an image. Computational models of attention predict that texture variation influences bottom-up attention mechanisms. Our method reduces the spatial variation of texture using power maps, high-order features describing local frequency content in an image. Modification of power maps results in effective regional de-emphasis. We validate our results quantitatively via a human subject search experiment and qualitatively with eye tracking data. / Singapore-MIT Alliance (SMA)

The self-power map is the function from the set of natural numbers to itself which sends the number $n$ to $n^n$. Motivated by applications to cryptography, we consider the image of this map modulo a prime $p$. We study the question of how large $x$ must be so that $n^n \equiv a \bmod p$ has a solution with $1 \le n \le x$, for every residue class $a$ modulo $p$. While $n^n \bmod p$ is not uniformly distributed, it does appear to behave in certain ways as a random function. We give a heuristic argument to show that the expected $x$ is approximately ${p^2\log \phi(p-1)/\phi(p-1)}$, using the coupon collector problem as a model. Rigorously, we prove the bound $x <p^{2-\alpha}$ for sufficiently large $p$ and a fixed constant $\alpha > 0$ independent of $p$, using a counting argument and exponential sum bounds. Additionally, we prove nontrivial bounds on the number of solutions of $n^n \equiv a \bmod p$ for a fixed residue class $a$ when $1 \le n \le x$, extending the known bounds when $1 \le n \le p-1$.

The self-power map is the function from the set of natural numbers to itself which sends the number $n$ to $n^n$. Motivated by applications to cryptography, we consider the image of this map modulo a prime $p$. We study the question of how large $x$ must be so that $n^n \equiv a \bmod p$ has a solution with $1 \le n \le x$, for every residue class $a$ modulo $p$. While $n^n \bmod p$ is not uniformly distributed, it does appear to behave in certain ways as a random function. We give a heuristic argument to show that the expected $x$ is approximately ${p^2\log \phi(p-1)/\phi(p-1)}$, using the coupon collector problem as a model. Rigorously, we prove the bound $x <p^{2-\alpha}$ for sufficiently large $p$ and a fixed constant $\alpha > 0$ independent of $p$, using a counting argument and exponential sum bounds. Additionally, we prove nontrivial bounds on the number of solutions of $n^n \equiv a \bmod p$ for a fixed residue class $a$ when $1 \le n \le x$, extending the known bounds when $1 \le n \le p-1$.

This report presents the results and findings gathered during the master thesis work performed by Madeleine Jareblom at Scania CV AB in Södertälje. Scania is a developer and manufacturer of trucks and buses. They always strive to improve their testing and simulations for current and future products.  In order to predict the outcome or to analyse the performance of components or systems, simulation models are a powerful tool to use. Realistic and adaptive models are of great interest for Scania and this thesis will cover a steering system performance simulation capability. A steering system consist of a hand wheel, steering gear and linkages down to the steering wheels. The purpose of a steering gear is to ease the resistance a driver has to apply in order to steer the wheels.  There are a lot of different steering systems that are being used in vehicles these days but one of the more common ones is Electric Hydraulic Power Steering (EHPS) which this paper will cover. The simulation model is of an open loop design for an EHPS system that takes input data and divide them into separate calculation blocks. Static variables and data from vehicle measurements were used, together with some assumptions such as; front wheel steering, only applicable for trucks, no roll inclination, 2- or 3-axel vehicles and some static angels in the suspension geometry. During the construction phase of the model, calibrations were performed and there it was found that the friction in the system was load dependent. When the model was calibrated the final output results consisted of; calculated trajectory of the vehicle, the required output torque from the steering gear, input and output power of the steering system together with the consumed energy. From the results of the trajectory output it could be seen that the model is sensitive to small deviations of the handwheel angle and possible road banking. This entailed that the calculated trajectory did not resemble the driven path gathered from vehicle test data. The calculated output torque from the model, was validated with the use of measured pressure and supplier specifications for the steering gear. The results indicated that the calculation model could capture torques from the steering gear close to reality. It could be concluded that the model could be used to describe resulting torques, output and input power together with the consumed energy.

This thesis summarizes a theory of magnetic resonance and the method of functional magnetic resonance. It is focused on the influence of motion artifacts and image preprocessing methods, especially realign. It deals with the possibility of using movement parameters obtained in the process of alignment of functional scans to create maps that show the expression of motion artifacts. In this thesis, three different methods were designed, implemented a tested. These methods lead to the creation of probability, power and statistical group maps showing areas typically affected by movement artifacts.