Parameterizing roots of polynomial congruences

We use the arithmetic of ideals in orders to parameterize the roots $\mu \pmod m$ of the polynomial congruence $F(\mu) \equiv 0 \pmod m$, $F(X) \in \mathbb{Z}[X]$ monic, irreducible and degree $d$. Our parameterization generalizes Gauss's classic parameterization of the roots of quadratic congruences using binary quadratic forms, which had previously only been extended to the cubic polynomial $F(X) = X^3 - 2$. We show that only a special class of ideals are needed to parameterize the roots $\mu \pmod m$, and that in the cubic setting, $d = 3$, general ideals correspond to pairs of roots $\mu_1 \pmod{m_1}$, $\mu_2 \pmod {m_2}$ satisfying $\gcd(m_1, m_2, \mu_1 - \mu_2) = 1$. At the end we illustrate our parameterization and this correspondence between roots and ideals with a few applications, including finding approximations to $\frac{\mu}{m} \in \mathbb{R}/ \mathbb{Z}$, finding an explicit Euler product for the co-type zeta function of $\mathbb{Z}[2^{\frac{1}{3}}]$, and computing the composition of cubic ideals in terms of the roots $\mu_1 \pmod {m_1}$ and $\mu_2 \pmod {m_2}$.Comment: 49 page

Factors contributing to Posttraumatic Growth in college students who have experienced parental divorce

Parental divorce can have a significant impact on college students, such as anxiety, relationship problems, and difficulty adjusting to college. However, some college students may also experience growth as a result of parental divorce. Posttraumatic growth describes the process of how a person experiences growth, change, or positive benefits after a traumatic experience. Some college students may experience posttraumatic growth after a traumatic event including a parental divorce. This presentation will look at whether a college student\u27s attachment style or coping style is related to posttraumatic growth in college students who have experienced parental divorce

Text generation for dataset augmentation in security classification tasks

Security classifiers, designed to detect malicious content in computer systems and communications, can underperform when provided with insufficient training data. In the security domain, it is often easy to find samples of the negative (benign) class, and challenging to find enough samples of the positive (malicious) class to train an effective classifier. This study evaluates the application of natural language text generators to fill this data gap in multiple security-related text classification tasks. We describe a variety of previously-unexamined language-model fine-tuning approaches for this purpose and consider in particular the impact of disproportionate class-imbalances in the training set. Across our evaluation using three state-of-the-art classifiers designed for offensive language detection, review fraud detection, and SMS spam detection, we find that models trained with GPT-3 data augmentation strategies outperform both models trained without augmentation and models trained using basic data augmentation strategies already in common usage. In particular, we find substantial benefits for GPT-3 data augmentation strategies in situations with severe limitations on known positive-class samples

Senior Recital: Matthew J. C. Welsh, baritone

This recital is presented in partial fulfillment of requirements for the degree Bachelor of Music in Performance. Mr. Welsh studies voice with Todd Wedge.https://digitalcommons.kennesaw.edu/musicprograms/2208/thumbnail.jp

Junior Recital: Deondria West, soprano and Matthew Welsh, baritone/bass

This joint recital is presented in partial fulfillment of requirements for the degrees Bachelor of Music in Performance. Ms. West and Mr. Welsh study voice with Todd Wedge.https://digitalcommons.kennesaw.edu/musicprograms/2067/thumbnail.jp

A Utility-Based Approach to Bandwidth Allocation and Link Scheduling in Wireless Networks

We study the problem of optimizing aggregate user utility in wireless ad-hoc networks under the constraints of wireless interference. We develop a market-oriented approach to bandwidth allocation with a tˆatonnement process and demonstrate its ability to effectively price bottleneck resource. One novelty is that we choose to price “interference goods” to capture the externality imposed by one application’s use of the network on other applications. In making progress we also propose a modification to the CSMA protocol that is robust enough to handle a non-schedulable bandwidth schedule. Experimental results on simulated network topologies show that the market-based approach has better scalability than alternate approximation methods and is much more efficient in terms of runtime.Engineering and Applied Science

3D Computational Ghost Imaging

Computational ghost imaging retrieves the spatial information of a scene using a single pixel detector. By projecting a series of known random patterns and measuring the back reflected intensity for each one, it is possible to reconstruct a 2D image of the scene. In this work we overcome previous limitations of computational ghost imaging and capture the 3D spatial form of an object by using several single pixel detectors in different locations. From each detector we derive a 2D image of the object that appears to be illuminated from a different direction, using only a single digital projector as illumination. Comparing the shading of the images allows the surface gradient and hence the 3D form of the object to be reconstructed. We compare our result to that obtained from a stereo- photogrammetric system utilizing multiple high resolution cameras. Our low cost approach is compatible with consumer applications and can readily be extended to non-visible wavebands.Comment: 13pages, 4figure

Senior Recital: Tessa Walker, mezzo-soprano

This recital is presented in partial fulfillment of requirements for the degree Bachelor of Music in Music Education. Ms. Walker studies voice with Jana Young and Karla Harris.https://digitalcommons.kennesaw.edu/musicprograms/2209/thumbnail.jp