On the Quantitative Hardness of CVP

$\newcommand{\eps}{\varepsilon} \newcommand{\problem}[1]{\ensuremath{\mathrm{#1}} } \newcommand{\CVP}{\problem{CVP}} \newcommand{\SVP}{\problem{SVP}} \newcommand{\CVPP}{\problem{CVPP}} \newcommand{\ensuremath}[1]{#1}$For odd integers $p \geq 1$ (and $p = \infty$), we show that the Closest Vector Problem in the $\ell_p$ norm (\CVP_p) over rank $n$ lattices cannot be solved in 2^{(1-\eps) n} time for any constant \eps > 0 unless the Strong Exponential Time Hypothesis (SETH) fails. We then extend this result to "almost all" values of $p \geq 1$, not including the even integers. This comes tantalizingly close to settling the quantitative time complexity of the important special case of \CVP_2 (i.e., \CVP in the Euclidean norm), for which a $2^{n +o(n)}$-time algorithm is known. In particular, our result applies for any $p = p(n) \neq 2$ that approaches $2$ as $n \to \infty$. We also show a similar SETH-hardness result for \SVP_\infty; hardness of approximating \CVP_p to within some constant factor under the so-called Gap-ETH assumption; and other quantitative hardness results for \CVP_p and \CVPP_p for any $1 \leq p < \infty$ under different assumptions

Importance and Satisfaction with Institutional Factors among Students in Technical Colleges in Georgia

The researcher\u27s purpose of this study was to examine the relationship of the student\u27s identification of importance and satisfaction with institutional factors (those factors that the institutions can control) of Georgia\u27s technical colleges and to determine the extent of the differences between importance of and satisfaction with institutional factors. For the study, two databases were analyzed that were comprised of data from Georgia\u27s technical college students who took the Noel Levitz Student Satisfaction Inventory questionnaire. To explain the findings from the analysis, discussion topics were derived from the themes and trends and were presented to two, five person focus groups of students who attended a technical college in Georgia for discussion. The researchers findings revealed that students ranked the factors of instructional effectiveness, registration effectiveness, and academic advising/counseling as the most important factors within the institution. The researcher found that service excellence, safety and security issues, and campus support services were ranked by technical college students in Georgia as factors with which they were least satisfied. Students reported the least differences between the importance and satisfaction of the factors in the categories of safety and security, admissions and financial aid, and registration effectiveness reflected the greatest differences. The focus group expressed discontent with safety and security and the student services department of the institutions. The students are most satisfied with the faculty of the college. Administrators and decision makers may use the information garnered by this research to promote the areas that students feel are important and those in which students are satisfied, while focusing on correcting the items within the institution in which students are not satisfied. Policies and procedures can focus on factors that students feel are important such as instructional effectiveness, registration effectives, and academic advising and counseling. Coupled with this, policies should bolster factors that students are satisfied with such as institutional effectiveness, student centeredness, and concern for the individual while adding or changing policies that affect the factors that students are not satisfied; academic services, safety and security, and campus support services

Towards dense object tracking in a 2D honeybee hive

From human crowds to cells in tissue, the detection and efficient tracking of multiple objects in dense configurations is an important and unsolved problem. In the past, limitations of image analysis have restricted studies of dense groups to tracking a single or subset of marked individuals, or to coarse-grained group-level dynamics, all of which yield incomplete information. Here, we combine convolutional neural networks (CNNs) with the model environment of a honeybee hive to automatically recognize all individuals in a dense group from raw image data. We create new, adapted individual labeling and use the segmentation architecture U-Net with a loss function dependent on both object identity and orientation. We additionally exploit temporal regularities of the video recording in a recurrent manner and achieve near human-level performance while reducing the network size by 94% compared to the original U-Net architecture. Given our novel application of CNNs, we generate extensive problem-specific image data in which labeled examples are produced through a custom interface with Amazon Mechanical Turk. This dataset contains over 375,000 labeled bee instances across 720 video frames at 2 FPS, representing an extensive resource for the development and testing of tracking methods. We correctly detect 96% of individuals with a location error of ~7% of a typical body dimension, and orientation error of 12 degrees, approximating the variability of human raters. Our results provide an important step towards efficient image-based dense object tracking by allowing for the accurate determination of object location and orientation across time-series image data efficiently within one network architecture.Comment: 15 pages, including supplementary figures. 1 supplemental movie available as an ancillary fil

The economic rationality of consumption in the Mycenaean political economy and its role in the reproduction of social personae: modeling prestige networks.

This thesis is a theoretical examination of the economic rationality of consumption as it existed within the Mycenaean political economy. Using a modified paradigm of social network analysis, a semiotic approach is used in the study of identity expression and economic stratification present at three Late Helladic cemeteries. In doing so, the claim that exchange strategies which existed outside of palatial redistribution were present in the Late Helladic was substantiated as a similar logic of mortuary stratification which existed during the palatial era was also found to have existed after the shift to the post-palatial era and the collapse of the prevailing redistributive mode of consumption

Letter, Alexander Stephens to Unknown, ca. 1873-1882

This handwritten, undated note is written from Alexander Stephens to an unidentified recipient requesting a copy of the constitution from each state.https://scholarsjunction.msstate.edu/fvw-manuscripts-original-manuscripts/1197/thumbnail.jp

Letter, Alexander H. Stephens to Levi P. Morton, August 10, 1882

This letter, dated August 10, 1882, is written from Alexander H. Stephens, an American politician who served as the vice president of the Confederate States from 1861 to 1865, to Levi P. Morton, the 22nd vice president of the United States from 1889 to 1893. The letter offers an introduction to a friend of Stephens, J. Barrett Cohen of South Carolina. This note was found tipped into volume three, between pages 198-199 of Abraham Lincoln : A History by John G. Nicolay and John Hay.https://scholarsjunction.msstate.edu/fvw-manuscripts-nicolay-and-hay-documents/1023/thumbnail.jp

Symphony Orchestra Concerto Competition Concert

Kennesaw State University School of Music presents Concerto Competition Concert featuring competition winner Theresa Stephens, clarinet.https://digitalcommons.kennesaw.edu/musicprograms/1618/thumbnail.jp

Totally disconnected semigroup compactifications of topological groups

We introduce the notion of an introverted Boolean algebra $\cal B$ of closed-and-open subsets of a topological group $G$, show that the associated Stone space $(\nu_{\cal B} G, \nu_{\cal B})$ is a totally disconnected semigroup compactification of $G$, and show that every totally disconnected semigroup compactification of $G$ takes this form. We identify and study the universal totally disconnected semigroup compactification, the universal totally disconnected semitopological semigroup compactification and the universal totally disconnected group compactification of $G$. Our main results are obtained independently of Gelfand theory and well-known properties of the (typically non-totally disconnected) universal compactifications $G^{LUC}$, $G^{WAP}$ and $G^{AP}$, though we do employ Gelfand theory to clarify the relationship between these familiar universal compactifications and their totally disconnected counterparts.Comment: 24 pages, to be published in the Quarterly Journal of Mathematic

Speech of Hon. Alexander H. Stephens of Georgia on the Bill to Admit Kansas as a State Under the Topeka Constitution

The House having under consideration the bill reported from the Committee on Territories, providing for the admission of Kansas into the Union as a State, with the constitution prepared at Topeka by the Free State Party