A group-theoretic approach to fast matrix multiplication

We develop a new, group-theoretic approach to bounding the exponent of matrix multiplication. There are two components to this approach: (1) identifying groups G that admit a certain type of embedding of matrix multiplication into the group algebra C[G], and (2) controlling the dimensions of the irreducible representations of such groups. We present machinery and examples to support (1), including a proof that certain families of groups of order n^(2 + o(1)) support n-by-n matrix multiplication, a necessary condition for the approach to yield exponent 2. Although we cannot yet completely achieve both (1) and (2), we hope that it may be possible, and we suggest potential routes to that result using the constructions in this paper.Comment: 12 pages, 1 figure, only updates from previous version are page numbers and copyright informatio

Trace Elements in Soils of the South Texas Uranium District: Concentrations, Origin, and Environmental Significance

UT Librarie

Report of Investigations No. 135 Oligocene Volcanism and Multiple Caldera Formation in the Chinati Mountains, Presidio County, Texas

UT Librarie

The IRX-β\beta relation: Insights from simulations

We study the relationship between the UV continuum slope and infrared excess (IRX$\equiv L_{\rm IR}/L_{\rm FUV}$) predicted by performing dust radiative transfer on a suite of hydrodynamical simulations of galaxies. Our suite includes both isolated disk galaxies and mergers intended to be representative of galaxies at both $z \sim 0$ and $z \sim 2-3$. Our low-redshift isolated disks and mergers often populate a region around the the locally calibrated \citet[][M99]{M99} relation but move well above the relation during merger-induced starbursts. Our high-redshift simulated galaxies are blue and IR-luminous, which makes them lie above the M99 relation. The value of UV continuum slope strongly depends on the dust type used in the radiative transfer calculations: Milky Way-type dust leads to significantly more negative (bluer) slopes compared with Small Magellanic Cloud-type dust. The effect on $\beta$ due to variations in the dust composition with galaxy properties or redshift can dominate over other sources of $\beta$ variations and is the dominant model uncertainty. The dispersion in $\beta$ is anticorrelated with specific star formation rate and tends to be higher for the $z \sim 2-3$ simulations. In the actively star-forming $z \sim 2-3$ simulated galaxies, dust attenuation dominates the dispersion in $\beta$, whereas in the $z \sim 0$ simulations, the contributions of SFH variations and dust are similar. For low-SSFR systems at both redshifts, SFH variations dominate the dispersion. Finally, the simulated $z \sim 2-3$ isolated disks and mergers both occupy a region in the \irxbeta\ plane consistent with observed $z \sim 2-3$ dusty star-forming galaxies (DSFGs). Thus, contrary to some claims in the literature, the blue colors of high-z DSFGs do not imply that they are short-lived starbursts.Comment: 20 pages+a 4-page appendix, Accepted for publication at Ap

Extending the CRESST-II commissioning run limits to lower masses

Motivated by the recent interest in light WIMPs of mass ~O(10 GeV), an extension of the elastic, spin-independent WIMP-nucleon cross-section limits resulting from the CRESST-II commissioning run (2007) are presented. Previously, these data were used to set cross-section limits from 1000 GeV down to ~17 GeV, using tungsten recoils, in 47.9 kg-days of exposure of calcium tungstate. Here, the overlap of the oxygen and calcium bands with the acceptance region of the commissioning run data set is reconstructed using previously published quenching factors. The resulting elastic WIMP cross section limits, accounting for the additional exposure of oxygen and calcium, are presented down to 5 GeV.Comment: 4 pages, 4 figure

Group-theoretic algorithms for matrix multiplication

We further develop the group-theoretic approach to fast matrix multiplication introduced by Cohn and Umans, and for the first time use it to derive algorithms asymptotically faster than the standard algorithm. We describe several families of wreath product groups that achieve matrix multiplication exponent less than 3, the asymptotically fastest of which achieves exponent 2.41. We present two conjectures regarding specific improvements, one combinatorial and the other algebraic. Either one would imply that the exponent of matrix multiplication is 2.Comment: 10 page

Impact of Vegetative Treatment Systems on Multiple Measures of Antibiotic Resistance in Agricultural Wastewater

Wastewater is an important vector of antibiotic resistant bacteria and antibiotic resistance genes (ARB/G). While there is broad agreement that ARB/G from agricultural (ag) wastewaters can be transported through the environment and may contribute to untreatable infectious disease in humans and animals, there remain large knowledge gaps surrounding applied details on the types and amounts of ARB/G associated with different agricultural wastewater treatment options and different ag production systems. This study evaluates a vegetative treatment system (VTS) built to treat the wastewater from a beef cattle feedlot. Samples were collected for three years, and plated on multiple media types to enumerate tetracycline and cefotaxime-resistant bacteria. Enterobacteriaceae isolates (n = 822) were characterized for carriage of tetracycline resistance genes, and E. coli isolates (n = 673) were phenotyped to determine multi-drug resistance (MDR) profiles. Tetracycline resistance in feedlot runoff wastewater was 2-to-3 orders of magnitude higher compared to rainfall runoff from the VTS fields, indicating efficacy of the VTA for reducing ARB over time following wastewater application. Clear differences in MDR profiles were observed based on the specific media on which a sample was plated. This result highlights the importance of method, especially in the context of isolate-based surveillance and monitoring of ARB in agricultural wastewaters