High Performance Sparse Multivariate Polynomials: Fundamental Data Structures and Algorithms

Polynomials may be represented sparsely in an effort to conserve memory usage and provide a succinct and natural representation. Moreover, polynomials which are themselves sparse – have very few non-zero terms – will have wasted memory and computation time if represented, and operated on, densely. This waste is exacerbated as the number of variables increases. We provide practical implementations of sparse multivariate data structures focused on data locality and cache complexity. We look to develop high-performance algorithms and implementations of fundamental polynomial operations, using these sparse data structures, such as arithmetic (addition, subtraction, multiplication, and division) and interpolation. We revisit a sparse arithmetic scheme introduced by Johnson in 1974, adapting and optimizing these algorithms for modern computer architectures, with our implementations over the integers and rational numbers vastly outperforming the current wide-spread implementations. We develop a new algorithm for sparse pseudo-division based on the sparse polynomial division algorithm, with very encouraging results. Polynomial interpolation is explored through univariate, dense multivariate, and sparse multivariate methods. Arithmetic and interpolation together form a solid high-performance foundation from which many higher-level and more interesting algorithms can be built

Hyaluronic acid gel fillers in the management of facial aging

Time affects facial aging by producing cellular and anatomical changes resulting in the consequential loss of soft tissue volume. With the advent of new technologies, the physician has the opportunity of addressing these changes with the utilization of dermal fillers. Hyaluronic acid (HA) dermal fillers are the most popular, non-permanent injectable materials available to physicians today for the correction of soft tissue defects of the face. This material provides an effective, non invasive, non surgical alternative for correction of the contour defects of the face due to its enormous ability to bind water and easiness of implantation. HA dermal fillers are safe and effective. The baby-boomer generation, and their desire of turning back the clock while enjoying an active lifestyle, has expanded the popularity of these fillers. In the US, there are currently eight HA dermal fillers approved for commercialization by the Food and Drug Administration (FDA). This article reviews the innate properties of FDA-approved HA fillers and provides an insight on future HA products and their utilization for the management of the aging face

Nature of perpendicular-to-parallel spin reorientation in a Mn-doped GaAs quantum well: Canting or phase separation?

It is well known that the magnetic anisotropy in a compressively strained Mn-doped GaAs film changes from perpendicular to parallel with increasing hole concentration p. We study this reorientation transition at T=0 in a quantum well with delta-doped Mn impurities. With increasing p, the angle θ that minimizes the energy E increases continuously from 0 (perpendicular anisotropy) to π/2 (parallel anisotropy) within some range of p. The shape of E min (p) suggests that the quantum well becomes phase separated with regions containing low hole concentrations and perpendicular moments interspersed with other regions containing high hole concentrations and parallel moments. However, because of the Coulomb energy cost associated with phase separation, the true magnetic state in the transition region is canted with 0\u3cθ\u3cπ/2. © 2007 The American Physical Society

Utilization of Round One of The Paycheck Protection Program

The Paycheck Protection Program (PPP) was created when the H.R Bill 758 (Cares Act) was signed into U.S law on March 27, 2020. With the bill, small businesses that were struggling due to the COVID-19 pandemic were able to apply for loans that were forgivable. For this study, we focused solely on the first round of loans that were sent out. We understand that with the ever-changing situation of COVID-19 businesses could receive more loan forgiveness, but we focused on just the first round of loans. This study consisted of email surveys that were sent to small businesses in Texas and Wisconsin to learn about how small businesses utilized the loans they received. The purpose of this study was to see how a small sample of roughly 15-20 small businesses used the loans it received and to formulate trends on the questions that we asked. Our major findings were that one third of the businesses had to lay off employees, most of the businesses used the loans primarily for payroll costs, almost all the businesses are applying for loan forgiveness, and a good number of businesses saw a substantial downturn in revenue compared to other years due to COVID-19

In Vitro Inhibition of Listeria Monocytogenes by Novel Combinations of Food Antimicrobials

Listeria monocytogenes is a foodborne pathogenic bacterium responsible for ~500 deaths and a financial burden of ~$2.3 billion each year in the United States. Though a zero tolerance policy is enforced with regard to its detection in cooked ready-to-eat foods, additional preemptive control alternatives are required for certain products. Among these alternatives are strategies permitting the usage of food antimicrobial combinations to control the pathogen. Research on antimicrobial combinations can provide insight into more efficient control of the pathogen, but is currently lacking. The purpose of this study was to evaluate the in vitro inhibition of L. monocytogenes exposed to the antimicrobials e-Poly-L-Lysine (EPL), lauric arginate ester (LAE), and sodium lactate (SL) at pH 7.3, octanoic acid (OCT) at pH 5.0, and nisin (NIS) and acidic calcium sulfate (ACS) at both pH 5.0 and 7.3. A broth dilution assay was used to determine single antimicrobial minimum inhibitory and bactericidal concentrations for L. monocytogenes Scott A, 310, NADC 2783, and NADC 2045. Optical density differences (delta<0.05 at 630 nm) were used to denote inhibition. Concentrations producing population decreases of greater than or equal to 3.0 log10 CFU/ml after incubation were considered bactericidal. Inhibition resulting from combinations of antimicrobials (NIS+ACS, EPL+ACS, SL+ACS, NIS+LAE, OCT+ACS, and OCT+NIS) was assessed using a checkerboard assay, and fractional inhibitory concentrations (FIC) were determined. FIC values were plotted on isobolograms and were used to create FIC indices (FICI). Isobologram curvature was used to classify combinations as synergistic, additive, or antagonistic. From FIC indices, interactions were defined as antagonistic (FICI >1.0), additive (FICI =1.0), or synergistic (FICI &lt;1.0). Strain-dependent factors had a bearing on MIC and MBC values for NIS and EPL. At pH 7.3, NIS+ACS displayed synergistic inhibition, NIS+LAE and EPL+ACS demonstrated additive-type interactions, and the SL+ACS pairing was unable to be defined. At pH 5.0, interpretation of the OCT+NIS interaction also presented challenges, while the OCT+ACS combination resulted in synergistic behavior. Additional studies are needed to validate in vitro findings on surfaces of ready-to-eat meats. Future in vivo studies should investigate the ability of synergistic combinations (NIS+ACS and OCT+ACS) to control the pathogen. Better characterizations of inhibitory mechanisms should also be performed

Design, synthesis and in vitro degradation of a novel co-drug for the treatment of psoriasis

Psoriasis is a common, chronic and relapsing inflammatory skin disease. It affects approximately 2% of the western population and has no cure. Combination therapy for psoriasis often proves more efficacious and better tolerated than monotherapy with a single drug. Combination therapy could be administered in the form of a co-drug, where two or more therapeutic compounds active against the same condition are linked by a cleavable covalent bond. Similar to the pro-drug approach, the liberation of parent moieties post-administration, by enzymatic and/or chemical mechanisms, is a pre-requisite for effective treatment. In this study, a series of co-drugs incorporating dithranol in combination with one of several non-steroidal anti-inflammatory drugs, both useful for the treatment of psoriasis, were designed, synthesized and evaluated. An ester co-drug comprising dithranol and naproxen in a 1:1 stoichiometric ratio was determined to possess the optimal physicochemical properties for topical delivery. The co-drug was fully hydrolyzed in vitro by porcine liver esterase within four hours. When incubated with homogenized porcine skin, 9.5% of the parent compounds were liberated after 24 h, suggesting in situ esterase-mediated cleavage of the co-drug would occur within the skin. The kinetics of the reaction revealed first order kinetics, Vmax = 10.3 μM/min and Km = 65.1 μM. The co-drug contains a modified dithranol chromophore that was just 37% of the absorbance of dithranol at 375 nm and suggests reduced skin/clothes staining. Overall, these findings suggest that the dithranol-naproxen co-drug offers an attractive, novel approach for the treatment of psoriasis

Assessing the use of artificial substrates to monitor Gambierdiscus populations in the Florida Keys

© The Author(s), 2017. This is the author's version of the work. It is posted here under a nonexclusive, irrevocable, paid-up, worldwide license granted to WHOI. It is made available for personal use, not for redistribution. The definitive version was published in Harmful Algae 68 (2017): 52-66, doi:10.1016/j.hal.2017.07.007.Four distinct coastal locations were sampled on a monthly basis near Long Key (Florida Keys, USA) over a 13-month period to study Gambierdiscus population dynamics on different substrates, including four macrophyte species (Dictyota spp., Halimeda spp., Laurencia spp., and Thalassia testudinum) and three artificial substrates (polyvinyl chloride (PVC) tiles, burlap, and fiberglass window screen). Cell densities of Gambierdiscus were generally lower on Dictyota versus Halimeda and Laurencia. Cell densities of Gambierdiscus were significantly correlated among macrophyte hosts in 54% of the comparisons, and between macrophyte hosts and artificial substrates in 72% of the comparisons. Predictive slopes determined from regression analyses between cell densities on artificial substrates and macrophyte hosts indicated that, on an areal basis, fewer cells were present on macrophytes versus artificial substrates (cells cm-2) and that slope variation (error) among the different macrophytes and sites ranged from 5% to 200%, averaging 61% overall. As the data required log-transformation prior to analyses, this level of error translates into two-orders of magnitude in range of estimation of the overall average abundance of Gambierdiscus cells on macrophytes (135 cells g-1 wet weight); 20 to 2690 cells g-1 ww. The lack of consistent correlation among Gambierdiscus cell densities on macrophytes versus artificial substrates, coupled with the high level of error associated with the predictive slope estimations, indicates that extreme caution should be taken when interpreting the data garnered from artificial substrate deployments, and that such deployments should be thoroughly vetted prior to routine use for monitoring purposes.Funding for this work was provided by NOAA NOS (Cooperative Agreements NA11NOS478-0060 and NA11NOS4780028)

X-ray Power Density Spectrum of the Narrow Line Seyfert 1 Galaxy Akn 564

Beginning in 1999 January, the bright, strongly variable Narrow-Line Seyfert 1 (NLS1) galaxy Akn 564 has been observed by RXTE once every ~4.3 days. It was also monitored every ~3.2 hr throughout 2000 July. These evenly-sampled observations have allowed the first quantitative comparison of long and short time-scale X-ray variability in an NLS1 and the derivation of an X-ray Power Density Spectrum (PDS). The variability amplitude in the short time-scale light curve is very similar to that in the long time-scale light curve, in marked contrast to the stronger variability on longer time-scales which is characteristic of "normal" broad-line Seyfert 1s (BLS1s). Furthermore, the Akn 564 PDS power law cuts off at a frequency of 8.7x10^-7 Hz corresponding to a timescale of ~13 d, significantly shorter than that seen in the PDS of NGC 3516, a BLS1 of comparable luminosity. This result is consistent with NLS1s showing faster (as opposed to larger amplitude) variations than BLS1s, providing further evidence that NLS1s harbour lower mass black holes than BLS1s of similar luminosity, accreting at a correspondingly higher relative rate.Comment: Accepted for publication in Ap

Vortex avalanches and magnetic flux fragmentation in superconductors

We report results of numerical simulations of non isothermal dendritic flux penetration in type-II superconductors. We propose a generic mechanism of dynamic branching of a propagating hotspot of a flux flow/normal state triggered by a local heat pulse. The branching occurs when the flux hotspot reflects from inhomogeneities or the boundary on which magnetization currents either vanish, or change direction. Then the hotspot undergoes a cascade of successive splittings, giving rise to a dissipative dendritic-type flux structure. This dynamic state eventually cools down, turning into a frozen multi-filamentary pattern of magnetization currents.Comment: 4 pages, 4 figures, accepted to Phys. Rev. Let