Phase Transition in Liquid Drop Fragmentation

A liquid droplet is fragmented by a sudden pressurized-gas blow, and the resulting droplets, adhered to the window of a flatbed scanner, are counted and sized by computerized means. The use of a scanner plus image recognition software enables us to automatically count and size up to tens of thousands of tiny droplets with a smallest detectable volume of approximately 0.02 nl. Upon varying the gas pressure, a critical value is found where the size-distribution becomes a pure power-law, a fact that is indicative of a phase transition. Away from this transition, the resulting size distributions are well described by Fisher's model at coexistence. It is found that the sign of the surface correction term changes sign, and the apparent power-law exponent tau has a steep minimum, at criticality, as previously reported in Nuclear Multifragmentation studies [1,2]. We argue that the observed transition is not percolative, and introduce the concept of dominance in order to characterize it. The dominance probability is found to go to zero sharply at the transition. Simple arguments suggest that the correlation length exponent is nu=1/2. The sizes of the largest and average fragments, on the other hand, do not go to zero but behave in a way that appears to be consistent with recent predictions of Ashurst and Holian [3,4].Comment: 10 pages, 11 figures. LaTeX (revtex4) with psfig/epsfi

Multiscale Soil Investigations: Physical Concepts And Mathematical Techniques

Soil variability has often been considered to be composed of “functional” (explained) variations plus random fl uctuations or noise. However, the distinction between these two components is scale dependent because increasing the scale of observation almost always reveals structure in the noise (Burrough, 1983). Soils can be seen as the result of spatial variation operating over several scales, indicating that factors infl uencing spatial variability differ with scale. Th is observation points to variability as a key soil attribute that should be studied

A hybrid DEIM and leverage scores based method for CUR index selection

The discrete empirical interpolation method (DEIM) may be used as an index selection strategy for formulating a CUR factorization. A notable drawback of the original DEIM algorithm is that the number of column or row indices that can be selected is limited to the number of input singular vectors. We propose a new variant of DEIM, which we call L-DEIM, a combination of the strength of deterministic leverage scores and DEIM. This method allows for the selection of a number of indices greater than the number of input singular vectors. Since DEIM requires singular vectors as input matrices, L-DEIM is particularly attractive for example in big data problems when computing a rank-k SVD approximation is expensive even for moderately small k since it uses a lower-rank SVD approximation instead of the full rank-k SVD. We empirically demonstrate the performance of L-DEIM, which despite its efficiency, may achieve comparable results to the original DEIM and even better approximations than some state-of-the-art methods

A Prospective Longitudinal Study of the Clinical Outcomes from Cryptococcal Meningitis following Treatment Induction with 800 mg Oral Fluconazole in Blantyre, Malawi

Introduction: Cryptococcal meningitis is the most common neurological infection in HIV infected patients in Sub Saharan Africa, where gold standard treatment with intravenous amphotericin B and 5 flucytosine is often unavailable or difficult to administer. Fluconazole monotherapy is frequently recommended in national guidelines but is a fungistatic drug compromised by uncertainty over optimal dosing and a paucity of clinical end-point outcome data. Methods: From July 2010 until March 2011, HIV infected adults with a first episode of cryptococcal meningitis were recruited at Queen Elizabeth Central Hospital, Blantyre, Malawi. Patients were treated with oral fluconazole monotherapy 800 mg daily, as per national guidelines. ART was started at 4 weeks. Outcomes and factors associated with treatment failure were assessed 4, 10 and 52 weeks after fluconazole initiation. Results: Sixty patients were recruited. 26/60 (43%) died by 4 weeks. 35/60 (58.0%) and 43/56 (77%) died or failed treatment by 10 or 52 weeks respectively. Reduced consciousness (Glasgow Coma Score ,14 of 15), moderate/severe neurological disability (modified Rankin Score .3 of 5) and confusion (Abbreviated Mental Test Score ,8 of 10) were all common at baseline and associated with death or treatment failure. ART prior to recruitment was not associated with better outcomes. Conclusions: Mortality and treatment failure from cryptococcal meningitis following initiation of treatment with 800 mg oral fluconazole is unacceptably high. To improve outcomes, there is an urgent need for better therapeutic strategies and point-of-care diagnostics, allowing earlier diagnosis before development of neurological deficit

A DEIM-CUR factorization with iterative SVDs

A CUR factorization is often utilized as a substitute for the singular value decomposition (SVD), especially when a concrete interpretation of the singular vectors is challenging. Moreover, if the original data matrix possesses properties like nonnegativity and sparsity, a CUR decomposition can better preserve them compared to the SVD. An essential aspect of this approach is the methodology used for selecting a subset of columns and rows from the original matrix. This study investigates the effectiveness of one-round sampling and iterative subselection techniques and introduces new iterative subselection strategies based on iterative SVDs. One provably appropriate technique for index selection in constructing a CUR factorization is the discrete empirical interpolation method (DEIM). Our contribution aims to improve the approximation quality of the DEIM scheme by iteratively invoking it in several rounds, in the sense that we select subsequent columns and rows based on the previously selected ones. Thus, we modify A after each iteration by removing the information that has been captured by the previously selected columns and rows. We also discuss how iterative procedures for computing a few singular vectors of large data matrices can be integrated with the new iterative subselection strategies. We present the results of numerical experiments, providing a comparison of one-round sampling and iterative subselection techniques, and demonstrating the improved approximation quality associated with using the latter.</p

A DEIM-CUR factorization with iterative SVDs

A CUR factorization is often utilized as a substitute for the singular value decomposition (SVD), especially when a concrete interpretation of the singular vectors is challenging. Moreover, if the original data matrix possesses properties like nonnegativity and sparsity, a CUR decomposition can better preserve them compared to the SVD. An essential aspect of this approach is the methodology used for selecting a subset of columns and rows from the original matrix. This study investigates the effectiveness of \emph{one-round sampling} and iterative subselection techniques and introduces new iterative subselection strategies based on iterative SVDs. One provably appropriate technique for index selection in constructing a CUR factorization is the discrete empirical interpolation method (DEIM). Our contribution aims to improve the approximation quality of the DEIM scheme by iteratively invoking it in several rounds, in the sense that we select subsequent columns and rows based on the previously selected ones. Thus, we modify $A$ after each iteration by removing the information that has been captured by the previously selected columns and rows. We also discuss how iterative procedures for computing a few singular vectors of large data matrices can be integrated with the new iterative subselection strategies. We present the results of numerical experiments, providing a comparison of one-round sampling and iterative subselection techniques, and demonstrating the improved approximation quality associated with using the latter

RSVD-CUR Decomposition for Matrix Triplets

We propose a restricted SVD based CUR (RSVD-CUR) decomposition for matrix triplets $(A, B, G)$. Given matrices $A$, $B$, and $G$ of compatible dimensions, such a decomposition provides a coordinated low-rank approximation of the three matrices using a subset of their rows and columns. We pick the subset of rows and columns of the original matrices by applying either the discrete empirical interpolation method (DEIM) or the L-DEIM scheme on the orthogonal and nonsingular matrices from the restricted singular value decomposition of the matrix triplet. We investigate the connections between a DEIM type RSVD-CUR approximation and a DEIM type CUR factorization, and a DEIM type generalized CUR decomposition. We provide an error analysis that shows that the accuracy of the proposed RSVD-CUR decomposition is within a factor of the approximation error of the restricted singular value decomposition of given matrices. An RSVD-CUR factorization may be suitable for applications where we are interested in approximating one data matrix relative to two other given matrices. Two applications that we discuss include multi-view/label dimension reduction, and data perturbation problems of the form $A_E=A + BFG$, where $BFG$ is a nonwhite noise matrix. In numerical experiments, we show the advantages of the new method over the standard CUR approximation for these applications

Block Discrete Empirical Interpolation Methods

We present two block variants of the discrete empirical interpolation method (DEIM); as a particular application, we will consider a CUR factorization. The block DEIM algorithms are based on the rank-revealing QR factorization and the concept of the maximum volume of submatrices. We also present a version of the block DEIM procedures, which allows for adaptive choice of block size. Experiments demonstrate that the block DEIM algorithms may provide a better low-rank approximation, and may also be computationally more efficient than the standard DEIM procedure

Fecal Coliform Transport through Intact Soil Blocks Amended with Poultry Manure

Poultry production in Kentucky increased almost 200% between 1991 and 1995. Their waste is typically land applied, and fecal pathogen runoff and infiltration may cause nonpoint source groundwater pollution. We looked at the preferential flow of fecal coliforms through undisturbed soil blocks since fecal bacteria typically infiltrate the soil profile to contaminate groundwater. Poultry manure was uniformly distributed on top of sod-covered or tilled (upper 12.5 cm) soil blocks and the blocks were irrigated. Drainage was collected in 100 uniformly spaced cells beneath each block and analyzed for fecal coliform content and drainage volume. The spatial distribution of drainage and fecal coliforms through the soil blocks was not uniform. Fecal coliforms appeared where most drainage flowed. Drainage water from each soil block consistently exceeded 200 000 fecal coliforms per 100 mL and was as great as 30 million fecal coliforms per 100 mL of leachate collected. Fecal coliforms leached as a pulse, but the breakthrough of fecal coliforms through tilled blocks was delayed with respect to the breakthrough of fecal coliforms through sod-covered blocks. Rainfall on a well-structured soil will cause the preferential movement of fecal bacteria, even with unsaturated flow conditions, and could contribute to fecal coliform concentrations in shallow groundwater that exceed standards for domestic discharge and primary contact water in Kentucky (200 fecal coliforms/100 mL)