Efficient certification of feasibility and objective value of linear programs and its applications

The use of linear programming in various areas has increased with the significant improvement of specialized solvers. Linear programs are used as such to model practical problems, or as subroutines in algorithms such as formal proofs or branch-and-cut frameworks. In many situations a certified answer is needed, for example the guarantee that the linear program is feasible or infeasible, or a provably safe bound on its objective value. Most of the available solvers work with floating-point arithmetic and are thus subject to its shortcomings such as rounding errors or underflow, therefore they can deliver incorrect answers. While adequate for some applications, this is unacceptable for critical applications like flight controlling or nuclear plant management due to the potential catastrophic consequences. We propose a method that gives a certified answer whether a linear program is feasible or infeasible, or returns unknown'. The advantage of our method is that it is reasonably fast and rarely answers unknown'. It works by computing a safe solution that is in some way the best possible in the relative interior of the feasible set. To certify the relative interior, we employ exact arithmetic, whose use is nevertheless limited in general to critical places, allowing us to rnremain computationally efficient. Moreover, when certain conditions are fulfilled, our method is able to deliver a provable bound on the objective value of the linear program. We test our algorithm on typical benchmark sets and obtain higher rates of success compared to previous approaches for this problem, while keeping the running times acceptably small. The computed objective value bounds are in most of the cases very close to the known exact objective values. We prove the usability of the method we developed by additionally employing a variant of it in a different scenario, namely to improve the results of a Satisfiability Modulo Theories solver. Our method is used as a black box in the nodes of a branch-and-bound tree to implement conflict learning based on the certificate of infeasibility for linear programs consisting of subsets of linear constraints. The generated conflict clauses are in general small and give good rnprospects for reducing the search space. Compared to other methods we obtain significant improvements in the running time, especially on the large instances.

Novel algorithms for electronic structure based molecular dynamics with linear system-size scaling

Die vorliegende Arbeit behandelt die Entwicklung und Verbesserung von linear skalierenden Algorithmen für Elektronenstruktur basierte Molekulardynamik. Molekulardynamik ist eine Methode zur Computersimulation des komplexen Zusammenspiels zwischen Atomen und Molekülen bei endlicher Temperatur. Ein entscheidender Vorteil dieser Methode ist ihre hohe Genauigkeit und Vorhersagekraft. Allerdings verhindert der Rechenaufwand, welcher grundsätzlich kubisch mit der Anzahl der Atome skaliert, die Anwendung auf große Systeme und lange Zeitskalen. Ausgehend von einem neuen Formalismus, basierend auf dem großkanonischen Potential und einer Faktorisierung der Dichtematrix, wird die Diagonalisierung der entsprechenden Hamiltonmatrix vermieden. Dieser nutzt aus, dass die Hamilton- und die Dichtematrix aufgrund von Lokalisierung dünn besetzt sind. Das reduziert den Rechenaufwand so, dass er linear mit der Systemgröße skaliert. Um seine Effizienz zu demonstrieren, wird der daraus entstehende Algorithmus auf ein System mit flüssigem Methan angewandt, das extremem Druck (etwa 100 GPa) und extremer Temperatur (2000 - 8000 K) ausgesetzt ist. In der Simulation dissoziiert Methan bei Temperaturen oberhalb von 4000 K. Die Bildung von sp²-gebundenem polymerischen Kohlenstoff wird beobachtet. Die Simulationen liefern keinen Hinweis auf die Entstehung von Diamant und wirken sich daher auf die bisherigen Planetenmodelle von Neptun und Uranus aus. Da das Umgehen der Diagonalisierung der Hamiltonmatrix die Inversion von Matrizen mit sich bringt, wird zusätzlich das Problem behandelt, eine (inverse) p-te Wurzel einer gegebenen Matrix zu berechnen. Dies resultiert in einer neuen Formel für symmetrisch positiv definite Matrizen. Sie verallgemeinert die Newton-Schulz Iteration, Altmans Formel für beschränkte und nicht singuläre Operatoren und Newtons Methode zur Berechnung von Nullstellen von Funktionen. Der Nachweis wird erbracht, dass die Konvergenzordnung immer mindestens quadratisch ist und adaptives Anpassen eines Parameters q in allen Fällen zu besseren Ergebnissen führt.

Screening and prediction of erosive potential

The literature on the erosive potential of drinks and other products is summarised, and aspects of the conduct of screening tests as well as possible correlations of the erosive potential with various solution parameters are discussed. The solution parameters that have been suggested as important include pH, acid concentration (with respect to buffer capacity and concentration of undissociated acid), degree of saturation, calcium and phosphate concentrations, and inhibitors of erosion. Based on the available data, it is concluded that the dominant factor in erosion is pH. The effect of buffer capacity seems to be pH dependent. The degree of saturation probably has a non-linear relationship with erosion. While calcium at elevated concentrations is known to reduce erosion effectively, it is not known whether it is important at naturally occurring concentrations. Fluoride at naturally occurring concentrations is inversely correlated with erosive potential, but phosphate is probably not. Natural plant gums, notably pectin, do not inhibit erosion, so they are unlikely to interfere with the prediction of erosive potential. The non-linearity of some solution factors and interactions with pH need to be taken into account when developing multivariate models for predicting the erosive potential of different solutions. Finally, the erosive potential of solutions towards enamel and dentine might differ.

Investigation of the Potential Energy Surface for the First Step in the Alkaline Hydrolysis of Methyl Acetate

The potential energy surface for the first step of the alkaline hydrolysis of methyl acetate was explored by a variety of methods. The conformational search routine within SPARTAN was used to determine the lowest energy am1 and pm3 structures for the anionic tetrahedral intermediate. Ab initio single point and geometry optimization calculations were performed to determine the lowest energy conformer, and the linear synchronous transition (lst) method was used to provide an initial structure for transition state optimization. Transition states were obtained at the am1, pm3, 3-21G, and 3-21 + G levels of theory. These transition states were compared with the anionic tetrahedral intermediates to examine the assumption that the intermediate is a good model for the transition state. In addition, the Cramer/Truhlar sm3 solvation model was used at the semiempirical level to compare gas phase and aqueous alkaline hydrolysis of methyl acetate.

Clinical and molecular characterization of the potential CF disease modifier syntaxin 1A

Cystic fibrosis (CF) is caused by mutations in the CF transmembrane conductance regulator gene (CFTR). Disease severity in CF varies greatly, and sibling studies strongly indicate that genes other than CFTR modify disease outcome. Syntaxin 1A (STX1A) has been reported as a negative regulator of CFTR and other ion channels. We hypothesized that STX1A variants act as a CF modifier by influencing the remaining function of mutated CFTR. We identified STX1A variants by genomic resequencing patients from the Bernese CF Patient Data Registry and applied linear mixed model analysis to establish genotype-phenotype correlations, revealing STX1A rs4363087 (c.467-38A>G) to significantly influence lung function. The same STX1A risk allele was recognized in the European CF Twin and Sibling Study (P=0.0027), demonstrating that the genotype-phenotype association of STX1A to CF disease severity is robust enough to allow replication in two independent CF populations. rs4363087 is in linkage disequilibrium to the exonic variant rs2228607 (c.204C>T). Considering that neither rs4363087 nor rs2228607 changes the amino-acid sequence of STX1A, we investigated their effects on mRNA level. We show that rs2228607 reinforces aberrant splicing of STX1A mRNA, leading to nonsense-mediated mRNA decay. In conclusion, we demonstrate the clinical relevance of STX1A variants in CF, and evidence the functional relevance of STX1A variant rs2228607 at molecular level. Our findings show that genes interacting with CFTR can modify CF disease progression.European Journal of Human Genetics advance online publication, 10 April 2013; doi:10.1038/ejhg.2013.57.

Analysis of the antibody response to an immunodominant epitope of the envelope glycoprotein of a lentivirus and its diagnostic potential

The envelope glycoprotein of small ruminant lentiviruses (SRLV) is a major target of the humoral immune response and contains several linear B-cell epitopes. We amplified and sequenced the genomic segment encoding the SU5 antigenic site of the envelope glycoprotein of several SRLV field isolates. With synthetic peptides based on the deduced amino acid sequences of SU5 in an enzyme-linked immunosorbent assay (ELISA), we have (i) proved the immunodominance of this region regardless of its high variability, (ii) defined the epitopes encompassed by SU5, (iii) illustrated the rapid and peculiar kinetics of seroconversion to this antigenic site, and (iv) shown the rapid and strong maturation of the avidity of the anti-SU5 antibody. Finally, we demonstrated the modular diagnostic potential of SU5 peptides. Under Swiss field conditions, the SU5 ELISA was shown to detect the majority of infected animals and, when applied in a molecular epidemiological context, to permit rapid phylogenetic classification of the infecting virus.

Correlation between Accurate Electron Density and Linear Optical Properties in Amino Acid Derivatives: L-Histidinium Hydrogen Oxalate

The accurate electron density and linear optical properties of L-histidinium hydrogen oxalate are discussed. Two high-resolution single crystal X-ray diffraction experiments were performed and compared with density functional calculations in the solid state as well as in the gas phase. The crystal packing and the hydrogen bond network are accurately investigated using topological analysis based on quantum theory of atoms in molecules, Hirshfeld surface analysis, and electrostatic potential mapping. The refractive indices are computed from couple perturbed Kohn-Sham calculations and measured experimentally. Moreover, distributed atomic polarizabilities are used to analyze the origin of the linear susceptibility in the crystal, in order to separate molecular and intermolecular causes. The optical properties are also correlated with the electron density distribution. This compound also offers the possibility to test the electron density building block approach for material science and different refinement schemes for accurate positions and displacement parameters of hydrogen atoms, in the absence of neutron diffraction data.

Effect sizes and standardization in neighbourhood models of forest stands: potential biases and misinterpretations

Effects of conspecific neighbours on survival and growth of trees have been found to be related to species abundance. Both positive and negative relationships may explain observed abundance patterns. Surprisingly, it is rarely tested whether such relationships could be biased or even spurious due to transforming neighbourhood variables or influences of spatial aggregation, distance decay of neighbour effects and standardization of effect sizes. To investigate potential biases, communities of 20 identical species were simulated with log-series abundances but without species-specific interactions. No relationship of conspecific neighbour effects on survival or growth with species abundance was expected. Survival and growth of individuals was simulated in random and aggregated spatial patterns using no, linear, or squared distance decay of neighbour effects. Regression coefficients of statistical neighbourhood models were unbiased and unrelated to species abundance. However, variation in the number of conspecific neighbours was positively or negatively related to species abundance depending on transformations of neighbourhood variables, spatial pattern and distance decay. Consequently, effect sizes and standardized regression coefficients, often used in model fitting across large numbers of species, were also positively or negatively related to species abundance depending on transformation of neighbourhood variables, spatial pattern and distance decay. Tests using randomized tree positions and identities provide the best benchmarks by which to critically evaluate relationships of effect sizes or standardized regression coefficients with tree species abundance. This will better guard against potential misinterpretations.

Bridged bicyclic peptides as potential drug scaffolds: synthesis, structure, protein binding and stability

Double cyclization of short linear peptides obtained by solid phase peptide synthesis was used to prepare bridged bicyclic peptides (BBPs) corresponding to the topology of bridged bicyclic alkanes such as norbornane. Diastereomeric norbornapeptides were investigated by 1H-NMR, X-ray crystallography and CD spectroscopy and found to represent rigid globular scaffolds stabilized by intramolecular backbone hydrogen bonds with scaffold geometries determined by the chirality of amino acid residues and sharing structural features of β-turns and α-helices. Proteome profiling by capture compound mass spectrometry (CCMS) led to the discovery of the norbornapeptide 27c binding selectively to calmodulin as an example of a BBP protein binder. This and other BBPs showed high stability towards proteolytic degradation in serum.

Using the Morse Potential to Understand Reaction Coördinates using Maple

The interactions employed in the “linear” reaction A(g)+BC(g) -> AB(g) + C(g) in a “one dimensional world” can be used to illustrate the “reaction coördinate”, using Maple, in a manner which allows students to inspect potential energy surfaces, make contour maps of those surfaces, and conceptually construct the “reaction coördinate” by tracing the local minimum path on the surface created.“one dimensional world” can be used to illustrate the “reaction coördinate”, using Maple, in a manner which allows students to inspect potential energy surfaces, make contour maps of those surfaces, and conceptually construct the “reaction coördinate” by tracing the local minimum path on the surface created.

Prevalence of symptoms of neurotoxicity and potential occupational pesticide and solvent exposures among high school students in Starr County, Texas: A pilot study

Numerous harmful occupational exposures affect working teens in the United States. Teens working in agriculture and other heavy-labor industries may be at risk for occupational exposures to pesticides and solvents. The neurotoxicity of pesticides and solvents at high doses is well-known; however, the long term effects of these substances at low doses on occupationally exposed adolescents have not been well-studied. To address this research gap, a secondary analysis of cross-sectional data was completed in order to estimate the prevalence of self-reported symptoms of neurotoxicity among a cohort of high school students from Starr County, Texas, a rural area along the Texas-Mexico border. Multivariable linear regression was used to estimate the association between work status (i.e., no work, farm work, and non-farm work) and symptoms of neurotoxicity, while controlling for age, gender, Spanish speaking preference, inhalant use, tobacco use, and alcohol use. The sample included 1,208 students. Of these, the majority (85.84%) did not report having worked during the prior nine months compared to 4.80% who did only farm work, 6.21% who did only non-farm work, and 3.15% who did both types of work. On average, students reported 3.26 symptoms with a range from 0-16. The most commonly endorsed items across work status were those related to memory impairment. Adolescents employed in non-farm work jobs reported more neurotoxicity symptoms than those who reported that they did not work (Mean 4.31; SD 3.97). In the adjusted multivariable regression model, adolescents reporting non-farm work status reported an average of 0.77 more neurotoxicity symptoms on the Q16 than those who did not work (P = 0.031). The confounding variables included in the final model were all found to be factors significantly associated with report of neurotoxicity symptoms. Future research should examine the relationship between these variables and self-report of symptoms of neurotoxicity.^

Sources and proxy potential of long chain alkyl diols in lacustrine environments

Long chain 1,13- and 1,15-alkyl diols form the base of a number of recently proposed proxies used for climate reconstruction. However, the sources of these lipids and environmental controls on their distribution are still poorly constrained. We have analyzed the long chain alkyl diol (LCD) composition of cultures of ten eustigmatophyte species, with three species from different families grown at various temperatures, to identify the effect of species composition and growth temperature on the LCD distribution. The results were compared with the LCD distribution of sixty-two lake surface sediments, and with previously reported LCD distributions from marine environments. The different families within the Eustigmatophyceae show distinct LCD patterns, with the freshwater family Eustigmataceae most closely resembling LCD distributions in both marine and lake environments. Unlike the other two eustigmatophyte families analyzed (Monodopsidaceae and Goniochloridaceae), C28 and C30 1,13-alkyl diols and C30 and C32 1,15-alkyl diols are all relatively abundant in the family Eustigmataceae, while the mono-unsaturated C32 1,15-alkyl diol was below detection limit. In contrast to the marine environment, LCD distributions in lakes did not show a clear relationship with temperature. The Long chain Diol Index (LDI), a proxy previously proposed for sea surface temperature reconstruction, showed a relatively weak correlation (R2 = 0.33) with mean annual air temperature used as an approximation for annual mean surface temperature of the lakes. A much-improved correlation (R2 = 0.74, p-value<0.001) was observed applying a multiple linear regression analysis between LCD distributions and lake temperatures reconstructed using branched tetraether lipid distributions. The obtained regression model provides good estimates of temperatures for cultures of the family Eustigmataceae, suggesting that algae belonging to this family have an important role as a source for LCDs in lacustrine environments, or, alternatively, that the main sources of LCDs are similarly affected by temperature as the Eustigmataceae. The results suggest that LCDs may have the potential to be applicable as a palaeotemperature proxy for lacustrine environments, although further calibration work is still required.

Midday measurements of leaf water potential and stomatal conductance are highly correlated with daily water use of Thompson Seedless grapevines

A study was conducted to determine the relationship between midday measurements of vine water status and daily water use of grapevines measured with a weighing lysimeter. Water applications to the vines were terminated on August 24th for 9 days and again on September 14th for 22 days. Daily water use of the vines in the lysimeter (ETLYS) was approximately 40 L vine−1 (5.3 mm) prior to turning the pump off, and it decreased to 22.3 L vine−1 by September 2nd. Pre-dawn leaf water potential (ΨPD) and midday Ψl on August 24th were −0.075 and −0.76 MPa, respectively, with midday Ψl decreasing to −1.28 MPa on September 2nd. Leaf g s decreased from ~500 to ~200 mmol m−2 s−1 during the two dry-down periods. Midday measurements of g s and Ψl were significantly correlated with one another (r = 0.96) and both with ETLYS/ETo (r = ~0.9). The decreases in Ψl, g s, and ETLYS/ETo in this study were also a linear function of the decrease in volumetric soil water content. The results indicate that even modest water stress can greatly reduce grapevine water use and that short-term measures of vine water status taken at midday are a reflection of daily grapevine water use

Simplified computational method for non-linear seismic analysis of bridges

After the experience gained during the past years it seems clear that nonlinear analysis of bridges are very important to compute ductility demands and to localize potential hinges. This is specially true for irregular bridges in which it is not clear weather or not it is possible to use a linear computation followed by a correction using a behaviour factor. To simplify the numerical effort several approximate methods have been proposed. Among them, the so-called Dynamic Plastic Hinge Method in which an evolutionary shape function is used to reduce the structure to a single degree of freedom system seems to mantein a good balance between accuracy and simplicity. This paper presents results obtained in a parametric study conducted under the auspicies of PREC-8 european research program.

Estimation of a probability in inverse binomial sampling under normalized linear-linear and inverse-linear loss

Sequential estimation of the success probability p in inverse binomial sampling is considered in this paper. For any estimator pˆ , its quality is measured by the risk associated with normalized loss functions of linear-linear or inverse-linear form. These functions are possibly asymmetric, with arbitrary slope parameters a and b for pˆ

p , respectively. Interest in these functions is motivated by their significance and potential uses, which are briefly discussed. Estimators are given for which the risk has an asymptotic value as p→0, and which guarantee that, for any p∈(0,1), the risk is lower than its asymptotic value. This allows selecting the required number of successes, r, to meet a prescribed quality irrespective of the unknown p. In addition, the proposed estimators are shown to be approximately minimax when a/b does not deviate too much from 1, and asymptotically minimax as r→∞ when a=b.