The Mathematics of Internet Search Engines

This article presents a survey of techniques for ranking results in search engines, with emphasis on link-based ranking methods and the PageRank algorithm. The problem of selecting, in relation to a user search query, the most relevant documents from an unstructured source such as the WWW is discussed in detail. The need for extending classical information retrieval techniques such as boolean searching and vector space models with link-based ranking methods is demonstrated. The PageRank algorithm is introduced, and its numerical and spectral properties are discussed. The article concludes with an alternative means of computing PageRank, along with some example applications of this new method.     

An Algorithmic Approach to Discrete Time Non-homogeneous Backward Semi-Markov Reward Processes with an Application to Disability Insurance

In this paper semi-Markov reward models are presented. Higher moments of the reward process is presented for the first time applied to in time non-homogeneous semi-Markov insurance problems. Also an example is presented based on real disability data. Different algorithmic approaches to solve the problem is described. This work is partly supported by the Knowledge Foundation and Sparbankens Stiftelse Nya. The authors would like to thank the anonymous referee.     

Development of a new damper to reduce resonant vibrations in lightweight steel joist floors

Floor vibrations annoying to humans often occur in lightweight constructions. A number of methods to solve the problem of resonant vibrations are reported in the literature. Tuned mass damper, semi-active tuned vibration absorber and active control system are all examples of existing methods. A new method has been tested in laboratory environment on a prefabricated floor containing a resilient ceiling with a size up to 6.8×4.8 m². The method takes advantage of small pieces of visco-elastic material connected between the ceiling joists and the primary beams. A finite element model is used to calculate the correct amount of visco-elastic material. The new damper is especially effective in damping mode shapes where the ceiling oscillates out of phase relative to the floor but shows improvements for other mode shapes as well.     

Model cellulose films exposed to H. insolens glucoside hydrolase family 45 endo-cellulase--the effect of the carbohydrate-binding module

The effects of enzyme structure and activity on the degradation of model cellulose substrates were investigated by ellipsometry for the cellulase Humicola insolens GH45. The inactive variant D10N was found to adsorb at the cellulose surface but also to be incorporated into the cellulose films to an extent that depended on pH. For the native protein, the initial adsorption monitored for the inactive variant D10N was followed by enzyme-mediated degradation of the cellulose films. Again, a dependence on pH was found, such that higher pH resulted in slower enzymatic degradation. Removing the carbohydrate-binding module eliminated this pH dependence but also resulted in a decreased adsorption to the cellulose surface, and in a decreased net catalytic effect.     

Efficient microwave assisted synthesis of optically active bicyclic 2-pyridinones via Δ2-thiazolines

A new efficient synthesis of optically active bicyclic 2-pyridiones has been developed using microwave irradiation. The synthesis is a two-step procedure via delta2-thiazolines, which only requires a 3 + 2 min reaction time compared to 2 days when using conventional heating. The optimized conditions proved to be suitable for the synthesis of a small library in excellent yields and with limited racemizations.     

Primary photoprocess in vision: minimal motion to reach the photo- and bathorhodopsin intermediates

According to time-resolved spectroscopic measurements, the initial step of the photoreaction of rhodopsin occurs with a time constant of approximately 200 fs. The whole or a part of the retinal molecule cannot move any significant distance in such a short time. In this paper, we propose instead a minimal motion that accomplishes the important task of guiding the molecule to a configuration where it can decay to the ground-state surface, with a minimal loss of strain energy. This motion is proposed to involve a -90 degrees twisting of the C11=C12 double bond and a simultaneous twisting around two other double bonds in retinal to minimize the geometrical changes along the reaction path. The ONIOM method (complete active space self-consistent field for retinal and AMBER for the peptides) is used in a chromophore-cavity model to elucidate and confirm important features of the mechanism. The potential energy surface (PES) obtained according to the proposed mechanism show all of the characteristics of a fast photoreaction, meaning a downhill reaction path from the Franck-Condon point to an avoided crossing between S(1) and S(0). In this motion, only a few carbon and hydrogen atoms move more than 0.3 A, and the retinal structure is conserved in the protein cavity. We propose that the photorhodopsin intermediate is a retinal molecule formed on the excited-state PES. Bathorhodopsin, however, is a ground-state intermediate, still located inside the protein cavity.     

Uniaxial magnetocrystalline anisotropy of metal/semiconductor interfaces: Fe/ZnSe(001)

A theoretical study of the magnetic moments and the in-plane magnetic anisotropy of an interface between a cubic ferromagnet and a cubic semiconductor, Fe/ZnSe(001), is presented. Theory confirms the observed, much debated, uniaxial anisotropy of the iron film. This result is important since the calculations are for perfect interfaces with squarelike environments, proving that the fourfolded symmetry of the interface Fe atoms is broken beyond the nearest neighboring semiconducting layer, effects that are usually assumed small. It is demonstrated how the uniaxial anisotropy is produced by the directional covalent bonds at the interface, even without atomic relaxations.     

Effects of sample preservation and storage on mercury speciation in natural stream water

Despite an increasing focus on low level methods for determination of mercury species in water over the last decades, few studies have paid attention to direct effects of different sample preparation methods (i.e. preservation techniques) on natural freshwater samples. In this study we show how different preservation techniques give significantly different concentrations of total and methylmercury in freshwaters (9 and 14% on average, respectively). Natural stream samples from a forested lake catchment were studied. Mean stream sample concentrations of total (3.6 ng/L) and methylmercury (0.06 ng/L) reflect levels typical for pristine humic boreal catchments. The main reason for the observed average differences in total and methylmercury concentrations is the use of one instead of two sample bottles and timing of sample acidification, respectively.     

Continuous lipid bilayers derived from cell membranes for spatial molecular manipulation

Progress with respect to enrichment and separation of native membrane components in complex lipid environments, such as native cell membranes, has so far been very limited. The reason for the slow progress can be related to the lack of efficient means to generate continuous and laterally fluid supported lipid bilayers (SLBs) made from real cell membranes. We show in this work how the edge of a hydrodynamically driven SLB can be used to induce rupture of adsorbed lipid vesicles of compositions that typically prevent spontaneous SLB formation, such as vesicles made of complex lipid compositions, containing high cholesterol content or being derived from real cell membranes. In particular, upon fusion between the moving edge of a preformed SLB and adsorbed vesicles made directly from 3T3 fibroblast cell membranes, the membrane content of the vesicles was shown to be efficiently transferred to the SLB. The molecular transfer was verified using cholera toxin B subunit (CTB) binding to monosialoganglioside receptors (G(M1) and G(M3)), and the preserved lateral mobility was confirmed by spatial manipulation of the G(M1/M3)-CTB complex using a hydrodynamic flow. Two populations of CTB with markedly different drift velocity could be identified, which from dissociation kinetics data were attributed to CTB bound with different numbers of ganglioside anchors.