Multidimensional scaling and visualization of large molecular similarity tables

Multidimensional scaling (MDS) is a collection of statistical techniques that attempt to embed a set of patterns described by means of a dissimilarity matrix into a low‐dimensional display plane in a way that preserves their original pairwise interrelationships as closely as possible. Unfortunately, current MDS algorithms are notoriously slow, and their use is limited to small data sets. In this article, we present a family of algorithms that combine nonlinear mapping techniques with neural networks, and make possible the scaling of very large data sets that are intractable with conventional methodologies. The method employs a nonlinear mapping algorithm to project a small random sample, and then “learns” the underlying transform using one or more multilayer perceptrons. The distinct advantage of this approach is that it captures the nonlinear mapping relationship in an explicit function, and allows the scaling of additional patterns as they become available, without the need to reconstruct the entire map. A novel encoding scheme is described, allowing this methodology to be used with a wide variety of input data representations and similarity functions. The potential of the algorithm is illustrated in the analysis of two combinatorial libraries and an ensemble of molecular conformations. The method is particularly useful for extracting low‐dimensional Cartesian coordinate vectors from large binary spaces, such as those encountered in the analysis of large chemical data sets. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 488–500, 2001     

Large deviations analysis of the generalized processor sharing policy

In this paper we consider a stochastic server (modeling a multiclass communication switch) fed by a set of parallel buffers. The dynamics of the system evolve in discrete-time and the generalized processor sharing (GPS) scheduling policy of [25] is implemented. The arrival process in each buffer is an arbitrary, and possibly autocorrelated, stochastic process. We obtain a large deviations asymptotic for the buffer overflow probability at each buffer. In the standard large deviations methodology, we provide a lower and a matching (up to first degree in the exponent) upper bound on the buffer overflow probabilities. We view the problem of finding a most likely sample path that leads to an overflow as an optimal control problem. Using ideas from convex optimization we analytically solve the control problem to obtain both the asymptotic exponent of the overflow probability and a characterization of most likely modes of overflow. These results have important implications for traffic management of high-speed networks. They extend the deterministic, worst-case analysis of [25] to the case where a detailed statistical model of the input traffic is available and can be used as a basis for an admission control mechanism. This revised version was published online in June 2006 with corrections to the Cover Date.     

Analytical study of the changes in the color of daylight due to sulfate droplets and soot grains in the atmosphere

Absorption of daylight by an atmospheric layer that comprises non-interacting water and sulfate droplets, interstitial soot grains, and composite sulfate-soot particles is determined by use of exact theories of Mie or extended-Mie scattering from all types of suspended particles. Interest is in the color of the sky, as observed from the ground underneath a light-absorbing atmospheric layer which has been synthesized as above. The end-result of the theory presented in this paper is the spectral radiant power distribution and the colorimetric features of daylight at ground level. The numerical application manifests that microlensing by sulfate droplets gives rise to enhanced absorption by soot grains, which results in attenuation and redshifts of daylight. An investigation is made of the changes in the color of the sky, as observed from the ground, due to pollution of the air by sulfuric acid and carbon.     

Stabilization of human urine doping control samples: IV. Human chorionic gonadotropin

The presence of proteolytic enzymes in urine samples, coming from exogenous or endogenous sources, enhances the cleavage of human chorionic gonadotropin (hCG). Moreover, elevated temperatures occurring occasionally during the delayed transportation of sport urine samples, favor the nicking of the hCG molecule. The aim of the current study, funded by the World Anti-Doping Agency (WADA), was the application of a stabilization mixture in athletes’ urine samples to chemically inactivate proteolytic enzymes coming from exogenous or endogenous sources so as to prevent the degradation of hCG. The stabilization mixture applied, already tested for the stabilization of endogenous steroids and recombinant erythropoietin (rEPO), was a combination of antibiotics, antimycotic substances, and protease inhibitors. Incubation experiments were conducted in the presence or absence of the stabilization mixture in urine aliquots spiked with six proteases (first series of experiments) and one microorganism associated with urinary tract infections (UTI) (second series of experiments). Intact hCG levels were evaluated by using the EIAgen Total hCG kit. In the first series of experiments, hCG levels were reduced in the untreated aliquots following incubation at 37 °C. The addition of the chemical stabilization mixture prevented degradation of hCG induced by four of the proteases applied. In the second series of experiments, no significant difference was found in urine inoculated with E. coli, between aliquots treated with chemical mixture and the untreated aliquots. The addition of the proposed chemical stabilization mixture improves the quality of athletes’ urine samples against possible deterioration due to high temperatures or attempts of proteolytic manipulation.     

A numerical procedure for the generation of orthogonal body-fitted co-ordinate systems with direct determination of grid points on the boundary

The procedure proposed is based on the solution by finite difference means of a set of Laplace's equations, by the application of a relaxation method. The curvilinear orthogonal grid so generated is fitted to a 2-D physical domain with closed boundary and the contribution of the present work consists in the arbitrary choice of grid points on two adjacent boundaries, in order to achieve the desired density of grid points where the geometry of the boundaries varies rapidly. The method proposed is rapid and stable. Some characteristic examples are finally presented.     

Study of the isotropic and anisotropic fluorescence of two oligothiophenes by femtosecond time-resolved spectroscopy

The excited-state dynamics of two oligothiophenes, 5,5'-dicarboxyhaldehyde 2,2',5',2' '-terthiophene and 5-carboxyhaldehyde 2,2',5',2' '-terthiophene, were studied by time-resolved fluorescence spectroscopy, in the femtosecond regime. The isotropic and anisotropic parameters of their fluorescence were calculated. The angle (alpha) between the absorption and emission molecular dipoles was estimated from the initial fluorescence anisotropy. The effect of the chemical substituents, at the ends of the main chain of the molecule, on the temporal behavior of the fluorescence was investigated. Particularly, the nonsymmetric oligothiophene molecule (containing one aldehyde group) exhibits shorter excited-state isotropic decay time than the symmetric one (containing two aldehyde groups). This is due to the higher value of the emission dipole moment of the nonsymmetric oligothiophene in comparison with that of the symmetric one. Additionally, the two materials have almost the same anisotropic fluorescence parameters, and this is attributed to the same rotational motions in the excited state due to their similar molecular structures.     

Nearest neighbor search in general metric spaces using a tree data structure with a simple heuristic

We present a new algorithm for nearest neighbor search in general metric spaces. The algorithm organizes the database into recursively partitioned Voronoi regions and represents these partitions in a tree. The separations between the Voronoi regions as well as the radius of each region are used with triangular inequality to derive the minimum possible distance between any point in a region and the query and to discard the region from further search if a smaller distance has already been found. The algorithm also orders the search sequence of the tree branches using the estimate of the minimum possible distance. This simple heuristic proves to considerably enhance the pruning of the search tree. The efficiency of the algorithm is demonstrated on several artificial data sets and real problems in computational chemistry.     

Dendrimer-based transient supramolecular networks

Association of a 16-fold excess of a monodisperse telechelic oligo(THF) (Mw = 1270 g/mol) containing two end groups that selectively bind to the 32 binding sites of a fifth generation dendritic host (Mw = 18,511 g/mol and radius R(h) = 2.4 nm) results in the formation of reversible and dynamic supramolecular complexes. The structure of these complexes in solution depends strongly on the concentration. At low concentration, the two end groups of one guest are proposed to complex to the same host, and flowerlike structures are formed with a radius of R(h) = 3.7 nm. At higher concentrations, both end groups of one guest are complexed to different hosts, forming a bridge between them. This gives rise to the formation of larger associates, and eventually to a transient supramolecular network. Dynamic light scattering unequivocally showed that three distinct relaxation processes, associated with the proposed structures, are present in this system. In addition to the dynamics related to the flowerlike (fast) and the transient network structures (slow), an intermediate dynamic process is attributed to the cooperative motion of a few (approximately 6) connected flowerlike structures. Rheological data elucidate the nature of the intermittent network responsible for the slowest process. A monofunctional guest, not capable of forming a network structure, was used as a reference, and starlike supramolecular structures are formed at all concentrations, indeed.     

Synthesis and comparative biodegradability studies of three poly(alkylene succinate)s

Poly(alkylene succinates) were synthesized from succinic acid and aliphatic diols with 2 to 4 methylene groups by melt polycondensation. DSC, ¹H NMR, WAXD and molecular weight measurements were used to characterise the polymers. Biodegradability studies of polyesters with the same average molecular weight, included enzymatic hydrolysis for several days using Rhizopus delemar lipase at pH 7.2 and 30 °C. DSC traces of biodegraded polyesters revealed that hydrolysis affected mainly the amorphous material. For all polyesters an increase in glass transition, melting point and heat of fusion was recorded. In the first days of enzymatic hydrolysis, fast rates of mass loss were observed accompanied by a rapid reduction of intrinsic viscosity and molecular weight, thus indicating a mixed endo- and exo-type hydrolysis mechanism. Afterwards, it turned to an exo-type mechanism, taking place in the crystalline phase, since after 15-25 days of enzymatic hydrolysis molecular weight was stabilized, while mass loss kept on decreasing though in a slower rate. End-group analysis revealed that carboxyl and hydroxyl groups increased due to ester bonds' scission. The biodegradation rates of the polymers decreased following the order PPSu > PESu ≥ PBSu and it was attributed to the lower crystallinity of PPSu compared to other polyesters, rather than to differences in chemical structure. Finally, a simple theoretical kinetic model was developed and Michaelis-Menten parameters were estimated.     

An exact FCFS waiting time analysis for a general class of G/G/s queueing systems

A closed form expression for the waiting time distribution under FCFS is derived for the queueing system MGE_k/MGE_m/s, where MGE_n is the class of mixed generalized Erlang probability density functions (pdfs) of ordern, which is a subset of the Coxian pdfs that have rational Laplace transform. Using the calculus of difference equations and based on previous results of the author, it is proved that the waiting time distribution is of the form 1- , under the assumption that the rootsU _j are distinct, i.e. belongs to the Coxian class of distributions of order . The present approach offers qualitative insight by providing exact and asymptotic expressions, generalizes and unifies the well known theories developed for the G/G/1,G/M/s systems and leads to an algorithm, which is polynomial if only one of the parameterss orm varies, and is exponential if both parameters vary. As an example, numerical results for the waiting time distribution of the MGE₂/MGE₂/s queueing system are presented.