Homology modeling and metabolism prediction of human carboxylesterase-2 using docking analyses by GriDock: a parallelized tool based on AutoDock 4.0.

Metabolic problems lead to numerous failures during clinical trials, and much effort is now devoted to developing in silico models predicting metabolic stability and metabolites. Such models are well known for cytochromes P450 and some transferases, whereas less has been done to predict the activity of human hydrolases. The present study was undertaken to develop a computational approach able to predict the hydrolysis of novel esters by human carboxylesterase hCES2. The study involved first a homology modeling of the hCES2 protein based on the model of hCES1 since the two proteins share a high degree of homology (congruent with 73%). A set of 40 known substrates of hCES2 was taken from the literature; the ligands were docked in both their neutral and ionized forms using GriDock, a parallel tool based on the AutoDock4.0 engine which can perform efficient and easy virtual screening analyses of large molecular databases exploiting multi-core architectures. Useful statistical models (e.g., r (2) = 0.91 for substrates in their unprotonated state) were calculated by correlating experimental pK(m) values with distance between the carbon atom of the substrate's ester group and the hydroxy function of Ser228. Additional parameters in the equations accounted for hydrophobic and electrostatic interactions between substrates and contributing residues. The negatively charged residues in the hCES2 cavity explained the preference of the enzyme for neutral substrates and, more generally, suggested that ligands which interact too strongly by ionic bonds (e.g., ACE inhibitors) cannot be good CES2 substrates because they are trapped in the cavity in unproductive modes and behave as inhibitors. The effects of protonation on substrate recognition and the contrasting behavior of substrates and products were finally investigated by MD simulations of some CES2 complexes.

Map of ecological networks for landscape planning

This paper presents a method based on a geographical information system (GIS) to model ecological networks in a fragmented landscape. The ecological networks are generated with the help of a landscape model (which integrate human activities) and with a wildlife dispersal model. The main results are maps which permit the analysis and the understanding of the impact of human activities on wildlife dispersal. Three applications in a study area are presented: ecological networks at the landscape scale, conflicting areas at the farmstead scale and ecological distance between biotopes. These applications show the flexibility of the model and its potential to give information on ecological networks at different planning scales.

Genetic compatibility affects division of labor in the argentine ant linepithema humile.

Division of labor is central to the organization of insect societies. Within-colony comparisons between subfamilies of workers (patrilines or matrilines) revealed genetic effects on division of labor in many social insect species. Although this has been taken as evidence for additive genetic effects on division of labor, it has never been experimentally tested. To determine the relative roles of additive and nonadditive genetic effects (e.g., genetic compatibility, epistasis, and parent-of-origin imprinting effects) on worker behavior, we performed controlled crosses using the Argentine ant Linepithema humile. Three of the measured behaviors (the efficiency to collect pupae, the foraging propensity, and the distance between non-brood-tenders and brood) were affected by the maternal genetic background and the two others (the efficiency to feed larvae and the distance between brood-tenders and brood) by the paternal genetic background. Moreover, there were significant interactions between the maternal and paternal genetic backgrounds for three of the five behaviors. These results are most consistent with parent-of-origin and genetic compatibility effects on division of labor. The finding of nonadditive genetic effects is in strong contrast with the current view and has important consequences for our understanding of division of labor in insect societies.

Dual-channel electrospray microchip.

A dual-channel electrospray microchip has been developed for electrospray ionization mass spectrometry (ESI-MS) where aqueous samples are mixed at the Taylor cone with an organic buffer. Due to the fast and effective mixing in the Taylor cone, the aqueous sample can be well ionized with a high ion intensity. The influence of geometric parameters such as the distance between the two microchannels at their junction at the tip of the emitter has been investigated together with chemical parameters such as the organic buffer composition.

Effect of immune pressure on hepatitis C virus evolution: insights from a single-source outbreak.

The host's immune response to hepatitis C virus (HCV) can result in the selection of characteristic mutations (adaptations) that enable the virus to escape this response. The ability of the virus to mutate at these sites is dependent on the incoming virus, the fitness cost incurred by the mutation, and the benefit to the virus in escaping the response. Studies examining viral adaptation in chronic HCV infection have shown that these characteristic immune escape mutations can be observed at the population level as human leukocyte antigen (HLA)-specific viral polymorphisms. We examined 63 individuals with chronic HCV infection who were infected from a single HCV genotype 1b source. Our aim was to determine the extent to which the host's immune pressure affects HCV diversity and the ways in which the sequence of the incoming virus, including preexisting escape mutations, can influence subsequent mutations in recipients and infection outcomes. Conclusion: HCV sequences from these individuals revealed 29 significant associations between specific HLA types within the new hosts and variations within their viruses, which likely represent new viral adaptations. These associations did not overlap with previously reported adaptations for genotypes 1a and 3a and possibly reflected a combination of constraint due to the incoming virus and genetic distance between the strains. However, these sites accounted for only a portion of the sites in which viral diversity was observed in the new hosts. Furthermore, preexisting viral adaptations in the incoming (source) virus likely influenced the outcomes in the new hosts.

Quantifying rock fabrics: a test of autocorrelation of the spatial distribution of cristals

A novel test of spatial independence of the distribution of crystals or phases in rocksbased on compositional statistics is introduced. It improves and generalizes the commonjoins-count statistics known from map analysis in geographic information systems.Assigning phases independently to objects in RD is modelled by a single-trial multinomialrandom function Z(x), where the probabilities of phases add to one and areexplicitly modelled as compositions in the K-part simplex SK. Thus, apparent inconsistenciesof the tests based on the conventional joins{count statistics and their possiblycontradictory interpretations are avoided. In practical applications we assume that theprobabilities of phases do not depend on the location but are identical everywhere inthe domain of de nition. Thus, the model involves the sum of r independent identicalmultinomial distributed 1-trial random variables which is an r-trial multinomialdistributed random variable. The probabilities of the distribution of the r counts canbe considered as a composition in the Q-part simplex SQ. They span the so calledHardy-Weinberg manifold H that is proved to be a K-1-affine subspace of SQ. This isa generalisation of the well-known Hardy-Weinberg law of genetics. If the assignmentof phases accounts for some kind of spatial dependence, then the r-trial probabilitiesdo not remain on H. This suggests the use of the Aitchison distance between observedprobabilities to H to test dependence. Moreover, when there is a spatial uctuation ofthe multinomial probabilities, the observed r-trial probabilities move on H. This shiftcan be used as to check for these uctuations. A practical procedure and an algorithmto perform the test have been developed. Some cases applied to simulated and realdata are presented.Key words: Spatial distribution of crystals in rocks, spatial distribution of phases,joins-count statistics, multinomial distribution, Hardy-Weinberg law, Hardy-Weinbergmanifold, Aitchison geometry

Anastomotic longitudinal stress due to modification of arterial longitudinal properties after anastomosis.

BACKGROUND: In our hands, in vivo segmental vessel length changes up to 5% because of blood pressure: increasing in arterial pressure is associated to decrease in segmental vessel length. METHODS AND MATERIAL: Using two piezoelectric crystals sutured on vessel wall and a high fidelity pressure probe, we recorded artery length variations as function of blood pressure, before and after an end-to-end anastomosis on four pigs carotid arteries. RESULTS: Mean arterial pressure before anastomosis = 73 mmHg (+/- 12); mean arterial pressure after anastomosis = 91 mmHg (+/- 14); mean crystals displacement before anastomosis during systole = -0.21 mm; mean crystals displacement after anastomosis during systole = +0.24 mm; mean distance between crystals before anastomosis = 12.3 mm (+/- 0.8) and after anastomosis = 11.2 mm (+/- 0.5). CONCLUSIONS: In the acute phase following an end-to-end anastomosis, an increase in blood pressure causes increasing in vessel length, with an exponential correlation. The anastomosis is constantly subjected to a longitudinal traction whose magnitude depends on blood pressure.

An ex-post view of inequality of opportunity in France and its regions

This paper proposes an ex-post measure of inequality of opportunity in France and its regions by assessing the inequality between individuals exerting the same effort. To this end, we define a fair income that fulfils ex-post equality of opportunity requirements. Unfairness is measured by an unfair Gini based on the distance between the actual income and the fair income. Our findings reveal that the measures of ex-post inequality of opportunity largely vary across regions, and that this is due to di_erences in reward schemes and in the impact of the non responsibility factors of income. We find that most regions have actual incomes closer to fair incomes than to average income, excepted Ile de France where the actual income looks poorly related to effort variables. Finally, we find that income inequality and inequality of opportunity are positively correlated among regions.

Estimation of electronic coupling in π -stacked donor-bridge-acceptor systems: correction of the two-state model

Comparison of donor-acceptor electronic couplings calculated within two-state and three-state models suggests that the two-state treatment can provide unreliable estimates of Vda because of neglecting the multistate effects. We show that in most cases accurate values of the electronic coupling in a π stack, where donor and acceptor are separated by a bridging unit, can be obtained as Ṽ da = (E2 - E1) μ12 Rda + (2 E3 - E1 - E2) 2 μ13 μ23 Rda2, where E1, E2, and E3 are adiabatic energies of the ground, charge-transfer, and bridge states, respectively, μij is the transition dipole moments between the states i and j, and Rda is the distance between the planes of donor and acceptor. In this expression based on the generalized Mulliken-Hush approach, the first term corresponds to the coupling derived within a two-state model, whereas the second term is the superexchange correction accounting for the bridge effect. The formula is extended to bridges consisting of several subunits. The influence of the donor-acceptor energy mismatch on the excess charge distribution, adiabatic dipole and transition moments, and electronic couplings is examined. A diagnostic is developed to determine whether the two-state approach can be applied. Based on numerical results, we showed that the superexchange correction considerably improves estimates of the donor-acceptor coupling derived within a two-state approach. In most cases when the two-state scheme fails, the formula gives reliable results which are in good agreement (within 5%) with the data of the three-state generalized Mulliken-Hush model

A 2D/3D image analysis system to track fluorescently labeled structures in rod-shaped cells: application to measure spindle pole asymmetry during mitosis.

BACKGROUND: The yeast Schizosaccharomyces pombe is frequently used as a model for studying the cell cycle. The cells are rod-shaped and divide by medial fission. The process of cell division, or cytokinesis, is controlled by a network of signaling proteins called the Septation Initiation Network (SIN); SIN proteins associate with the SPBs during nuclear division (mitosis). Some SIN proteins associate with both SPBs early in mitosis, and then display strongly asymmetric signal intensity at the SPBs in late mitosis, just before cytokinesis. This asymmetry is thought to be important for correct regulation of SIN signaling, and coordination of cytokinesis and mitosis. In order to study the dynamics of organelles or large protein complexes such as the spindle pole body (SPB), which have been labeled with a fluorescent protein tag in living cells, a number of the image analysis problems must be solved; the cell outline must be detected automatically, and the position and signal intensity associated with the structures of interest within the cell must be determined. RESULTS: We present a new 2D and 3D image analysis system that permits versatile and robust analysis of motile, fluorescently labeled structures in rod-shaped cells. We have designed an image analysis system that we have implemented as a user-friendly software package allowing the fast and robust image-analysis of large numbers of rod-shaped cells. We have developed new robust algorithms, which we combined with existing methodologies to facilitate fast and accurate analysis. Our software permits the detection and segmentation of rod-shaped cells in either static or dynamic (i.e. time lapse) multi-channel images. It enables tracking of two structures (for example SPBs) in two different image channels. For 2D or 3D static images, the locations of the structures are identified, and then intensity values are extracted together with several quantitative parameters, such as length, width, cell orientation, background fluorescence and the distance between the structures of interest. Furthermore, two kinds of kymographs of the tracked structures can be established, one representing the migration with respect to their relative position, the other representing their individual trajectories inside the cell. This software package, called "RodCellJ", allowed us to analyze a large number of S. pombe cells to understand the rules that govern SIN protein asymmetry. CONCLUSIONS: "RodCell" is freely available to the community as a package of several ImageJ plugins to simultaneously analyze the behavior of a large number of rod-shaped cells in an extensive manner. The integration of different image-processing techniques in a single package, as well as the development of novel algorithms does not only allow to speed up the analysis with respect to the usage of existing tools, but also accounts for higher accuracy. Its utility was demonstrated on both 2D and 3D static and dynamic images to study the septation initiation network of the yeast Schizosaccharomyces pombe. More generally, it can be used in any kind of biological context where fluorescent-protein labeled structures need to be analyzed in rod-shaped cells. AVAILABILITY: RodCellJ is freely available under http://bigwww.epfl.ch/algorithms.html, (after acceptance of the publication).

Intravascular ultrasound underestimates vessel dimensions.

The information gathered with intravascular ultrasound (IVUS) are of great value in endovascular techniques. The aim of this study was to evaluate the reliability of IVUS when measuring vessel dimensions by comparison with an established reference method. The left carotid artery was exposed in 4 pigs (45-55 kg) and two piezoelectric crystals were sutured on the adventitia in the same cross-sectional plane. The distance between them was measured either by IVUS and by sonomicrometers. The mean distance between the two crystals calculated by the sonomicrometer was 4.7+/-0.4 mm (mean systolic distance was 4.9+/-0.2 mm, mean diastolic distance was 4.6+/-0.1 mm). The mean distance between the two targets calculated by IVUS was 4. 5+/-0.2 mm (mean systolic distance was 4.6+/-0.2 mm and mean diastolic 4.4+/-0.2 mm). Regression analysis of the two series of data shows a R(2)=0.9984. IVUS measurements are an average 5% smaller than sonomicrometer measurements (3.6% up to 8.3%) and the difference is statistically significant ( p <0.05). The underestimation of IVUS measurements will affect the accuracy, and probably the long-term outcome, of endovascular procedures.

Financial Markets and Real Ecinomy: Four Essays in International Trade

Financial markets play an important role in an economy performing various functions like mobilizing and pooling savings, producing information about investment opportunities, screening and monitoring investments, implementation of corporate governance, diversification and management of risk. These functions influence saving rates, investment decisions, technological innovation and, therefore, have important implications for welfare. In my PhD dissertation I examine the interplay of financial and product markets by looking at different channels through which financial markets may influence an economy.My dissertation consists of four chapters. The first chapter is a co-authored work with Martin Strieborny, a PhD student from the University of Lausanne. The second chapter is a co-authored work with Melise Jaud, a PhD student from the Paris School of Economics. The third chapter is co-authored with both Melise Jaud and Martin Strieborny. The last chapter of my PhD dissertation is a single author paper.Chapter 1 of my PhD thesis analyzes the effect of financial development on growth of contract intensive industries. These industries intensively use intermediate inputs that neither can be sold on organized exchange, nor are reference-priced (Levchenko, 2007; Nunn, 2007). A typical example of a contract intensive industry would be an industry where an upstream supplier has to make investments in order to customize a product for needs of a downstream buyer. After the investment is made and the product is adjusted, the buyer may refuse to meet a commitment and trigger ex post renegotiation. Since the product is customized to the buyer's needs, the supplier cannot sell the product to a different buyer at the original price. This is referred in the literature as the holdup problem. As a consequence, the individually rational suppliers will underinvest into relationship-specific assets, hurting the downstream firms with negative consequences for aggregate growth. The standard way to mitigate the hold up problem is to write a binding contract and to rely on the legal enforcement by the state. However, even the most effective contract enforcement might fail to protect the supplier in tough times when the buyer lacks a reliable source of external financing. This suggests the potential role of financial intermediaries, banks in particular, in mitigating the incomplete contract problem. First, financial products like letters of credit and letters of guarantee can substantially decrease a risk and transaction costs of parties. Second, a bank loan can serve as a signal about a buyer's true financial situation, an upstream firm will be more willing undertake relationship-specific investment knowing that the business partner is creditworthy and will abstain from myopic behavior (Fama, 1985; von Thadden, 1995). Therefore, a well-developed financial (especially banking) system should disproportionately benefit contract intensive industries.The empirical test confirms this hypothesis. Indeed, contract intensive industries seem to grow faster in countries with a well developed financial system. Furthermore, this effect comes from a more developed banking sector rather than from a deeper stock market. These results are reaffirmed examining the effect of US bank deregulation on the growth of contract intensive industries in different states. Beyond an overall pro-growth effect, the bank deregulation seems to disproportionately benefit the industries requiring relationship-specific investments from their suppliers.Chapter 2 of my PhD focuses on the role of the financial sector in promoting exports of developing countries. In particular, it investigates how credit constraints affect the ability of firms operating in agri-food sectors of developing countries to keep exporting to foreign markets.Trade in high-value agri-food products from developing countries has expanded enormously over the last two decades offering opportunities for development. However, trade in agri-food is governed by a growing array of standards. Sanitary and Phytosanitary standards (SPS) and technical regulations impose additional sunk, fixed and operating costs along the firms' export life. Such costs may be detrimental to firms' survival, "pricing out" producers that cannot comply. The existence of these costs suggests a potential role of credit constraints in shaping the duration of trade relationships on foreign markets. A well-developed financial system provides the funds to exporters necessary to adjust production processes in order to meet quality and quantity requirements in foreign markets and to maintain long-standing trade relationships. The products with higher needs for financing should benefit the most from a well functioning financial system. This differential effect calls for a difference-in-difference approach initially proposed by Rajan and Zingales (1998). As a proxy for demand for financing of agri-food products, the sanitary risk index developed by Jaud et al. (2009) is used. The empirical literature on standards and norms show high costs of compliance, both variable and fixed, for high-value food products (Garcia-Martinez and Poole, 2004; Maskus et al., 2005). The sanitary risk index reflects the propensity of products to fail health and safety controls on the European Union (EU) market. Given the high costs of compliance, the sanitary risk index captures the demand for external financing to comply with such regulations.The prediction is empirically tested examining the export survival of different agri-food products from firms operating in Ghana, Mali, Malawi, Senegal and Tanzania. The results suggest that agri-food products that require more financing to keep up with food safety regulation of the destination market, indeed sustain longer in foreign market, when they are exported from countries with better developed financial markets.Chapter 3 analyzes the link between financial markets and efficiency of resource allocation in an economy. Producing and exporting products inconsistent with a country's factor endowments constitutes a serious misallocation of funds, which undermines competitiveness of the economy and inhibits its long term growth. In this chapter, inefficient exporting patterns are analyzed through the lens of the agency theories from the corporate finance literature. Managers may pursue projects with negative net present values because their perquisites or even their job might depend on them. Exporting activities are particularly prone to this problem. Business related to foreign markets involves both high levels of additional spending and strong incentives for managers to overinvest. Rational managers might have incentives to push for exports that use country's scarce factors which is suboptimal from a social point of view. Export subsidies might further skew the incentives towards inefficient exporting. Management can divert the export subsidies into investments promoting inefficient exporting.Corporate finance literature stresses the disciplining role of outside debt in counteracting the internal pressures to divert such "free cash flow" into unprofitable investments. Managers can lose both their reputation and the control of "their" firm if the unpaid external debt triggers a bankruptcy procedure. The threat of possible failure to satisfy debt service payments pushes the managers toward an efficient use of available resources (Jensen, 1986; Stulz, 1990; Hart and Moore, 1995). The main sources of debt financing in the most countries are banks. The disciplining role of banks might be especially important in the countries suffering from insufficient judicial quality. Banks, in pursuing their rights, rely on comparatively simple legal interventions that can be implemented even by mediocre courts. In addition to their disciplining role, banks can promote efficient exporting patterns in a more direct way by relaxing credit constraints of producers, through screening, identifying and investing in the most profitable investment projects. Therefore, a well-developed domestic financial system, and particular banking system, would help to push a country's exports towards products congruent with its comparative advantage.This prediction is tested looking at the survival of different product categories exported to US market. Products are identified according to the Euclidian distance between their revealed factor intensity and the country's factor endowments. The results suggest that products suffering from a comparative disadvantage (labour-intensive products from capital-abundant countries) survive less on the competitive US market. This pattern is stronger if the exporting country has a well-developed banking system. Thus, a strong banking sector promotes exports consistent with a country comparative advantage.Chapter 4 of my PhD thesis further examines the role of financial markets in fostering efficient resource allocation in an economy. In particular, the allocative efficiency hypothesis is investigated in the context of equity market liberalization.Many empirical studies document a positive and significant effect of financial liberalization on growth (Levchenko et al. 2009; Quinn and Toyoda 2009; Bekaert et al., 2005). However, the decrease in the cost of capital and the associated growth in investment appears rather modest in comparison to the large GDP growth effect (Bekaert and Harvey, 2005; Henry, 2000, 2003). Therefore, financial liberalization may have a positive impact on growth through its effect on the allocation of funds across firms and sectors.Free access to international capital markets allows the largest and most profitable domestic firms to borrow funds in foreign markets (Rajan and Zingales, 2003). As domestic banks loose some of their best clients, they reoptimize their lending practices seeking new clients among small and younger industrial firms. These firms are likely to be more risky than large and established companies. Screening of customers becomes prevalent as the return to screening rises. Banks, ceteris paribus, tend to focus on firms operating in comparative-advantage sectors because they are better risks. Firms in comparative-disadvantage sectors finding it harder to finance their entry into or survival in export markets either exit or refrain from entering export markets. On aggregate, one should therefore expect to see less entry, more exit, and shorter survival on export markets in those sectors after financial liberalization.The paper investigates the effect of financial liberalization on a country's export pattern by comparing the dynamics of entry and exit of different products in a country export portfolio before and after financial liberalization.The results suggest that products that lie far from the country's comparative advantage set tend to disappear relatively faster from the country's export portfolio following the liberalization of financial markets. In other words, financial liberalization tends to rebalance the composition of a country's export portfolio towards the products that intensively use the economy's abundant factors.

Pollicipes caboverdensis sp. nov. (Crustacea: Cirripedia: Scalpelliformes), an intertidal barnacle from the Cape Verde Islands

Recently, genetic evidence supported the existence of a new species of the genus Pollicipes from the Cape Verde Islands, previously considered a population of P. pollicipes. However, P. pollicipes was not sampled at its southern limit of distribution (Dakar, Senegal), which is geographically separated from the Cape Verde Islands by about 500 km. Herein we describe Pollicipes caboverdensis sp. nov. from the Cape Verde Islands and compare its morphology with the other three species of Pollicipes: P. pollicipes, P. elegans and P. polymerus. Pollicipes pollicipes was sampled at both the middle (Portugal) and southern limit (Dakar, Senegal) of its geographical distribution. The genetic divergence among and within these two regions and Cape Verde was calculated through the analysis of partial mtDNA CO1 gene sequences. Pollicipes caboverdensis sp. nov. has a single whorl of capitular plates below the subrostrum, peduncular scales pointing up toward the capitulum and multi-articulate caudal appendages (all characters shared with P. pollicipesand P. elegans), reddish-orange capitular plates (large specimens), a single rostral median latus between the median latus and the rostrolatus (both characters shared with P. elegans), and uniquely possesses peduncular scales that are approximately the same width as height. The genetic distance between the Cape Verde population and the Senegal and Portugal populations is 13–14%, whilst between Senegal and Portugal it is < 1%.

Carotid-Subclavian Artery Index : Validation of an Echocardiographic Index to Detect Coarctation : P67

Introduction: Due to patency of the arterial duct and the parallel circulation during the fetal life, coarctation remains a difficult diagnosis prenatally and even shortly after birth. Fisrtly, our study aimed to assess accuracy of a new cardiographie index based on morphologie measurements of the distal aortic arch, the Carotid-Subclavian Artery Index (CSA Index), the ratio of the distal transverse aortic arch diameter to the distance between the left carotid artery and the left subclavian artery, in detecting coarctation in newborns, infants and children, independently of other cardiac lesions. Secondly, to assess the additive value of another morphologie index in predicting coarctation, the 1/0 ratio, the ratio of isthmus to descending aorta diameter. Methods: It is a retrospective cohort study in a tertiary care children's hospital. Offline echocardiographic measurements of great vessels and aortic arch dimensions were done in 69 patients with coarctation. We calculate their CSA index, and their 1/0 ratio. Values of CSA Index and 1/0 ratio from coarctation group were compared with those from a normal local control population. Results: 69 echocardiograms from patients with coarctation were analysed. Compared with controls, patients with coarctation had a significantly lower CSA index (0.88 ±0.49 vs 2.65 ±0.82, p <0.0001) and 1/0 ratio. The same significant difference was observed, independently of age and other associated defects, even complex ones. CSA Index confirmed its good sensitivity and specificity (99% and 96% respectively). This was not improved by adding the I/D ratio. Conclusions: An abnormal CSA index is highly suggestive of coarctation independently of age, of the presence of a patent ductus arteriosus or of other cardiac defects. The addition of another anatomie index, the I/D ratio, was not helpful in our study.

Unfolding a symmetric matrix

Graphical displays which show inter--sample distances are importantfor the interpretation and presentation of multivariate data. Except whenthe displays are two--dimensional, however, they are often difficult tovisualize as a whole. A device, based on multidimensional unfolding, isdescribed for presenting some intrinsically high--dimensional displays infewer, usually two, dimensions. This goal is achieved by representing eachsample by a pair of points, say $R_i$ and $r_i$, so that a theoreticaldistance between the $i$-th and $j$-th samples is represented twice, onceby the distance between $R_i$ and $r_j$ and once by the distance between$R_j$ and $r_i$. Self--distances between $R_i$ and $r_i$ need not be zero.The mathematical conditions for unfolding to exhibit symmetry are established.Algorithms for finding approximate fits, not constrained to be symmetric,are discussed and some examples are given.