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Showing papers by "École Normale Supérieure published in 1998"


Journal ArticleDOI
01 Jan 1998
TL;DR: In this article, a graph transformer network (GTN) is proposed for handwritten character recognition, which can be used to synthesize a complex decision surface that can classify high-dimensional patterns, such as handwritten characters.
Abstract: Multilayer neural networks trained with the back-propagation algorithm constitute the best example of a successful gradient based learning technique. Given an appropriate network architecture, gradient-based learning algorithms can be used to synthesize a complex decision surface that can classify high-dimensional patterns, such as handwritten characters, with minimal preprocessing. This paper reviews various methods applied to handwritten character recognition and compares them on a standard handwritten digit recognition task. Convolutional neural networks, which are specifically designed to deal with the variability of 2D shapes, are shown to outperform all other techniques. Real-life document recognition systems are composed of multiple modules including field extraction, segmentation recognition, and language modeling. A new learning paradigm, called graph transformer networks (GTN), allows such multimodule systems to be trained globally using gradient-based methods so as to minimize an overall performance measure. Two systems for online handwriting recognition are described. Experiments demonstrate the advantage of global training, and the flexibility of graph transformer networks. A graph transformer network for reading a bank cheque is also described. It uses convolutional neural network character recognizers combined with global training techniques to provide record accuracy on business and personal cheques. It is deployed commercially and reads several million cheques per day.

42,067 citations


Journal ArticleDOI
TL;DR: The operation and philosophy of the monitoring system, the precision and accuracy of the measuring radiometers, a brief description of the processing system, and access to the database are discussed.

6,535 citations


Journal ArticleDOI
TL;DR: In this paper, an efficient primal-dual interior-point method for solving second-order cone programs (SOCP) is presented. But it is not a generalization of interior point methods for convex problems.

2,215 citations


Journal ArticleDOI
TL;DR: In this article, a one-dimensional scattering amplitude and effective 1D interaction potential for atoms confined transversally by an atom waveguide or highly elongated ''cigar''-shaped atomic trap was calculated.
Abstract: We calculate, within the pseudopotential approximation, a one-dimensional scattering amplitude and effective one-dimensional interaction potential for atoms confined transversally by an atom waveguide or highly elongated ``cigar''-shaped atomic trap. We show that, in the low-energy scattering regime, the scattering process degenerates to a total reflection, suggesting an experimental realization of a famous model in theoretical physics---a one-dimensional gas of impenetrable bosons (``Tonks'' gas). We give an estimate for suitable experimental parameters for alkali atoms confined in waveguides.

1,481 citations


Journal ArticleDOI
TL;DR: The develop-ment of functional foods for the gut is in its infancy and will be successful only if more fundamental research is done on digestive physiology, the gut microflora, immune system and mucosal function.
Abstract: The gut is an obvious target for the development of functional foods, acting as it does as the interface between diet and the metabolic events which sustain life. The key processes in digestive physiology which can be regulated by modifying diet are satiety, the rate and extent of macronutrient breakdown and absorption from the small bowel, sterol metabolism, the colonic microflora, fermentation, mucosal function and bowel habit, and the gut immune system. The intestinal microflora is the main focus of many current functional foods. Probiotics are foods which contain live bacteria which are beneficial to health whilst prebiotics, such as certain non-digestible oligosaccharides which selectively stimulate the growth of bifidobacteria in the colon, are already on the market. Their claimed benefits are to alleviate lactose maldigestion, increase resistance to invasion by pathogenic species of bacteria in the gut, stimulate the immune system and possibly protect against cancer. There are very few reports of well-designed human intervention studies with prebiotics as yet. Certain probiotic species have been shown to shorten the duration of rotavirus diarrhoea in children but much more work is needed on the mechanism of immunomodulation and of competitive exclusion and microflora modification. The development of functional foods for the gut is in its infancy and will be successful only if more fundamental research is done on digestive physiology, the gut microflora, immune system and mucosal function.

1,416 citations


Journal ArticleDOI
TL;DR: The design of a new methodology for representing the relationship between two sets of spectral envelopes and the proposed transform greatly improves the quality and naturalness of the converted speech signals compared with previous proposed conversion methods.
Abstract: Voice conversion, as considered in this paper, is defined as modifying the speech signal of one speaker (source speaker) so that it sounds as if it had been pronounced by a different speaker (target speaker). Our contribution includes the design of a new methodology for representing the relationship between two sets of spectral envelopes. The proposed method is based on the use of a Gaussian mixture model of the source speaker spectral envelopes. The conversion itself is represented by a continuous parametric function which takes into account the probabilistic classification provided by the mixture model. The parameters of the conversion function are estimated by least squares optimization on the training data. This conversion method is implemented in the context of the HNM (harmonic+noise model) system, which allows high-quality modifications of speech signals. Compared to earlier methods based on vector quantization, the proposed conversion scheme results in a much better match between the converted envelopes and the target envelopes. Evaluation by objective tests and formal listening tests shows that the proposed transform greatly improves the quality and naturalness of the converted speech signals compared with previous proposed conversion methods.

1,109 citations


Journal Article
TL;DR: In this article, the relative strengths of popular notions of security for public key encryption schemes are compared under chosen plaintext attack and two kinds of chosen ciphertext attack, and the goals of privacy and non-malleability are considered.
Abstract: We compare the relative strengths of popular notions of security for public key encryption schemes. We consider the goals of privacy and non-malleability, each under chosen plaintext attack and two kinds of chosen ciphertext attack. For each of the resulting pairs of definitions we prove either an implication (every scheme meeting one notion must meet the other) or a separation (there is a scheme meeting one notion but not the other, assuming the first notion can be met at all). We similarly treat plaintext awareness, a notion of security in the random oracle model. An additional contribution of this paper is a new definition of non-malleability which we believe is simpler than the previous one.

1,057 citations


Journal ArticleDOI
TL;DR: An iterative decoding algorithm for any product code built using linear block codes based on soft-input/soft-output decoders for decoding the component codes so that near-optimum performance is obtained at each iteration.
Abstract: This paper describes an iterative decoding algorithm for any product code built using linear block codes. It is based on soft-input/soft-output decoders for decoding the component codes so that near-optimum performance is obtained at each iteration. This soft-input/soft-output decoder is a Chase decoder which delivers soft outputs instead of binary decisions. The soft output of the decoder is an estimation of the log-likelihood ratio (LLR) of the binary decisions given by the Chase decoder. The theoretical justifications of this algorithm are developed and the method used for computing the soft output is fully described. The iterative decoding of product codes is also known as the block turbo code (BTC) because the concept is quite similar to turbo codes based on iterative decoding of concatenated recursive convolutional codes. The performance of different Bose-Chaudhuri-Hocquenghem (BCH)-BTCs are given for the Gaussian and the Rayleigh channel. Performance on the Gaussian channel indicates that data transmission at 0.8 dB of Shannon's limit or more than 98% (R/C>0.98) of channel capacity can be achieved with high-code-rate BTC using only four iterations. For the Rayleigh channel, the slope of the bit-error rate (BER) curve is as steep as for the Gaussian channel without using channel state information.

970 citations


Journal ArticleDOI
TL;DR: The unexpected properties of penetratins, a class of peptides with translocating properties and capable of carrying hydrophilic compounds across the plasma membrane, are summarized, allowing direct targeting of oligopeptides and oligonucleotides to the cytoplasm and nucleus.

842 citations


Journal ArticleDOI
TL;DR: In this article, it was shown that in certain superstring compactifications, gauge theories on noncommutative tori will naturally appear as D-brane world volume theories.
Abstract: We show that in certain superstring compactifications, gauge theories on noncommutative tori will naturally appear as D-brane world-volume theories. This gives strong evidence that they are well-defined quantum theories. It also gives a physical derivation of the identification proposed by Connes, Douglas and Schwarz of Matrix theory compactification on the noncommutative torus with M theory compactification with constant background three-form tensor field.

837 citations


Journal ArticleDOI
TL;DR: The science base that underpins the argument that oxidative damage is a significant causative factor in the development of human diseases and that antioxidants are capable of preventing or ameliorating these disease processes is assessed critically.
Abstract: This paper assesses critically the science base that underpins the argument that oxidative damage is a significant causative factor in the development of human diseases and that antioxidants are capable of preventing or ameliorating these disease processes. The assessment has been carried out under a number of headings, and some recommendations for future research are made based on the present day knowledge base. The knowledge database (1) Consideration of the basic science that underlies understanding of the role of free radicals in causing cellular pathologies, and the role of antioxidants in preventing this, shows that an imbalance of reactive oxygen species and antioxidant defence systems may lead to chemical modifications of biologically relevant macromolecules. This imbalance provides a logical pathobiochemical mechanism for the initiation and development of several disease states. Experimental data obtained in vivo provide evidence that antioxidants function in systems that scavenge reactive oxygen species and that these are relevant to what occurs in vivo. The relevance in vivo of these observations depends inter alia on knowledge of the uptake and distribution of the antioxidant within the human body, and on what tissue levels of the antioxidant may be expected in relation to dietary levels. (2) There is some way to go until validated precise methods are available for measuring biomarkers of oxidative damage in human subjects in vivo under minimally invasive conditions. With respect to oxidative damage in DNa, HPLC and GC-mass spectrophotometry methods have both merits and limitations. Lipid oxidation products in plasma are best measured as isoprostanes or as lipid hydroperoxides using specific HPLC techniques. Development of isoprostane measurement will advance specificity and precision. The measurement of oxidative damage to proteins has some potential but such methods have not been effectively exploited. (3) Epidemiological studies support the hypothesis that the major antioxidant nutrients vitamin E and vitamin C, and beta-carotene (which may or may not be acting as an antioxidant in vivo), may play a beneficial role in prevention of several chronic disorders. More research is needed on the impact of other non-nutrient compounds, such as other carotenoids and flavonoids, on human health. In general, human intervention studies using hard end-points are the gold standard. Trials are restricted mainly to the major antioxidants and do not allow firm conclusions because of inconsistent findings, an insufficient number of studies and the use of varying doses. There is evidence that large doses of beta-carotene may be deleterious to the health of certain subgroups of the population such as heavy habitual smokers. (4) With respect to the safety of administration of supplementary vitamins, vitamin C is safe at levels of supplementation up to 600 mg/d, and higher levels, up to 2000 mg/d, are without risk. Vitamin E has a very low human toxicity and an intake of 1000 mg/d is without risk; 3200 mg/d has been shown to be without any consistent risk. Large intakes of beta-carotene must be viewed with caution because they have been shown to confer detriment to a population at high risk of lung cancer when administered after many years of high risk (smoking) behaviour. Until further work clarifies the situation in heavy smokers with respect to taking supplements, larger doses should be avoided by such individuals. There is little reliable information about the human toxicology of flavonoids and related non-nutrient antioxidant constituents of the diet. (5) The food industry has long experience in the control of oxidative damage in foods and this experience can be used to advantage for the protection of food antioxidants which are beneficial. Some of these, such as vitamins C and E and beta-carotene, are well known, and strategies for their protection in foods are already exploited by food technologies. (ABSTRACT TRUNCATED)

Journal ArticleDOI
TL;DR: In this article, a number of exact results have been obtained recently for the one-dimensional asymmetric simple exclusion process, a model of particles which hop to their right at random times, on a 1D lattice, provided that the target site is empty.

Journal ArticleDOI
TL;DR: This zebrafish gene map will facilitate molecular identification of mutated zebra-fish genes, which can suggest functions for human genes known only by sequence, and is likely that two polyploidization events occurred prior to the divergence of fish and mammal lineages.
Abstract: In chordate phylogeny, changes in the nervous system, jaws, and appendages transformed meek filter feeders into fearsome predators. Gene duplication is thought to promote such innovation. Vertebrate ancestors probably had single copies of genes now found in multiple copies in vertebrates and gene maps suggest that this occurred by polyploidization. It has been suggested that one genome duplication event occurred before, and one after the divergence of ray-finned and lobe-finned fishes. Holland et al., however, have argued that because various vertebrates have several HOX clusters, two rounds of duplication occurred before the origin of jawed fishes. Such gene-number data, however, do not distinguish between tandem duplications and polyploidization events, nor whether independent duplications occurred in different lineages. To investigate these matters, we mapped 144 zebrafish genes and compared the resulting map with mammalian maps. Comparison revealed large conserved chromosome segments. Because duplicated chromosome segments in zebrafish often correspond with specific chromosome segments in mammals, it is likely that two polyploidization events occurred prior to the divergence of fish and mammal lineages. This zebrafish gene map will facilitate molecular identification of mutated zebrafish genes, which can suggest functions for human genes known only by sequence.

Journal ArticleDOI
TL;DR: The protein-polysaccharide complexes exhibit better functional properties than that of the proteins and polysaccharides alone, and could be attributed to the simultaneous presence of the two biopolymers, as well as the structure of the complexes.
Abstract: Food proteins and polysaccharides are the two key structural entities in food materials. Generally, interactions between proteins and polysaccharides in aqueous media can lead to one- or two-phase systems, the latter being generally observed. In some cases of protein-polysaccharide net attraction, mainly mediated through electrostatic interactions, complex coac-ervation or associative phase separation occurs, giving rise to the formation of protein-polysac-charide complexes. Physicochemical factors such as pH, ionic strength, ratio of protein to polysaccharide, polysaccharide and protein charge, and molecular weight affect the formation and stability of such complexes. Additionally, the temperature and mechanical factors (pressure, shearing rate, and time) have an influence on phase separation and time stability of the system. The protein-polysacchaide complexes exhibit better functional properties than that of the proteins and polysaccharides alone. This improvement could be attributed to the simultaneou...


Journal ArticleDOI
TL;DR: This article investigated the ability of French newborns to discriminate between sets of sentences in different foreign languages and found that infants use prosodic and, more specifically, rhythmic information to classify utterances into broad language classes defined according to global rhythmic properties.
Abstract: Three experiments investigated the ability of French newborns to discriminate between sets of sentences in different foreign languages. The sentences were low-pass filtered to reduce segmental information while sparing prosodic information. Infants discriminated between stress-timed English and mora-timed Japanese (Experiment 1) but failed to discriminate between stress-timed English and stress-timed Dutch (Experiment 2). In Experiment 3, infants heard different combinations of sentences from English, Dutch, Spanish, and Italian. Discrimination was observed only when English and Dutch sentences were contrasted with Spanish and Italian sentences. These results suggest that newborns use prosodic and, more specifically, rhythmic information to classify utterances into broad language classes defined according to global rhythmic properties. Implications of this for the acquisition of the rhythmic properties of the native language are discussed.

Journal ArticleDOI
TL;DR: In this article, a possible way to valorize citrus peels and seeds, which are byproducts of the juice extraction industry, is to use them as natural antioxidants, and the antioxidant activity of several citrus peel and...
Abstract: A possible way to valorize citrus peels and seeds, which are byproducts of the juice extraction industry, is to use them as natural antioxidants. The antioxidant activity of several citrus peel and...

Journal ArticleDOI
TL;DR: MBCP implants with 565 microm pore diameter and 40% macroporosity represented the optimal association for homogeneous and abundant bone ingrowth and provided more abundant newly formed bone both in peripheral and deep pores.

Journal ArticleDOI
TL;DR: This study demonstrates the existence of acidic phosphate, observable by Raman microspectrometry, in mature biominerals, and suggests that even low levels of carbonate substitution induce modifications of the hydroxyapatite spectrum.
Abstract: The carbonate and phosphate vibrational modes of different synthetic and biological carbonated apatites were investigated by Raman microspectroscopy, and compared with those of hydroxyapatite. The ν1 phosphate band at 960 cm−1 shifts slightly due to carbonate substitution in both A and B sites. The spectrum of type A carbonated apatite exhibits two ν1 PO43− bands at 947 and 957 cm−1. No significant change was observed in the ν2 and ν4 phosphate mode regions in any carbonated samples. The ν3 PO43− region seems to be more affected by carbonation: two main bands were observed, as in the hydroxyapatite spectrum, but at lower wave numbers. The phosphate spectra of all biominerals apatite were consistent with type AB carbonated apatite. In the enamel spectrum, bands were observed at 3513 and at 3573 cm−1 presumably due to two different hydroxyl environments. Two different bands due to the carbonate ν1 mode were identified depending on the carbonate substitution site A or B, at 1107 and 1070 cm−1, respectively. Our results, compared with the infrared data already reported, suggest that even low levels of carbonate substitution induce modifications of the hydroxyapatite spectrum. Increasing substitution ratios, however, do not bring about any further alteration. The spectra of dentine and bone showed a strong similarity at a micrometric level. This study demonstrates the existence of acidic phosphate, observable by Raman microspectrometry, in mature biominerals. The HPO42− and CO32− contents increase from enamel to dentine and bone, however, these two phenomena do not seem to be correlated.

Book ChapterDOI
23 Aug 1998
TL;DR: In this article, the relative strengths of popular notions of security for public key encryption schemes are compared under chosen plaintext attack and two kinds of chosen ciphertext attack, and the goals of privacy and non-malleability are considered.
Abstract: We compare the relative strengths of popular notions of security for public key encryption schemes. We consider the goals of privacy and non-malleability, each under chosen plaintext attack and two kinds of chosen ciphertext attack. For each of the resulting pairs of definitions we prove either an implication (every scheme meeting one notion must meet the other) or a separation (there is a scheme meeting one notion but not the other, assuming the first notion can be met at all). We similarly treat plaintext awareness, a notion of security in the random oracle model. An additional contribution of this paper is a new definition of non-malleability which we believe is simpler than the previous one.

Journal ArticleDOI
TL;DR: In this article, the stability properties of and modelling issues by generalized fractional differential systems of commensurate and incommensurate nature are addressed. And when necessary a distinction is made between fractional ARMA systems and general fractional DDE systems.
Abstract: In the last decades, fractional differential equations have become popular among scientists in order to model various stable physical phenomena with anomalous decay, say that are not of exponential type. Moreover in discrete-time series analysis, so-called fractional ARMA models have been proposed in the literature in order to model stochastic processes, the autocorrelation of which also exhibits an anomalous decay. Both types of models stem from a common property of complex variable functions: namely, multivalued functions and their behaviour in the neighborhood of the branching point, and asymptotic expansions performed along the cut between branching points. This more abstract point of view proves very much useful in order to extend these models by changing the location of the classical branching points (the origin of the complex plane, for continuous-time systems). Hence, stability properties of and modelling issues by generalized fractional differential systems will be adressed in the present paper: systems will be considered both in the time-domain and in the frequency-domain; when necessary a distinction will be made between fractional differential systems of commensurate and incommensurate.

Journal ArticleDOI
TL;DR: A mechanistic model of a spatially structured ecosystem in which plants compete for a limiting soil nutrient shows that plant species richness does not necessarily enhance ecosystem processes, but it identifies two types of factors that could generate such an effect: complementarity among species in the space they occupy below ground and positive correlation between mean resource-use intensity and diversity.
Abstract: Recent experiments have provided some evidence that loss of biodiversity may impair the functioning and sustainability of ecosystems. However, we still lack adequate theories and models to provide robust generalizations, predictions, and interpretations for such results. Here I present a mechanistic model of a spatially structured ecosystem in which plants compete for a limiting soil nutrient. This model shows that plant species richness does not necessarily enhance ecosystem processes, but it identifies two types of factors that could generate such an effect: (i) complementarity among species in the space they occupy below ground and (ii) positive correlation between mean resource-use intensity and diversity. In both cases, the model predicts that plant biomass, primary productivity, and nutrient retention all increase with diversity, similar to results reported in recent field experiments. These two factors, however, have different implications for the understanding of the relationship between biodiversity and ecosystem functioning. The model also shows that the effect of species richness on productivity or other ecosystem processes is masked by the effects of physical environmental parameters on these processes. Therefore, comparisons among sites cannot reveal it, unless abiotic conditions are very tightly controlled. Identifying and separating out the mechanisms behind ecosystem responses to biodiversity should become the focus of future experiments.

Journal ArticleDOI
TL;DR: The authors found that a stable link exists between oil price shocks and the US real effective exchange rate over the post-Bretton Woods period, suggesting that oil prices may have been the dominant source of persistent real exchange rate shocks.

Journal ArticleDOI
TL;DR: The authors propose a two-step algorithm for almost unsupervised detection of linear structures, in particular, main axes in road networks, as seen in synthetic aperture radar (SAR) images.
Abstract: The authors propose a two-step algorithm for almost unsupervised detection of linear structures, in particular, main axes in road networks, as seen in synthetic aperture radar (SAR) images. The first step is local and is used to extract linear features from the speckle radar image, which are treated as road-segment candidates. The authors present two local line detectors as well as a method for fusing information from these detectors. In the second global step, they identify the real roads among the segment candidates by defining a Markov random field (MRF) on a set of segments, which introduces contextual knowledge about the shape of road objects. The influence of the parameters on the road detection is studied and results are presented for various real radar images.

Journal ArticleDOI
TL;DR: In this article, an approximate approach is used showing the importance of small cavity order m/sub c/ and of the m/ sub c/n/sup 2/ ratio.
Abstract: We address the long-standing issue of extracting light as efficiently as possible from a high-index material, n/spl ges/2, where as little as 2%-10% of light not suffering total internal reflection is extracted at standard plane faces due to the small critical angle /spl sim/1/n. Using a planar microcavity to redirect spontaneous emission toward the surface, constructive interferences can bring 15%-50% of the light out, enhancing brightness and efficiency. In this first of two papers, an approximate approach is used showing the importance of small cavity order m/sub c/ and of the m/sub c//n/sup 2/ ratio. We define a condition for microcavity regime as m/sub c/<2n/sup 2/. It is shown that most of light extraction is usually attained for moderate mirror reflectivities /spl sim/1-m/sub c//n/sup 2/ typically below 90%, and without strong directionality. Balance between emission directionality, radiance (brightness), and spectral narrowing is discussed. We define a brightness enhancement factor B given by Bm/sub c//spl Delta//spl Omega/=4/spl pi/ where /spl Delta//spl Omega/ is the largest internal solid angle of either the cavity mode or that deduced from the material emission linewidth. Design rules are applied to distributed dielectric mirrors yielding an optimal number of periods. The underlying physical competition between emission into guided modes, Fabry-Perot modes and the so-called "leaky modes" is analyzed.

Journal ArticleDOI
TL;DR: The authors review the recent developments that have provided an increased understanding of the basis of integrin activation and identify novel cytoplasmic partners for integrins and the emerging characterization of the signal-transduction pathways that regulate integrin 'inside-out' signalling.

Journal ArticleDOI
TL;DR: In this paper, the advantages, types, formation, and properties of agricultural packaging materials based on proteins, with examples, are reviewed in detail, and two technological processes have been investigated: the wet (or solvent) process, based on dispersion or solubilization of proteins in a solvent medium, and the dry process based on the thermoplastic properties of proteins under low water content conditions.
Abstract: Advantages, types, formation, and properties of agricultural packaging materials based on proteins, with examples, are reviewed in detail. Proteins have long and empirically been used to make biodegradable, renewable, and edible packaging materials. Numerous cereal and vegetable proteins (such as corn zein, wheat gluten, and soy proteins) and animal proteins (such as milk proteins, collagen, gelatin, keratin, and myofibrillar proteins) are commonly used to form agricultural packaging materials. Two technological processes have been investigated to make materials based on proteins: the “wet (or solvent) process” based on dispersion or solubilization of proteins in a solvent medium, and the “dry process” based on the thermoplastic properties of proteins under low water content conditions. The macroscopic properties (including solubility in water, mechanical properties, and barrier properties) of agricultural packaging materials based on proteins are dependent mainly on the structure of the macromol...

Journal ArticleDOI
TL;DR: In this article, the spatially homogeneous Boltzmannian equation without cut-off, the Fokker-Planck Landau equation, and the asymptotics of grazing collisions for a broad class of potentials were derived.
Abstract: This paper deals with the spatially homogeneous Boltzmann equation when grazing collisions are involved.We study in a unified setting the Boltzmann equation without cut-off, the Fokker-Planck-Landau equation, and the asymptotics of grazing collisions for a very broad class of potentials; in particular, we are able to derive rigorously the Landau equation for the Coulomb potential. In order to do so, we introduce a new definition of weak solutions, based on entropy production.


Book ChapterDOI
TL;DR: In this article, a set of methods addressed to the study of solvation problems at the quantum mechanical level with the use of polarizable continuum model (PCM) are presented.
Abstract: Publisher Summary This chapter presents a set of methods addressed to the study of solvation problems at the quantum mechanical level with the use of polarizable continuum model (PCM). The chapter describes the evolution of continuous methods since the first proposals or the first formulation at a QM level, semiempirical, or ab initio. PCM belongs to the family of methods in which focuses on a limited portion of matter, the ‘solute’ (one or more molecules) while the remaining, and larger, portion of the solution, called here the ‘solvent’, is treated at a lower level of accuracy. PCM is a quantum mechanical (QM) method in which use is made of an effective Hamiltonian for the solute M , and the corresponding Schrodinger equation is generally (but not compulsory) treated at the ab initio level. PCM makes use of continuous solvent distributions to describe the solute-solvent interaction potential. The chapter demonstrates that PCM manages to treat not only the well known model based on a uniform isotropic dielectric description of the solvent, whose interactions are limited to the electrostatic terms, but also more complex models including interactions of different physical origin and other solvent distribution functions.