Bayesian Analysis of Linear Inverse Problems with Applications in Economics and Finance

In my PhD thesis I propose a Bayesian nonparametric estimation method for structural econometric models where the functional parameter of interest describes the economic agent's behavior. The structural parameter is characterized as the solution of a functional equation, or by using more technical words, as the solution of an inverse problem that can be either ill-posed or well-posed. From a Bayesian point of view, the parameter of interest is a random function and the solution to the inference problem is the posterior distribution of this parameter. A regular version of the posterior distribution in functional spaces is characterized. However, the infinite dimension of the considered spaces causes a problem of non continuity of the solution and then a problem of inconsistency, from a frequentist point of view, of the posterior distribution (i.e. problem of ill-posedness). The contribution of this essay is to propose new methods to deal with this problem of ill-posedness. The first one consists in adopting a Tikhonov regularization scheme in the construction of the posterior distribution so that I end up with a new object that I call regularized posterior distribution and that I guess it is solution of the inverse problem. The second approach consists in specifying a prior distribution on the parameter of interest of the g-prior type. Then, I detect a class of models for which the prior distribution is able to correct for the ill-posedness also in infinite dimensional problems. I study asymptotic properties of these proposed solutions and I prove that, under some regularity condition satisfied by the true value of the parameter of interest, they are consistent in a "frequentist" sense. Once I have set the general theory, I apply my bayesian nonparametric methodology to different estimation problems. First, I apply this estimator to deconvolution and to hazard rate, density and regression estimation. Then, I consider the estimation of an Instrumental Regression that is useful in micro-econometrics when we have to deal with problems of endogeneity. Finally, I develop an application in finance: I get the bayesian estimator for the equilibrium asset pricing functional by using the Euler equation defined in the Lucas'(1978) tree-type models.

Computational methods for the analysis of protein structure and function

The vast majority of known proteins have not yet been experimentally characterized and little is known about their function. The design and implementation of computational tools can provide insight into the function of proteins based on their sequence, their structure, their evolutionary history and their association with other proteins. Knowledge of the three-dimensional (3D) structure of a protein can lead to a deep understanding of its mode of action and interaction, but currently the structures of <1% of sequences have been experimentally solved. For this reason, it became urgent to develop new methods that are able to computationally extract relevant information from protein sequence and structure. The starting point of my work has been the study of the properties of contacts between protein residues, since they constrain protein folding and characterize different protein structures. Prediction of residue contacts in proteins is an interesting problem whose solution may be useful in protein folding recognition and de novo design. The prediction of these contacts requires the study of the protein inter-residue distances related to the specific type of amino acid pair that are encoded in the so-called contact map. An interesting new way of analyzing those structures came out when network studies were introduced, with pivotal papers demonstrating that protein contact networks also exhibit small-world behavior. In order to highlight constraints for the prediction of protein contact maps and for applications in the field of protein structure prediction and/or reconstruction from experimentally determined contact maps, I studied to which extent the characteristic path length and clustering coefficient of the protein contacts network are values that reveal characteristic features of protein contact maps. Provided that residue contacts are known for a protein sequence, the major features of its 3D structure could be deduced by combining this knowledge with correctly predicted motifs of secondary structure. In the second part of my work I focused on a particular protein structural motif, the coiled-coil, known to mediate a variety of fundamental biological interactions. Coiled-coils are found in a variety of structural forms and in a wide range of proteins including, for example, small units such as leucine zippers that drive the dimerization of many transcription factors or more complex structures such as the family of viral proteins responsible for virus-host membrane fusion. The coiled-coil structural motif is estimated to account for 5-10% of the protein sequences in the various genomes. Given their biological importance, in my work I introduced a Hidden Markov Model (HMM) that exploits the evolutionary information derived from multiple sequence alignments, to predict coiled-coil regions and to discriminate coiled-coil sequences. The results indicate that the new HMM outperforms all the existing programs and can be adopted for the coiled-coil prediction and for large-scale genome annotation. Genome annotation is a key issue in modern computational biology, being the starting point towards the understanding of the complex processes involved in biological networks. The rapid growth in the number of protein sequences and structures available poses new fundamental problems that still deserve an interpretation. Nevertheless, these data are at the basis of the design of new strategies for tackling problems such as the prediction of protein structure and function. Experimental determination of the functions of all these proteins would be a hugely time-consuming and costly task and, in most instances, has not been carried out. As an example, currently, approximately only 20% of annotated proteins in the Homo sapiens genome have been experimentally characterized. A commonly adopted procedure for annotating protein sequences relies on the "inheritance through homology" based on the notion that similar sequences share similar functions and structures. This procedure consists in the assignment of sequences to a specific group of functionally related sequences which had been grouped through clustering techniques. The clustering procedure is based on suitable similarity rules, since predicting protein structure and function from sequence largely depends on the value of sequence identity. However, additional levels of complexity are due to multi-domain proteins, to proteins that share common domains but that do not necessarily share the same function, to the finding that different combinations of shared domains can lead to different biological roles. In the last part of this study I developed and validate a system that contributes to sequence annotation by taking advantage of a validated transfer through inheritance procedure of the molecular functions and of the structural templates. After a cross-genome comparison with the BLAST program, clusters were built on the basis of two stringent constraints on sequence identity and coverage of the alignment. The adopted measure explicity answers to the problem of multi-domain proteins annotation and allows a fine grain division of the whole set of proteomes used, that ensures cluster homogeneity in terms of sequence length. A high level of coverage of structure templates on the length of protein sequences within clusters ensures that multi-domain proteins when present can be templates for sequences of similar length. This annotation procedure includes the possibility of reliably transferring statistically validated functions and structures to sequences considering information available in the present data bases of molecular functions and structures.

Existence of solutions and asymtptotic limits of the Euler-Poisson and the quantum drift-diffusion systems

My work concerns two different systems of equations used in the mathematical modeling of semiconductors and plasmas: the Euler-Poisson system and the quantum drift-diffusion system. The first is given by the Euler equations for the conservation of mass and momentum, with a Poisson equation for the electrostatic potential. The second one takes into account the physical effects due to the smallness of the devices (quantum effects). It is a simple extension of the classical drift-diffusion model which consists of two continuity equations for the charge densities, with a Poisson equation for the electrostatic potential. Using an asymptotic expansion method, we study (in the steady-state case for a potential flow) the limit to zero of the three physical parameters which arise in the Euler-Poisson system: the electron mass, the relaxation time and the Debye length. For each limit, we prove the existence and uniqueness of profiles to the asymptotic expansion and some error estimates. For a vanishing electron mass or a vanishing relaxation time, this method gives us a new approach in the convergence of the Euler-Poisson system to the incompressible Euler equations. For a vanishing Debye length (also called quasineutral limit), we obtain a new approach in the existence of solutions when boundary layers can appear (i.e. when no compatibility condition is assumed). Moreover, using an iterative method, and a finite volume scheme or a penalized mixed finite volume scheme, we numerically show the smallness condition on the electron mass needed in the existence of solutions to the system, condition which has already been shown in the literature. In the quantum drift-diffusion model for the transient bipolar case in one-space dimension, we show, by using a time discretization and energy estimates, the existence of solutions (for a general doping profile). We also prove rigorously the quasineutral limit (for a vanishing doping profile). Finally, using a new time discretization and an algorithmic construction of entropies, we prove some regularity properties for the solutions of the equation obtained in the quasineutral limit (for a vanishing pressure). This new regularity permits us to prove the positivity of solutions to this equation for at least times large enough.

Mitochondrial inheritance and germ line determination in a bivalve species with Doubly Uniparental Inheritance (DUI)

Mitochondria are inherited maternally in most metazoans. However, in some bivalves, two mitochondrial lineages are present: one transmitted through eggs (F), the other through sperm (M). This is called Doubly Uniparental Inheritance (DUI). During male embryo development, spermatozoon mitochondria aggregate and end up in the primordial germ cells, while they are dispersed in female embryos. The molecular mechanisms of segregation patterns are still unknown. In the DUI species Ruditapes philippinarum, I examined sperm mitochondria distribution by MitoTracker, microtubule staining and TEM, and I localized germ line determinants with immunocytochemical analysis. I also analyzed the gonad transcriptome, searching for genes involved in reproduction and sex determination. Moreover, I analyzed an M-type specific open reading frame that could be responsible for maintenance/degradation of M mitochondria during embryo development. These transcripts were also localized in tissues using in situ hybridization. As in Mytilus, two distribution patterns of M mitochondria were detected in R. philippinarum, supporting that they are related to DUI. Moreover, the first division midbody concurs in positioning aggregated M mitochondria on the animal-vegetal axis of the male embryo: in organisms with spiral segmentation this zone is not involved in further cleavages, so aggregation is maintained. Moreover, sperm mitochondria reach the same embryonic area where germ plasm is transferred, suggesting their contribution in male germ line formation. The finding of reproduction and ubiquitination transcripts led to formulate a model in which ubiquitination genes stored in female oocytes during gametogenesis would activate sex-gene expression in the early embryonic developmental stages (preformation). Only gametogenetic cells were labeled by in situ hybridization, proving their specific transcription in developing gametes. Other than having a role in sex determination, some ubiquination factors could also be involved in mitochondrial inheritance, and their differential expression could be responsible for the different fate of sperm mitochondria in the two sexes.

Geochemistry, petrogenesis and tectonic setting of ophiolites and mafic-ultramafic complexes in the Northeastern Aegean Region

In this study two ophiolites and a mafic-ultramafic complexes of the northeastern Aegean Sea, Greece, have been investigated to re-evaluate their petrogenetic evolution and tectonic setting. These complexes are: the mafic-ultramafic complex of Lesvos Island and the ophiolites of Samothraki Island and the Evros area. In order to examine these complexes in detail whole-rock major- and trace-elements as well as Sr and Nd isotopes, and minerals were analysed and U-Pb SHRIMP ages on zircons were determined. The mafic-ultramafic complex of Lesvos Island consists of mantle peridotite thrusted over a tectonic mélange containing metasediments, metabasalts and a few metagabbros. This succession had previously been interpreted as an ophiolite of Late Jurassic age. The new field and geochemical data allow a reinterpretation of this complex as representing an incipient continental rift setting that led to the subsequent formation of the Meliata-Maliac-Vardar branches of Neotethys in Upper Permian times (253 ± 6 Ma) and the term “Lesvos ophiolite” should be abandoned. With proceeding subduction and closure of the Maliac Ocean in Late Jurassic times (155 Ma) the Lesvos mafic-ultramafic complex was obducted. Zircon ages of 777, 539 and 338 Ma from a gabbro strongly suggest inheritance from the intruded basement and correspond to ages of distinct terranes recently recognized in the Hellenides (e.g. Florina terrane). Geochemical similar complexes which contain rift associations with Permo-Triassic ages can be found elsewhere in Greece and Turkey, namely the Teke Dere Thrust Sheet below the Lycian Nappes (SW Turkey), the Pindos subophiolitic mélange (W Greece), the Volcanosedimentary Complex on Central Evia Island (Greece) and the Karakaya Complex (NW Turkey). This infers that the rift-related rocks from Lesvos belong to an important Permo-Triassic rifting episode in the eastern Mediterranean. The ‘in-situ’ ophiolite of Samothraki Island comprises gabbros, sparse dykes and basalt flows as well as pillows cut by late dolerite dykes and had conventionally been interpreted as having formed in an ensialic back-arc basin. The results of this study revealed that none of the basalts and dolerites resemble mid-ocean ridge or back-arc basin basalts thus suggesting that the Samothraki ophiolite cannot represent mature back-arc basin crust. The age of the complex is regarded to be 160 ± 5 Ma (i.e. Oxfordian; early Upper Jurassic), which precludes any correlation with the Lesvos mafic-ultramafic complex further south (253 ± 6 Ma; Upper Permian). Restoration of the block configuration in NE Greece, before extensional collapse of the Hellenic hinterland and exhumation of the Rhodope Metamorphic Core Complex (mid-Eocene to mid-Miocene), results in a continuous ophiolite belt from Guevgueli in the NW to Samothraki in the SE, thus assigning the latter to the Innermost Hellenic Ophiolite Belt. In view of the data of this study, the Samothraki ophiolite represents a rift propagation of the Sithonia ophiolite spreading ridge into the Chortiatis calc-alkaline arc. The ophiolite of the Evros area consists of a plutonic sequence comprising cumulate and non-cumulate gabbros with plagiogranite veins, and an extrusive sequence of basalt dykes, massive and pillow lavas as well as pyroclastic rocks. Furthermore, in the Rhodope Massif tectonic lenses of harzburgites and dunites can be found. All rocks are spatially separated. The analytical results of this study revealed an intra-oceanic island arc setting for the Evros ophiolitic rocks. During late Middle Jurassic times (169 ± 2 Ma) an intra-oceanic arc has developed above a northwards directed intra-oceanic subduction zone of the Vardar Ocean in front of the Rhodope Massif. The boninitic, island arc tholeiitic and calc-alkaline rocks reflect the evolution of the Evros island arc. The obduction of the ophiolitic rocks onto the Rhodope basement margin took place during closure of the Vardar ocean basins. The harzburgites and dunites of the Rhodope Massif are strongly depleted and resemble harzburgites from recent oceanic island arcs. After melt extraction they underwent enrichment processes by percolating melts and fluids from the subducted slab. The relationship of the peridotites and the Evros ophiolite is still ambiguous, but the stratigraphic positions of the peridotites and the ophiolitic rocks indicate separated origin. The harzburgites and dunites most probably represent remnants of the mantle wedge of the island arc of the Rhodope terrane formed above subducted slab of the Nestos Ocean in late Middle Jurassic times. During collision of the Thracia terrane with the Rhodope terrane thrusting of the Rhodope terrane onto the Thracia terrane took place, whereas the harzburgites and dunites were pushed between the two terranes now cropping out on top of the Thracia terrane of the Rhodope Massif.

Analysis of Copy Number Variants identifies new candidate genes for Autism Spectrum Disorder and Intellectual Disability

Autism spectrum disorder (ASD) and Intellectual Disability (ID) are complex neuropsychiatric disorders characterized by extensive clinical and genetic heterogeneity and with overlapping risk factors. The aim of my project was to further investigate the role of Copy Numbers Variants (CNVs), identified through genome-wide studies performed by the Autism Geome Project (AGP) and the CHERISH consortium in large cohorts of ASD and ID cases, respectively. Specifically, I focused on four rare genic CNVs, selected on the basis of their impact on interesting ASD/ID candidate genes: a) a compound heterozygous deletion involving CTNNA3, predicted to cause the lack of functional protein; b) a 15q13.3 duplication containing CHRNA7; c) a 2q31.1 microdeletion encompassing KLHL23, SSB and METTL5; d) Lastly, I investigated the putative imprinting regulation of the CADPS2 gene, disrupted by a maternal deletion in two siblings with ASD and ID. This study provides further evidence for the role of CTNNA3, CHRNA7, KLHL23 and CADPS2 as ASD and/or ID susceptibility genes, and highlights that rare genetic variation contributes to disease risk in different ways: some rare mutations, such as those impacting CTNNA3, act in a recessive mode of inheritance, while other CNVs, such as those occurring in the 15q13.3 region, are implicated in multiple developmental and/or neurological disorders possibly interacting with other susceptibility variants elsewhere in the genome. On the other hand, the discovery of a tissue-specific monoallelic expression for the CADPS2 gene, implicates the involvement of epigenetic regulatory mechanisms as risk factors conferring susceptibility to ASD/ID.

Analysis of the Kohn Laplacian on the Heisenberg Group and on Cauchy-Riemann Manifolds

The purpose of this study is to analyse the regularity of a differential operator, the Kohn Laplacian, in two settings: the Heisenberg group and the strongly pseudoconvex CR manifolds. The Heisenberg group is defined as a space of dimension 2n+1 with a product. It can be seen in two different ways: as a Lie group and as the boundary of the Siegel UpperHalf Space. On the Heisenberg group there exists the tangential CR complex. From this we define its adjoint and the Kohn-Laplacian. Then we obtain estimates for the Kohn-Laplacian and find its solvability and hypoellipticity. For stating L^p and Holder estimates, we talk about homogeneous distributions. In the second part we start working with a manifold M of real dimension 2n+1. We say that M is a CR manifold if some properties are satisfied. More, we say that a CR manifold M is strongly pseudoconvex if the Levi form defined on M is positive defined. Since we will show that the Heisenberg group is a model for the strongly pseudo-convex CR manifolds, we look for an osculating Heisenberg structure in a neighborhood of a point in M, and we want this structure to change smoothly from a point to another. For that, we define Normal Coordinates and we study their properties. We also examinate different Normal Coordinates in the case of a real hypersurface with an induced CR structure. Finally, we define again the CR complex, its adjoint and the Laplacian operator on M. We study these new operators showing subelliptic estimates. For that, we don't need M to be pseudo-complex but we ask less, that is, the Z(q) and the Y(q) conditions. This provides local regularity theorems for Laplacian and show its hypoellipticity on M.

Analysis and numerical solution of the Peterlin viscoelastic model

Liquids and gasses form a vital part of nature. Many of these are complex fluids with non-Newtonian behaviour. We introduce a mathematical model describing the unsteady motion of an incompressible polymeric fluid. Each polymer molecule is treated as two beads connected by a spring. For the nonlinear spring force it is not possible to obtain a closed system of equations, unless we approximate the force law. The Peterlin approximation replaces the length of the spring by the length of the average spring. Consequently, the macroscopic dumbbell-based model for dilute polymer solutions is obtained. The model consists of the conservation of mass and momentum and time evolution of the symmetric positive definite conformation tensor, where the diffusive effects are taken into account. In two space dimensions we prove global in time existence of weak solutions. Assuming more regular data we show higher regularity and consequently uniqueness of the weak solution. For the Oseen-type Peterlin model we propose a linear pressure-stabilized characteristics finite element scheme. We derive the corresponding error estimates and we prove, for linear finite elements, the optimal first order accuracy. Theoretical error of the pressure-stabilized characteristic finite element scheme is confirmed by a series of numerical experiments.

Córdoban Discourses: A Drama of Interreligious Dialogue

SETTING: Cordoba, Spain, 1135 CE, 29th year of the reign of ‘Ali “amir al-muslimin,” second king of the Berber Almoravid dynasty, rulers of Moorish Spain from 1071 to 1147. Cordoba, the capital of Andalus and the center of the Almoravid holdings in Spain, is a bustling cosmopolitan center, a crossroads for Europe and the Middle East, and the meeting-point of three religious traditions. Most significantly, Cordoba at this time is the hub of European intellectual activity. From the square—itself impressively large and surrounded by a massive collonade, the regularity and ordered beauty of which typifies the Moorish taste for symmetry (so beloved of M.C. Escher)—can be seen the huge Cordoban mosque, erected in the 8th-century by Khalif Abd-er-Rahman I to the glory of Allah, oft forgiving, most merciful. It is the second largest building in Islam, and the bastion of the still entrenched but soon to fade Muslim presence in western Europe. SCENE: Three figures sit upon stone benches beneath the westernmost colonnade of the Cordoban mosque, involved in an animated, though friendly discussion on matters of faith and reason, knowledge and God, language and logic. The host is none other than Jehudah Halevi, and his esteemed guests Master Peter Abelard and the venerable Råmånuja, whose obviously advanced age belies his youthful voice, gleaming eye, quick hands, and general exuberance. It is autumn, early evening…

Epidemiological and genetic study of exertional rhabdomyolysis in a Warmblood horse family in Switzerland

REASONS FOR PERFORMING STUDY: Exertional rhabdomyolysis (ER) and its familial basis in Warmblood horses is incompletely understood. OBJECTIVES: To describe the case details, clinical signs and management of ER-affected Warmblood horses from a family with a high prevalence of ER, to determine if histopathological signs of polysaccharide storage myopathy (PSSM) and the glycogen synthase (GYS1) mutation are associated with ER in this family, and to investigate potential risk factors for development of ER. METHODS: A family consisting of a sire with ER and 71 of his descendants was investigated. History of episodes of ER, husbandry, feeding and use was assessed by interviewing horse owners using a standardised questionnaire. All horses were genotyped for GYS1. In 10 ER-affected horses, muscle histopathology was evaluated. RESULTS: Signs of ER were reported in 39% of horses and 51% of the entire family possessed the GYS1 mutation. Horses possessing the GYS1 mutation had a 7.1-times increased risk for developing ER compared to those with the normal genotype (95% confidence interval [CI] 2.37-21.23, P = 0.0005). All muscle samples from horses in the family with ER showed polysaccharide accumulation typical for PSSM, amylase-resistant in 9/10 cases. There was evidence (odds ratio 5.6, CI 1.00-31.32, P = 0.05) that fat or oil feeding improved clinical signs of ER. No other effects of environmental factors associated with clinical signs of ER were identified. CONCLUSION AND POTENTIAL RELEVANCE: PSSM associated with the GYS1 mutation is one identifiable cause of ER in Warmblood horses. Signs of ER are not always manifest in GYS1 positive horses and there are also other causes for ER in Warmblood horses. Breeding animals with the GYS1 mutation results in a high prevalence of ER due to its dominant mode of inheritance.

Huntington's like conditions in China, A review of published Chinese cases

Background: Knowledge about HD in China is lacking in the international literature. We have therefore analyzed the Chinese literature to thoroughly explore the clinical characteristics of Huntington disease in China. Methods: A computer-based online search of China National Knowledge Infrastructure was performed to review case reports concerning HD published between January 1980 and April of 2011, and the clinical characteristics were extracted. Results: A total of 92 studies involving 279 patients (157 males and 122 females) were collected, 82.0% of which were from provinces of North China. Most of the cases (97.8%) had a family history of HD, and paternal inheritance (65.5%) was higher than maternal inheritance (34.5%). Onset age was 35.8 (± 11.8) years, death occurred with 45.6 (± 13.5) years after a course of 11.6 (± 5.6) years. Involuntary movements were the most frequent reported presentation (found in 52.3%, including 64.4% in the entire body, 19.8% in the upper limbs, and 13.7% in the head and face). Psychiatric symptoms at onset were reported in 16.1%, and cognitive impairment in 1.8%. With disease progression, 99.6% of patients had abnormal movements, 67.9% cognitive impairment, and 35.0% suffered psychiatric symptoms. Of the reported patients, only 22 underwent IT15 gene testing with positive results. Conclusion: HD is a well-reported entity in Chinese medical literature, however, only a small number of instances have been proven by molecular diagnosis. Most of the features resemble what is known in other countries. The highly predominant motor presentation, and the higher male prevalence as well as the apparent concentration in Northern China may be due to observational bias. There is therefore a need to prospectively examine cohorts of patients with appropriate comprehensive assessment tools including genetic testing.

Characterization of the canine CLCN3 gene and evaluation as candidate for late-onset NCL

BACKGROUND: The neuronal ceroid lipofuscinoses (NCL) are a heterogenous group of inherited progressive neurodegenerative diseases in different mammalian species. Tibetan Terrier and Polish Owczarek Nizinny (PON) dogs show rare late-onset NCL variants with autosomal recessive inheritance, which can not be explained by mutations of known human NCL genes. These dog breeds represent animal models for human late-onset NCL. In mice the chloride channel 3 gene (Clcn3) encoding an intracellular chloride channel was described to cause a phenotype similar to NCL. RESULTS: Two full-length cDNA splice variants of the canine CLCN3 gene are reported. The current canine whole genome sequence assembly was used for gene structure analyses and revealed 13 coding CLCN3 exons in 52 kb of genomic sequence. Sequence analysis of the coding exons and flanking intron regions of CLCN3 using six NCL-affected Tibetan terrier dogs and an NCL-affected Polish Owczarek Nizinny (PON) dog, as well as eight healthy Tibetan terrier dogs revealed 13 SNPs. No consistent CLCN3 haplotype was associated with NCL. CONCLUSION: For the examined animals we excluded the complete coding region and adjacent intronic regions of canine CLCN3 to harbor disease-causing mutations. Therefore it seems to be unlikely that a mutation in this gene is responsible for the late-onset NCL phenotype in these two dog breeds.

Genetic analysis of syndactyly in German Holstein cattle

Congenital syndactyly with a variable number of affected feet was observed in eight black and white German Holstein calves. Analysis of the pedigree data revealed that all affected individuals could be traced back to a single founder. The pedigree was consistent with monogenic autosomal recessive inheritance and variable expressivity. Bovine syndactyly or "mulefoot" has been previously shown to map on the telomeric end of bovine chromosome 15 and we performed PCR genotyping of microsatellite markers spanning 27 cM of this chromosomal region to test the new cases for genetic linkage with the phenotype. The haplotype segregation confirmed the suggested inheritance pattern of the mulefoot mutation in this family and markers RM004, BM848 and BMS820 showed significant linkage to the phenotype. The results confirmed the chromosomal location of the mulefoot gene in this pedigree. Furthermore the study demonstrated that although marker testing has been available for nearly a decade the use of mulefoot carriers in cattle breeding remains uncontrolled. The presented family provides a resource for positional cloning of the causative mutation.