Academic literature on the topic 'Degeneracy locus'

In this paper, we study the irreducible decompositions of the degeneracy loci of matrices which are defined by rank conditions on upper left submatrices. By introducing the concepts of standard and essential rank functions, we give an explicit classification of these degeneracy loci. Based on standard rank functions, we design an algorithm to write a degeneracy locus as a union of its irreducible components. This gives an answer to a problem raised by Sturmfels.

Hurtubise showed that the singular locus of the complexification of a BPS monopole intersects the degeneracy locus of the complex Higgs field in a null curve [Formula: see text] has a dual [Formula: see text]: by adapting a criterion of Hitchin it is shown that for a generic charge 2 monopole, [Formula: see text], the monopole's spectral curve.

We consider compact Kählerian manifolds $X$ of even dimension 4 or more, endowed with a log-symplectic holomorphic Poisson structure $\unicode[STIX]{x1D6F1}$ which is sufficiently general, in a precise linear sense, with respect to its (normal-crossing) degeneracy divisor $D(\unicode[STIX]{x1D6F1})$. We prove that $(X,\unicode[STIX]{x1D6F1})$ has unobstructed deformations, that the tangent space to its deformation space can be identified in terms of the mixed Hodge structure on $H^{2}$ of the open symplectic manifold $X\setminus D(\unicode[STIX]{x1D6F1})$, and in fact coincides with this $H^{2}$ provided the Hodge number $h_{X}^{2,0}=0$, and finally that the degeneracy locus $D(\unicode[STIX]{x1D6F1})$ deforms locally trivially under deformations of $(X,\unicode[STIX]{x1D6F1})$.

Let C C be a smooth projective curve of genus g ≥ 3 g\geq 3 and let η \eta be an odd theta characteristic on it such that h 0 ( C , η ) = 1 h^0(C,\eta ) = 1 . Pick a point p p from the support of η \eta and consider the one-dimensional linear system | η + p | |\eta + p| . In general this linear system is base-point free and all its ramification points are simple. The locus in the moduli space of odd spin curves is studied where the linear system | η + p | |\eta + p| fails to have this general behavior. This locus is stratified with respect to multiplicities of degeneracies; these strata are called degeneracy schemes and their geometry is explored. Conormal spaces to these schemes are described in intrinsic terms and some consequences of this are presented.

Vanishing eigenvalues of a gyroscopic system are always repeated and, as a result of this degeneracy, their eigenfunctions represent a combination of constant displacements with zero velocity and the displacements derived from constant, nonzero velocity. In a second-order formulation of the equations of motion, the assumption of harmonic vibration is not sufficiently general to represent this motion as the displacements derived from constant, nonzero velocity are not included. In a first order formulation, however, the assumption of harmonic vibration is sufficient. Solvability criteria are required to determine the complete form of such eigenfunctions and in particular whether or not their velocities are identically zero. A conjecture for gyroscopic systems is proposed that predicts whether the eigenvalue locus is imaginary or complex in the neighborhood of a vanishing eigenvalue. If the velocities of all eigenfunctions with vanishing eigenvalues are identically zero, the eigenvalues are imaginary; if any eigenfunction exists whose eigenvalue is zero but whose velocity is nonzero, the corresponding eigenvalue locus is complex. The conjecture is shown to be true for many commonly studied gyroscopic systems; no counter examples have yet been found. The conjecture can be used to predict divergence instability in many cases without extensive computation.

Transcription activator-like effectors (TALEs) have been effectively used for targeted genome editing, transcriptional regulation, epigenetic modification, and locus-specific DNA imaging. However, with the advent of the clustered regularly interspaced short palindromic repeat/Cas9 system, an easy-to-use tool with the same function as TALEs, TALEs have recently been abandoned because of their complexity, time consumption, and difficult handling in common labs. Here, we described a degenerated codon-based TALE assembly system for simple, rapid, and efficient TALE assembly. TALE trimers with nonrepetitive DNA sequences were amplified by PCR and sequentially assembled via Gibson assembly. Our method is cost-effective, requires only commonly used basic molecular biology reagents, and takes only 2 h from target sequence analysis to completion. This simple, rapid, and lab-friendly TALE assembly method will restore the value of TALEs in DNA targeting.

La retinitis pigmentària (RP) és la degeneració retinal hereditària més prevalent i una de les causes principals de ceguesa en humans. Des d'un punt de vista clínic es manifesta com a ceguesa nocturna, progressa amb la reducció del camp visual i en estadis avançats condueix a la ceguesa completa. Es caracteritza per la mort apoptòtica de les cèl·lules fotoreceptores de la retina com a conseqüència de l'alteració d'algun dels 32 gens que, fins a dia d'avui, han estat identificats com a gens causals de la malaltia.
L'objectiu principal d'aquest treball de tesi doctoral ha estat la cerca d'un nou gen de retinitis pigmentària autosòmica recessiva en el locus RP26. Aquest locus havia estat definit prèviament, pel nostre grup, en el braç llarg del cromosoma 2, mitjançant una anàlisi de lligament. En aquest treball de tesi, es presenta la caracterització funcional d'un nou gen del locus RP26, el gen ORMDL1, identificat com a pressumpte candidat, i la descripció de la família gènica a què pertany: una nova família de gens que codifiquen proteïnes transmembrana del reticle endoplasmàtic, molt conservades i presents exclusivament en els eucariotes. A partir de l'anàlisi funcional realitzada amb la generació de soques knockout dels gens ORM1 i ORM2 del llevat, es proposa una implicació d'aquestes proteïnes en la resposta del reticle endoplasmàtic a proteïnes malplegades.
En la segona part del treball, s'exposen els resultats de la cerca del gen responsable d'RP del locus RP26. Gràcies a una aproximació que va incloure el refinament dels marges del locus, l'anàlisi de gens candidats i un extens mapatge d'homozigositat, realitzat al llarg d'un interval de cosegregació de 12 Mb, vam definir una regió candidata que contenia 9 gens descrits. Tot ells van ser descartats per seqüenciació com a responsables de la malatia. La cerca in silico de nous gens ens va conduir a la identificació d'un nou gen, que vam anomenar CERKL (ceramide kinase-like) perquè codifica una proteïna similar a ceramida quinasa. La seqüenciació de la regió codificant de CERKL en la família RP26, ens va permetre identificar una mutació puntual (R257X) en l'exó 5 del gen, en homozigosi en els individus afectes. Aquesta mutació produeix el truncament prematur de la proteïna CERKL, al bell mig del pressumpte domini quinàsic. El gen CERKL s'expressa en diversos teixits adults, inclosa la retina, i fetals. L'ortòleg del ratolí s'expressa en la capa de cèl·lules ganglionars i en els fotoreceptors de la retina. La descoberta de CERKL com a gen RP26 vincula per primer cop l'apoptosi característica de la degeneració retinal amb una alteració del metabolisme dels esfingolípids, que ha estat implicat en nombrosos processos de supervivènica i mort cel·lular.
Retinitis Pigmentosa (RP), the main cause of adult blindness, is a genetically heterogeneous disorder characterized by progressive loss of photoreceptor cells through apoptosis. Up to now, 32 genes have been implicated in RP.
The main goal of this PhD thesis has been the search of a novel autosomal recessive RP gene within the RP26 locus. This locus was identified by linkage analysis on 2q31.2-q32.3. As no obvious positional candidates were found among known genes, an expressed sequence tag (EST) database search was undertaken to identify sequences expressed in the retina. Following this approach, we characterized a novel gene within the RP26 locus, ORMDL1. This gene belonged to a eukaryotic gene family that encoded highly conserved endoplasmic reticulum transmembrane proteins.
In the second part of the thesis, we refined the RP26 locus down to 2.5 Mb by homozygosity mapping. After unsuccessful mutational analysis of the nine genes initially reported in this region, a detailed gene search based on expressed-sequence-tag data was undertaken. We finally identified a novel gene encoding a ceramide kinase (CERKL), which encompassed 13 exons. All of the patients from the RP26 family bear a homozygous mutation in exon 5, which generates a premature termination codon. The same mutation was also characterized in another, unrelated, Spanish pedigree with arRP. Human CERKL is expressed in the retina, among other adult and fetal tissues. A more detailed analysis by in situ hybridization on adult murine retina sections shows expression of Cerkl in the ganglion cell layer. Ceramide kinases convert the sphingolipid metabolite ceramide into ceramide-1-phosphate, both key mediators of cellular apoptosis and survival. Ceramide metabolism plays an essential role in the viability of neuronal cells, the membranes of which are particularly rich in sphingolipids. Therefore, CERKL deficiency could shift the relative levels of the signaling sphingolipid metabolites and increase sensitivity of photoreceptor and other retinal cells to apoptotic stimuli. This is the first genetic report suggesting a direct link between retinal neurodegeneration in RP and sphingolipid-mediated apoptosis.

We describe the implementation of a holographic heteroassociative memory and the modeling of the nonlinear dynamics of the system. The system uses thermoplastic plates for storing associative images and a Hughes liquid crystal light valve (LCLV) for image amplification and thresholding. Planar holographic interconnections are used for interconnecting patterns from one layer to another. The problem of degenerate readouts in planar holographic interconnections is analyzed and the technique of using sampling grids for specifying unique interconnections is described. The optical system is arranged as a feedback loop. It locks the recognized input and its associative image as a stable state in the loop. We show that the main factors determining the dynamics of the system are the optical gain and the similarity between input and the stored images. The optical system is equivalent to a two-layer network with feedback. Equations describing the dynamics of the system are derived, including the effects of the square-law detection by the neural plane. A geometric method is introduced which allows us to analyze how the system state evolves and how the parameters influence the evolution.