Matemáticas
http://hdl.handle.net/10347/2913
2024-03-29T12:50:53ZDevelopment of an epigenetic age predictor for costal cartilage with a simultaneous somatic tissue differentiation system
http://hdl.handle.net/10347/33226
Development of an epigenetic age predictor for costal cartilage with a simultaneous somatic tissue differentiation system
Freire Aradas, Ana María; Ambroa Conde, Adrián; Casares de Cal, María Ángeles; Gómez Tato, Antonio; Álvarez Dios, José Antonio; Phillips, C.; Branicki, Wojciech
Age prediction from DNA has been a topic of interest in recent years due to the promising results obtained when using epigenetic markers. Since DNA methylation gradually changes across the individual’s lifetime, prediction models have been developed accordingly for age estimation. The tissue-dependence for this biomarker usually necessitates the development of tissue-specific age prediction models, in this way, multiple models for age inference have been constructed for the most commonly encountered forensic tissues (blood, oral mucosa, semen). The analysis of skeletal remains has also been attempted and prediction models for bone have now been reported. Recently, the VISAGE Enhanced Tool was developed for the simultaneous DNA methylation analysis of 8 age-correlated loci using targeted high-throughput sequencing. It has been shown that this method is compatible with epigenetic age estimation models for blood, buccal cells, and bone. Since when dealing with decomposed cadavers or postmortem samples, cartilage samples are also an important biological source, an age prediction model for cartilage has been generated in the present study based on methylation data collected using the VISAGE Enhanced Tool. In this way, we have developed a forensic cartilage age prediction model using a training set composed of 109 samples (19–74 age range) based on DNA methylation levels from three CpGs in FHL2, TRIM59 and KLF14, using multivariate quantile regression which provides a mean absolute error (MAE) of ± 4.41 years. An independent testing set composed of 72 samples (19–75 age range) was also analyzed and provided an MAE of ± 4.26 years. In addition, we demonstrate that the 8 VISAGE markers, comprising EDARADD, TRIM59, ELOVL2, MIR29B2CHG, PDE4C, ASPA, FHL2 and KLF14, can be used as tissue prediction markers which provide reliable blood, buccal cells, bone, and cartilage differentiation using a developed multinomial logistic regression model. A training set composed of 392 samples (n = 87 blood, n = 86 buccal cells, n = 110 bone and n = 109 cartilage) was used for building the model (correct classifications: 98.72%, sensitivity: 0.988, specificity: 0.996) and validation was performed using a testing set composed of 192 samples (n = 38 blood, n = 36 buccal cells, n = 46 bone and n = 72 cartilage) showing similar predictive success to the training set (correct classifications: 97.4%, sensitivity: 0.968, specificity: 0.991). By developing both a new cartilage age model and a tissue differentiation model, our study significantly expands the use of the VISAGE Enhanced Tool while increasing the amount of DNA methylation-based information obtained from a single sample and a single forensic laboratory analysis. Both models have been placed in the open-access Snipper forensic classification website.
2023-01-01T00:00:00ZOn the derivations of the quadratic Jordan product in the space of rectangular matrices
http://hdl.handle.net/10347/33223
On the derivations of the quadratic Jordan product in the space of rectangular matrices
Isidro Gómez, José María
Let Mn,m be a rectangular finite dimensional Cartan factor, i.e. the space L(Cn, Cm) with 1 ≤n ≤m, and let δ:Mn,m→ Mn,m be a quadratic Jordan derivation of Mn,m, i.e., a map (neither linearity nor continuity of δ is assumed) that satisfies the functional equation δ{ABA}={δ(A)BA}+{Aδ(B)A}+{ABδ(A)}, (A,B ∈ Mn,m), where (A, B, C) →{A B, C} := 1/2 (AB∗C+CB∗A) stands for the Jordan triple product in Mn,m. We prove that then δ automatically is a continuous complex linear map on Mn,m. More precisely we show that δ admits a representation of the form δ(A) =UA +AV, (A ∈ Mn,m), for a suitable pair U, V of square skew symmetric matrices with complex entries U ∈ Mn,n and V ∈ Mm,m.
2023-01-01T00:00:00ZOn the derivations of the quadratic Jordan product in classical finite dimensional Cartan factors
http://hdl.handle.net/10347/33222
On the derivations of the quadratic Jordan product in classical finite dimensional Cartan factors
Isidro Gómez, José María
Let R be a unital *-ring which contains a complex unit and in which the unit can be halved. Conmutativity of R is not assumed. Let Mn and Sn be the Jordan *-triples of the square n × n matrices (respectively, n × n symmetric matrices) (n ≥2) with entries in R. The additive groups Der(Mn) and Der(Sn) of the quadratic Jordan derivations of Mn (respectively, Sn) are described in terms of Der(R), the group of quadratic Jordan derivations of R. Particular attention is paid to the case R = C.
2023-01-01T00:00:00ZIsoparametric hypersurfaces in symmetric spaces of non-compact type and higher rank
http://hdl.handle.net/10347/33000
Isoparametric hypersurfaces in symmetric spaces of non-compact type and higher rank
Domínguez Vázquez, Miguel; Sanmartín López, Víctor
We construct inhomogeneous isoparametric families of hypersurfaces with non-austere focal set on each symmetric space of non-compact type and rank ≥3. If the rank is ≥4, there are infinitely many such examples. Our construction yields the first examples of isoparametric families on any Riemannian manifold known to have a non-austere focal set. They can be obtained from a new general extension method of submanifolds from Euclidean spaces to symmetric spaces of non-compact type. This method preserves the mean curvature and isoparametricity, among other geometric properties
2024-01-01T00:00:00Z