A computability theoretic equivalent to Vaught's conjecture

We prove that, for every theory $T$ which is given by an ${\mathcal L}_{\omega_1,\omega}$ sentence, $T$ has less than $2^{\aleph_0}$ many countable models if and only if we have that, for every $X\in 2^\omega$ on a cone of Turing degrees, every $X$-hyperarithmetic model of $T$ has an $X$-computable copy. We also find a concrete description, relative to some oracle, of the Turing-degree spectra of all the models of a counterexample to Vaught's conjecture

The spark of synchronization in heterogeneous networks of chaotic maps

We investigate the emergence of synchronization in heterogeneous networks of chaotic maps. Our findings reveal that a small cluster of highly connected maps is responsible for triggering the spark of synchronization. After the spark, the synchronized cluster grows in size and progressively moves to less connected maps, eventually reaching a cluster that may remain synchronized over time. We explore how the shape of the network's degree distribution affects the onset of synchronization and derive an expression based on the network's construction that determines the expected time for a network to synchronize. Understanding how the network structure affects the spark of synchronization is particularly important for the control and design of more robust systems that require some level of coherence between a subset of units for better functioning. Numerical simulations in finite-sized networks are consistent with this analysis

The Complements of Lower Cones of Degrees and the Degree Spectra of Structures

We study Turing degrees a for which there is a countable structure whose degree spectrum is the collection {x : x ≰ a}. In particular, for degrees a from the interval [0′, 0″], such a structure exists if a′ = 0″, and there are no such structures if a″ \u3e 0‴

De Volkswagen a KIA, coreanización y desarrollo sustentable: el caso de Pesquería.

¿Repetimos errores, a pesar de lo que la Historia nos enseña? ¿Podemos amortiguarlo? Estas son las cuestiones iniciales que nos convocan al trabajo. Por nuestra vocación antropológica y de estudios orientales nos interesa especialmente el proceso de establecimiento y desarrollo de un importante proyecto de construcción y puesta en marcha de una planta de la automotriz coreana KIA en el entorno del municipio de Pesquería en el Estado mexicano de Nuevo León, en pleno perímetro metropolitano de su capital, Monterrey.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Influence of the LILRA3 Deletion on Multiple Sclerosis Risk : Original Data and Meta-Analysis

Altres ajuts: Junta de Andalucía (JA)- Fondos Europeos de Desarrollo Regional (FEDER) (grant number CTS2704 to FM).Multiple sclerosis (MS) is a neurodegenerative, autoimmune disease of the central nervous system. Genome-wide association studies (GWAS) have identified over hundred polymorphisms with modest individual effects in MS susceptibility and they have confirmed the main individual effect of the Major Histocompatibility Complex. Additional risk loci with immunologically relevant genes were found significantly overrepresented. Nonetheless, it is accepted that most of the genetic architecture underlying susceptibility to the disease remains to be defined. Candidate association studies of the leukocyte immunoglobulin-like receptor LILRA3 gene in MS have been repeatedly reported with inconsistent results. In an attempt to shed some light on these controversial findings, a combined analysis was performed including the previously published datasets and three newly genotyped cohorts. Both wild-type and deleted LILRA3 alleles were discriminated in a single-tube PCR amplification and the resulting products were visualized by their different electrophoretic mobilities. Overall, this meta-analysis involved 3200 MS patients and 3069 matched healthy controls and it did not evidence significant association of the LILRA3 deletion [carriers of LILRA3 deletion: p = 0.25, OR (95% CI) = 1.07 (0.95-1.19)], even after stratification by gender and the HLA-DRB1*15 : 01 risk allele

Physics-Informed Neural Networks for an optimal counterdiabatic quantum computation

We introduce a novel methodology that leverages the strength of Physics-Informed Neural Networks (PINNs) to address the counterdiabatic (CD) protocol in the optimization of quantum circuits comprised of systems with $N_{Q}$ qubits. The primary objective is to utilize physics-inspired deep learning techniques to accurately solve the time evolution of the different physical observables within the quantum system. To accomplish this objective, we embed the necessary physical information into an underlying neural network to effectively tackle the problem. In particular, we impose the hermiticity condition on all physical observables and make use of the principle of least action, guaranteeing the acquisition of the most appropriate counterdiabatic terms based on the underlying physics. The proposed approach offers a dependable alternative to address the CD driving problem, free from the constraints typically encountered in previous methodologies relying on classical numerical approximations. Our method provides a general framework to obtain optimal results from the physical observables relevant to the problem, including the external parameterization in time known as scheduling function, the gauge potential or operator involving the non-adiabatic terms, as well as the temporal evolution of the energy levels of the system, among others. The main applications of this methodology have been the $\mathrm{H_{2}}$ and $\mathrm{LiH}$ molecules, represented by a 2-qubit and 4-qubit systems employing the STO-3G basis. The presented results demonstrate the successful derivation of a desirable decomposition for the non-adiabatic terms, achieved through a linear combination utilizing Pauli operators. This attribute confers significant advantages to its practical implementation within quantum computing algorithms.Comment: 28 pages, 10 figures, 1 algorithm, 1 tabl