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In this paper we explore the capabilities of MoS2 and WS2 2D monolayers to produce radiation in the terahertz range by generation of high-order harmonics. This phenomenon, which is a result of the non-linear response of the electronic carrier population to the applied electric field, is studied by using a particle ensemble stochastic simulation approach based on the Monte Carlo method. The power of the produced harmonic signals is studied against the electric field amplitude, the external temperature, and the frequency of the excitation. Additionally, the stochastic nature of the simulation tool enables to discern the purely discrete harmonic signal from the background spectral noise that comes from the intrinsic carrier velocity fluctuations in the diffusive regime, permitting to set bandwidth thresholds for harmonic extraction. It was found that both TMDs showed similar thresholds bandwidths when compared to III-V semiconductor at low temperatures, while WS2 would be by far a better choice, over MoS2, for exploitation of the 7th and 9th harmonic generation., Comment: 6 pages, 5 figures. Published in Appl. Phys. Lett., 119, 012101 (2021)

The effect of degeneracy and the impact of free-carrier screening on a low-field mobility and a high-field drift velocity in MoS2 and WS2 are explored using an in-house ensemble Monte Carlo simulator. Electron low field mobility increases to 8400 cm2/Vs for MoS2 and to 12040 cm2/Vs for WS2 when temperature decreases to 77 K and carrier concentration is around 5e12 cm-2. In the case of holes, best mobility values were 9320 cm2/Vs and 13290 cm2 per Vs, reached at 77 K, while at room temperature these fall to 80 cm2/Vs and 150 cm2/Vs for MoS2 and WS2, respectively. The carrier screening effect plays a major role at low fields, and low and intermediate temperatures, where a combination of large occupancy of primary valleys and carrier-phonon interactions dominated by relatively low energy exchange processes results in an enhanced screening of intrinsic scattering. For electrons, degeneracy yields to transport in secondary valleys, which plays an important role in the decrease of the low field mobility at high concentrations and/or at room temperature. The high-field drift velocity is not much affected by carrier screening because of an increased carrier scattering with surface optical polar phonons, favouring larger phonon wavevector interactions with small dielectric function values., Comment: 10 pages, 5 figures. Published in 2D Materials, 14, 025011 (2023)

Epistasis can be defined as the statistical interaction of genes during the expression of a phenotype. It is believed that it plays a fundamental role in gene expression, as individual genetic variants have reported a very small increase in disease risk in previous Genome-Wide Association Studies. The most successful approach to epistasis detection is the exhaustive method, although its exponential time complexity requires a highly parallel implementation in order to be used. This work presents Fiuncho, a program that exploits all levels of parallelism present in \textit{x86\_64} CPU clusters in order to mitigate the complexity of this approach. It supports epistasis interactions of any order, and when compared with other exhaustive methods, it is on average 358, 7 and 3 times faster than MDR, MPI3SNP and BitEpi, respectively., Comment: Submitted to The Journal of Supercomputing. Source code available at https://github.com/UDC-GAC/fiuncho

We review the relation between the classical formulas of the pre-Schwarzian and Schwarzian derivatives of locally univalent analytic functions and the derivatives of the generating functions of the methods due to Newton and Halley, respectively, for approximating zeros. We extend these relations to the cases when the functions considered are harmonic.

Epistasis is a phenomenon in which a phenotype outcome is determined by the interaction of genetic variation at two or more loci and it cannot be attributed to the additive combination of effects corresponding to the individual loci. Although it has been more than 100 years since William Bateson introduced this concept, it still is a topic under active research. Locating epistatic interactions is a computationally expensive challenge that involves analyzing an exponentially growing number of combinations. Authors in this field have resorted to a multitude of hardware architectures in order to speed up the search, but little to no attention has been paid to the vector instructions that current CPUs include in their instruction sets. This work extends an existing third-order exhaustive algorithm to support the search of epistasis interactions of any order and discusses multiple SIMD implementations of the different functions that compose the search using Intel AVX Intrinsics. Results using the GCC and the Intel compiler show that the 512-bit explicit vector implementation proposed here performs the best out of all of the other implementations evaluated. The proposed 512-bit vectorization accelerates the original implementation of the algorithm by an average factor of 7 and 12, for GCC and the Intel Compiler, respectively, in the scenarios tested., Comment: Submitted to Future Generation Computer Systems. Codes used are available at https://github.com/UDC-GAC/fiuncho

We provide two new formulas for quasiconformal extension to $\overline{\mathbb{C}}$ for harmonic mappings defined in the unit disk and having sufficiently small Schwarzian derivative. Both are generalizations of the Ahlfors-Weill extension for holomorphic functions., Comment: 14 pages

We obtain a necessary and sufficient condition for a weighted composition operator to be co-isometric on a general weighted Hardy space of analytic functions in the unit disk whose reproducing kernel has the usual natural form. This turns out to be equivalent to the property of being unitary. The result reveals a dichotomy identifying a specific family of weighted Hardy spaces as the only ones that support non-trivial operators of this kind., Comment: The proof of Proposition 1 has been corrected and reorganized. Various misprints have been corrected and various other minor changes have been made

There are not too many known explicit solutions to the 2-dimensional incompressible Euler equations in Lagrangian coordinates. Special mention must be made of the well-known ones due Gerstner and Kirchhoff, which were already discovered in the 19th century. These two classical solutions share a common characteristic, namely, the dependence of the coordinates from the initial location is determined by a harmonic map, as recognized by Abrashkin and Yakubovich, who more recently -- in the 1980s -- obtained new explicit solutions with a similar feature. We present a more general method for constructing new explicit solutions in Lagrangian coordinates which contain as special cases all previously known ones. This new approach shows that in fact "harmonic labelings" are special cases of a much larger family. In the classical solutions, the matrix Lie groups were essential in describing the time evolution. We see that also the geodesics in these groups are important.

It is well-known that two locally univalent analytic functions $\varphi$ and $\psi$ have equal Schwarzian derivative if and only if there exists a non-constant M\"obius transformation $T$ such that $\varphi=T\circ \psi$. In this paper, we identify completely the relationship between two locally univalent harmonic mappings with equal (harmonic) Schwarzian derivative., Comment: 28 pages

Brannan showed that a normalized univalent polynomial of the form $P(z)=z+a_2 z^2+\ldots + a_{n-1}z^{n-1}+\frac{z^n}{n}$ is starlike if and only if $a_2=\ldots=a_{n-1}=0$. We give a new and simple proof of his result, showing further that it is also equivalent to the membership of $P$ in the Noshiro-Warschawski class of univalent functions whose derivative has positive real part in the disk. Both proofs are based on the Fej\'er lemma for trigonometric polynomials with positive real part., Comment: 6 pages. In the last submission two misprints have been corrected

The quality of graphene in nanodevices has increased hugely thanks to the use of hexagonal boron nitride as a supporting layer. This paper studies to which extent hBN together with channel length scaling can be exploited in graphene field effect transistors (GFETs) to get a competitive radio frequency (RF) performance. Carrier mobility and saturation velocity were obtained from an ensemble Monte Carlo simulator that accounted for the relevant scattering mechanisms (intrinsic phonons, scattering with impurities and defects, etc.). This information is fed into a self consistent simulator, which solves the drift diffusion equation coupled with the two dimensional Poisson's equation to take full account of short channel effects. Simulated GFET characteristics were benchmarked against experimental data from our fabricated devices. Our simulations show that scalability is supposed to bring to RF performance an improvement that is, however, highly limited by instability. Despite the possibility of a lower performance, a careful choice of the bias point can avoid instability. Nevertheless, maximum oscillation frequencies are still achievable in the THz region for channel lengths of a few hundreds of nanometers., Comment: 29 pages, 7 figures, 1 table, Supplementary Information (10 pages) Funded by: 1 Micronova Nanofabrication Centre 2 European Union's Horizon 2020 (696656) 3 MINECO (TEC2013-42622-R, TEC2015-67462-C2-1-R, TEC2016-80839-P, MINECO/FEDER, FJCI-2014-19643) 4 MECD (CAS16/00043) 5 Generalitat de Catalunya (2014 SGR 384)

We consider harmonic maps on simply connected Riemann surfaces into the group $\mathrm{U}(n)$ of unitary matrices of order $n$. It is known that a harmonic map with an associated algebraic extended solution can be deformed into a new harmonic map that has an $S^1$-invariant associated extended solution. We study this deformation in detail and show that the corresponding unitons are smooth functions of the deformation parameter and real analytic along any line through the origin., Comment: 9 pages

In 1984, Gehring and Pommerenke proved that if the Schwarzian derivative $S(f)$ of a locally univalent analytic function $f$ in the unit disk satisfies that $\limsup_{|z|\to 1} |S(f)(z)| (1-|z|^2)^2 < 2$, then there exists a positive integer $N$ such that $f$ takes every value at most $N$ times. Recently, Becker and Pommerenke have shown that the same result holds in those cases when the function $f$ satisfies that $\limsup_{|z|\to 1} |f"(z)/f'(z)|\, (1-|z|^2)< 1$. In this paper, we generalize these two criteria for bounded valence of analytic functions to the cases when $f$ is merely harmonic., Comment: 10 pages

We characterize in various ways the weighted composition transformations which preserve the class ${\mathcal P}$ of normalized analytic functions in the disk with positive real part. We analyze the meaning of the criteria obtained for various special cases of symbols and identify the fixed points of such transformations., Comment: 16 pages, 1 figure. A new comment and one minor correction were included in this version

We study, by means of a Monte Carlo simulator, the hot phonon effect on the relaxation dynamics in photoexcited graphene and its quantitative impact as compared to considering an equilibrium phonon distribution. Our multi-particle approach indicates that neglecting the hot phonon effect significantly underestimates the relaxation times in photoexcited graphene. The hot phonon effect is more important for a higher energy of the excitation pulse and photocarrier densities between $1$ and $3\times 10^{12} \mathrm{~cm}^{-2}$. Acoustic intervalley phonons play a non-negligible role, and emitted phonons with wavelengths limited up by a maximum (determined by the carrier concentration) induce a slower carrier cooling rate. Intrinsic phonon heating is damped in graphene on a substrate due to additional cooling pathways, with the hot phonon effect showing a strong inverse dependence with the carrier density., Comment: 12 pages, 5 figures

Background: The increasing volume and variety of genotypic and phenotypic data is a major defining characteristic of modern biomedical sciences. At the same time, the limitations in technology for generating data and the inherently stochastic nature of biomolecular events have led to the discrepancy between the volume of data and the amount of knowledge gleaned from it. A major bottleneck in our ability to understand the molecular underpinnings of life is the assignment of function to biological macromolecules, especially proteins. While molecular experiments provide the most reliable annotation of proteins, their relatively low throughput and restricted purview have led to an increasing role for computational function prediction. However, accurately assessing methods for protein function prediction and tracking progress in the field remain challenging. Methodology: We have conducted the second Critical Assessment of Functional Annotation (CAFA), a timed challenge to assess computational methods that automatically assign protein function. One hundred twenty-six methods from 56 research groups were evaluated for their ability to predict biological functions using the Gene Ontology and gene-disease associations using the Human Phenotype Ontology on a set of 3,681 proteins from 18 species. CAFA2 featured significantly expanded analysis compared with CAFA1, with regards to data set size, variety, and assessment metrics. To review progress in the field, the analysis also compared the best methods participating in CAFA1 to those of CAFA2. Conclusions: The top performing methods in CAFA2 outperformed the best methods from CAFA1, demonstrating that computational function prediction is improving. This increased accuracy can be attributed to the combined effect of the growing number of experimental annotations and improved methods for function prediction., Comment: Submitted to Genome Biology