arXiv subjects
Publications and source records attributed to João Lourenço.
We construct lepton flavour models based on two $A_4$ modular symmetries. The two $A_4$ are broken by a bi-triplet field to the diagonal $A_4$ subgroup, resulting in an effective modular $A_4$ flavour symmetry with two moduli. We employ these moduli as stabilisers, that preserve distinct residual symmetries, enabling us to obtain Tri-Maximal 2 (TM2) mixing with a minimal field content (without flavons).
In this work, we introduce an optoelectronic spiking artificial neuron capable of operating at ultrafast rates ($\approx$ 100 ps/optical spike) and with low energy consumption ($<$ pJ/spike). The proposed system combines an excitable resonant tunnelling diode (RTD) element exhibiting negative differential conductance, coupled to a nanoscale light source (forming a master node) or a photodetector (forming a receiver node). We study numerically the spiking dynamical responses and information propagation functionality of an interconnected master-receiver RTD node system. Using the key functionality of pulse thresholding and integration, we utilize a single node to classify sequential pulse patterns and perform convolutional functionality for image feature (edge) recognition. We also demonstrate an optically-interconnected spiking neural network model for processing of spatiotemporal data at over 10 Gbps with high inference accuracy. Finally, we demonstrate an off-chip supervised learning approach utilizing spike-timing dependent plasticity for the RTD-enabled photonic spiking neural network. These results demonstrate the potential and viability of RTD spiking nodes for low footprint, low energy, high-speed optoelectronic realization of neuromorphic hardware.
We extend the work of Pappas-Rapoport-Zhu on twisted affine Grassmannians to wildly ramified, quasi-split, and residually split groups, assuming the maximal torus is induced. This relies on the construction, inspired by Tits, of certain smooth, affine, and connected $\mathbb{Z}[t]$-groups of parahoric type, which should be regarded as $\mathbb{Z}$-families of parahoric group schemes, and naturally extends a similar construction in the above articles after inverting $e$. The resulting $\mathbb{F}_p(t)$-groups are pseudo-reductive possibly non-standard in the sense of Conrad--Gabber--Prasad, and their $\mathbb{F}_p[[t]]$-models are parahoric in our generalized sense. We study their affine Grassmannians, establishing normality of Schubert varieties and Zhu's coherence theorem.
We extend (scheme-theoretic) Bruhat-Tits theory to quasi-reductive groups i.e. with trivial split unipotent radical over discretely valued henselian non-archimedean fields $K$, whose ring of integers is excellent and residue field is perfect, building on Bruhat-Tits I et II and the classification of pseudo-reductive groups by Conrad-Gabber-Prasad. The buildings had been constructed previously by Solleveld in a different manner, but they ultimately coincide with ours. We were motivated by the geometry of affine Grassmannians and give some applications at the end (compare also with previously submitted work arXiv:1912.11918).
--- Portuguese version As falhas de software estão com frequência associadas a acidentes com graves consequências económicas e/ou humanas, pelo que se torna imperioso investir na validação do software, nomeadamente daquele que é crítico. Este artigo endereça a temática da qualidade do software através de uma análise comparativa da usabilidade e eficácia de quatro ferramentas de análise estática de programas em C/C++. Este estudo permitiu compreender o grande potencial e o elevado impacto que as ferramentas de análise estática podem ter na validação e verificação de software. Como resultado complementar, foram identificados novos erros em programas de código aberto e com elevada popularidade, que foram reportados. --- English version Software bugs are frequently associated with accidents with serious economical and/or human consequences, being thus imperative the investment in the validation of software, namely of the critical one. This article addresses the topic of software quality by making a comparative analysis of the usability and efficiency of four static analysis tools for C/C++ programs. This study allow to understand the big potential and high impact that these tools may have in the validation and verification of software. As a complementary result, we identified new errors in very popular open source projects, which have been reported.