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The evolution, as functions of the "ticking time" $\ell =0,1,2,...$, of the solutions of the system of $N$ quadratic recursions \begin{eqnarray*} x_{n}\left( \ell +1\right) =c_{n}+\sum_{m=1}^{N}\left[ C_{nm}x_{m}\left( \ell \right) \right] +\sum_{m=1}^{N}\left\{ d_{nm}\left[ x_{m}\left( \ell \right) \right] ^{2}\right\} +\sum_{m_{1}>m_{2}=1}^{N}\left[ D_{nm_{1}m_{2}}x_{m_{1}}\left( \ell \right) x_{m_{2}}\left( \ell \right) \right] ~,~~~n=1,2,...,N~, && \end{eqnarray*} featuring $N+N^{2}+N^{2}+N\left( N-1\right) N/2=N\left( N+1\right) \left( N+2\right) /2$ ($\ell $-independent) coefficients $c_{n}$, $C_{nm}$, $d_{nm}$ and $D_{nm_{1}m_{2}}$, may be easily ascertained, if these coefficients are given, in terms of $N+N^{2}=N\left( N+1\right) $ a priori arbitrary parameters $a_{n}$ and $b_{nm}$, by $N\left( N+1\right) \left( N+2\right) /2$ explicit formulas provided in this paper. Here $N$ is an arbitrary positive integer.

A kinetic model for the dynamics of collisionless spin neutral particles in a spacetime with torsion is proposed. The fundamental matter field is the kinetic density $f(x,u,s)$ of particles with four-velocity $u$ and four-spin $s$. The stress-energy tensor and the spin current of the particles distribution are defined as suitable integral moments of $f$ in the $(u,s)$ variables. By requiring compatibility with the contracted Bianchi identity in Einstein-Cartan theory, we derive a transport equation on the kinetic density $f$ that generalizes the well-known Vlasov equation for spinless particles. The total number of particles in the new model is not conserved. To restore this important property we assume the existence in spacetime of a second species of particles with the same mass and spin magnitude. The Vlasov equation on the kinetic density $\overline{f}$ of the new particles is derived by requiring that the sum of total numbers of particles of the two species should be conserved., Comment: 26 pages, no figures

In this paper a procedure is described which allows to identify new systems of nonlinear recursions whose solutions are controllable and which may be asymptotically isochronous as functions of the independent variable (considered a ticking time).

In this paper we firstly review how to \textit{explicitly} solve a system of $3$ \textit{first-order linear recursions }and outline the main properties of these solutions. Next, via a change of variables, we identify a class of systems of $3$ \textit{first-order nonlinear recursions} which also are \textit{explicitly solvable}. These systems might be of interest for practitioners in \textit{applied} sciences: they allow a complete display of their solutions, which may feature interesting behaviors, for instance be \textit{completely periodic} ("isochronous systems", if the independent variable $n=0,1,2,3...$is considered a \textit{ticking time}), or feature this property \textit{only asymptotically} (as\textit{\ }$n\rightarrow \infty $).

In this paper a class of simple, but nonlinear, systems of recursions involving $2$ dependent variables $x_{j}\left( n\right) $ is identified, such that the solutions of their initial-values problems -- with arbitrary initial data $x_{j}\left( 0\right) $ -- may be explicitly obtained.

Bottom-up on-surface synthesis enables the fabrication of carbon nanostructures with atomic precision. Good examples are graphene nanoribbons (GNRs), 1D conjugated polymers, and nanoporous graphenes (NPGs), which are gathering increasing attention for future carbon nanoelectronics. A key step is the ability to manipulate current flow within these nanomaterials. Destructive quantum interference (QI), long studied in the field of single-molecule electronics, has been proposed as the most effective way to achieve such control with molecular-scale precision. However, for practical applications, it is essential that such QI-engineering remains effective near or above room temperature. To assess this important point, here we combine large-scale molecular dynamics simulations and quantum transport calculations and focus our study on NPGs formed as arrays of laterally bonded GNRs. By considering various NPGs with different inter-GNR chemical connections we disentangle the different factors determining electronic transport in these carbon nanomaterials at 300 K. Our findings unequivocally demonstrate that QI survives at room temperature, with thermal vibrations weakly restricting current flow along GNRs while completely blocking transport across GNRs. Our results thus pave the way towards the future realization of QI-engineered carbon nanocircuitry operating at room temperature, which is a fundamental step towards carbon-based nanoelectronics and quantum technologies., Comment: 21 pages, 4 figures

Some simple nonlinear recursions which can be completely managed are identified and the behaviour of all their solutions is ascertained.

In the last years, artificial intelligence (AI) in clinical decision support systems (CDSS) played a key role in harnessing machine learning and deep learning architectures. Despite their promising capabilities, the lack of transparency and explainability of AI models poses significant challenges, particularly in medical contexts where reliability is a mandatory aspect. Achieving transparency without compromising predictive accuracy remains a key challenge. This paper presents a novel method, namely Rad4XCNN, to enhance the predictive power of CNN-derived features with the interpretability inherent in radiomic features. Rad4XCNN diverges from conventional methods based on saliency map, by associating intelligible meaning to CNN-derived features by means of Radiomics, offering new perspectives on explanation methods beyond visualization maps. Using a breast cancer classification task as a case study, we evaluated Rad4XCNN on ultrasound imaging datasets, including an online dataset and two in-house datasets for internal and external validation. Some key results are: i) CNN-derived features guarantee more robust accuracy when compared against ViT-derived and radiomic features; ii) conventional visualization map methods for explanation present several pitfalls; iii) Rad4XCNN does not sacrifice model accuracy for their explainability; iv) Rad4XCNN provides global explanation insights enabling the physician to analyze the model outputs and findings. In addition, we highlight the importance of integrating interpretability into AI models for enhanced trust and adoption in clinical practice, emphasizing how our method can mitigate some concerns related to explainable AI methods.

Ultraviolet nanosecond laser annealing (UV-NLA) proves to be an important technique, particularly when tightly controlled heating and melting are necessary. In the realm of semiconductor technologies, the significance of nanosecond laser annealing (NLA) grows in tandem with the escalating intricacy of integration schemes in nano-scaled devices. Silicon-germanium alloys have been studied for decades for their compatibility with silicon devices. Indeed, they enable the manipulation of properties like strain, carrier mobilities and bandgap. In this framework, they can for instance boost the performances of p-type MOSFETs but also enable near infra-red absorption and emission for applications in photo-detection and photonics. Laser melting on such type of layers, however results, up to now, in the development of extended defects and poor control over layer morphology and homogeneity. In our study, we investigate the laser melting of ~700 nm thick relaxed silicon-germanium samples coated with SiO2 nano-arrays, observing the resulting material to maintain an unaltered lattice. We found the geometrical parameters of the silicon oxide having an impact on the thermal budget samples see, influencing melt threshold, melt depth and germanium distribution.

The properties of liquid Si-Ge binary systems at melting conditions deviate from those expected by the ideal alloy approximation. Particularly, a non-linear dependence of the dielectric functions occurs with the reflectivity of liquid Si-Ge reaching a maximum at 50\% Ge content, being 10\% higher than in pure Si or Ge. Using \textit{ab initio} methodologies, we modelled liquefied Si-Ge alloys, unveiling very high coordination numbers and poor symmetry in the first coordination shell with respect to Si and Ge, related to different bonding properties. We simulated optical functions, quantitatively replicating the aforementioned reflectivity trend and we highlighted a direct relationship between atomic structure and optical properties, indicating that the unusual optics arises from Si-Ge higher local coordination characterized by low symmetry. We forecast further implications for the overall class of these alloys. These findings expand our comprehension of liquefied semiconductors and are essential for implementing controlled laser melting procedures to highly dope these materials for advanced transistors, superconductors, sensors and plasmonic devices.

Controlling ultrafast material transformations with atomic precision is essential for future nanotechnology. Pulsed laser annealing (LA), inducing extremely rapid and localized phase transitions, is a powerful way to achieve this, but it requires careful optimization together with the appropriate system design. We present a multiscale LA computational framework able to simulate atom-by-atom the highly out-of-equilibrium kinetics of a material as it interacts with the laser, including effects of structural disorder. By seamlessly coupling a macroscale continuum solver to a nanoscale super-lattice Kinetic Monte Carlo code, this method overcomes the limits of state-of-the-art continuum-based tools. We exploit it to investigate nontrivial changes in composition, morphology and quality of laser-annealed SiGe alloys. Validations against experiments and phase-field simulations, as well as advanced applications to strained, defected, nanostructured and confined SiGe are presented, highlighting the importance of a multiscale atomistic-continuum approach. Current applicability and potential generalization routes are finally discussed.