Search

Programmable integrated photonics has emerged as a powerful platform for implementing diverse optical functions on a single chip through software-driven reconfiguration. At the core of these processors, photonic waveguide meshes enable flexible light routing and manipulation. However, recirculating waveguide meshes are fundamentally limited by the fixed dimensions of their unit cells, constraining their spectral and temporal resolution. These limitations hinder broadband signal processing and high-precision delay-line applications. Here, we introduce the concept of non-uniform programmable waveguide meshes by incorporating defect cells into an otherwise uniform hexagonal architecture. These defect cells preserve an external hexagonal perimeter for seamless integration while embedding smaller internal subcells that modify the spectral response via the Vernier effect. By coupling cells with different optical path lengths, we achieve a free spectral range multiplication of up to tenfold, reaching 133 GHz-surpassing the capabilities of conventional silicon ring resonators. Additionally, we demonstrate a dramatic reduction in sampling times from 75 ps to 7.5 ps, enabling ultra-fast optical signal processing and high-precision delay tuning. This approach unlocks new degrees of freedom in programmable photonic circuits, offering enhanced spectral and temporal tunability. Beyond broadband signal processing, it paves the way for advanced applications in topological photonics, quantum information processing, and high-speed optical computing.

We show that for every g greater or equal than 5, the locus of Prym varieties in the moduli space of principally polarized abelian varieties of dimension g-1 that possess a pseudoreflection of geometric origin is the union of three different non-empty explicit irreducible families. This is in stark contrast to the loci of Jacobian varieties that possess a pseudoreflection of geometric origin, which is empty for any genus greater than 3. In g=6, a distinguished example of Prym varieties with a pseudoreflection is given by intermediate Jacobians of cubic threefolds that possess an Eckardt point., Comment: 17 pages, comments are welcome

An analogue of Kakutani's representation theorem for Banach lattice algebras is provided. We characterize Banach lattice algebras that embed as a closed sublattice-algebra of $C(K)$ precisely as those with a positive approximate identity $(e_\gamma)$ such that $x^{*}(e_\gamma)\to \|x^{*}\|$ for every positive functional $x^{*}$. We also show that every Banach lattice algebra with identity other than $C(K)$ admits different product operations which are compatible with the order and the algebraic identity. This complements the classical result, due to Martignon, that on $C(K)$ spaces pointwise multiplication is the unique compatible product.

The present research aims to enhance the efficiency of a DTU-10MW Horizontal Axis Wind Turbine (HAWT) via Active Flow Control (AFC) implementation and using Synthetic Jets (SJ). In the initial part of the study the flow around two airfoil sections cut along the wing turbine blade and for a wind speed of 10m/s is simulated using CFD-2D-RANS-K{\omega}-SST turbulence model, in order to obtain the time averaged boundary layer separation point and the associated vortex shedding frequency. This information is used, on a second stage of the paper, to set, in one of these two airfoils where the boundary layer is having an early separation, two of the AFC parameters while optimizing the remaining three. The optimization is performed employing a parametric analysis and demonstrates that a considerable WT power increase can be obtained when managing to reattach the former separated boundary layer. This is further clarified thanks to the energy assessment presented in the final part of the paper. Although the AFC optimization needs to be extended for the rest of the blade sections, the procedure outlined in the present research clarifies the different steps to be followed to optimize the performance of any HAWT under any operating conditions. The Reynolds numbers associated to the respective airfoil sections analyzed in the present manuscript are Re = 14.088 e6 and Re = 14.877 e6, the characteristic length being the corresponding chord length for each airfoil., Comment: 35 pages, 17 figures

The Prym map $\mathcal{P}_6$ in genus 6 is dominant and generically finite of degree 27. When restricted to the divisor of curves with an odd semicanonical pencil $\mathcal{T}_6^o$, it is still generically finite, but of degree strictly smaller. In this paper, we prove that $\mathcal{P}_6$ restricted to $\mathcal{T}_6^o$ is birational and that the monodromy group over the image of $\mathcal{T}_6^o$ is the Weyl group $WD_5$. Thus, there are two other irreducible divisors in the moduli space of Prym curves $\mathcal{R}_6$ and the degree of $\mathcal{P}_6$ restricted to them is 10 and 16. Moreover, we study the geometry of the divisor where $\mathcal{P}_6$ has degree 10., Comment: 16 pages, comments are welcome

The growth of quantum technologies is attracting the interest of many students eager to learn concepts such as quantum entanglement or quantum superposition. However, the non-intuitive nature of these concepts poses a challenge to understanding them. Here, we present an entangled photon system which can perform a Bell test, i.e. the CHSH inequality, and can obtain the complete tomography of the two-photon state. The proposed setup is versatile, cost-effective and allows for multiple classroom operating modes. We present two variants, both facilitating the measurement of Bell inequalities and quantum state tomography. Experimental results showcase successful manipulation of the quantum state of the photons, achieving high-fidelity entangled states and significant violations of Bell's inequalities. Our setup's simplicity and affordability enhances accessibility for less specialized laboratories, allowing students to familiarize themselves with quantum physics concepts.

Motivated by recent work about band projections on spaces of regular operators over a Banach lattice, given a Banach lattice algebra $A$, we will say an element $a \in A_+$ is a band projection if the multiplication operator $L_aR_a\in \mathcal L_r(A)$ is a band projection. Our aim in this note is to explore the relations between this and the notion of order idempotent (those elements $a$ in a Banach lattice algebra $A$ with identity $e$ such that $0\leq a\leq e$ and $a^2=a$). We also revisit the properties of the ideal generated by the identity on a Banach lattice algebra, motivated by those of the centre of a Banach lattice.

We introduce inner band projections in the space of regular operators on a Dedekind complete Banach lattice and study some structural properties of this class. In particular, we provide a new characterization of atomic order continuous Banach lattices as those for which all band projections in the corresponding space of regular operators are inner. We also characterize the multiplication operators $L_AR_B$ which are band projections precisely as those with $A,B$ being band projections up to a scalar multiple.

The newest generation of radio telescopes are able to survey large areas with high sensitivity and cadence, producing data volumes that require new methods to better understand the transient sky. Here we describe the results from the first citizen science project dedicated to commensal radio transients, using data from the MeerKAT telescope with weekly cadence. Bursts from Space: MeerKAT was launched late in 2021 and received ~89000 classifications from over 1000 volunteers in 3 months. Our volunteers discovered 142 new variable sources which, along with the known transients in our fields, allowed us to estimate that at least 2.1 per cent of radio sources are varying at 1.28 GHz at the sampled cadence and sensitivity, in line with previous work. We provide the full catalogue of these sources, the largest of candidate radio variables to date. Transient sources found with archival counterparts include a pulsar (B1845-01) and an OH maser star (OH 30.1-0.7), in addition to the recovery of known stellar flares and X-ray binary jets in our observations. Data from the MeerLICHT optical telescope, along with estimates of long time-scale variability induced by scintillation, imply that the majority of the new variables are active galactic nuclei. This tells us that citizen scientists can discover phenomena varying on time-scales from weeks to several years. The success both in terms of volunteer engagement and scientific merit warrants the continued development of the project, whilst we use the classifications from volunteers to develop machine learning techniques for finding transients., Comment: Accepted to MNRAS, 14 pages + an appendix containing our main data table

Latent Class Choice Models (LCCM) are extensions of discrete choice models (DCMs) that capture unobserved heterogeneity in the choice process by segmenting the population based on the assumption of preference similarities. We present a method of efficiently incorporating attitudinal indicators in the specification of LCCM, by introducing Artificial Neural Networks (ANN) to formulate latent variables constructs. This formulation overcomes structural equations in its capability of exploring the relationship between the attitudinal indicators and the decision choice, given the Machine Learning (ML) flexibility and power in capturing unobserved and complex behavioural features, such as attitudes and beliefs. All of this while still maintaining the consistency of the theoretical assumptions presented in the Generalized Random Utility model and the interpretability of the estimated parameters. We test our proposed framework for estimating a Car-Sharing (CS) service subscription choice with stated preference data from Copenhagen, Denmark. The results show that our proposed approach provides a complete and realistic segmentation, which helps design better policies., Comment: 25 pages, 8 figures

The Schrodinger equation is one of the most important equations in physics and chemistry and can be solved in the simplest cases by computer numerical methods. Since the beginning of the 70s of the last century the computer began to be used to solve this equation in elementary quantum systems, e.g. and in the most complex case a hydrogen-like system. Obtaining the solution means finding the wave function, which allows predicting the physical and chemical properties of the quantum system. However, when a quantum system is more complex than a hydrogen-like system then we must be satisfied with an approximate solution of the equation. During the last decade the application of algorithms and principles of quantum computation in disciplines other than physics and chemistry, such as biology and artificial intelligence, has led to the search for alternative techniques with which to obtain approximate solutions of the Schrodinger equation. In this paper, we review and illustrate the application of genetic algorithms, i.e. stochastic optimization procedures inspired by Darwinian evolution, in elementary quantum systems and in quantum models of artificial intelligence. In this last field, we illustrate with two toy models how to solve the Schrodinger equation in an elementary model of a quantum neuron and in the synthesis of quantum circuits controlling the behavior of a Braitenberg vehicle., Comment: preprint

The linearization of a microwave photonic link based on a dual-parallel Mach-Zehnder modulator is theoretically described and experimentally demonstrated. Up to four different radio frequency tones are considered in the study, which allow us to provide a complete mathematical description of all third-order distortion terms that arise at the photodetector. Simulations show that a complete linearization is obtained by properly tuning the DC bias voltages and processing the optical carrier and. As a result, a suppression of 17 dBm is experimentally obtained for the third-order distortion terms, as well as a SDFR improvement of 3 dB. The proposed linearization method enables the simultaneous modulation of four different signals without the need of additional radio frequency components, which is desirable to its implementation in integrated optics and makes it suitable for several applications in microwave photonics.

We investigate the ultimate precision limits for quantum phase estimation in terms of the coherence, $C$, of the probe. For pure states, we give the minimum estimation variance attainable, $V(C)$, and the optimal state, in the asymptotic limit when the probe system size, $n$, is large. We prove that pure states are optimal only if $C$ scales as $n$ with a sufficiently large proportionality factor, and that the rank of the optimal state increases with decreasing $C$, eventually becoming full-rank. We show that the variance exhibits a Heisenberg-like scaling, $V(C) \sim a_n/C^2$, where $a_n$ decreases to $\pi^2/3$ as $n$ increases, leading to a dimension-independent relation., Comment: 10 pages, 5 figures

In the moduli space $\mathcal{R}_g$ of double \'etale covers of curves of a fixed genus $g$, the locus formed by covers of curves with a semicanonical pencil consists of two irreducible divisors $\mathcal T^e_g$ and $\mathcal T^o_g$. We study the Prym map on these divisors, which shows significant differences between them and has a rich geometry in the cases of low genus. In particular, the analysis of $\mathcal T^o_5$ has enumerative consequences for lines on cubic threefolds., Comment: Fixed an inaccuracy in Theorem A and Section 3, and improved the exposition. Final version, to appear in Mathematische Nachrichten

We introduce Chern degree functions for complexes of coherent sheaves on a polarized surface, which encode information given by stability conditions on the boundary of the $(\alpha, \beta)$-plane. We prove that these functions extend to continuous real valued functions and we study their differentiability in terms of stability. For abelian surfaces, Chern degree functions coincide with the cohomological rank functions defined by Jiang-Pareschi. We illustrate in some geometrical situations a general strategy to compute these functions., Comment: Minor changes. Final version, to appear in Commun. Contemp. Math

Bacteria have been a source of inspiration for the design of evolutionary algorithms. At the beginning of the 20th century synthetic biology was born, a discipline whose goal is the design of biological systems that do not exist in nature, for example, programmable synthetic bacteria. In this paper, we introduce as a novelty the designing of evolutionary algorithms where all the steps are conducted by synthetic bacteria. To this end, we designed a genetic algorithm, which we have named BAGA, illustrating its utility solving simple instances of optimization problems such as function optimization, 0/1 knapsack problem, Hamiltonian path problem. The results obtained open the possibility of conceiving evolutionary algorithms inspired by principles, mechanisms and genetic circuits from synthetic biology. In summary, we can conclude that synthetic biology is a source of inspiration either for the design of evolutionary algorithms or for some of their steps, as shown by the results obtained in our simulation experiments.

We prove that the kernel of the evaluation morphism of global sections - namely the syzygy bundle - of a sufficiently ample line bundle on an abelian variety is stable. This settles a conjecture of Ein-Lazarsfeld-Mustopa, in the case of abelian varieties., Comment: Final version. To appear in Bull. Lond. Math. Soc