Absolutely Koszul algebras and the Backelin-Roos property

We study absolutely Koszul algebras, Koszul algebras with the Backelin-Roos property and their behavior under standard algebraic operations. In particular, we identify some Veronese subrings of polynomial rings that have the Backelin-Roos property and conjecture that the list is indeed complete. Among other things, we prove that every universally Koszul ring defined by monomials has the Backelin-Roos property

Linear resolutions of powers and products

The goal of this paper is to present examples of families of homogeneous ideals in the polynomial ring over a field that satisfy the following condition: every product of ideals of the family has a linear free resolution. As we will see, this condition is strongly correlated to good primary decompositions of the products and good homological and arithmetical properties of the associated multi-Rees algebras. The following families will be discussed in detail: polymatroidal ideals, ideals generated by linear forms and Borel fixed ideals of maximal minors. The main tools are Gr\"obner bases and Sagbi deformation

Radical Generic Initial Ideals

In this paper, we survey the theory of Cartwright\u2013Sturmfels ideals. These are \u2124n-graded ideals, whose multigraded generic initial ideal is radical. Cartwright\u2013Sturmfels ideals have surprising properties, mostly stemming from the fact that their Hilbert scheme only contains one Borel-fixed point. This has consequences, e.g., on their universal Gr\uf6bner bases and on the family of their initial ideals. In this paper, we discuss several known classes of Cartwright\u2013Sturmfels ideals and we find a new one. Among determinantal ideals of same-size minors of a matrix of variables and Schubert determinantal ideals, we are able to characterize those that are Cartwright\u2013Sturmfels

Cynoglossum clandestinum Desf. (Boraginaceae), a new especies for the flora of the Catalan Countries

Es dóna a conèixer una localitat nova de Cynoglossum clandestinum Desf. a la comarca de la Vall d’Albaida, que representa una novetat per a la flora dels Països Catalans. Es realitzen comentaris sobre els caràcters morfològics, l’hàbitat i l’estat de conservació. Es discuteix també sobre la seva inclusió en alguna de les categories del Decret 70/2009, que inclou el «Catàleg Valencià d’Espècies de Flora Amenaçada».Cynoglossum clandestinum Desf. has been found in Catalan Countries for the first time. Several comments on the morphological characterization, the habitat and the convervation estatus are reported. We discussed about the need to include it in the Decree 70/2009, in which includes the “Valencian Catalogue of Threatened Plant Species”

Cynoglossum clandestinum Desf. (Boraginaceae), una espècie nova per a la flora dels Països Catalans

Es dóna a conèixer una localitat nova de Cynoglossum clandestinum Desf. a la comarca de la Vall d'Albaida, que representa una novetat per a la flora dels Països Catalans. Es realitzen comentaris sobre els caràcters morfològics, l'hàbitat i l'estat de conservació. Es discuteix també sobre la seva inclusió en alguna de les categories del Decret 70/2009, que inclou el «Catàleg Valencià d'Espècies de Flora Amenaçada».Cynoglossum clandestinum Desf. has been found in Catalan Countries for the first time. Several comments on the morphological characterization, the habitat and the convervation estatus are reported. We discussed about the need to include it in the Decree 70/2009, in which includes the "Valencian Catalogue of Threatened Plant Species"

Fast-Gated 16 x 16 SPAD Array With 16 on-Chip 6 ps Time-to-Digital Converters for Non-Line-of-Sight Imaging

We present the design and characterization of a fully-integrated array of 16 x 16 Single-Photon Avalanche Diodes (SPADs) with fast-gating capabilities and 16 on-chip 6 ps time-to-digital converters, which has been embedded in a compact imaging module. Such sensor has been developed for Non-Line-Of-Sight imaging applications, which require: i) a narrow instrument response function, for a centimeter-accurate single-shot precision; ii) fast-gated SPADs, for time-filtering of directly reflected photons; iii) high photon detection probability, for acquiring faint signals undergoing multiple scattering events. Thanks to a novel multiple differential SPAD-SPAD sensing approach, SPAD detectors can be swiftly activated in less than 500 ps and the full-width at half maximum of the instrument response function is always less than 75 ps (60 ps on average). Temporal responses are consistently uniform throughout the gate window, showing just few picoseconds of time dispersion when 30 ns gate pulses are applied, while the differential non-linearity is as low as 250 fs. With a photon detection probability peak of 70% at 490 nm, a fill-factor of 9.6% and up to 1.6 . 10(8) photon time-tagging measurements per second, such sensor fulfills the demand for fully-integrated imaging solutions optimized for non-line-of-sight imaging applications, enabling to cut exposure times while also optimizing size, weight, power and cost, thus paving the way for further scaled architectures