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

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

Suggestive hypothesis on a case report: Patient presenting with cyclical ovarian cysts coupled to increased cholestatic enzymes

We describe the case of a childbearing-age woman presenting with spontaneous recurrent functional ovarian cysts and, more interestingly, chronic and asymptomatic elevation of cholestatic parameters. The patient showed no history of chronic viral infections, immunological and metabolic disorders, alcohol abuse and environmental toxins exposition. Hepatic ultrasonography and cholangio-pancreatography-magnetic-resonance excluded any morphological and structural abnormalities, while liver biopsy evidenced only minimal and not specific features of inflammation. Cholestasis indices obtained prompt recovery after each cycle of synthetic hormone therapy, implanted to treat functional ovarian cysts. She has continuously experienced the off-therapy asynchronous recurrence of liver laboratory abnormalities and functional ovarian cysts. The favorable effect of the synthetic hormone therapy to obtaining a stable recovery of this unexplained long-lasting cholestatic syndrome could be likely explained by downregulation of an endogenous ovarian overproduction, although estrogen-regulated local intracellular transduction pathways cannot be excluded

Performance optimization of InGaAs/InP SPADs for either low noise or high photon detection efficiency applications

InGaAs/InP Single-Photon Avalanche Diodes ( SPADs) can achieve high photon detection efficiency (PDE) with a thick absorber, but at the expense of higher dark count rate ( DCR). PDE and DCR also depend on the electric field inside the structure, which can be tailored in the design phase and influences the overall performance. We present the design and the experimental characterization of two different 10 mu m-diameter InGaAs/InP SPADs. The first one is intended for applications where low noise is the key requirement: at 225 K and 5 V excess bias, it features 1 kcps DCR, 25% PDE at 1550 nm and a timing jitter of 100 ps (FWHM). The second device is an InGaAs/InP SPAD optimized for PDE-enhanced applications, having a PDE up to 50% at 1550 nm, with a DCR of 20 kcps and a timing jitter of 70 ps (FWHM) at 225 K. Alternatively, it features a PDE of 37% at 1550 nm, with a DCR of just 3 kcps and a timing jitter of 100 ps (FWHM). When combined with a custom integrated circuit we developed, both devices show an afterpulsing probability as low as few percent with a gating frequency of 1 MHz and hold-off time of few microseconds at 225 K, allowing to achieve a photon count rate towards 1 Mcps