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

On the symbolic powers of binomial edge ideals

We show that under some conditions, if the initial ideal in$_<(I)$ of an ideal $I$ in a polynomial ring has the property that its symbolic and ordinary powers coincide, then the ideal $I$ shares the same property. We apply this result to prove the equality between symbolic and ordinary powers for binomial edge ideals with quadratic Gr\"obner basis

Epitaxial Co2Cr0.6Fe0.4Al thin films and magnetic tunneling junctions

Epitaxial thin films of the theoretically predicted half metal Co2Cr0.6Fe0.4Al were deposited by dc magnetron sputtering on different substrates and buffer layers. The samples were characterized by x-ray and electron beam diffraction (RHEED) demonstrating the B2 order of the Heusler compound with only a small partition of disorder on the Co sites. Magnetic tunneling junctions with Co2Cr0.6Fe0.4Al electrode, AlOx barrier and Co counter electrode were prepared. From the Julliere model a spin polarisation of Co2Cr0.6Fe0.4Al of 54% at T=4K is deduced. The relation between the annealing temperature of the Heusler electrodes and the magnitude of the tunneling magnetoresistance effect was investigated and the results are discussed in the framework of morphology and surface order based of in situ STM and RHEED investigations.Comment: accepted by J. Phys. D: Appl. Phy

Powers of componentwise linear ideals

We give criteria for graded ideals to have the property that all their powers are componentwise linear. Typical examples to which our criteria can be applied include the vertex cover ideals of certain finite graphs

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