Induced log-concavity of equivariant matroid invariants

Inspired by the notion of equivariant log-concavity, we introduce the concept of induced log-concavity for a sequence of representations of a finite group. For an equivariant matroid equipped with a symmetric group action or a finite general linear group action, we transform the problem of proving the induced log-concavity of matroid invariants to that of proving the Schur positivity of symmetric functions. We prove the induced log-concavity of the equivariant Kazhdan-Lusztig polynomials of $q$-niform matroids equipped with the action of a finite general linear group, as well as that of the equivariant Kazhdan-Lusztig polynomials of uniform matroids equipped with the action of a symmetric group. As a consequence of the former, we obtain the log-concavity of Kazhdan-Lusztig polynomials of $q$-niform matroids, thus providing further positive evidence for Elias, Proudfoot and Wakefield's log-concavity conjecture on the matroid Kazhdan-Lusztig polynomials. From the latter we obtain the log-concavity of Kazhdan-Lusztig polynomials of uniform matroids, which was recently proved by Xie and Zhang by using a computer algebra approach. We also establish the induced log-concavity of the equivariant characteristic polynomials and the equivariant inverse Kazhdan-Lusztig polynomials for $q$-niform matroids and uniform matroids.Comment: 36 page

Scenarios about the long-time damage of silicon as material and detectors operating beyond LHC collider conditions

For the new hadron collider LHC and some of its updates in luminosity and energy, as SLHC and VLHC, the silicon detectors could represent an important option, especially for the tracking system and calorimetry. The main goal of this paper is to analyse the expected long-time degradation in the bulk of the silicon as material and for silicon detectors, in continuous radiation field, in these hostile conditions. The behaviour of silicon in relation to various scenarios for upgrade in energy and luminosity is discussed in the frame a phenomenological model developed previously by the authors. Different silicon material parameters resulting from different technologies are considered to evaluate what materials are harder to radiation and consequently could minimise the degradation of device parameters in conditions of continuous long time operation.Comment: submitted to Physica Scripta Work in the frame of CERN RD-50 Collaboratio

Photodissociation dynamics of the iodide-uracil (I-U) complex

Photofragment action spectroscopy and femtosecond time-resolved photoelectron imaging are utilized to probe the dissociation channels in iodide-uracil (I− ⋅ U) binary clusters upon photoexcitation. The photofragment action spectra show strong I− and weak [U- H]− ion signal upon photoexcitation. The action spectra show two bands for I− and [U- H]− production peaking around 4.0 and 4.8 eV. Time-resolved experiments measured the rate of I− production resulting from excitation of the two bands. At 4.03 eV and 4.72 eV, the photoelectron signal from I− exhibits rise times of 86 ± 7 ps and 36 ± 3 ps, respectively. Electronic structure calculations indicate that the lower energy band, which encompasses the vertical detachment energy (4.11 eV) of I−U, corresponds to excitation of a dipole-bound state of the complex, while the higher energy band is primarily a π-π∗ excitation on the uracil moiety. Although the nature of the two excited states is very different, the long lifetimes for I− production suggest that this channel results from internal conversion to the I− ⋅ U ground state followed by evaporation of I−. This hypothesis was tested by comparing the dissociation rates to Rice-Ramsperger-Kassel-Marcus calculations

Clinical and Molecular Aspects of Senataxin Mutations in Amyotrophic Lateral Sclerosis 4

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/154673/1/ana25681_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/154673/2/ana25681.pd

Confinement and Processing Can Alter the Morphology and Periodicity of Bottlebrush Block Copolymers in Thin Films

Bottlebrush block copolymers (BBCPs) are intriguing architectural variations on linear BCPs with highly tunable structure. Confinement can have a significant impact on polymer assembly, giving rise to changes in morphology, assembly kinetics, and properties like the glass transition. Given that confinement leads to significant changes in the persistence length of bottlebrush homopolymers, it is reasonable to expect that BBCPs will see significant changes in their structure and periodicity relative to the bulk morphology. Understanding how confinement influences assembly will be important for designing BBCPs for thin film applications including membranes, integrated photonic structures, and potentially BCP lithography. In order to study the effects of confinement on BBCP conformation and morphology, a blade coating was used to prepare films with continuous variation in film thickness. Unlike thin films of linear BCPs, islands/holes were not observed, and instead mixtures of parallel and perpendicular morphologies emerge after annealing. The lamellar periodicity (L₀) of the morphologies is found to be thickness dependent, increasing L₀ with decreasing film thickness for blade coated films. Films coated out of tetrahydrofuran (THF) resulted in a single well-defined lamellar periodicity, verified through atomic force microscopy (AFM) and grazing incidence small-angle X-ray scattering (GISAXS), which increases dramatically from the bulk value (30.6 nm) and continues to increase as the film thickness decreases. The largest observed L₀ was 65.5 nm, and this closely approaches the estimated upper limit of 67 nm corresponding to a fully extended backbone in a bilayer arrangement. Films coated out of propylene glycol methyl ether acetate (PGMEA) resulted in a mixture of perpendicular lamellae and a smaller, likely cylindrical morphology. The lamellar portion of the film shows the same thickness dependence as the lamellae observed in the THF coated films. The scaling of the lamellar L₀ with respect to film thickness follows predictions for confined semiflexible polymers with weak excluded volume interactions and can be related to models for confinement of DNA. Spin coated films shows the same reduction in periodicity, although at very different film thicknesses. This result suggests that the material has shallow free-energy barriers to transitioning between different L₀ and morphologies, a property that could be taken advantage of for patterning diverse structures with a single material