Centrally symmetric polytopes with many faces

We present explicit constructions of centrally symmetric polytopes with many faces: first, we construct a d-dimensional centrally symmetric polytope P with about (1.316)^d vertices such that every pair of non-antipodal vertices of P spans an edge of P, second, for an integer k>1, we construct a d-dimensional centrally symmetric polytope P of an arbitrarily high dimension d and with an arbitrarily large number N of vertices such that for some 0 < delta_k < 1 at least (1-delta_k^d) {N choose k} k-subsets of the set of vertices span faces of P, and third, for an integer k>1 and a>0, we construct a centrally symmetric polytope Q with an arbitrary large number N of vertices and of dimension d=k^{1+o(1)} such that least (1 - k^{-a}){N choose k} k-subsets of the set of vertices span faces of Q.Comment: 14 pages, some minor improvement

Neighborliness of the symmetric moment curve

We consider the convex hull B_k of the symmetric moment curve U(t)=(cos t, sin t, cos 3t, sin 3t, ..., cos (2k-1)t, sin (2k-1)t) in R^{2k}, where t ranges over the unit circle S= R/2pi Z. The curve U(t) is locally neighborly: as long as t_1, ..., t_k lie in an open arc of S of a certain length phi_k>0, the convex hull of the points U(t_1), ..., U(t_k) is a face of B_k. We characterize the maximum possible length phi_k, proving, in particular, that phi_k > pi/2 for all k and that the limit of phi_k is pi/2 as k grows. This allows us to construct centrally symmetric polytopes with a record number of faces.Comment: 28 pages, proofs are simplified and results are strengthened somewha

Customer perceived value—Conceptualization and avenues for future research

Given the present dynamic consumption environment due to technological innovations as well as interlinked economic developments on the macro-, micro-, and societal-level, researchers and managers have been increasingly showing interest in the concept of customer perceived value. However, especially given its vast empirical application, surprisingly little effort has been paid to synthesize various perspectives on the dimensionality, abstraction, and model taxonomy of customer perceived value. Therefore, based on a comprehensive literature review, this article identifies the predominant conceptualization of customer perceived value, thus also providing a sound basis for future empirical assessments of this concept, and discusses avenues for future research. In addition to contributing to research, this study also contributes to practice by comprehensively positioning customer perceived value as a key source of competitive advantage in the context of relationship marketing, management, and business models

Exploring AGN Activity over Cosmic Time with the SKA

In this Chapter we present the motivation for undertaking both a wide and deep survey with the SKA in the context of studying AGN activity across cosmic time. With an rms down to 1 $\mu$Jy/beam at 1 GHz over 1,000 - 5,000 deg$^2$ in 1 year (wide tier band 1/2) and an rms down to 200 nJy/beam over 10 - 30 deg$^2$ in 2000 hours (deep tier band 1/2), these surveys will directly detect faint radio-loud and radio-quiet AGN (down to a 1 GHz radio luminosity of about $2\times10^{23}$ W/Hz at $z=6$). For the first time, this will enable us to conduct detailed studies of the cosmic evolution of radio AGN activity to the cosmic dawn ($z\gtrsim6$), covering all environmental densities.Comment: 17 pages, 7 figures, to appear as part of 'Continuum Science' in Proceedings 'Advancing Astrophysics with the SKA (AASKA14)

Probing the Tavis-Cummings level splitting with intermediate-scale superconducting circuits

We demonstrate the local control of up to eight two-level systems interacting strongly with a microwave cavity. Following calibration, the frequency of each individual two-level system (qubit) is tunable without influencing the others. Bringing the qubits one by one on resonance with the cavity, we observe the collective coupling strength of the qubit ensemble. The splitting scales up with the square root of the number of the qubits, which is the hallmark of the Tavis-Cummings model. The local control circuitry causes a bypass shunting the resonator, and a Fano interference in the microwave readout, whose contribution can be calibrated away to recover the pure cavity spectrum. The simulator's attainable size of dressed states with up to five qubits is limited by reduced signal visibility, and -- if uncalibrated -- by off-resonance shifts of sub-components. Our work demonstrates control and readout of quantum coherent mesoscopic multi-qubit system of intermediate scale under conditions of noise

Validation of a Diagnostic Marker for Primocane-Fruiting in Blackberry

Typical blackberries (Rubus subgenus Rubus) have perennial crowns and roots and biennial canes. The first-year canes (primocanes) are usually vegetative, while second-year canes (floricanes) produce fruit. Primocane-fruiting blackberries produce fruit on first-year canes and are desirable to growers because they potentially allow for a longer harvest season in temperate regions and enable production in tropical areas where no natural chill hours are accumulated. The development of molecular markers for desirable traits can potentially increase efficiency in blackberry breeding. However, to date, there are no diagnostic molecular markers for economically important traits in blackberries. Primocane-fruiting is recessively inherited, and tetraploid blackberries must have four copies of the primocane allele for the trait to be expressed. A single locus strongly associated with primocane fruiting was recently identified on chromosome Ra03, and a new KASP marker (PF2) was developed within this locus. In this study, we validated the performance of the new PF2 marker in a seedling population (Population 1937) segregating for primocane-fruiting at the University of Arkansas System Division of Agriculture\u27s Fruit Breeding Program. In 2022, 170 seedlings in the population were evaluated for primocane-fruiting. Of these seedlings, 68 were floricane-fruiting, 86 were primocane-fruiting, and 16 could not be phenotyped due to poor plant growth. The PF2 marker correctly predicted the phenotype for 146 of 154 progeny that were scored in the 1937 population. Some of the inconsistencies between the marker prediction and the observed phenotypes could have been due to weak plants shaded out by neighbors or human error

Validation of a Diagnostic Marker for Primocane-Fruiting in Blackberry

Typical blackberries (Rubus subgenus Rubus) have perennial crowns and roots and biennial canes. The first-year canes (primocanes) are usually vegetative, while second-year canes (floricanes) produce fruit. Primocane-fruiting blackberries produce fruit on first-year canes and are desirable to growers because they potentially allow for a longer harvest season in temperate regions and enable production in tropical areas where no natural chill hours are accumulated. The development of molecular markers for desirable traits can potentially increase efficiency in blackberry breeding. However, to date, there are no diagnostic molecular markers for economically important traits in blackberries. Primocane-fruiting is recessively inherited, and tetraploid blackberries must have four copies of the primocane allele for the trait to be expressed. A single locus strongly associated with primocane fruiting was recently identified on chromosome Ra03, and a new KASP marker (PF2) was developed within this locus. In this study, we validated the performance of the new PF2 marker in a seedling population (Population 1937) segregating for primocane-fruiting at the University of Arkansas System Division of Agriculture\u27s Fruit Breeding Program. In 2022, 170 seedlings in the population were evaluated for primocane-fruiting. Of these seedlings, 68 were floricane-fruiting, 86 were primocane-fruiting, and 16 could not be phenotyped due to poor plant growth. The PF2 marker correctly predicted the phenotype for 146 of 154 progeny that were scored in the 1937 population. Some of the inconsistencies between the marker prediction and the observed phenotypes could have been due to weak plants shaded out by neighbors or human error

Population Inversion in Monolayer and Bilayer Graphene

The recent demonstration of saturable absorption and negative optical conductivity in the Terahertz range in graphene has opened up new opportunities for optoelectronic applications based on this and other low dimensional materials. Recently, population inversion across the Dirac point has been observed directly by time- and angle-resolved photoemission spectroscopy (tr-ARPES), revealing a relaxation time of only ~ 130 femtoseconds. This severely limits the applicability of single layer graphene to, for example, Terahertz light amplification. Here we use tr-ARPES to demonstrate long-lived population inversion in bilayer graphene. The effect is attributed to the small band gap found in this compound. We propose a microscopic model for these observations and speculate that an enhancement of both the pump photon energy and the pump fluence may further increase this lifetime.Comment: 18 pages, 6 figure