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

Non-local two-photon correlations using interferometers physically separated by 35 meters

An experimental demonstration of quantum correlations is presented. Energy and time entangled photons at wavelengths of 704 and 1310 nm are produced by parametric downconversion in KNbO3 and are sent through optical fibers into a bulk-optical (704 nm) and an all-fiber Michelson-interferometer (1310 nm), respectively. The two interferometers are located 35 meters aside from one another. Using Faraday-mirrors in the fiber-interferometer, all birefringence effects in the fibers are automatically compensated. We obtained two-photon fringe visibilities of up to 95 % from which one can project a violation of Bell's inequality by 8 standard deviations. The good performance and the auto-aligning feature of Faraday-mirror interferometers show their potential for a future test of Bell's inequalities in order to examine quantum-correlations over long distances.Comment: 9 pages including 3 postscript figures, to be published in Europhys. Let

Can We Study Titin Properties in Passive Myofibrils?

Titin is a giant molecular spring in skeletal and cardiac muscles. It has a variety of important passive, structural, sensing and force-regulatory functions, and thus has been investigated widely (Granzier & Labeit, 2007). Studying the mechanical properties of isolated titin has been difficult because of the enormous size and great instability of this protein. However, the passive properties in single myofibrils are almost exclusively explained by titin, and thus we asked the question if we can study titin properties in intact, passive myofibrils (Bartoo et al., 1997). Single myofibrils were isolated in a standard way (Leonard & Herzog, 2010) and three consecutive stretches of 1.0-3.5μm/sarcomere magnitude were performed at a nominal stretch speed of 0.1 sarcomere length/sarcomere/s. Sarcomere length were measured using a high resolution photo diode array and forces were measured using micro-electronically machined silicon nitrate levers. Single myofibrils frequently showed a distinct change in stiffness upon stretch at sarcomere length of approximately 3.6-3.8μm, they showed a decrease in loading energy with repeat stretch cycles and their efficiency decreased for all loading cycles with increasing stretch magnitude. These properties are in agreement with results observed in single titin preparations (Kellermayer et al., 1997). Therefore, we conclude that titin properties can be studied using single myofibrils. This has at least two significant advantages over tests with isolated titin proteins: (i) testing is technically much easier and (ii) titin is arranged in its intact structural arrangement. In the future, we would like to study titin properties in calcium activated myofibrils in which active (actin-myosin based cross-bridges forces) are eliminated either by chemical inhibition or by deletion of regulatory proteins on actin, as we have done before (Joumaa et al., 2008)

Anomalous dimensions and splitting functions beyond the next-to-next-to-leading order

We report on recent progress on the splitting functions for the evolution of parton distributions and related quantities, the (lightlike) cusp anomalous dimensions, in perturbative QCD. New results are presented for the four-loop (next-to-next-to-next-to-leading order, N^3LO) contributions to the flavour-singlet splitting functions and the gluon cusp anomalous dimension. We present first results, the moments N=2 and N=3, for the five-loop (N^4LO) non-singlet splitting functions.Comment: 10 pages, LaTeX (PoS style), 3 eps-figures. Contribution to the proceedings of `Loops & Legs 2018', St. Goar (Germany), April/May 201

Betti numbers for numerical semigroup rings

We survey results related to the magnitude of the Betti numbers of numerical semigroup rings and of their tangent cones.Comment: 22 pages; v2: updated references. To appear in Multigraded Algebra and Applications (V. Ene, E. Miller Eds.

Temperature- and Magnetic-Field-Dependent Optical Properties of Heavy Quasiparticles in YbIr2Si2

We report the temperature- and magnetic-field-dependent optical conductivity spectra of the heavy electron metal YbIr$_2$Si$_2$. Upon cooling below the Kondo temperature ($T_{\rm K}$), we observed a typical charge dynamics that is expected for a formation of a coherent heavy quasiparticle state. We obtained a good fitting of the Drude weight of the heavy quasiparticles by applying a modified Drude formula with a photon energy dependence of the quasiparticle scattering rate that shows a similar power-law behavior as the temperature dependence of the electrical resistivity. By applying a magnetic field of 6T below $T_{\rm K}$, we found a weakening of the effective dynamical mass enhancement by about 12% in agreement with the expected decrease of the $4f$-conduction electron hybridization on magnetic field.Comment: 5 pages, 4 figures. to be published in Journal of the Physical Society of Japan Vol. 79 (2010) No. 1

Far-infrared optical conductivity of CeCu2Si2

Journal ref.: J. Phys.: Condens. Matter 25, 065602 (2013): We investigated the optical reflectivity of the heavy-fermion metal CeCu2Si2 in the energy range 3 meV - 30 eV for temperatures between 4K - 300K. The results for the charge dynamics indicate a behavior that is expected for the formation of a coherent heavy quasiparticle state: Upon cooling the spectra of the optical conductivity indicate a narrowing of the coherent response. Below temperatures of 30 K a considerable suppression of conductivity evolves below a peak structure at 13 meV. We assign this gap-like feature to strong electron correlations due to the 4f-conduction electron hybridization.Comment: 7 pages, 3 figure

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

Spinning Dragging Strings

We use the AdS/CFT correspondence to compute the drag force experienced by a heavy quark moving through a maximally supersymmetric SU(N) super Yang-Mills plasma at nonzero temperature and R-charge chemical potential and at large 't Hooft coupling. We resolve a discrepancy in the literature between two earlier studies of such quarks. In addition, we consider small fluctuations of the spinning strings dual to these probe quarks and find no evidence of instabilities. We make some comments about suitable D7-brane boundary conditions for the dual strings.Comment: 25 pages, 4 figures; v2 refs added; v3 to appear in JHEP, clarifying comment