5,034 research outputs found
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
Boundary between the thermal and statistical polarization regimes in a nuclear spin ensemble
As the number of spins in an ensemble is reduced, the statistical uctuations
in its polarization eventually exceed the mean thermal polarization. This
transition has now been surpassed in a number of recent nuclear magnetic
resonance experiments, which achieve nanometer-scale detection volumes. Here,
we measure nanometer- scale ensembles of nuclear spins in a KPF6 sample using
magnetic resonance force microscopy. In particular, we investigate the
transition between regimes dominated by thermal and statistical nuclear
polarization. The ratio between the two types of polarization provides a
measure of the number of spins in the detected ensemble
Reproducibility or Producibility? Metrics and their masters
Reproducibility of indicators and metrics is an important topic as it underlies an increasing part of the approach taken to research evaluation. But reproducibility of metrics is not the critical question. The more important question is around access to the data to create metrics, and around who owns the metrics and the transparency of the algorithms and data elements. In short, is it not about producibility rather than reproducibility? With Dimensions, Digital Science has taken a first step in making publication and citation data more openly available. But, perhaps more importantly, Dimensions links other types of data to the familiar bibliometrics landscape to allow the community to go beyond citation-based indicators. The team at Digital Science believes in the “separation of powers” - data should be developed and hosted by providers and the community should own the metrics used to measure itself. Work has started to collaborate with the scientometric and research management community to support their development and implementation of metrics based on the Dimensions data and platform
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
The Runaway Quiver
We point out that some recently proposed string theory realizations of
dynamical supersymmetry breaking actually do not break supersymmetry in the
usual desired sense. Instead, there is a runaway potential, which slides down
to a supersymmetric vacuum at infinite expectation values for some fields. The
runaway direction is not on a separated branch; rather, it shows up as
a"tadpole" everywhere on the moduli space of field expectation values.Comment: 12 pages, no figures. v2: reference chang
New results on superconformal quivers
All superconformal quivers are shown to satisfy the relation c = a and are
thus good candidates for being the field theory living on D3 branes probing CY
singularities. We systematically study 3 block and 4 block chiral quivers which
admit a superconformal fixed point of the RG equation. Most of these theories
are known to arise as living on D3 branes at a singular CY manifold, namely
complex cones over del Pezzo surfaces. In the process we find a procedure of
getting a new superconformal quiver from a known one. This procedure is termed
"shrinking" and, in the 3 block case, leads to the discovery of two new models.
Thus, the number of superconformal 3 block quivers is 16 rather than the
previously known 14. We prove that this list exausts all the possibilities. We
suggest that all rank 2 chiral quivers are either del Pezzo quivers or can be
obtained by shrinking a del Pezzo quiver and verify this statement for all 4
block quivers, where a lot of "shrunk'' del Pezzo models exist.Comment: 51 pages, many figure
Active control in an anechoic room : Theory and first simulations
International audienceNoise control and source design require the measurement of sound radiation at low frequencies. Anechoic rooms, which are designed for this purpose, allow echo-free measurements at medium or high frequency but passive wall treatment is less effective at low frequency and in practice no facility provides anechoicity below 50Hz. This paper discusses the applicability of an active control algorithm which has been previously introduced to minimize the echoes from a scattering object to the cancellation of the low frequency wall echoes in an anechoic room including wall-embedded secondary sources. At first the paper discusses, in the general case then for a free half-space as a model case, the algorithm key which consists in estimating the scattered acoustic pressure from total pressure measurements. Boundary Element Method computations are secondly used to simulate estimation and active control of error signals accounting for the low-frequency scattered pressure in an anechoic room. The simulations show that control with a few dozen microphones and noise sources allows a large reduction of the noise scattered from the walls at low-frequency
Exceptional Collections and del Pezzo Gauge Theories
Stacks of D3-branes placed at the tip of a cone over a del Pezzo surface
provide a way of geometrically engineering a small but rich class of
gauge/gravity dualities. We develop tools for understanding the resulting
quiver gauge theories using exceptional collections. We prove two important
results for a general quiver gauge theory: 1) we show the ordering of the nodes
can be determined up to cyclic permutation and 2) we derive a simple formula
for the ranks of the gauge groups (at the conformal point) in terms of the
numbers of bifundamentals. We also provide a detailed analysis of four node
quivers, examining when precisely mutations of the exceptional collection are
related to Seiberg duality.Comment: 26 pages, 1 figure; v2 footnote 2 amended; v3 ref adde
Heavy flavor diffusion in weakly coupled N=4 Super Yang-Mills theory
We use perturbation theory to compute the diffusion coefficient of a heavy
quark or scalar moving in N=4 SU(N_c) Super Yang-Mills plasma to leading order
in the coupling and the ratio T/M<<1. The result is compared both to recent
strong coupling calculations in the same theory and to the corresponding weak
coupling result in QCD. Finally, we present a compact and simple formulation of
the Lagrangian of our theory, N=4 SYM coupled to a massive fundamental N=2
hypermultiplet, which is well-suited for weak coupling expansions.Comment: 22 pages, 4 figures; v3: error corrected in calculations, figures and
discussion modified accordingl
Energy Loss of Heavy Quarks from Asymptotically AdS Geometries
We investigate some universal features of AdS/CFT models of heavy quark
energy loss. In addition, as a specific example, we examine quark damping in
the spinning D3-brane solution dual to N=4 SU(N_c) super Yang-Mills at finite
temperature and R-charge chemical potential.Comment: 17 pages, 9 figures; v2 refs added, typo fixe
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