Emergent multipolar spin correlations in a fluctuating spiral - The frustrated ferromagnetic S=1/2 Heisenberg chain in a magnetic field

We present the phase diagram of the frustrated ferromagnetic S=1/2 Heisenberg J_1-J_2 chain in a magnetic field, obtained by large scale exact diagonalizations and density matrix renormalization group simulations. A vector chirally ordered state, metamagnetic behavior and a sequence of spin-multipolar Luttinger liquid phases up to hexadecupolar kind are found. We provide numerical evidence for a locking mechanism, which can drive spiral states towards spin-multipolar phases, such as quadrupolar or octupolar phases. Our results also shed light on previously discovered spin-multipolar phases in two-dimensional $S=1/2$ quantum magnets in a magnetic field.Comment: 4+ pages, 4 figure

Exact EGB models for spherical static perfect fluids

We obtain a new exact solution to the field equations in the EGB modified theory of gravity for a 5-dimensional spherically symmetric static distribution. By using a transformation, the study is reduced to the analysis of a single second order nonlinear differential equation. In general the condition of pressure isotropy produces a first order differential equation which is an Abel equation of the second kind. An exact solution is found. The solution is examined for physical admissability. In particular a set of constants is found which ensures that a pressure-free hypersurface exists which defines the boundary of the distribution. Additionally the isotropic pressure and the energy density are shown to be positive within the radius of the sphere. The adiabatic sound speed criterion is also satisfied within the fluid ensuring a subluminal sound speed. Furthermore, the weak, strong and dominant conditions hold throughout the distribution. On setting the Gauss-Bonnet coupling to zero, an exact solution for 5-dimensional perfect fluids in the standard Einstein theory is obtained. Plots of the dynamical quantities for the Gauss-Bonnet and the Einstein case reveal that the pressure is unaffected while the the energy density increases under the influence of the Gauss-Bonnet term.Comment: 18 pages, Submitted for publicatio

Derandomization of auctions

We study the role of randomization in seller optimal (i.e., profit maximization) auctions. Bayesian optimal auctions (e.g., Myerson, 1981) assume that the valuations of the agents are random draws from a distribution and prior-free optimal auctions either are randomized (e.g., Goldberg et al., 2006) or assume the valuations are randomized (e.g., Segal, 2003). Is randomization fundamental to profit maximization in auctions? Our main result is a general approach to derandomize single-item multi-unit unit-demand auctions while approximately preserving their performance (i.e., revenue). Our general technique is constructive but not computationally tractable. We complement the general result with the explicit and computationally-simple derandomization of a particular auction. Our results are obtained through analogy to hat puzzles that are interesting in their own right

The vanishing ideal of a finite set of points with multiplicity structures

Given a finite set of arbitrarily distributed points in affine space with arbitrary multiplicity structures, we present an algorithm to compute the reduced Groebner basis of the vanishing ideal under the lexicographic ordering. Our method discloses the essential geometric connection between the relative position of the points with multiplicity structures and the quotient basis of the vanishing ideal, so we will explicitly know the set of leading terms of elements of I. We split the problem into several smaller ones which can be solved by induction over variables and then use our new algorithm for intersection of ideals to compute the result of the original problem. The new algorithm for intersection of ideals is mainly based on the Extended Euclidean Algorithm.Comment: 12 pages,12 figures,ASCM 201

A New View on Worst-Case to Average-Case Reductions for NP Problems

We study the result by Bogdanov and Trevisan (FOCS, 2003), who show that under reasonable assumptions, there is no non-adaptive worst-case to average-case reduction that bases the average-case hardness of an NP-problem on the worst-case complexity of an NP-complete problem. We replace the hiding and the heavy samples protocol in [BT03] by employing the histogram verification protocol of Haitner, Mahmoody and Xiao (CCC, 2010), which proves to be very useful in this context. Once the histogram is verified, our hiding protocol is directly public-coin, whereas the intuition behind the original protocol inherently relies on private coins

Index

The interest in relativistic beam-plasma instabilities has been greatly rejuvenated over the past two decades by novel concepts in laboratory and space plasmas. Recent advances in this long-standing field are here reviewed from both theoretical and numerical points of view. The primary focus is on the two-dimensional spectrum of unstable electromagnetic waves growing within relativistic, unmagnetized, and uniform electron beam-plasma systems. Although the goal is to provide a unified picture of all instability classes at play, emphasis is put on the potentially dominant waves propagating obliquely to the beam direction, which have received little attention over the years. First, the basic derivation of the general dielectric function of a kinetic relativistic plasma is recalled. Next, an overview of two-dimensional unstable spectra associated with various beam-plasma distribution functions is given. Both cold-fluid and kinetic linear theory results are reported, the latter being based on waterbag and Maxwell–Jüttner model distributions. The main properties of the competing modes (developing parallel, transverse, and oblique to the beam) are given, and their respective region of dominance in the system parameter space is explained. Later sections address particle-in-cell numerical simulations and the nonlinear evolution of multidimensional beam-plasma systems. The elementary structures generated by the various instability classes are first discussed in the case of reduced-geometry systems. Validation of linear theory is then illustrated in detail for large-scale systems, as is the multistaged character of the nonlinear phase. Finally, a collection of closely related beam-plasma problems involving additional physical effects is presented, and worthwhile directions of future research are outlined.Original Publication: Antoine Bret, Laurent Gremillet and Mark Eric Dieckmann, Multidimensional electron beam-plasma instabilities in the relativistic regime, 2010, Physics of Plasmas, (17), 12, 120501-1-120501-36. http://dx.doi.org/10.1063/1.3514586 Copyright: American Institute of Physics http://www.aip.org/</p

New high magnetic field phase of the frustrated S=1/2S=1/2 chain compound LiCuVO4_4

Magnetization of the frustrated $S=1/2$ chain compound LiCuVO$_4$, focusing on high magnetic field phases, is reported. Besides a spin-flop transition and the transition from a planar spiral to a spin modulated structure observed recently, an additional transition was observed just below the saturation field. This newly observed magnetic phase is considered as a spin nematic phase, which was predicted theoretically but was not observed experimentally. The critical fields of this phase and its dM/dH curve are in good agreement with calculations performed in a microscopic model (M. E. Zhitomirsky and H. Tsunetsugu, preprint, arXiv:1003.4096v2).Comment: 5 pages, 4 figure

Renal function at two years in liver transplant patients receiving everolimus: results of a randomized, multicenter study

Abstract In a 24-month prospective, randomized, multicenter, open-label study, de novo liver transplant patients were randomized at 30 days to everolimus (EVR) + Reduced tacrolimus (TAC; n = 245), TAC Control (n = 243) or TAC Elimination (n = 231). Randomization to TAC Elimination was stopped prematurely due to a significantly higher rate of treated biopsy-proven acute rejection (tBPAR). The incidence of the primary efficacy endpoint, composite efficacy failure rate of tBPAR, graft loss or death postrandomization was similar with EVR + Reduced TAC (10.3%) or TAC Control (12.5%) at month 24 (difference -2.2%, 97.5% confidence interval [CI] -8.8%, 4.4%). BPAR was less frequent in the EVR + Reduced TAC group (6.1% vs. 13.3% in TAC Control, p = 0.010). Adjusted change in estimated glomerular filtration rate (eGFR) from randomization to month 24 was superior with EVR + Reduced TAC versus TAC Control: difference 6.7 mL/min/1.73 m(2) (97.5% CI 1.9, 11.4 mL/min/1.73 m(2), p = 0.002). Among patients who remained on treatment, mean (SD) eGFR at month 24 was 77.6 (26.5) mL/min/1.73 m(2) in the EVR + Reduced TAC group and 66.1 (19.3) mL/min/1.73 m(2) in the TAC Control group (p < 0.001). Study medication was discontinued due to adverse events in 28.6% of EVR + Reduced TAC and 18.2% of TAC Control patients. Early introduction of everolimus with reduced-exposure tacrolimus at 1 month after liver transplantation provided a significant and clinically relevant benefit for renal function at 2 years posttransplant