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

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

Small-scale-field Dynamo

Generation of magnetic field energy, without mean field generation, is studied. Isotropic mirror-symmetric turbulence of a conducting fluid amplifies the energy of small-scale magnetic perturbations if the magnetic Reynolds number is high, and the dimensionality of space d satisfies 2.103 < d <8.765. The result does not depend on the model of turbulence, incompressibility and isotropy being the only requirements.Comment: 11 pages Plain TeX, no figures, Accepted by Phys. Rev. Let

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

A Hypergraph Dictatorship Test with Perfect Completeness

A hypergraph dictatorship test is first introduced by Samorodnitsky and Trevisan and serves as a key component in their unique games based \PCP construction. Such a test has oracle access to a collection of functions and determines whether all the functions are the same dictatorship, or all their low degree influences are $o(1).$ Their test makes $q\geq3$ queries and has amortized query complexity $1+O(\frac{\log q}{q})$ but has an inherent loss of perfect completeness. In this paper we give an adaptive hypergraph dictatorship test that achieves both perfect completeness and amortized query complexity $1+O(\frac{\log q}{q})$.Comment: Some minor correction

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

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

Cloning and Expression of Major Surface Antigen 1 Gene of Toxoplasma gondii RH Strain Using the Expression Vector pVAX1 in Chinese Hamster Ovary Cells

Background: Toxoplasmosis is an opportunistic protozoan infection with a high prevalence in a broad range of hosts infecting up to onethird of the world human population. Toxoplasmosis leads to serious medical problems in immunocompromised individuals and fetuses and also induces abortion and mortality in domestic animals. Therefore, there is a huge demand for the development of an effective vaccine. Surface Antigen 1 (SAG1) is one of the important immunodominant surface antigens of Toxoplasma gondii, which interacts with host cells and primarily involved in adhesion, invasion and stimulation of host immune response. Surface antigen 1 is considered as the leading candidate for development of an effective vaccine against toxoplasmosis. Objectives: The purpose of this study was to clone the major surface antigen1 gene (SAG1) from the genotype 1 of T. gondii, RH strain into the eukaryotic expression vector pVAX1 in order to use for a DNA vaccine. Materials and Methods: Genomic DNA was extracted from tachyzoite of the parasite using the QIAamp DNA mini kit. After designing the specific primers, SAG1 gene was amplified by Polymerase Chain Reaction (PCR). The purified PCR products were then cloned into a pPrime plasmid vector. The aforementioned product was subcloned into the pVAX1 eukaryotic expression vector. The recombinant pVAX1-SAG1 was then transfected into Chinese Hamster Ovary (CHO) cells and expression of SAG1 antigen was evaluated using Reverse Transcriptase Polymerase Chain Reaction (RT-PCR), Immunofluorescence Assay (IFA) and Western Blotting (WB). Results: The cloning and subcloning products (pPrime-SAG1 and pVAX1-SAG1 plasmid vectors) of SAG1 gene were verified and confirmed by enzyme digestion and sequencing. A 30 kDa recombinant protein was expressed in CHO cells as shown by IFA and WB methods. Conclusions: The pVAX1 expression vector and CHO cells are a suitable system for high-level recombinant protein production for SAG1 gene from T. gondii parasites and are promising approaches for antigen preparation in vaccine development

Entanglement study of the 1D Ising model with Added Dzyaloshinsky-Moriya interaction

We have studied occurrence of quantum phase transition in the one-dimensional spin-1/2 Ising model with added Dzyaloshinsky-Moriya (DM) interaction from bi- partite and multi-partite entanglement point of view. Using exact numerical solutions, we are able to study such systems up to 24 qubits. The minimum of the entanglement ratio R $\equiv$ \tau 2/\tau 1 < 1, as a novel estimator of QPT, has been used to detect QPT and our calculations have shown that its minimum took place at the critical point. We have also shown both the global-entanglement (GE) and multipartite entanglement (ME) are maximal at the critical point for the Ising chain with added DM interaction. Using matrix product state approach, we have calculated the tangle and concurrence of the model and it is able to capture and confirm our numerical experiment result. Lack of inversion symmetry in the presence of DM interaction stimulated us to study entanglement of three qubits in symmetric and antisymmetric way which brings some surprising results.Comment: 18 pages, 9 figures, submitte

Sublinear-Time Language Recognition and Decision by One-Dimensional Cellular Automata

After an apparent hiatus of roughly 30 years, we revisit a seemingly neglected subject in the theory of (one-dimensional) cellular automata: sublinear-time computation. The model considered is that of ACAs, which are language acceptors whose acceptance condition depends on the states of all cells in the automaton. We prove a time hierarchy theorem for sublinear-time ACA classes, analyze their intersection with the regular languages, and, finally, establish strict inclusions in the parallel computation classes $\mathsf{SC}$ and (uniform) $\mathsf{AC}$. As an addendum, we introduce and investigate the concept of a decider ACA (DACA) as a candidate for a decider counterpart to (acceptor) ACAs. We show the class of languages decidable in constant time by DACAs equals the locally testable languages, and we also determine $\Omega(\sqrt{n})$ as the (tight) time complexity threshold for DACAs up to which no advantage compared to constant time is possible.Comment: 16 pages, 2 figures, to appear at DLT 202