In this work, we study the problem of testing properties spectrum a mixed quantum state. Here one is given n copies state $$\rho \in \mathbb {C}^{d\times d}$$ ρ ∈ C d × and goal to distinguish (with high probability) whether $$ ’s satisfies some property $${\mathcal {P}}$$ P or it at least $$\epsilon ϵ -far in $$\ell _1$$ ℓ 1 -distance from satisfying . This was promoted survey Montanaro de Wol...

In this paper, we study the structure of nite Frobenius groups whose non-rational or non-real irreducible characters are linear.

vspace{0.2cm}In this paper, we design a data structure for the following problem. Let $pi$ be an $x$-monotone trajectory with $n$ vertices in the plane and $epsilon >0$. We show how to preprocess $pi$ and $epsilon$ into a data structure such that for any horizontal query segment $Q$ in the plane, one can quickly determine the minimal continuous fraction of $pi$ whose Fr{'e}chet and Hausdo...

We study the determinant line bundle over moduli space of stable bundles on abelian surfaces. We evaluate their analytic torsions. We extend Mukai's version of the Parseval Theorem to L 2 metrics on cohomology groups. We prove that the Mukai transform preserves the determinant line bundle as a hermitian line bundle. This is done by induction via the natural boundary of the moduli spaces.

We generalize the Second Oversampling Theorem for wavelet frames and dual wavelet frames from the setting of integer dilations to real dilations. We also study the relationship between dilation matrix oversampling of semi-orthogonal Parseval wavelet frames and the additional shift invariance gain of the core subspace.

A generalized filter construction is used to build non-MRA Parseval wavelets for dilation by 2 in L2(R2). These examples have the same multiplicity functions as wavelet sets, yet can be made to be Cr with Cr Fourier transform for any fixed positive integer r.

The use of random samples to approximate properties of geometric configurations has been an influential idea for both combinatorial and algorithmic purposes. This chapter considers two related notions— -approximations and -nets—that capture the most important quantitative properties that one would expect from a random sample with respect to an underlying geometric configuration. An example prob...

A population of cells that express mast cell markers, including the membrane protein p161, but that lack expression of the high affinity IgE receptor, Fc epsilon RI, can be routinely grown from bone marrow. Ionomycin, but not IgE immune complexes, causes these cells to release serotonin and to express IL-3 and IL-13 mRNA, consistent with their being FC epsilon RI-deficient mast cells. These p16...

We present extensive molecular dynamics simulation results for the structure and the static and dynamical responses of a droplet of 1000 soft spheres carrying extended dipoles and confined to spherical cavities of radii R=2.5, 3, and 4 nm embedded in a dielectric continuum of permittivity epsilon(')>or=1. The polarization of the external medium by the charge distribution inside the cavity is ac...

Protein kinase C (PKC) plays a prominent role in immune signaling, and the paradigms for isoform selective signaling are beginning to be elucidated. Real-time microscopy was combined with molecular and biochemical approaches to demonstrate a role for PKC- epsilon in Fc gamma receptor (Fc gammaR)-dependent phagocytosis. RAW 264.7 macrophages were transfected with GFP-conjugated PKC isoforms, and...