This note provides some corrections to the aforementioned paper. In [1, eq. (7)], C and aMkE1 cannot be added because the dimensions of the matrices are different. Therefore, the consequent derivations have to be adjusted. We propose two methods that can be used to correct this problem without harming the main idea of [1]. The first method is zero padding to zk 2 < to make zk 2 <. This can be w...

Let χc(H) denote the circular chromatic number of a graph H. For graphs F and G, the circular chromatic Ramsey number Rχc(F,G) is the infimum of χc(H) over graphs H such that every red/blue edge-coloring of H contains a red copy of F or a blue copy of G. We characterize Rχc(F,G) in terms of a Ramsey problem for the families of homomorphic images of F and G. Letting zk = 3 − 2 −k, we prove that ...

It is known that some polynomial mappings φ : Ck → Cn are recti able in the sense that there exists a polynomial mapping α : Cn → Cn whose inverse is also polynomial and for which α(φ(z1, . . . , zk)) = (z1, . . . , zk, 0, . . . , 0) for all z1, . . . , zk. In many cases, the existence of such a recti cation is proven indirectly, without an explicit construction of the mapping α. In this paper,...

The motivation for this paper comes from the Halperin–Carlsson conjecture for (real) moment-angle complexes. We first give an algebraic combinatorics formula for the Möbius transform of an abstract simplicial complex K on [m] = {1, . . . ,m} in terms of the Betti numbers of the Stanley–Reisner face ring k(K) of K over a field k. We then employ a way of compressing K to provide the lower bound o...

where μ(.) is an unknown smooth function, the i are independent and identically distributed errors, i.e. i ∼ (0, σ2 ), and the xi take values in [0, 1], for simplicity. We estimate μ(.) by some high dimensional spline of the form X(x)β + ZK(x)uK . Here, X(.) is a low dimensional basis while ZK(.) is built from truncated polynomials, i.e. we set X(x) = (1, x, x2/2!, . . . , xq/q!) and ZK(x) = ( ...

BACKGROUND ZK 200775 is an antagonist at the alpha-Amino-3-hydroxy-5-methyl-4-isoxazolepropionate (AMPA) receptor and had earned attention as a possible neuroprotective agent in cerebral ischemia. Probands receiving the agent within phase I trials reported on an alteration of visual perception. In this trial, the effects of ZK 200775 on the visual system were analyzed in detail. METHODOLOGY I...

Zero-knowledge proofs of knowledge (ZK-PoK) play an important role in many cryptographic applications. Direct anonymous attestation (DAA) and the identity mixer anonymous authentication system are first real world applications using ZKPoK as building blocks. But although being used for many years now, design and implementation of sound ZK-PoK remains challenging. In fact, there are security fla...

Let k ≥ 3 be a fixed integer and let Zk(G) be the number of k-colourings of the graph G. For certain values of the average degree, the random variable Zk(G(n,m)) is known to be concentrated in the sense that 1 n (lnZk(G(n,m)) − lnE[Zk(G(n,m))]) converges to 0 in probability [Achlioptas and Coja-Oghlan: Proc. FOCS 2008]. In the present paper we prove a significantly stronger concentration result...

We construct 3-round proofs and arguments with negligible soundness error satisfying two relaxed notions of zero-knowledge (ZK): weak ZK and witness hiding (WH). At the heart of our constructions lie new techniques based on point obfuscation with auxiliary input (AIPO). It is known that such protocols cannot be proven secure using blackbox reductions (or simulation). Our constructions circumven...