The legality of the " rooting trick " in dynamical staggered fermion simulations is discussed, i.e. whether the theory with the Boltzmann weight det 1/4 (D st) yields the right continuum limit. Since the problem is unsolved, pieces of evidence in favor and against are collected and examined.

The log-det estimator is a measure of divergence (evolutionary distance) between sequences of biological characters, DNA or amino acids, for example, and has been shown to be robust to biases in composition that can cause problems for other estimators. We provide a statistical framework to construct high-accuracy confidence intervals for log-det estimates and compare the efficiency of the estim...

" Der Mensch ist jenes Nicht-bleiben-können und doch nicht von der Stelle Können." (Martin Heidegger) "Den klara himlen har ställt sig på lut mot väggen. det är som en bön till det tomma. Och det tomma vänder sitt ansikte till oss och viskar ' Jag är inte tom, jag är öppen'"

Let H 0 (t); H 1 (t) be real 2 2 matrix{functions with entries from L 1 (0; 1), H 1 (t) = H 1 (t); H 0 (t) 0. We associate with these data the solution of the Cauchy problem for the diierential system dA(t; z) dt = A(t;z)fzH 0 (t) + H 1 (t)gJ; A(0;z) = 1 2 ; where J = 0 1 ?1 0 : The matrix{function A(z) = A(1;z) is called the monodromy matrix of the corresponding system 5]. More generally, let ...

For a finitely-generated vertex operator algebra V of central charge c ∈ C, a locally convex topological completion HV is constructed. We construct on HV a structure of an algebra over the operad of the c 2 -th power Det c/2 of the determinant line bundle Det over the moduli space of genus-zero Riemann surfaces with ordered analytically parametrized boundary components. In particular, HV is a m...

The affine synthesis operator Sc = P j>0 P k∈Zd cj,kψj,k is shown to map the mixed-norm sequence space `(`) surjectively onto L(R), 1 ≤ p < ∞, under mild conditions on the synthesizer ψ ∈ L(R) (say, having a radially decreasing L majorant near infinity) and assuming R Rd ψ dx = 1. Here ψj,k(x) = | det aj |ψ(ajx− k), for some dilation matrices aj that expand. Therefore the standard norm on f ∈ L...

Knowledge based methods in the domain of process and factory planning could lead to substantial savings for products with a high number of variants and production facilities. Although knowledge based approaches are already state of the art in the engineering and data management of complex products, these methods have not yet been applied to the planning of processes and production facilities so...

We notice that there is a 2-cover P of S 1 SO(3) (we denote this group D 1/2 ) by the group U(2): P sends a matrix z into a pair (det z,v). The matrix v here is the image of u under a standard covering map p from SU(2) onto SO(3), see (3.4) below. Finally, u (being a matrix from SU(2) ) is determined (up to a sign) from the decomposition z = du, here d 2 = det z. Both P and p are group homomorp...

Let B = (bjk)p×n = (Y1, Y2, · · · , Yn) be a collection of independent real random variables with mean zero and variance one. Suppose that Σ is a p by p population covariance matrix. Let Xk = Σ Yk for k = 1, 2, · · · , n and Σ̂1 = 1 n ∑n k=1XkX T k . Under the moment condition supp,n max1≤j≤p,1≤k≤n Ebjk < ∞, we prove that the log determinant of the sample covariance matrix Σ̂1 satisfies log det Σ̂...

We obtainC2,β estimates up to the boundary for solutions to degenerate Monge–Ampère equations of the type det D2u = f in , f ∼ distα(·, ∂ ) near ∂ , α > 0. As a consequence we obtain global C∞ estimates up to the boundary for the eigenfunctions of the Monge–Ampère operator (det D2u)1/n on smooth, bounded, uniformly convex domains in Rn .