Related papers: Simplified exact SICs
The majority-voter model is studied by Monte Carlo simulations on hypercubic lattices of dimension $d=2$ to 7 with periodic boundary conditions. The critical exponents associated to the Finite-Size Scaling of the magnetic susceptibility are…
We discuss the existence of an orthogonal basis consisting of decomposable vectors for some symmetry classes of tensors associated with Semi-Dihedral groups $SD_{8n}$. The dimensions of these symmetry classes of tensors are also computed.
We find families of simplicial complexes where the simplicial chromatic polynomials defined by Cooper--de Silva--Sazdanovic \cite{CdSS} are Hilbert series of Stanley--Reisner rings of auxiliary simplicial complexes. As a result, such…
We work out all of the details required for implementation of the conformal bootstrap program applied to the four-point function of two scalars and two vectors in an abstract conformal field theory in arbitrary dimension. This includes a…
Verma modules of superconfomal algebras can have singular vector spaces with dimensions greater than 1. Following a method developed for the Virasoro algebra by Kent, we introduce the concept of adapted orderings on superconformal algebras.…
We prove the Plancherel formula for a four-parameter family of discrete Fourier transforms and their multivariate generalizations stemming from corresponding generalized Schur polynomials. For special choices of the parameters, this…
The NP-hard Distinct Vectors problem asks to delete as many columns as possible from a matrix such that all rows in the resulting matrix are still pairwise distinct. Our main result is that, for binary matrices, there is a complexity…
A system of commutative complex numbers in 5 dimensions of the form u=x_0+h_1x_1+h_2x_2+h_3x_3+h_4x_4 is described in this paper, the variables x_0, x_1, x_2, x_3, x_4 being real numbers. The operations of addition and multiplication of the…
In this article, we combine the periodic sinc basis set with a curvilinear coordinate system for electronic structure calculations. This extension allows for variable resolution across the computational domain, with higher resolution close…
We present solutions to the matrix completion problems proposed by the Alignment Research Center that have a polynomial dependence on the precision $\varepsilon$. The motivation for these problems is to enable efficient computation of…
We prove equality of the vector field (iterated commutator) type and the regular contact type, which together with the Bloom theorem on equality of the Levi-form type and the regular contact type provides a complete solution of a long…
We study 6d $(1,0)$ superconformal theories. These have a natural lightlike conformal Killing vector, the Dirac current. We perform a conformal dimensional reduction along the Dirac current down to five-dimensions in such a way that we…
It is proved that quasi-exactly soluble potentials corresponding to an oscillator with harmonic, quartic and sextic terms, for which the $n+1$ lowest levels of a given parity can be determined exactly, may be approximated by WKB equivalent…
We introduce a suitable adapted ordering for the twisted N=2 superconformal algebra (i.e. with mixed boundary conditions for the fermionic fields). We show that the ordering kernels for complete Verma modules have two elements and the…
We use the conformal bootstrap to perform a precision study of the operator spectrum of the critical 3d Ising model. We conjecture that the 3d Ising spectrum minimizes the central charge c in the space of unitary solutions to crossing…
We consider complex rational vector fields in dimension $n>2$ (equivalently, differential forms of degree $n-1$ in $n$ variables) which admit a Liouvillian first integral. Extending a classical result by Singer for $n=2$, our main result…
A spinorial approach to 6-dimensional differential geometry is constructed and used to analyze tensor fields of low rank, with special attention to the Weyl tensor. We perform a study similar to the 4-dimensional case, making full use of…
We study the Lorentz and Dirac algebra, including antisymmetric $\epsilon$ tensors and the $\gamma_5$ matrix, in implicit gauge-invariant regularization/renormalization methods defined in fixed integer dimensions. They include constrained…
Obtaining meaningful solutions for inverse problems has been a major challenge with many applications in science and engineering. Recent machine learning techniques based on proximal and diffusion-based methods have shown promising results.…
We show that translations and dilations of a p-adic wavelet coincides (up to the multiplication by some root of one) with a vector from the known basis of discrete p-adic wavelets. In this sense the continuous p-adic wavelet transform…