A new generalized inversion for square matrices based on projections is introduced. It includes as special cases known generalized inverses such as the Moore-Penrose and the Drazin inverses. When associated with a regular matrix pencil, it can be expressed by a contour integral formula and can be used, in particular, to write down an explicit representation of the solutions of linear differenti...

We compute the singular value decomposition of the radial distribution function g(r) for hard sphere, and square well solutions. We find that g(r) decomposes into a small set of basis vectors allowing for an extremely accurate representation at all interpolated densities and potential strengths. In addition, we find that the coefficient vectors describing the magnitude of each basis vector are ...

A new generalized inversion for square matrices based on projections is introduced. It includes as special cases known generalized inverses such as the Moore-Penrose and the Drazin inverses. When associated with a regular matrix pencil, it can be expressed by a contour integral formula and can be used, in particular, to write down an explicit representation of the solutions of linear differenti...

The nonarchimedean local analogues of modular forms of half-integral weight with level and character are certain vectors in irreducible, admissible, genuine representations of the metaplectic group over a nonarchimedean local field of characteristic zero. Two natural level raising operators act on such vectors, leading to the concepts of oldforms and newforms. We prove that the number of newfor...

Memories are thought to be attractor states of neuronal representations, with the hippocampus a likely substrate for context-dependent episodic memories. However, such states have not been directly observed. For example, the hippocampal place cell representation of location was previously found to respond continuously to changes in environmental shape alone. We report that exposure to novel squ...

The near-horizon properties of a black hole are studied within an algebraic framework, using a scalar field as a simple probe to analyze the geometry. The operator H governing the near-horizon dynamics of the scalar field contains an inverse square interaction term. It is shown that the operators appearing in the corresponding algebraic description belong to the representation space of the Vira...

In this note we use Clifford algebras and their Fock representations to build representations of LU(N) and LSU(N). Let H be the Hilbert space of square-integrable sections of the trivial rank N complex vector bundle over S and P : H → H the projection onto the space spanned by non-negative Fourier modes. To this data we can associate the Fermionic Fock space FP . FP is a representation of level...

When delegations to an assembly or council represent differently sized constituencies, they are often allocated voting weights which increase in population numbers (EU Council, US Electoral College, etc.). The Penrose square root rule (PSRR) is the main benchmark for ‘fair representation’ of all bottom-tier voters in the top-tier decision making body, but rests on the restrictive assumption of ...

This paper combines linear sparse coding and nonnegative matrix factorization into sparse non-negative matrix factorization. In contrast to non-negative matrix factorization, the new model can leam much sparser representation via imposing sparseness constraints explicitly; in contrast to a close model non-negative sparse coding, the new model can learn parts-based representation via fully multi...

The six-vertex model on an N × N square lattice with domain wall boundary conditions is considered. A Fredholm determinant representation for the partition function of the model is given. The kernel of the corresponding integral operator is of the so-called integrable type, and involves classical orthogonal polynomials. From this representation, a " reconstruction " formula is proposed, which e...