Recent observations of Type 1a supernovae indicating an accelerating universe have once more drawn attention to the possible existence, at the present epoch, of a small positive Λ-term (cosmological constant). In this paper we review both observational and theoretical aspects of a small cosmological Λ-term. We discuss the current observational situation focusing on cosmological tests of Λ inclu...

In this document we give supplementary details to the paper " The Solution Path of the Generalized Lasso ". We use the prefix " GL " when referring to equations, sections, etc. in the original paper, as in equation (GL-1) or Section GL-1 (this stands for Generalized Lasso). 1 Proof of the boundary lemma We prove the boundary lemma when D = D 1d , but first we give a helpful lemma. Lemma 1. Let ...

An account is given of the structure and representations of chiral bosonic meromorphic conformal field theories (CFT's), and, in particular, the conditions under which such a CFT may be extended by a representation to form a new theory. This general approach is illustrated by considering the untwisted and Z 2-twisted theories, H(Λ) and˜H(Λ) respectively , which may be constructed from a suitabl...

It is shown that the problem of reduction can be formulated in a uniform way using the theory of invariants. This provides a powerful tool of analysis and it opens the road to new applications of these algebras, beyond the context of integrable systems. Moreover, it is proven that sl2(C)–Automorphic Lie Algebras associated to the icosahedral group I, the octahedral group O, the tetrahedral grou...

Suppose λ,x,ζ traverse the ordered sets Λ, X and Z, respectively and consider the functions f(λ,x,ζ) and g(λ,ζ) satisfying the following conditions, (a) f(λ,x,ζ) > 0 and f is TP2 in each pairs of variables when the third variable is held fixed and (b) g(λ,ζ) is TP2. Then the function h(λ,x) =∫Z f(λ,x,ζ)g(λ,ζ)dµ(ζ), defined on Λ×X is TP2 in (λ,x). The aim of this note is to use a new stochast...

We consider effects of symmetries on renormalization properties of the collinear effective theory. We investigate which types of operators are possible in the effective theory satisfying gauge invariance, reparameterization invariance and residual energy invariance. Each symmetry puts a constraint on the possible structure of the theory, and there can appear only specific combinations of operat...

Two-dimensional lattices provide the arena for many physics problems of essential importance, a scale symmetry, which rarely exists as noticed by Galileo, in such lattices can help reveal the underlying physics. Here we report the discovery and proof of directional scaling symmetry for high symmetry 2D lattices, i.e., the square lattice, the equilateral triangular lattice and thus the honeycomb...

We study positronium’s fine structure in a light-front hamiltonian approach. Starting with a bare cutoff QED hamiltonian, H B , with matrix elements between free states of drastically different energies removed, we perform a similarity transformation that removes the matrix elements between free states with energy differences between the bare cutoff, Λ, and final cutoff, λ (λ < Λ). This generat...

In this talk I summarize our recent works on the chiral phase transition in the large flavor QCD studied by the hidden local symmetry (HLS). Bare parameters in the HLS are determined by matching the HLS with the underlying QCD at the matching scale through the Wilsonian matching. This leads to the vector manifestation of the Wigner realization of the chiral symmetry in which the symmetry is res...

We determine the helicity amplitudes A1/2 and radiative decay widths in the transition Λ(1670) → γY (Y = Λ or Σ). The Λ(1670) is treated as a dynamically generated resonance in mesonbaryon chiral dynamics. We obtain the radiative decay widths of the Λ(1670) to γΛ as 3 ± 2 keV and to γΣ as 120 ± 50 keV. Also, the Q dependence of the helicity amplitudes A1/2 is calculated. We find that the KΞ com...