In the geometric realization of a cubical complex without degeneracies, a 2-set, dipaths and dihomotopies may not be combinatorial, i.e., not geometric realizations of combinatorial dipaths and equivalences. When we want to use geometric/topological tools to classify dipaths on the 1-skeleton, combinatorial dipaths, up to dihomotopy, and in particular up to combinatorial dihomotopy, we need tha...

Strong evidence indicates that the spectrum of planar anomalous dimensions of N = 4 super Yang-Mills theory is given asymptotically by Bethe equations. A curious observation is that the Bethe equations for the psu(1, 1|2) subsector lead to very large degeneracies of 2 multiplets, which apparently do not follow from conventional integrable structures. In this article, we explain such degeneracie...

We compute the boundary entropies for the allowed boundary conditions of the SU (2)-invariant principal chiral model at level k = 1. We used the reflection factors determined in previous work. As a by-product we obtain some miscellaneous results such as the ground-state energy for mixed boundary conditions as well as the degeneracies of the Kondo model in the underscreened and exactly screened ...

We update a recent work devoted to resolve the degeneracies that appear in the simultaneous extraction of θ13 and δ at future Neutrino Factories (NF, that exploit the golden channels, i.e. νe → νμ (ν̄e → ν̄μ)) and Superbeam experiments (SB, that measure the νμ → νe (ν̄μ → ν̄e) transitions). We consider the neutrino fluxes obtained with a new optics design for the CERNSPL SB and assume the solar par...

Topological sweep can contribute to efficient implementations of various algorithms for data analysis. Real data, however, has degeneracies. The modification of the topological sweep algorithm presented here handles degenerate cases such as parallel or multiply concurrent lines without requiring numerical perturbations to achieve general position. Our method maintains the O(n) and O(n) time and...

(1.4) h(x, z) := detΦxz(x, z). If C is locally the graph of a canonical transformation, i.e., h(x, z) 6= 0, then ‖Tλ‖ = O(λ−d/2) (see Hörmander [15], [16]). If the projections have singularities then there is less decay in λ and in various specific cases the decay has been determined. In dimension d = 1 Phong and Stein [21] obtained a complete description of the L mapping properties, for the ca...

Continuing our first paper in this series, we study multiple limits in infinite-dimensional multiple categories. The general setting is chiral multiple categories a weak, partially lax form with directed interchanges. After defining multiple limits we prove that all of them can be constructed from (multiple) products, equalisers and tabulators all of them assumed to be respected by faces and de...

Distance measurements to Type Ia supernovae (SNe Ia) at cosmological distances indicate that the Universe is accelerating and that a large fraction of the critical energy density exists in a component with negative pressure. Various hypotheses on the nature of this “dark energy” can be tested via their prediction for the equation of state of this component. If the dark energy is due to a scalar...

Three propositions about Jordan matrices are proved and applied to algebraically classify the Ricci tensor in n-dimensional Kaluza-Klein-type spacetimes. We show that the possible Segre types are [1, 1 . . . 1], [21 . . . 1], [31 . . . 1], [zz̄1 . . . 1] and degeneracies thereof. A set of canonical forms for the Segre types is obtained in terms of semi-null bases of vectors.

{In this paper, we propose a highly reliable RAID architecture called a Dual-Crosshatch Disk Array. It uses the proposed interleaved 2d-parity scheme, a low overhead triple-erasure correcting parity organization. It is a hybrid approach of RAID-4 and RAID-5 with one dedicated parity group and another parity group using block interleaved data and parity. The results obtained from simulations ind...