A note on spin-s duality

Duality is investigated for higher spin (s ≥ 2), free, massless, bosonic gauge fields. We show how the dual formulations can be derived from a common "parent", first-order action. This goes beyond most of the previous treatments where higher-spin duality was investigated at the level of the equations of motion only. In D = 4 spacetime dimensions, the dual theories turn out to be described by the same Pauli-Fierz (s = 2) or Fronsdal (s ≥ 3) action (as it is the case for spin 1). In the particular s = 2 D = 5 case, the Pauli-Fierz action and the Curtright action are shown to be related through duality. A crucial ingredient of the analysis is given by the first-order, gauge-like, reformulation of higher spin theories due to Vasiliev. © SISSA/ISAS 2003.

Salted fish products from the Coptic monastery at Bawit, Egypt: evidence from the bones and texts

Fish bone assemblages are described that were recently discovered in the storage area of two rooms, dated to the 7th century AD, from the monastery of Bawit, Egypt. The species composition, the reconstructed sizes of the fish and the find contexts show that this material represents pickled fish (salsamenta). This product was made in one case of medium-sized Clarias catfish, whereas another assemblage, found inside an amphora, consisted of small-sized fish, mainly cyprinids and alestiids. The latter product was stored in a Late Roman Amphora 5/6 of Palestinian origin, traditionally considered as a container for wine. The amphora was clearly re-used since the fish found in it are Nilotic species which excludes that the salsamenta came from outside Egypt. A few additional finds of fish inside amphorae were available, but due to the low number of bones it was unclear if salted fish products were stored in them. Textual information provided by ostraca and papyri from the same site shows that the monks exerted fishing activities themselves and also suggests that the production of pickled fish took place locally. One of the two Nilotic fish taxa (Labeo) that is specifically mentioned by written evidence is the most common ingredient found in the amphora with abundant fish remains. The paper ends with a brief summary of other faunal evidence for salted fish products from monastic and other historic sites in Egypt.

Approximation limits of linear programs (beyond hierarchies)

We develop a framework for proving approximation limits of polynomial size linear programs (LPs) from lower bounds on the nonnegative ranks of suitably defined matrices. This framework yields unconditional impossibility results that are applicable to any LP as opposed to only programs generated by hierarchies. Using our framework, we prove that O(n^1/2-ε)-approximations for CLIQUE require LPs of size 2^nΩ(ε). This lower bound applies to LPs using a certain encoding of CLIQUE as a linear optimization problem. Moreover, we establish a similar result for approximations of semidefinite programs by LPs. Our main technical ingredient is a quantitative improvement of Razborov's [38] rectangle corruption lemma for the high error regime, which gives strong lower bounds on the nonnegative rank of shifts of the unique disjointness matrix.