Metric-like Lagrangian Formulations for Higher-Spin Fields of Mixed Symmetry

We review the structure of local Lagrangians and field equations for free bosonic and fermionic gauge fields of mixed symmetry in flat space. These are first presented in a constrained setting extending the metric formulation of linearized gravity, and then the ($\gamma$-)trace constraints on fields and gauge parameters are eliminated via the introduction of auxiliary fields. We also display the emergence of Weyl-like symmetries in particular classes of models in low space-time dimensions.Comment: 136 pages, LaTeX. References added. Final version to appear in La Rivista del Nuovo Cimento

On oblivious branching programs with bounded repetition that cannot efficiently compute CNFs of bounded treewidth

In this paper we study complexity of an extension of ordered binary decision diagrams (OBDDs) called c-OBDDs on CNFs of bounded (primal graph) treewidth. In particular, we show that for each k ≥ 3 there is a class of CNFs of treewidth k for which the equivalent c-OBDDs are of size Ω(nk/(8c−4)). Moreover, this lower bound holds if c-OBDDs are non-deterministic and semantic. Our second result uses the above lower bound to separate the above model from sentential decision diagrams (SDDs). In order to obtain the lower bound, we use a structural graph parameter called matching width. Our third result shows that matching width and pathwidth are linearly related

The beginning of time? Evidence for catastrophic drought in Baringo in the early nineteenth century

New developments in the collection of palaeo-data over the past two decades have transformed our understanding of climate and environmental history in eastern Africa. This article utilises instrumental and proxy evidence of historical lake-level fluctuations from Baringo and Bogoria, along with other Rift Valley lakes, to document the timing and magnitude of hydroclimate variability at decadal to century time scales since 1750. These data allow us to construct a record of past climate variation not only for the Baringo basin proper, but also across a sizable portion of central and northern Kenya. This record is then set alongside historical evidence, from oral histories gathered amongst the peoples of northern Kenya and the Rift Valley and from contemporary observations recorded by travellers through the region, to offer a reinterpretation of human activity and its relationship to environmental history in the nineteenth century. The results reveal strong evidence of a catastrophic drought in the early nineteenth century, the effects of which radically alters our historical understanding of the character of settlement, mobility and identity within the Baringo–Bogoria basin

Logical Characterization of Weighted Pebble Walking Automata

International audienceWeighted automata are a conservative quantitative extension of finite automata that enjoys applications, e.g., in language processing and speech recognition. Their expressive power, however, appears to be limited, especially when they are applied to more general structures than words, such as graphs. To address this drawback, weighted automata have recently been generalized to weighted pebble walking automata, which proved useful as a tool for the specification and evaluation of quantitative properties over words and nested words. In this paper, we establish the expressive power of weighted pebble walking automata in terms of transitive closure logic, lifting a similar result by Engelfriet and Hoogeboom from the Boolean case to a quantitative setting. This result applies to a general class of graphs that subsumes all the aforementioned classes

Elevated Oestrogen Receptor Splice Variant ERαΔ5 Expression in Tumour-adjacent Hormone-responsive Tissue

Susceptibility to prostate or endometrial cancer is linked with obesity, a state of oestrogen excess. Oestrogen receptor (ER) splice variants may be responsible for the tissue-level of ER activity. Such micro-environmental regulation may modulate cancer initiation and/or progression mechanisms. Real-time reverse transcriptase (RT) polymerase chain reaction (PCR) was used to quantitatively assess the levels of four ER splice variants (ERαΔ3, ERαΔ5, ERβ2 and ERβ5), plus the full-length parent isoforms ERα and ERβ1, in high-risk [tumour-adjacent prostate (n = 10) or endometrial cancer (n = 9)] vs. low-risk [benign prostate (n = 12) or endometrium (n = 9)], as well as a comparison of UK (n = 12) vs. Indian (n = 15) benign prostate. All three tissue groups expressed the ER splice variants at similar levels, apart from ERαΔ5. This splice variant was markedly raised in all of the tumour-adjacent prostate samples compared to benign tissues. Immunofluorescence analysis for ERβ2 in prostate tissue demonstrated that such splice variants are present in comparable, if not greater, amounts as the parent full-length isoform. This small pilot study demonstrates the ubiquitous nature of ER splice variants in these tissue sites and suggests that ERαΔ5 may be involved in progression of prostate adenocarcinoma