The Isomorphism Relation Between Tree-Automatic Structures

An $\omega$-tree-automatic structure is a relational structure whose domain and relations are accepted by Muller or Rabin tree automata. We investigate in this paper the isomorphism problem for $\omega$-tree-automatic structures. We prove first that the isomorphism relation for $\omega$-tree-automatic boolean algebras (respectively, partial orders, rings, commutative rings, non commutative rings, non commutative groups, nilpotent groups of class n >1) is not determined by the axiomatic system ZFC. Then we prove that the isomorphism problem for $\omega$-tree-automatic boolean algebras (respectively, partial orders, rings, commutative rings, non commutative rings, non commutative groups, nilpotent groups of class n >1) is neither a $\Sigma_2^1$-set nor a $\Pi_2^1$-set

Spurious shear induced by the tree rings of the LSST CCDs

We present an analysis of the impact of the tree rings seen in the candidate sensors of the Large Synoptic Survey Telescope (LSST) on galaxy-shape measurements. The tree rings are a consequence of transverse electric fields caused by circularly symmetric impurity gradients in the silicon of the sensors. They effectively modify the pixel area and shift the photogenerated charge around, displacing the observed photon positions. The displacement distribution generates distortions that cause spurious shears correlated with the tree-rings patterns, potentially biasing cosmic shear measurements. In this paper we quantify the amplitude of the spurious shear caused by the tree rings on the LSST candidate sensors, and calculate its 2-point correlation function. We find that 2-point correlation function of the spurious shear on an area equivalent to the LSST field of view is order of about $10^{-13}$, providing a negligible contribution to the 2-point correlation of the cosmic shear signal. Additional work is underway, and the final results and analysis will be published elsewhere (Okura et al. (2015), in prep.

Branch Rings, Thinned Rings, Tree Enveloping Rings

We develop the theory of ``branch algebras'', which are infinite-dimensional associative algebras that are isomorphic, up to taking subrings of finite codimension, to a matrix ring over themselves. The main examples come from groups acting on trees. In particular, for every field k we construct a k-algebra K which (1) is finitely generated and infinite-dimensional, but has only finite-dimensional quotients; (2) has a subalgebra of finite codimension, isomorphic to $M_2(K)$; (3) is prime; (4) has quadratic growth, and therefore Gelfand-Kirillov dimension 2; (5) is recursively presented; (6) satisfies no identity; (7) contains a transcendental, invertible element; (8) is semiprimitive if k has characteristic $\neq2$; (9) is graded if k has characteristic 2; (10) is primitive if k is a non-algebraic extension of GF(2); (11) is graded nil and Jacobson radical if k is an algebraic extension of GF(2).Comment: 35 pages; small changes wrt previous versio

Does Cedrela always form annual rings? Testing ring periodicity across South America using radiocarbon dating

Tropical tree rings have the potential to yield valuable ecological and climate information, on the condition that rings are annual and accurately dated. It is important to understand the factors controlling ring formation, since regional variation in these factors could cause trees in different regions to form tree rings at different times. Here, we use ‘bomb-peak’ radiocarbon (¹⁴C) dating to test the periodicity of ring formation in Cedrela trees from four sites across tropical South America. We show that trees from Bolivia, Ecuador and Venezuela have reliably annual tree rings, while trees from Suriname regularly form two rings per year. This proves that while tree rings of a particular species may be demonstrably annual at one site, this does not imply that rings are formed annually in other locations. We explore possible drivers of variation in ring periodicity and find that Cedrela growth rhythms are most likely caused by precipitation seasonality, with a possible degree of genetic control. Therefore, tree-ring studies undertaken at new locations in the tropics require independent validation of the annual nature of tree rings, irrespective of how the studied species behaves in other location

Nonannual tree rings in a climate-sensitive Prioria copaifera chronology in the Atrato River, Colombia

In temperate climates, tree growth dormancy usually ensures the annual nature of tree rings, but in tropical environments, determination of annual periodicity can be more complex. The purposes of the work are as follows: (1) to generate a reliable tree‐ring width chronology for Prioria copaifera Griseb. (Leguminoceae), a tropical tree species dwelling in the Atrato River floodplains, Colombia; (2) to assess the climate signal recorded by the tree‐ring records; and (3) to validate the annual periodicity of the tree rings using independent methods. We used standard dendrochronological procedures to generate the P. copaifera tree‐ring chronology. We used Pearson correlations to evaluate the relationship of the chronology with the meteorological records, climate regional indices, and gridded precipitation/sea surface temperature products. We also evaluated 24 high‐precision 14C measurements spread over a range of preselected tree rings, with assigned calendar years by dendrochronological techniques, before and after the bomb spike in order to validate the annual nature of the tree rings. The tree‐ring width chronology was statistically reliable, and it correlated significantly with local records of annual and October–December (OND) streamflow and precipitation across the upper river watershed (positive), and OND temperature (negative). It was also significantly related to the Oceanic Niño Index, Pacific Decadal Oscillation, and the Southern Oscillation Index, as well as sea surface temperatures over the Caribbean and the Pacific region. However, 14C high‐precision measurements over the tree rings demonstrated offsets of up to 40 years that indicate that P. copaifera can produce more than one ring in certain years. Results derived from the strongest climate–growth relationship during the most recent years of the record suggest that the climatic signal reported may be due to the presence of annual rings in some of those trees in recent years. Our study alerts about the risk of applying dendrochronology in species with challenging anatomical features defining tree rings, commonly found in the tropics, without an independent validation of annual periodicity of tree rings. High‐precision 14C measurements in multiple trees are a useful method to validate the identification of annual tree rings

X-ray based tree ring analyses

In this thesis, two x-ray based dendro-analyses (batch-wise microdensitometry and energy dispersive x-ray fluorescence (EDXRF)) and the conditions under which these methods could be used on the two typical boreal conifers Norway spruce (Picea abies (L.) Karst.) and Scots pine (Pinus sylvestris L.) were evaluated. For density measurements using batch scanning x-ray densitometry, sample preparation and density calibration are vital to acquire high resolution and precision in densitometric measurements. Thickness and alignment should be adapted to give optimal resolution without loss of precision. Samples should be extracted to remove resins before wood density measurements. Ca, Mn, Fe, and Sr and in most cases K and Zn could thus be measured in an efficient way using EDXRF. Significant differences in concentrations between tree rings were found for all of these elements except Sr, indicating that tree ring concentrations of these elements could be correlated to changes in the tree environment. For Mn a correlation between soil pH and Mn concentration in tree rings was found. Other correlations between tree ring element concentration and tree environmental factors were also found. For most elements in tree-rings of Scots pine and Norway spruce it seems that the concentration is due to environmental conditions during the year the tree-ring was developed and several years afterwards. It is concluded that microdensitometry and EDXRF analyses on increment cores are cost-efficient and non-destructive analyses of wood properties. Batch-wise, x-ray based dendrochemical analysis provides opportunities for more property-based use of wood raw material and for environmental monitoring

Fingerprints of extreme climate events in Pinus sylvestris tree rings from Bulgaria

Tree-ring studies may help better understand climate variability and extreme climate event frequency and are especially useful in regions where detailed meteorological records lack. We studied the effect of droughts and unusually cold periods on Pinus sylvestris tree-ring width and wood anatomy. Study sites were selected along an altitudinal gradient on Vitosha Mountain, Bulgaria. Drought conditions caused the formation of narrow tree rings or light rings if the drought occurred in July-August at the lower altitude sites. In years with droughts in June and the first half of July, followed by precipitation in the middle of July, intra-annual density fluctuations (IADFs) were formed. Trees in the zone with optimal growth conditions produced fewer light rings and narrow rings in years with either strongest droughts or unusually cold summers. At the timberline zone, low summer temperature triggered narrow tree rings and light rings. Frost rings were formed when there was a drop in temperatures below the freezing point in the second half of May or at the beginning of June. Our findings show that studies of tree-ring anatomy may contribute to obtain further knowledge about extreme climatic events in the Balkan Peninsula and in other regions where meteorological data lac