Global Response Sensitivity Analysis of Randomly Excited Dynamic Structures

The response of structural dynamical systems excited by multiple random excitations is considered. Two new procedures for evaluating global response sensitivity measures with respect to the excitation components are proposed. The first procedure is valid for stationary response of linear systems under stationary random excitations and is based on the notion of Hellinger's metric of distance between two power spectral density functions. The second procedure is more generally valid and is based on the l2 norm based distance measure between two probability density functions. Specific cases which admit exact solutions are presented, and solution procedures based on Monte Carlo simulations for more general class of problems are outlined. Illustrations include studies on a parametrically excited linear system and a nonlinear random vibration problem involving moving oscillator-beam system that considers excitations attributable to random support motions and guide-way unevenness. (C) 2015 American Society of Civil Engineers.

A Bayesian wavelet-based multidimensional deconvolution with sub-band emphasis

This paper proposes a new algorithm for waveletbased multidimensional image deconvolution which employs subband-dependent minimization and the dual-tree complex wavelet transform in an iterative Bayesian framework. In addition, this algorithm employs a new prior instead of the popular ℓ1 norm, and is thus able to embed a learning scheme during the iteration which helps it to achieve better deconvolution results and faster convergence. © 2008 IEEE.

Image deconvolution using a Gaussian scale mixtures model to approximate the wavelet sparseness constraint

This paper proposes to use an extended Gaussian Scale Mixtures (GSM) model instead of the conventional ℓ1 norm to approximate the sparseness constraint in the wavelet domain. We combine this new constraint with subband-dependent minimization to formulate an iterative algorithm on two shift-invariant wavelet transforms, the Shannon wavelet transform and dual-tree complex wavelet transform (DTCWT). This extented GSM model introduces spatially varying information into the deconvolution process and thus enables the algorithm to achieve better results with fewer iterations in our experiments. ©2009 IEEE.

Hacia una ética de la responsabilidad: Derrida y el otro “por venir” en Lévinas

Resumen: La tesis del trabajo es que la deconstrucción entraña en sí misma una actitud ética, y que ésta radica intrínsecamente en su apertura al otro y en la responsabilidad frente a ese otro. Para ello, se intenta en primer lugar una elucidación del concepto, caracterizándola como un protocolo de lectura compuesto de dos fases: des-sedimentación y reinscripción, siendo este último momento el que la identifica como una lectura singular y no universalizable. Posteriormente, a través de las nociones de “sujeto” y “alteridad del texto”, se muestra cómo las bases de la ética deconstructiva giran en torno a las nociones de “yo” y “otro”, conceptos que Derrida, como se demuestra, toma de Lévinas. La instancia ética es la apertura al otro, que se verifica por la responsabilidad que supone concebir al otro como aquello incapaz de apropiación. Dicha responsabilidad configura la aporía ética de lo general-particular, al concebirse como la posibilidad imposible de una opción general que es al mismo tiempo una decisión personal o singular, o, en otros términos, la indecidibilidad entre la norma general y la decisión concreta, que es a su vez la tensión entre “justicia”, “hospitalidad” y “negociación”. Lo anterior demuestra que el acto ético (o acto deconstructivo) tiene la misma estructura de la différance, imbricada siempre en la iteración del significante.

Ausência de política pública de cotas raciais para ingresso em instituições públicas de ensino superior no Brasil

Descreve o atual panorama normativo para as cotas raciais no Brasil com base em estudo realizado com utilização de a análise documental e bibliográfica. Os resultados indicaram que a ausência de uma norma federal implicou baixa adesão ao sistema de cotas, o que é ratificado pelo insignificante número de Instituições Públicas de Ensino Superior (Ipes) que adotaram norma de cota racial - apenas 17,79%. Verificou-se, ainda, que essa ausência cria lacunas na adoção de diretrizes nacionais para a interpretação e a compreensão das ações afirmativas. Tais lacunas refletem diretamente no ciclo da política pública, comprometendo a avaliação e o acompanhamento da efetividade e do sucesso da política, o que é extremamente perigoso para a segurança jurídica na área de direitos humanos e para a garantia da equidade de fato nos espaços político, econômico e social.

Política de cotas raciais para ingresso em instituições públicas de ensino superior no Brasil : ausência de política pública

Descreve o atual panorama normativo para as cotas raciais no Brasil. Os resultados indicaram que a ausência de uma norma federal implicou na baixa adesão ao sistema de cotas, o que é ratificado pelo insignificante número de Instituições Públicas de Ensino Superior - IPES que adotaram norma de cota racial - apenas 17,79%. Verificou-se, ainda, que essa ausência cria lacunas na adoção de diretrizes nacionais para a interpretação e a compreensão das ações afirmativas. Tais lacunas refletem diretamente no ciclo da política pública, comprometendo a avaliação e o acompanhamento da efetividade e do sucesso da política, o que é extremamente perigoso para a segurança jurídica na área de direitos humanos e para a garantia da equidade de fato nos espaços político, econômico e sociais.

Prosocial norms and degree heterogeneity in social networks

We provide empirical evidence to support the claims that social diversity promotes prosocial behavior. We elicit a real-life social network and its members’ adherence to a social norm, namely inequity aversion. The data reveal a positive relationship between subjects’ prosociality and several measures of centrality. This result is in line with the theoretical literature that relates the evolution of social norms to the structure of social interactions and argues that central individuals are crucial for the emergence of prosocial behavior.

The ontogeny of haematopoiesis in the marine teleost Leiostomus xanthurus and a comparison of the site of initial haematopoiesis with Opsanus tau

The ontogeny of haematopoiesis in the perciform fish, spot Leiostomus xanthurus, differed from that reported as the norm for fishes, as exemplified by the cypriniform zebrafish Danio rerio, and observed in the batrachoidiform oyster toadfish Opsanus tau. Erythropoiesis in spot was first evident in the head kidney of yolk-sac larvae 3 days after hatching (DAH). No embryonic intermediate cell mass (ICM) of primitive stem cells or blood islands on the yolk were apparent within embryos. Erythrocytes were first evident in circulation near the completion of yolk absorption, c. 5 DAH, when larvae were c. 20 mm notochord length (LN). Erythrocyte abundance increased rapidly with larval development for c. 14 to 16 DAH, then became highly variable following changes in cardiac chamber morphology and volume. Erythrocytic haemoglobin (Hb) was not detected within whole larvae until they were 12 DAH or c. 31 mm LN, well after yolk and oil-globule absorption. The Hb was not quantified until larvae were >47 DAH or >7 mm standard length. The delayed appearance of erythrocytes and Hb in spot was similar to that reported for other marine fishes with small embryos and larvae. In oyster toadfish, a marine teleost that exhibits large embryos and larvae, the ICM and Hb were first evident in two bilateral slips of erythropoietic tissue in the embryos, c. 5 days after fertilization. Soon thereafter, erythrocytes were evident in the heart, and peripheral and vitelline circulation. Initial haematopoiesis in oyster toadfish conformed with that described for zebrafish. While the genes that code for the development of haematopoiesis are conserved among vertebrates, gene expression lacks phylogenetic pattern among fishes and appears to conform more closely with phenotypic expression related to physiological and ecological influences of overall body size and environmental oxygen availability.

U.S. Caribbean fish trap fishery costs and earnings study

Executive Summary: This study describes the socio-economic characteristics of the U.S. Caribbean trap fishery that encompasses the Commonwealth of Puerto Rico and Territory of the U.S. Virgin Islands. In-person interviews were administered to one hundred randomly selected trap fishermen, constituting nearly 25% of the estimated population. The sample was stratified by geographic area and trap tier. The number of traps owned or fished to qualify for a given tier varied by island. In Puerto Rico, tier I consisted of fishermen who had between 1-40 fish traps, tier II was made up of fishermen who possessed between 41 and 100 fish traps, and tier III consisted of fishermen who held in excess of 100 fish traps. In St. Thomas and St. John, tier I was composed of fishermen who held between 1 and 50 fish traps, tier II consisted of fishermen who had between 51-150 fish traps and tier III was made up of fishermen who had in excess of 150 fish traps. Lastly, in St. Croix, tier I was made up of fishermen who had less than 20 fish traps and tier II consisted of fishermen who had 20 or more fish traps. The survey elicited information on household demographics, annual catch and revenue, trap usage, capital investment on vessels and equipment, fixed and variable costs, behavioral response to a hypothetical trap reduction program and the spatial distribution of traps. The study found that 79% of the sampled population was 40 years or older. The typical Crucian trap fisherman was older than their Puerto Rican and St. Thomian and St. Johnian counterparts. Crucian fishermen’s average age was 57 years whereas Puerto Rican fishermen’s average age was 51 years, and St. Thomian and St. Johnian fishermen’s average age was 48 years. As a group, St. Thomian and St. Johnian fishermen had 25 years of fishing experience, and Puerto Rican and Crucian fishermen had 30, and 29 years, respectively. Overall, 90% of the households had at least one dependent. The average number of dependents across islands was even, ranging between 2.8 in the district of St. Thomas and St. John and 3.4 in the district of St. Croix. The percentage utilization of catch for personal or family use was relatively low. Regionally, percentage use of catch for personal or family uses ranged from 2.5% in St. Croix to 3.8% in the St. Thomas and St. John. About 47% of the respondents had a high school degree. The majority of the respondents were highly dependent on commercial fishing for their household income. In St. Croix, commercial fishing made up 83% of the fishermen’s total household income, whereas in St. Thomas and St. John and Puerto Rico it contributed 74% and 68%, respectively. The contribution of fish traps to commercial fishing income ranged from 51% in the lowest trap tier in St. Thomas and St. John to 99% in the highest trap tier in St. Croix. On an island basis, the contribution of fish traps to fishing income was 75% in St. Croix, 61% in St. Thomas and St. John, and 59% in Puerto Rico. The value of fully rigged vessels ranged from $400 to $250,000. Over half of the fleet was worth $10,000 or less. The St. Thomas and St. John fleet reported the highest mean value, averaging $58,518. The Crucian and Puerto Rican fleets were considerably less valuable, averaging $19,831 and $8,652, respectively. The length of the vessels ranged from 14 to 40 feet. Fifty-nine percent of the sampled vessels were at least 23 feet in length. The average length of the St. Thomas and St. John fleet was 28 feet, whereas the fleets based in St. Croix and Puerto Rico averaged 21 feet. The engine’s propulsion ranged from 8 to 400 horsepower (hp). The mean engine power was 208 hp in St. Thomas and St. John, 108 hp in St. Croix, and 77 hp in Puerto Rico. Mechanical trap haulers and depth recorders were the most commonly used on-board equipment. About 55% of the sampled population reported owning mechanical trap haulers. In St. Thomas and St. John, 100% of the respondents had trap haulers compared to 52% in Puerto Rico and 20% in St. Croix. Forty-seven percent of the fishermen surveyed stated having depth recorders. Depth recorders were most common in the St. Thomas and St. John fleet (80%) and least common in the Puerto Rican fleet (37%). The limited presence of emergency position indication radio beacons (EPIRBS) and radar was the norm among the fish trap fleet. Only 8% of the respondents had EPIRBS and only 1% had radar. Interviewees stated that they fished between 1 and 350 fish traps. Puerto Rican respondents fished on average 39 fish traps, in contrast to St. Thomian and St. Johnian and Crucian respondents, who fished 94 and 27 fish traps, respectively. On average, Puerto Rican respondents fished 11 lobster traps, and St. Thomian and St. Johnian respondents fished 46 lobster traps. None of the Crucian respondents fished lobster traps. The number of fish traps built or purchased ranged between 0 and 175, and the number of lobster traps built or bought ranged between 0 and 200. Puerto Rican fishermen on average built or purchased 30 fish traps and 14 lobster traps, and St. Thomian and St. Johnian fishermen built or bought 30 fish traps and 11 lobster traps. Crucian fishermen built or bought 25 fish traps and no lobster traps. As a group, fish trap average life ranged between 1.3 and 5 years, and lobster traps lasted slightly longer, between 1.5 and 6 years. The study found that the chevron or arrowhead style was the most common trap design. Puerto Rican fishermen owned an average of 20 arrowhead traps. St. Thomian and St. Johnian and Crucian fishermen owned an average of 44 and 15 arrowhead fish traps, respectively. The second most popular trap design was the square trap style. Puerto Rican fishermen had an average of 9 square traps, whereas St. Thomian and St. Johnian fishermen had 33 traps and Crucian fishermen had 2 traps. Antillean Z (or S) -traps, rectangular and star traps were also used. Although Z (or S) -traps are considered the most productive trap design, fishermen prefer the smaller-sized arrowhead and square traps because they are easier and less expensive to build, and larger numbers of them can be safely deployed. The cost of a fish trap, complete with rope and buoys, varied significantly due to the wide range of construction materials utilized. On average, arrowhead traps commanded $94 in Puerto Rico, $251 in St. Thomas and St. John, and $119 in St. Croix. The number of trips per week ranged between 1 and 6. However, 72% of the respondents mentioned that they took two trips per week. On average, Puerto Rican fishermen took 2.1 trips per week, St. Thomian and St. Johnian fishermen took 1.4 trips per week, and Crucian fishermen took 2.5 trips per week. Most fishing trips started at dawn and finished early in the afternoon. Over 82% of the trips lasted 8 hours or less. On average, Puerto Rican fishermen hauled 27 fish traps per trip whereas St. Thomian and St. Johnian fishermen and Crucian fishermen hauled 68 and 26 fish traps per trip, respectively. The number of traps per string and soak time varied considerably across islands. In St. Croix, 84% of the respondents had a single trap per line, whereas in St. Thomas and St. John only 10% of the respondents had a single trap per line. Approximately, 43% of Puerto Rican fishermen used a single trap line. St. Thomian and St. Johnian fishermen soaked their traps for 6.9 days while Puerto Rican and Crucian fishermen soaked their traps for 5.7 and 3.6 days, respectively. The heterogeneity of the industry was also evidenced by the various economic surpluses generated. The survey illustrated that higher gross revenues did not necessarily translate into higher net revenues. Our analysis also showed that, on average, vessels in the trap fishery were able to cover their cash outlays, resulting in positive vessel income (i.e., financial profits). In Puerto Rico, annual financial profits ranged from $4,760 in the lowest trap tier to $32,467 in the highest tier, whereas in St. Thomas and St. John annual financial profits ranged from $3,744 in the lowest tier to $13,652 in the highest tier. In St. Croix, annual financial profits ranged between $9,229 and $15,781. The survey also showed that economic profits varied significantly across tiers. Economic profits measure residual income after deducting the remuneration required to keep the various factors of production in their existing employment. In Puerto Rico, annual economic profits ranged from ($9,339) in the lowest trap tier to $ 8,711 in the highest trap tier. In St. Thomas and St. John, annual economic profits ranged from ($7,920) in the highest tier to ($18,486) in the second highest tier. In St. Croix, annual economic profits ranged between ($7,453) to $10,674. The presence of positive financial profits and negative economic profits suggests that higher economic returns could be earned from a societal perspective by redirecting some of these scarce capital and human resources elsewhere in the economy. Furthermore, the presence of negative economic earnings is evidence that the fishery is overcapitalized and that steps need to be taken to ensure the long-run economic viability of the industry. The presence of positive financial returns provides managers with a window of opportunity to adopt policies that will strengthen the biological and economic performance of the fishery while minimizing any adverse impacts on local fishing communities. Finally, the document concludes by detailing how the costs and earnings information could be used to develop economic models that evaluate management proposals. (PDF contains 147 pages)

Caribbean connectivity: implications for Marine Protected Area Management. Proceedings of a Special Symposium, 9-11 November 2006, 59th Annual Meeting of the Gulf and Caribbean Fisheries Institute, Belize City, Belize

Executive Summary: Tropical marine ecosystems in the Caribbean region are inextricably linked through the movement of pollutants, nutrients, diseases, and other stressors, which threaten to further degrade coral reef communities. The magnitude of change that is occurring within the region is considerable, and solutions will require investigating pros and cons of networks of marine protected areas (MPAs), cooperation of neighboring countries, improved understanding of how external stressors degrade local marine resources, and ameliorating those stressors. Connectivity can be broadly defined as the exchange of materials (e.g., nutrients and pollutants), organisms, and genes and can be divided into: 1) genetic or evolutionary connectivity that concerns the exchange of organisms and genes, 2) demographic connectivity, which is the exchange of individuals among local groups, and 3) oceanographic connectivity, which includes flow of materials and circulation patterns and variability that underpin much of all these exchanges. Presently, we understand little about connectivity at specific locations beyond model outputs, and yet we must manage MPAs with connectivity in mind. A key to successful MPA management is how to most effectively work with scientists to acquire the information managers need. Oceanography connectivity is poorly understood, and even less is known about the shape of the dispersal curve for most species. Dispersal kernels differ for various systems, species, and life histories and are likely highly variable in space and time. Furthermore, the implications of different dispersal kernels on population dynamics and management of species is unknown. However, small dispersal kernels are the norm - not the exception. Linking patterns of dispersal to management options is difficult given the present state of knowledge. The behavioral component of larval dispersal has a major impact on where larvae settle. Individual larval behavior and life history details are required to produce meaningful simulations of population connectivity. Biological inputs are critical determinants of dispersal outcomes beyond what can be gleaned from models of passive dispersal. There is considerable temporal and spatial variation to connectivity patterns. New models are increasingly being developed, but these must be validated to understand upstream-downstream neighborhoods, dispersal corridors, stepping stones, and source/sink dynamics. At present, models are mainly useful for providing generalities and generating hypotheses. Low-technology approaches such as drifter vials and oceanographic drogues are useful, affordable options for understanding local connectivity. The “silver bullet” approach to MPA design may not be possible for several reasons. Genetic connectivity studies reveal divergent population genetic structures despite similar larval life histories. Historical stochasticity in reproduction and/or recruitment likely has important, longlasting consequences on present day genetic structure. (PDF has 200 pages.)

On a Class of Self-Adjoint Compact Operators in Hilbert Spaces and Their Relations with Their Finite-Range Truncations

This paper investigates a class of self-adjoint compact operators in Hilbert spaces related to their truncated versions with finite-dimensional ranges. The comparisons are established in terms of worst-case norm errors of the composite operators generated from iterated computations. Some boundedness properties of the worst-case norms of the errors in their respective fixed points in which they exist are also given. The iterated sequences are expanded in separable Hilbert spaces through the use of numerable orthonormal bases.

The Relevance of Relative Position in Ultimatum Games

This paper investigates the effect of focal points and initial relative position in the outcome of a bargaining process. We conduct two on-line experiments. In the first experiment we attempt to replicate Güth, Huck and Müller's (2001) results about the relevance of equal splits. In our second experiment, we recover the choices of participants in forty mini-ultimatum games. This design allows us to test whether the equal split or any other distribution or set of distributions are salient. Our data provide no support for a focal-point explanation but we find support for an explanation based on relative position. Our results confirm that there is a norm against hyper-fair offers. Proposers are expected to behave selfishly when the unselfish distribution leads to a change in the initial relative position.

Topics in randomized numerical linear algebra

This thesis studies three classes of randomized numerical linear algebra algorithms, namely: (i) randomized matrix sparsification algorithms, (ii) low-rank approximation algorithms that use randomized unitary transformations, and (iii) low-rank approximation algorithms for positive-semidefinite (PSD) matrices.

Randomized matrix sparsification algorithms set randomly chosen entries of the input matrix to zero. When the approximant is substituted for the original matrix in computations, its sparsity allows one to employ faster sparsity-exploiting algorithms. This thesis contributes bounds on the approximation error of nonuniform randomized sparsification schemes, measured in the spectral norm and two NP-hard norms that are of interest in computational graph theory and subset selection applications.

Low-rank approximations based on randomized unitary transformations have several desirable properties: they have low communication costs, are amenable to parallel implementation, and exploit the existence of fast transform algorithms. This thesis investigates the tradeoff between the accuracy and cost of generating such approximations. State-of-the-art spectral and Frobenius-norm error bounds are provided.

The last class of algorithms considered are SPSD "sketching" algorithms. Such sketches can be computed faster than approximations based on projecting onto mixtures of the columns of the matrix. The performance of several such sketching schemes is empirically evaluated using a suite of canonical matrices drawn from machine learning and data analysis applications, and a framework is developed for establishing theoretical error bounds.

In addition to studying these algorithms, this thesis extends the Matrix Laplace Transform framework to derive Chernoff and Bernstein inequalities that apply to all the eigenvalues of certain classes of random matrices. These inequalities are used to investigate the behavior of the singular values of a matrix under random sampling, and to derive convergence rates for each individual eigenvalue of a sample covariance matrix.

Projections in a normed linear space and a generalization of the pseudo-inverse

The concept of a "projection function" in a finite-dimensional real or complex normed linear space H (the function P_M which carries every element into the closest element of a given subspace M) is set forth and examined.

If dim M = dim H - 1, then P_M is linear. If P_N is linear for all k-dimensional subspaces N, where 1 ≤ k < dim M, then P_M is linear.

The projective bound Q, defined to be the supremum of the operator norm of P_M for all subspaces, is in the range 1 ≤ Q < 2, and these limits are the best possible. For norms with Q = 1, P_M is always linear, and a characterization of those norms is given.

If H also has an inner product (defined independently of the norm), so that a dual norm can be defined, then when P_M is linear its adjoint P_M^H is the projection on (kernel P_M)^⊥ by the dual norm. The projective bounds of a norm and its dual are equal.

The notion of a pseudo-inverse F⁺ of a linear transformation F is extended to non-Euclidean norms. The distance from F to the set of linear transformations G of lower rank (in the sense of the operator norm ∥F - G∥) is c/∥F⁺∥, where c = 1 if the range of F fills its space, and 1 ≤ c < Q otherwise. The norms on both domain and range spaces have Q = 1 if and only if (F⁺)⁺ = F for every F. This condition is also sufficient to prove that we have (F⁺)^H = (F^H)⁺, where the latter pseudo-inverse is taken using dual norms.

In all results, the real and complex cases are handled in a completely parallel fashion.

The variations and climatic significance of D/H ratios in the carbon-bound hydrogen of cellulose in trees

The σD values of nitrated cellulose from a variety of trees covering a wide geographic range have been measured. These measurements have been used to ascertain which factors are likely to cause σD variations in cellulose C-H hydrogen.

It is found that a primary source of tree σD variation is the σD variation of the environmental precipitation. Superimposed on this are isotopic variations caused by the transpiration of the leaf water incorporated by the tree. The magnitude of this transpiration effect appears to be related to relative humidity.

Within a single tree, it is found that the hydrogen isotope variations which occur for a ring sequence in one radial direction may not be exactly the same as those which occur in a different direction. Such heterogeneities appear most likely to occur in trees with asymmetric ring patterns that contain reaction wood. In the absence of reaction wood such heterogeneities do not seem to occur. Thus, hydrogen isotope analyses of tree ring sequences should be performed on trees which do not contain reaction wood.

Comparisons of tree σD variations with variations in local climate are performed on two levels: spatial and temporal. It is found that the σD values of 20 North American trees from a wide geographic range are reasonably well-correlated with the corresponding average annual temperature. The correlation is similar to that observed for a comparison of the σD values of annual precipitation of 11 North American sites with annual temperature. However, it appears that this correlation is significantly disrupted by trees which grew on poorly drained sites such as those in stagnant marshes. Therefore, site selection may be important in choosing trees for climatic interpretation of σD values, although proper sites do not seem to be uncommon.

The measurement of σD values in 5-year samples from the tree ring sequences of 13 trees from 11 North American sites reveals a variety of relationships with local climate. As it was for the spatial σD vs climate comparison, site selection is also apparently important for temporal tree σD vs climate comparisons. Again, it seems that poorly-drained sites are to be avoided. For nine trees from different "well-behaved" sites, it was found that the local climatic variable best related to the σD variations was not the same for all sites.

Two of these trees showed a strong negative correlation with the amount of local summer precipitation. Consideration of factors likely to influence the isotopic composition of summer rain suggests that rainfall intensity may be important. The higher the intensity, the lower the σD value. Such an effect might explain the negative correlation of σD vs summer precipitation amount for these two trees. A third tree also exhibited a strong correlation with summer climate, but in this instance it was a positive correlation of σD with summer temperature.

The remaining six trees exhibited the best correlation between σD values and local annual climate. However, in none of these six cases was it annual temperature that was the most important variable. In fact annual temperature commonly showed no relationship at all with tree σD values. Instead, it was found that a simple mass balance model incorporating two basic assumptions yielded parameters which produced the best relationships with tree σD values. First, it was assumed that the σD values of these six trees reflected the σD values of annual precipitation incorporated by these trees. Second, it was assumed that the σD value of the annual precipitation was a weighted average of two seasonal isotopic components: summer and winter. Mass balance equations derived from these assumptions yielded combinations of variables that commonly showed a relationship with tree σD values where none had previously been discerned.

It was found for these "well-behaved" trees that not all sample intervals in a σD vs local climate plot fell along a well-defined trend. These departures from the local σD VS climate norm were defined as "anomalous". Some of these anomalous intervals were common to trees from different locales. When such widespread commonalty of an anomalous interval occurred, it was observed that the interval corresponded to an interval in which drought had existed in the North American Great Plains.

Consequently, there appears to be a combination of both local and large scale climatic information in the σD variations of tree cellulose C-H hydrogen.