Logarithm Of Size Research Articles

Seeflow: A Visualization System Using 2T Hybrid Graph for Characteristics Analysis of Abnormal Netflow

With the network expansion, the development of information highway, and the numerous data generated by applications, Netflow log size has been rapidly expanding. This paper proposes the use of visualization techniques to quickly and effectively identify network attacks and abnormal events, as well as perceive network security situation. A 2T (combination with Time-series and Treemap) graph visualization system, named Seeflow, is developed, which uses information entropy of Netflow’s features to draw a Time-series graph and use cross-entropies to distinguish between the normal and abnormal flow stream. Time-series graph can overview the network state from macro level. And Treemap graph is used to drill down into details from micro level. In addition, the exponential function is used to conduct quantitative analysis for the performance of Treemap. The Seeflow system also creates graphical features to visually analyze attacks and find interesting patterns. In experiment, VAST Challenge2013 competition dataset is analyzed by Seeflow system. Comparing with the prize-winning works shows that Seeflow can intuitively display network security situation from both of macro and micro level and effectively identify network attacks as well as support decision-making.

Size diversity in Swiss Bronze Age cattle.

To date, osteometric data for Swiss Bronze Age cattle, particularly from Alpine sites, are scarce. In the present study, using a large dataset generated by combining preexisting data with recent data obtained from a large Alpine site, cattle size from the Late Neolithic to the Late Bronze Age (LBA) in populations from different sites and regions was evaluated using the logarithmic size index and other statistical analysis. Additionally, the finite mixture model and a meta‐analytic technique were used to observe possible effects of sex ratios on cattle size. Results indicated that sex ratios did not affect size distribution. Cattle populations did not differ over time, but the Alpine cattle were smaller than the Central Plateau cattle. There were two distinct sizes in the Alpine cattle populations. It is suggested that the different economic interrelationships between Alpine and other geographically related communities might have led to the emergence of size diversity in Swiss Bronze Age cattle. Further interdisciplinary studies with larger sample sizes are required to confirm these possibilities.

Log sequence clustering for workflow mining in multi-workflow systems

Current workflow mining efforts aim to discover process knowledge from user-system interaction logs and represent it as high-level workflow models. They assume there is one single workflow model in a system, or rely on the information that can explicitly link each log sequence to the underlying workflow model. Such assumptions may not be applicable to multi-workflow systems where the instances of different workflow models are mixed together without being differentiated. To address this issue, this paper proposes to apply sequence clustering methods to group similar log sequences together. Each sequence cluster corresponds to a workflow model and the log sequences in the cluster are the corresponding instances. This paper investigates different similarity measures, including structure-based and user-based, as well as different clustering algorithms, including one-side clustering and co-clustering. In order to incorporate user factors into sequence clustering, which is novel to the current sequence clustering methods, this paper proposes to model User Behavior Patterns (UBPs) as probabilistic distributions over sequences and learn it from the event log. We represent a UBP as a Probabilistic Suffix Tree and use it to measure sequence similarity. The co-clustering method leverages the dyad relationship between UBPs and log sequences to improve the clustering accuracy. An experimental study has been conducted and the result indicates that user-based methods outperform structure-based methods in terms of accuracy and they are more effective on dealing with noises in the log and the increase of log size. The UBP-sequence co-clustering method achieves the best performance which indicates the effectiveness of incorporating user factors and applying co-clustering.

LongLine: Visual Analytics System for Large-scale Audit Logs

Audit logs are different from other software logs in that they record the most primitive events (i.e., system calls) in modern operating systems. Audit logs contain a detailed trace of an operating system, and thus have received great attention from security experts and system administrators. However, the complexity and size of audit logs, which increase in real time, have hindered analysts from understanding and analyzing them. In this paper, we present a novel visual analytics system, LongLine, which enables interactive visual analyses of large-scale audit logs. LongLine lowers the interpretation barrier of audit logs by employing human-understandable representations (e.g., file paths and commands) instead of abstract indicators of operating systems (e.g., file descriptors) as well as revealing the temporal patterns of the logs in a multi-scale fashion with meaningful granularity of time in mind (e.g., hourly, daily, and weekly). LongLine also streamlines comparative analysis between interesting subsets of logs, which is essential in detecting anomalous behaviors of systems. In addition, LongLine allows analysts to monitor the system state in a streaming fashion, keeping the latency between log creation and visualization less than one minute. Finally, we evaluate our system through a case study and a scenario analysis with security experts.

Definability of Cai-Fürer-Immerman Problems in Choiceless Polynomial Time

Choiceless Polynomial Time (CPT) is one of the most promising candidates in the search for a logic capturing P time . The question whether there is a logic that expresses exactly the polynomial-time computable properties of finite structures, which has been open for more than 30 years, is one of the most important and challenging problems in finite model theory. The strength of Choiceless Polynomial Time is its ability to perform isomorphism-invariant computations over structures, using hereditarily finite sets as data structures. But, because of isomorphism-invariance, it is choiceless in the sense that it cannot select an arbitrary element of a set—an operation that is crucial for many classical algorithms. CPT can define many interesting P time queries, including (a certain version of) the Cai-Fürer-Immerman (CFI) query. The CFI-query is particularly interesting, because it separates fixed-point logic with counting from P time and has since remained the main benchmark for the expressibility of logics within P time . The CFI-construction associates with each connected graph a set of CFI-graphs that can be partitioned into exactly two isomorphism classes called odd and even CFI-graphs. The problem is to decide, given a CFI-graph, whether it is odd or even. For the case where the CFI-graphs arise from ordered graphs, Dawar, Richerby, and Rossman proved that the CFI-query is CPT-definable. However, definability of the CFI-query over general graphs remains open. Our first contribution generalises the result by Dawar, Richerby, and Rossman to the variant of the CFI-query derived from graphs with colour classes of logarithmic size, instead of colour class size one. Second, we consider the CFI-query over graph classes where the maximal degree is linear in the size of the graphs. For the latter, we establish CPT-definability using only sets of small, constant rank, which is known to be impossible for the general case. In our CFI-recognising procedures we strongly make use of the ability of CPT to create sets, rather than tuples only, and we further prove that, if CPT worked over tuples instead, then no such procedure would be definable. We introduce a notion of “sequencelike objects” based on the structure of the graphs’ symmetry groups, and we show that no CPT-program that only uses sequencelike objects can decide the CFI-query over complete graphs, which have linear maximal degree. From a broader perspective, this generalises a result by Blass, Gurevich, and van den Bussche about the power of isomorphism-invariant machine models (for polynomial time) to a setting with counting.

Equations to estimate processing and forwarding costs, while considering log size: clear-cutting operations in Nasunogahara, Tochigi prefecture, Japan

ABSTRACTThis study develops equations by which one can estimate processing and forwarding costs for clear-cutting operations, while considering log size and assuming moderately and gently sloping sites. Processing cycle times were estimated by using the average delimbing and bucking times related to average log volume and piling time related to the number of logs extracted from the stem. Forwarding cycle times were estimated by using the forwarding distance, the out-hauling and in-hauling travel velocities, and the loading and unloading time related to the number of loaded logs. The forwarding volume was estimated by using the relationship between the average log volume and the number of logs loaded on the forwarder. Differences in processing costs between 0.02 and 0.20 m3/log worked out to around USD 10.00/m3, whereas differences in forwarding costs between 0.02 and 0.20 m3/log worked out to around USD 4.00 and USD 7.00/m3 for thinning and clear-cutting operations, respectively. Finally, operational system costs were estimated: differences in operational system costs with the extraction of small-sized logs (and while not considering log size) between maximizing revenues and profits were USD 9.08, USD 9.05, and USD 9.36/m3 at Site A, Site B, and thinning operations, respectively. However, those costs ranged from USD 36.65 to USD 87.65/m3 for Site A, from USD 28.75 to USD 70.21/m3 for Site B, and from USD 27.71 to USD 70.81/m3 for thinning operations. Thus, costs should be estimated while duly considering log size.

Analysis Framework for Logs in Communication Devices

This article describes how logging is an important mechanism that is being used in almost all kinds of devices. It is used for tracking events during the running of a software. In this case, programs are developed by the software developers in such a way that whenever an event happens it can be recorded. Among its many uses, system troubleshooting is of greatest importance. Manual methods of logging can be adopted when dealing with a smaller process but mostly log sizes can go from kilobytes to terabytes in size for which log analyzing tools are required. In addition to that, those tools should be capable of extracting all the relevant information so that it becomes easy to highlight the ongoing issues in an effective manner. This article proposes a dedicated analysis framework for deep log analysis in communication devices.

Efficient dynamic malware analysis using virtual time control mechanics

Efficient detection of stealthy malware attacks in suspicious files is very challenging as dynamic malware analysis is time consuming. This paper proposes a virtual time control mechanics-based method to overcome the challenge. The proposed method utilizes a modified Xen hypervisor, in which a virtual clock source is generated according to a predefined speed ratio, such that sandbox systems running on the modified hypervisor can be accelerated. Thus, it does not modify operating system kernels nor intercept system function calls, and is therefore compatible with various operating systems. Further, it utilizes an entropy-based measure that adjusts its execution time according to various malware inputs as an early termination criterion. The results of experiments conducted to verify the efficacy of the proposed method indicate that it speeds up the system timer and significantly increases the logged record size by up to 42% or obtains the same log size within a shorter period compared with conventional sandboxes. Thus, the proposed virtual time control mechanics-based method efficiently detects nontrivial anomalous codes that may be neglected by conventional sandboxing techniques.

Development of a Downed Woody Debris Forecasting Tool Using Strategic-Scale Multiresource Forest Inventories

The increasing interest in forest biomass for energy or carbon cycle purposes has raised the need for forest resource managers to refine their understanding of downed woody debris (DWD) dynamics. We developed a DWD forecasting tool using field measurements (mean size and stage of stage of decay) for three common forest types across the eastern United States using field observations of DWD from the US Department of Agriculture Forest Service's Forest Inventory and Analysis program. Residence times for DWD ranged from as short as 20.3 ± 9.7 years (mean ± SD) for loblolly pine biomass in the southeastern United States to as long as 41.7 ± 20.9 years for aspen biomass in the Lake States. Although we suggest numerous improvements through refined DWD measurements and models, our proposed tool can be considered a rapid assessment technique to assist natural resource managers in forecasting DWD populations. Beginning with using log size and decay stage to understand deadwood dynamics, future researchers should seek to refine DWD metrics through implementing enhanced forest inventory information and exploring the impacts of forest disturbances on inputs to the DWD pool. Management and Policy Implications Downed woody debris (DWD) is an integral component of forest health and is of interest to managers involved in forest management, wildlife habitat, and forest fuel assessment and fire risk. The presence and abundance of woody debris encourages biodiversity by serving as cover and habitat for deadwood-dependent plants and animals. To date, the majority of research has focused on how to accurately assess forest DWD attributes at a given time period. Our study highlights the ability to inform DWD dynamics through the development of a forecasting tool that allows managers to forecast woody debris populations. We estimated shorter residence times in southeastern US forests than in northern forest types. Through a rapid assessment of average deadwood diameter and stage of decay, trends in future deadwood stocks can be understood. Applying these results can aid natural resource managers in meeting management objectives and policy requirements that seek to maintain and/or promote the abundance of forest DWD. These results can enhance the value of using existing forest inventory information to provide insights into future forest composition and structure as a part of forest management plans.

Breakdown of instream wood in low order forested streams of the Southern Chilean mountain ranges

We analyzed instream wood depletion or breakdown in terms of wood breakage (defined as the reduction in length) and decay (reduction in diameter) on channel segments of three low-order mountain streams located in southern Chile. We used a unique database, composed of 1049 individually tagged logs, which were measured and their position was georeferenced between 2005 and 2014, and re-measured and re-georeferenced after the rainy winter period of 2015. Results showed that median breakdown at the end of the survey ranged between 5 and 27% and between 10 and 25% for median decay, with highest values of 83 and 72% respectively. While median annual breakage ranged between less than 1 and 4 %·year−1 and median annual decay between 1 and 4 %·year−1. According to our results, breakdown of instream wood is influenced by many factors, the most significant being initial log size (both length and diameter), their orientation, residence time and fluvial transport (i.e. displacement length). Wood density and initial tree height at the time of recruitment were also analyzed, aiming to better understand breakage and decay processes. Results showed that in-channel logs were, as expected, less dense than living trees, and very decayed logs significant loose density compared to fresh logs. The differences between initial log size and potential minimum tree height at the time of recruitment ranged between 29 and 64%. We believe that our findings illuminates on wood depletion processes on low order streams in the Chilean mountain ranges, and can be easily extrapolated to other streams with similar conditions; however, the natural heterogeneity among river environments and hydrological conditions during the survey period may influence breakage and decay processes. Therefore, we encourage other researchers to provide data on breakdown of instream wood from different regions.

The impact of log surface damage caused by harvester Eucalyptus debarking on pulp value recovery

Mechanised harvesting operations are growing in popularity in South Africa, as motor-manual and manual harvesting operations pose significant health and safety risks to workers. Potential damage inflicted by single-grip harvester feed rollers and delimbing knives on the log surface during debranching and debarking of eucalypts may affect chip size distributions during chip production. Chip size is important as it influences pulp quality and recovery in the kraft pulping process. The study investigated the influence of two mechanised debarking treatments in eucalypts (three feed roller passes and five feed roller passes along the stem surface) with feed-roller-induced log surface damage on pulp value recovery. The two mechanised treatments were compared against chips produced from manually debarked logs with no surface damage. In addition, the effect of two log drying periods (one week and two weeks) and three log classes (base, middle and top logs) on chip quality were also analysed. An economic evaluation was conducted to quantify potential recoverable pulp value losses associated with debarking treatments and log drying periods. Logs subject to manual debarking produced significantly less undesired sized chips than both three-pass and five-pass mechanically debarked logs and therefore had significantly greater pulp value recovery. Mechanically debarked logs had a projected pulp value recovery of R62, R86 and R123 less per bone dry tonne of chips produced from base, middle and top logs, respectively, when compared with manually debarked logs with no log surface damage after a one-week log drying period. Mechanically debarked logs also had a projected pulp value recovery of R77, R40 and R59 less per bone dry tonne of chips produced from base, middle and top logs, respectively, when compared with manually debarked logs with no log surface damage after a two-week log drying period. Logs dried for two weeks also produced significantly less under-sized chips than chips produced from one-week-dried logs and therefore had greater pulp value recovery. However, two-week-dried logs produced wood chips with significantly more over-thick chips than logs dried for one week. The volume of undesirable-sized chips produced during chipping increased with decreasing log size.

Insights into the ecology, genetics and distribution of Lucanus elaphus Fabricius (Coleoptera: Lucanidae), North America's giant stag beetle

Abstract Little is known about the biology or conservation status of Lucanus elaphus Fabricius in North America despite well‐documented declines of a related species, Lucanus cervus (L.), in Europe. This study provides information critical to developing conservation plans for L. elaphus including the species’ larval substrate requirements, genetic data and range‐wide estimates of habitat suitability. In Mississippi floodplain forests, larval L. elaphus were recovered from a wide range of log sizes and rot types and were either found tunnelling within the wood or feeding beneath logs at the soil–wood interface. The species appears to require 1–2 years to complete development, exhibits a 1:1 sex ratio and is parasitised by Zelia vertebrata (Say) (Diptera: Tachinidae). Flight intercept traps placed at three heights at both the edge and interior of hardwood‐dominated forests in Georgia yielded six adult male L. elaphus, all of which were captured in traps placed at 15 m on the forest edge. Because L. elaphus larvae are morphologically indistinguishable from related species, DNA sequence data from the mitochondrial cytochrome oxidase I gene were generated to facilitate molecular identification. Genetic data revealed modest intra‐specific variation, with up to 1.3% sequence divergence among haplotypes sampled from the same forest. Based on assembled occurrence records, ecological niche models suggest that environmental conditions are suitable for L. elaphus across much of the southeastern United States, provided that adequate lowland forest cover and dead wood substrates are available.

Log moisture capacity does not predict epixylic bryophyte growth under thinned and unthinned forest canopies

Summary Coarse woody debris (CWD) serves as habitat for diverse and rare taxa in forest systems. Because the abundance of mosses appears to be correlated with log size and stage of decay, many have suggested that CWD serves as a moisture reservoir, ensuring a humid microclimate and facilitating moss growth, but no one has tested this connection. Intact forest canopies are also thought to maintain humid conditions that benefit moss growth. If microclimatic regulation is the primary mechanism contributing to high moss abundance on CWD, then epixylic moss growth should increase with the capacity of the log moisture reservoir, and the importance of the reservoir size should increase with canopy opening. Three types of synthetic logs, identical in size and shape but differing in moisture capacity, and two natural substrates, well‐decayed birch and cedar logs, were used to test the effects of log moisture capacity on growth of Dicranum flagellare under thinned and intact canopies of a spruce plantation over 20 months. Surface humidity was positively associated with moisture capacity, but did not reach the water compensation point outside of precipitation events. Under a closed forest canopy, moss growth was negligible across all log types. Under an open forest canopy, moss growth was greater on natural substrates than synthetic ones, and negatively related to moisture capacity. Coarse woody debris facilitates a sufficiently humid surface for only a short time after precipitation, presumably when a film of liquid water is maintained near the surface. For D. flagellare, canopy condition is a more accurate predictor of growth than CWD‐moisture capacity; any beneficial properties of CWD appear to be lessened by a dense forest canopy (as in silvicultural plantations), probably because it reduces access to liquid water from precipitation. We propose that the surface moisture availability of CWD depends on optimal depth of a ‘resisting layer’ below the log surface, representing a tradeoff between water retention and loss (via percolation or runoff at extremely deep vs. shallow resisting layer depth). Coarse woody debris may possess microclimate‐regulating traits that benefit moss growth, but it does not appear to act as a moisture capacitor. A lay summary is available for this article.

On the energy landscape of the mixed even p-spin model

We investigate the energy landscape of the mixed even $p$-spin model with Ising spin configurations. We show that for any given energy level between zero and the maximal energy, with overwhelming probability there exist exponentially many distinct spin configurations such that their energies stay near this energy level. Furthermore, their magnetizations and overlaps are concentrated around some fixed constants. In particular, at the level of maximal energy, we prove that the Hamiltonian exhibits exponentially many orthogonal peaks. This improves the results of Chatterjee and Ding-Eldan-Zhai, where the former established a logarithmic size of the number of the orthogonal peaks, while the latter proved a polynomial size. Our second main result obtains disorder chaos at zero temperature and at any external field. As a byproduct, this implies that the fluctuation of the maximal energy is superconcentrated when the external field vanishes and obeys a Gaussian limit law when the external field is present.

Pareto-Lognormal Modeling of Known and Unknown Metal Resources. II. Method Refinement and Further Applications

Pareto-lognormal modeling of worldwide metal deposit size–frequency distributions was proposed in an earlier paper (Agterberg in Nat Resour 26:3–20, 2017). In the current paper, the approach is applied to four metals (Cu, Zn, Au and Ag) and a number of model improvements are described and illustrated in detail for copper and gold. The new approach has become possible because of the very large inventory of worldwide metal deposit data recently published by Patino Douce (Nat Resour 25:97–124, 2016c). Worldwide metal deposits for Cu, Zn and Ag follow basic lognormal size–frequency distributions that form straight lines on lognormal Q–Q plots. Au deposits show a departure from the straight-line model in the vicinity of their median size. Both largest and smallest deposits for the four metals taken as examples exhibit hyperbolic size–frequency relations and their Pareto coefficients are determined by fitting straight lines on log rank–log size plots. As originally pointed out by Patino Douce (Nat Resour Res 25:365–387, 2016d), the upper Pareto tail cannot be distinguished clearly from the tail of what would be a secondary lognormal distribution. The method previously used in Agterberg (2017) for fitting the bridge function separating the largest deposit size–frequency Pareto tail from the basic lognormal is significantly improved in this paper. A new method is presented for estimating the approximate deposit size value at which the upper tail Pareto comes into effect. Although a theoretical explanation of the proposed Pareto-lognormal distribution model is not a required condition for its applicability, it is shown that existing double Pareto-lognormal models based on Brownian motion generalizations of the multiplicative central limit theorem are not applicable to worldwide metal deposits. Neither are various upper tail frequency amplification models in their present form. Although a physicochemical explanation remains possible, it is argued that preferential mining of the largest and smallest orebodies can have economic historical reasons. The size–frequency distribution of uranium can be regarded as lognormal without Pareto tails. At the end of the paper, it is shown that original copper deposit size data can be used for forward projection of discovery trends toward the end of this century.

Wood Quality of Old-Growth Koa Logs and Lumber

Abstract Acacia koa trees are ecologically, economically, and culturally significant to the Hawaiian Islands. Koa wood is one of the most valuable species in the world and sale of koa products represents a majority of all the Hawaiian wood products sold by Hawaiian retailers. Today, there is concern in Hawaii among foresters, forest landowners and managers, wood products manufacturers, and the public that the remaining old-growth koa resource has become scarce, is suffering from declining health and diseases, and is characterized by poor growth form. Current practices require harvest of only dead and dying trees and using downed material in wood products manufacturing. We examined lumber volume and value recovery from logs sawn from dead and dying trees and from relic logs (logs that have been on the ground) from four sites on the island of Hawaii. Gross lumber recovery from all study logs was 71 percent. Log size did not significantly influence lumber volume recovery. Forty-five percent of the lumber manufactured from relic logs was below grade compared with 26 percent of the lumber sawn from standing dead and dying trees. Variables that affect lumber quality, such as different defects and heartwood proportion, were measured. Decay-type defects were the most prominent.

Efficient Methods for Influence-Based Network-Oblivious Community Detection

We study the problem of detecting social communities when the social graph is not available but instead we have access to a log of user activity, that is, a dataset of tuples ( u , i , t ) recording the fact that user u “adopted” item i at time t . We propose a stochastic framework that assumes that the adoption of items is governed by an underlying diffusion process over the unobserved social network and that such a diffusion model is based on community-level influence . That is, we aim at modeling communities through the lenses of social contagion . By fitting the model parameters to the user activity log, we learn the community membership and the level of influence of each user in each community. The general framework is instantiated with two different diffusion models, one with discrete time and one with continuous time, and we show that the computational complexity of both approaches is linear in the number of users and in the size of the propagation log. Experiments on synthetic data with planted community structure show that our methods outperform non-trivial baselines. The effectiveness of the proposed techniques is further validated on real-word data, on which our methods are able to detect high-quality communities.

The invariances of power law size distributions

Size varies. Small things are typically more frequent than large things. The logarithm of frequency often declines linearly with the logarithm of size. That power law relation forms one of the common patterns of nature. Why does the complexity of nature reduce to such a simple pattern? Why do things as different as tree size and enzyme rate follow similarly simple patterns? Here I analyze such patterns by their invariant properties. For example, a common pattern should not change when adding a constant value to all observations. That shift is essentially the renumbering of the points on a ruler without changing the metric information provided by the ruler. A ruler is shift invariant only when its scale is properly calibrated to the pattern being measured. Stretch invariance corresponds to the conservation of the total amount of something, such as the total biomass and consequently the average size. Rotational invariance corresponds to pattern that does not depend on the order in which underlying processes occur, for example, a scale that additively combines the component processes leading to observed values. I use tree size as an example to illustrate how the key invariances shape pattern. A simple interpretation of common pattern follows. That simple interpretation connects the normal distribution to a wide variety of other common patterns through the transformations of scale set by the fundamental invariances.

Landscape variation in tree regeneration and snag fall drive fuel loads in 24-year old post-fire lodgepole pine forests.

Escalating wildfire in subalpine forests with stand-replacing fire regimes is increasing the extent of early-seral forests throughout the western USA. Post-fire succession generates the fuel for future fires, but little is known about fuel loads and their variability in young post-fire stands. We sampled fuel profiles in 24-year-old post-fire lodgepole pine (Pinus contorta var. latifolia) stands (n=82) that regenerated from the 1988 Yellowstone Fires to answer three questions. (1) How do canopy and surface fuel loads vary within and among young lodgepole pine stands? (2) How do canopy and surface fuels vary with pre- and post-fire lodgepole pine stand structure and environmental conditions? (3) How have surface fuels changed between eight and 24years post-fire? Fuel complexes varied tremendously across the landscape despite having regenerated from the same fires. Available canopy fuel loads and canopy bulk density averaged 8.5Mg/ha (range 0.0-46.6) and 0.24kg/m3 (range: 0.0-2.3), respectively, meeting or exceeding levels in mature lodgepole pine forests. Total surface-fuel loads averaged 123Mg/ha (range: 43-207), and 88% was in the 1,000-h fuel class. Litter, 1-h, and 10-h surface fuel loads were lower than reported for mature lodgepole pine forests, and 1,000-h fuel loads were similar or greater. Among-plot variation was greater in canopy fuels than surface fuels, and within-plot variation was greater than among-plot variation for nearly all fuels. Post-fire lodgepole pine density was the strongest positive predictor of canopy and fine surface fuel loads. Pre-fire successional stage was the best predictor of 100-h and 1,000-h fuel loads in the post-fire stands and strongly influenced the size and proportion of sound logs (greater when late successional stands had burned) and rotten logs (greater when early successional stands had burned). Our data suggest that 76% of the young post-fire lodgepole pine forests have 1,000-h fuel loads that exceed levels associated with high-severity surface fire potential, and 63% exceed levels associated with active crown fire potential. Fire rotations in Yellowstone National Park are predicted to shorten to a few decades and this prediction cannot be ruled out by a lack of fuels to carry repeated fires.

Power laws in EU country exports

International trade flows are highly concentrated in the top units of analysis. In this paper, we study the size distribution of exports at the product level, using Comext data for the 28 EU countries over the period 2002–2014. We fit power law relationships running log rank–log size regressions. The estimated Pareto exponent may be interpreted as a single measure of the inequality between the top products; it thus constitutes an alternative to other measures of export diversification. The Pareto exponent estimates are quite stable for most EU countries between 2002 and 2014. However, some countries stand out for their increase or decrease in the Pareto exponent. Some preliminary evidence suggesting negative correlation between volatility in EU country exports and export diversification at the product level is also provided.