Logarithm Of Size Research Articles

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.

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.

The invariances of power law size distributions.

Size varies. Small things are typically more frequent than large things. The logarithmof frequency often declines linearly with the logarithm of size. That power law relationforms one of the common patterns of nature. Why does the complexity of nature reduceto such a simple pattern? Why do things as different as tree size and enzymerate follow similarly simple patterns? Here I analyze such patterns by their invariantproperties. For example, a common pattern should not change when adding a constantvalue to all observations. That shift is essentially the renumbering of the pointson a ruler without changing the metric information provided by the ruler. A ruler isshift 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 invariancecorresponds to pattern that does not depend on the order in which underlying processesoccur, for example, a scale that additively combines the component processesleading to observed values. I use tree size as an example to illustrate how the keyinvariances shape pattern. A simple interpretation of common pattern follows. Thatsimple interpretation connects the normal distribution to a wide variety of other commonpatterns through the transformations of scale set by the fundamental invariances.

Regressive computations characterize logarithmic space

We consider the function class E generated by the constant functions, the projection functions, the predecessor function, the substitution operator and the recursion on notation operator. Furthermore, we introduce regressive register machines, which have division by 2 and the predecessor on natural numbers as basic operations. We show that E is the class of functions computable by regressive machines and that the sharply bounded functions (functions with logarithmic size values) of E coincide with the sharply bounded logspace computable functions.

Horse size and domestication: Early equid bones from the Czech Republic in the European context

ABSTRACT We collected and evaluated, by the ‘logarithmic size index’ (LSI) method, all available postcranial equid bones found in the Czech Republic from the Neolithic to the Early Bronze Age. Material from the Upper Paleolithic (Magdalenien) and Bohemian Late Bronze Age (Knoviz culture) was also included. Two different species of equids were documented: Equus hydruntinus Regalia, 1907 and Equus ferus Boddaert, 1785. The variation in the size of true horses was compared with data published for neighbouring countries. In most periods, the horses are found to be larger in the eastern part of Central Europe than in the western part. The Czech lands appear to span the border of two worlds: the Pannonian plains and the western, geomorphologically diverse regions. The status of horses in the Neolithic Lengyel period from Moravia remains disputable. However, a high size variability in Eneolithic Funnel Beaker culture (TRB, 3800-3350 BC) together with a non-homogeneous distribution in Řivnac culture (3100-2800 BC...

Species shade tolerance affects tree basal area growth behaviour in two eucalypt species in thinned and unthinned even-aged monoculture

ABSTRACTIndividual tree and stand basal area growth were studied in a thinning experiment established over two sites in subtropical eastern Australia. The experiment compared the less shade tolerant species Eucalyptus dunnii with the more shade tolerant Corymbia citriodora var. variegata, both grown in plantation monoculture. Growth was compared over a 2½−3 year period that immediately followed thinning at 5½−7½ years of age. Towards the end of the growth period, tree crown depths and leaf mass per unit area were measured at one site. Crown depth and leaf mass per area of C. citriodora were greater than of E. dunnii, characteristics consistent with a more shade tolerant species. Gross stand basal area growth of E. dunnii was faster than that of C. citriodora. Individual-tree basal area growth behaviour was consistent with inter-tree competition involving asymmetric competition for light. Opening the stand by thinning reduced inter-tree competition to near zero. In unthinned control stands, smaller, more shaded trees of C. citriodora were better able to retain their basal area growth rates than those of E. dunnii in the face of competition. In consequence, the more shade tolerant C. citriodora developed a more evenly spread frequency distribution of tree diameters than less shade tolerant E. dunnii. This would have consequences for the assortment of log sizes that would be available ultimately from monocultures of the two species.

A User-Friendly Log Viewer for Storage Systems

System log files contains messages emitted from several modules within a system and carries valuable information about the system state such as device status and error conditions and also about the various tasks within the system such as program names, execution path, including function names and parameters, and the task completion status. For customers with remote support, the system collects and transmits these logs to a central enterprise repository, where these are monitored for alerts, problem forecasting, and troubleshooting. Very large log files limit the interpretability for the support engineers. For an expert, a large volume of log messages may not pose any problem; however, an inexperienced person may get flummoxed due to the presence of a large number of log messages. Often it is desired to present the log messages in a comprehensive manner where a person can view the important messages first and then go into details if required. In this article, we present a user-friendly log viewer where we first hide the unimportant or inconsequential messages from the log file. A user can then click a particular hidden view and get the details of the hided messages. Messages with low utility are considered inconsequential as their removal does not impact the end user for the aforesaid purpose such as problem forecasting or troubleshooting. We relate the utility of a message to the probability of its appearance in the due context. We present machine-learning-based techniques that computes the usefulness of individual messages in a log file. We demonstrate identification and discarding of inconsequential messages to shrink the log size to acceptable limits. We have tested this over real-world logs and observed that eliminating such low value data can reduce the log files significantly (30% to 55%), with minimal error rates (7% to 20%). When limited user feedback is available, we show modifications to the technique to learn the user intent and accordingly further reduce the error.

Features of the deterministic replay in the case of a minimum device set

A technology of the deterministic replay of an execution process in virtual machines can be used for debugging, improving reliability and robustness, software development and incident investigation (including reverse engineering of malware). The paper describes an implementation of deterministic replay for guest machines based on IA-32 in the emulator QEMU. This implementation minimizes the list of replayed devices. The organization of QEMU is discussed in detail, and the techniques used in the implementation are thoroughly explained. The key performance characteristics, such as the size of log of nondeterministic events and slowdown are experimentally measured.

Screening efficacy of a simplified logMAR chart

Background: Snellen acuity charts are the most commonly used method for visual acuity (VA) testing in screening programmes despite comparative studies verifying that the logarithm of minimum angle of resolution (logMAR) acuity measurement charts are more accurate than the Snellen chart acuity measurements. LogMAR acuity measurement charts however are not well implemented in routine clinical practice because of the increased testing time and the complexity of scoring. To implement the logMAR method in a screening programme, there has to be some simplification of it.Aim: This study evaluates the efficacy of a simplified logMAR chart, designed for VA testing over the conventional Snellen chart, in a school-based vision-screening programme.Methods: We designed a simplified logMAR chart by employing the principles of the Early Treatment Diabetic Retinopathy Study (ETDRS) chart in terms of logarithmic letter size progression, inter-letter spacing, and inter-line spacing. Once the simplified logMAR chart was validated by students in the Elite school vision-screening programme, we set out to test the chart in 88 primary and middle schools in the Tiruporur block of Kancheepuram district in Tamil Nadu. One school teacher in each school was trained to screen a cross-sectional population of 10 354 primary and secondary school children (girls: 5488; boys: 4866) for VA deficits using a new, simplified logMAR algorithm. An experienced paediatric optometrist was recruited to validate the screening methods and technique used by the teachers to collect the data. Results: The optometrist screened a subset of 1300 school children from the total sample. The optometrist provided the professional insights needed to validate the clinical efficacy of the simplified logMAR algorithm and verified the reliability of the data collected by the teachers. The mean age of children sampled for validation was 8.6 years (range: 9–14 years). The sensitivity and the specificity of the simplified logMAR chart when compared to the standard logMAR chart were found to be 95% and 98%, respectively. Kappa value was 0.97. Sensitivity of the teachers’ screening was 66.63% (95% confidence interval [CI]: 52.73–77.02) and the specificity was 98.33% (95% CI: 97.49–98.95). Testing of VA was done under substandard illumination levels in 87% of the population. A total of 10 354 children were screened, 425 of whom were found to have some form of visual and/or ocular defect that was identified by the teacher or optometrist.Conclusion: The simplified logMAR testing algorithm proved to be less time consuming than the standard logMAR test. This suggests that the simplified logMAR chart is effective in vision-screening programmes and would be a reliable alternative to the standard logMAR chart and therefore replace the use of Snellen chart acuity tests in vision-screening programmes. The study also showed that non-healthcare providers, such as teachers, can reliably administer the simplified logMAR test.Keywords: vision screening; school children; vision screening standards; screening reliability

The impact of mechanical log surface damage on chip size uniformity during debranching and debarking Eucalyptus pulpwood logs using a single-grip harvester

Mechanised harvesting operations are becoming more prevalent in South Africa with the realisation that motormanual and manual harvesting operations pose significant health and safety risks to workers. The damage inflicted by single-grip harvester feed rollers and delimbing knives on log surfaces during debranching and debarking eucalypts, may affect eventual chip quality. Chip quality influences pulp quality and recovery in the kraft pulping process. This study investigates the influence of two mechanised debranching and debarking treatments on Eucalyptus pulp logs (threeand five-feed roller passes along the stem surface) by feed rollers and delimbing knives on chip uniformity, size and purity. The two mechanised treatments to three log classes (base, middle and top logs) were compared with chips produced from manually debarked logs. Manually debarked logs produced significantly less undesirable-sized chips than both three and five-pass processed logs. The volume of undesirablesized chips produced during chipping also increased with decreasing log size. Manually debarked logs produced chips with significantly less bark than three-pass-processed logs (0.008% vs 0.062%), and five-pass-processed logs produced chips with significantly less bark than three-pass-processed logs (0.018% vs 0.062%). Middle logs also produced chips with significantly less bark than base logs (0.016% vs 0.056%), and top logs produced chips with significantly less bark than base logs (0.017% vs 0.056%). In all cases the bark content on logs was considerably less than the maximum of 1.0% generally specified by kraft pulp mills.

The contingency of medicare physician spending on population densities and sizes

The exploration of the spatial association between Medicare physician spending and population densities and sizes could possibly facilitate the investigation of the causal mechanisms beneath the variation in medical care. We acquired the U.S. Medicare physician expenditures and regional demographic and geographic data in 2006 from the Dartmouth Atlas of Health Care. Six geographic units—states, counties, Hospital Referral Regions, Hospital Service Areas, Metropolitan Statistical Areas, and state non-Metropolitan Statistical Areas—were used as units of study. Pearson correlation analysis, multivariable regression, and partial correlation analysis were employed. Among six geographic units, Pearson correlation coefficients between Medicare physician expenditures and logarithmic population densities ranged from 0.42 to 0.63 (p < 0.05 for all), and between the expenditures and logarithmic population sizes from 0.31 to 0.65 (p < 0.05 for all). When population health, differential demand, market structure, and data reporting bias were controlled, population densities and sizes were positively associated with Medicare physician expenditures in most models. Population densities and sizes could explain considerable amounts of regional variation in Medicare physician spending. We concluded that Medicare physician spending was contingent on population densities and sizes. Because population densities and sizes are produced by more fundamental qualities such as natural environments and resources and thus are not easily manipulated, they are suggestive in health policy studies. Further research might investigate population distribution associated properties such as geographic distribution of health care resources, spatial dynamics of medical technology distribution, and cultural and psychological factors.

Direct estimates of downslope deadwood movement over 30 years in a temperature forest illustrate impacts of treefall on forest ecosystem dynamics

Deadwood plays important roles in forest ecosystems by storing carbon, influencing hydrology, and provisioning countless organisms. Models for these processes often assume that deadwood does not move and ignore redistribution that occurs when trees fall. To evaluate the effects of treefall, we provide the first direct estimates for the magnitude, direction, and drivers of deadwood movement in a long-term oak–hickory forest dynamics plot in Missouri, USA. Among 1871 total pieces of deadwood, logs today pointed downslope more often than branches and occurred at lower elevation than snags. Of these, 477 logs retained tags from which we reconstructed movement using new formulae for reconciling survey coordinates and calculating log shape. Relocated logs occurred at lower elevation than their original rooting location, with the magnitude of the drop dependent on log size, degree of decay, and slope. Although changes in elevation were modest, the log centroids moved up to several meters horizontally. Consequently, as large trees fall, they predictably redistribute deadwood downhill, suggesting that models of deadwood dynamics in small inventory plots may gain accuracy by incorporating import and export along with recruitment and decay. We highlight implications of small-scale deadwood movement for forest inventories, carbon dynamics, and biodiversity.

Resonances for thin barriers on the circle

We study high energy resonances for the operator when V has strong frequency dependence. The operator is a Hamiltonian used to model both quantum corrals (Aligia and Lobos 2005 J. Phys.: Condens. Matter 17 S1095, Barr 2010 Nano Lett. 10 3253–60) and leaky quantum graphs (Exner P 2008 Analysis on Graphs and its Applications (Providence, RI: American Mathematical Society) pp 523–564). Since highly frequency dependent delta potentials are out of reach of the more general techniques in (Galkowski J 2015 arXiv:1511.05894, Galkowski J and Smith H 2014 Int. Math. Res. Not.) we study the special case where and with . Here is the frequency. We give sharp bounds on the size of resonance free regions for and the location of bands of resonances when . Finally, we give a lower bound on the number of resonances in logarithmic size strips: .

AND-Compression of NP-Complete Problems: Streamlined Proof and Minor Observations

Drucker (2012) proved the following result: Unless the unlikely complexity-theoretic collapse coNP is in NP/poly occurs, there is no AND-compression for SAT. The result has implications for the compressibility and kernelizability of a whole range of NP-complete parameterized problems. We present a streamlined proof of Drucker's theorem. An AND-compression is a deterministic polynomial-time algorithm that maps a set of SAT-instances $x_1,\dots,x_t$ to a single SAT-instance of size poly(max $|x_i|$) such that is if and only if all are The in the name stems from the fact that the predicate $y$ is satisfiable can be written as the AND of all predicates $x_i$ is satisfiable. Drucker's result complements the result by Bodlaender et al. (2009) and Fortnow and Santhanam (2010), who proved the analogous statement for OR-compressions, and Drucker's proof not only subsumes that result but also extends it to randomized compression algorithms that are allowed to have a certain probability of failure. Drucker (2012) presented two proofs: The first uses information theory and the minimax theorem from game theory, and the second is an elementary, iterative proof that is not as general. In our proof, we realize the iterative structure as a generalization of the arguments of Ko (1983) for P-selective sets, which use the fact that tournaments have dominating sets of logarithmic size. We generalize this fact to hypergraph tournaments. Our proof achieves the full generality of Drucker's theorem, avoids the minimax theorem, and restricts the use of information theory to a single, intuitive lemma about the average noise sensitivity of compressive maps. To prove this lemma, we use the same information-theoretic inequalities as Drucker.

Robust reconstruction of Barabási‐Albert networks in the broadcast congested clique model

In the broadcast version of the congested clique model, nodes communicate in synchronous rounds by writing ‐bit messages on a whiteboard, which is visible to all of them. The joint input to the nodes is an undirected ‐node graph , with node receiving the list of its neighbors in . Our goal is to design a protocol at the end of which the information contained in the whiteboard is enough for reconstructing . It has already been shown that there is a one‐round protocol for reconstructing graphs with bounded degeneracy. The main drawback of that protocol is that the degeneracy of the input graph must be known a priori by the nodes. Moreover, the protocol fails when applied to graphs with degeneracy larger than . In this article, we address this issue by looking for robust reconstruction protocols, that is, protocols which always give the correct answer and work efficiently when the input is restricted to a certain class. We introduce a very simple, two‐round protocol that we call Robust‐Reconstruction. We prove that this protocol is robust for reconstructing the class of Barabási‐Albert trees with (expected) message size . Moreover, we present computational evidence suggesting that Robust‐Reconstruction also generates logarithmic size messages for arbitrary Barabási‐Albert networks. Finally, we stress the importance of the preferential attachment mechanism (used in the construction of Barabási‐Albert networks) by proving that Robust‐Reconstruction does not generate short messages for random recursive trees. © 2015 Wiley Periodicals, Inc. NETWORKS, Vol. 67(1), 82–91 2016

임베디드 소프트웨어의 단위 테스팅을 위한 로그 기반 테스팅 프레임워크 개발

As Internet of Things (IoT) is recently serviced in several fields, the reliability and safety issues for IoT embedded systems are emerged. During the development of embedded systems, it is not easy to build the virtual execution environment and to test the developing version. Therefore, it is difficult to ensure its reliability due to lack of unit testing. In this paper, we propose a log-based unit testing framework for embedded software, which performs on real target board by extracting information of function execution. And, according to execution paths, duplicated logs are eliminated to keep a minimal log size. As a result, during system testing, testers can efficiently decide whether the executed paths of each function are correctly performed or not.

Deterministic Replay

Deterministic replay is a type of emerging technique dedicated to providing deterministic executions of computer programs in the presence of nondeterministic factors. The application scopes of deterministic replay are very broad, making it an important research topic in domains such as computer architecture, operating systems, parallel computing, distributed computing, programming languages, verification, and hardware testing. In this survey, we comprehensively review existing studies on deterministic replay by introducing a taxonomy. Basically, existing deterministic replay schemes can be classified into two categories, single-processor (SP) schemes and multiprocessor (MP) schemes. By reviewing the details of these two categories of schemes respectively, we summarize and compare how existing schemes address technical issues such as log size, record slowdown, replay slowdown, implementation cost, and probe effect, which may shed some light on future studies on deterministic replay.

Trade‐offs in parasitism efficiency and brood size mediate parasitoid coexistence, with implications for biological control of the invasive emerald ash borer

Summary Parasitoids often are selected for use as biological control agents because of their high host specificity, yet such host specificity can result in strong interspecific competition. Few studies have examined whether and how various extrinsic factors (such as parasitism efficiency, i.e. the ability to optimize host‐finding attack rates) influence the outcome of competition between parasitoids, even though they could have profound effects on the implementation of classical biological control programmes. To determine the potential influence of extrinsic competition and coexistence on host suppression efficacy, we compared parasitism by two larval parasitoids (Tetrastichus planipennisi and Spathius galinae) of the invasive emerald ash borer (EAB) Agrilus planipennis, under different host densities, parasitoid densities, host plant sizes and parasitoid–host ratios. Spathius galinae had significantly higher parasitism efficiency (≈4 times), but significantly lower brood size (&gt;6 times) than that of T. planipennisi. The attack rates of hosts increased significantly with parasitoid density, whereas host density did not significantly affect multiparasitism. The parasitism rate of T. planipennisi on small host logs was significantly higher than that on large logs, while host plant (log) size had no significant impact on S. galinae parasitism. The multiparasitism rate was rather low regardless of host log size and parasitoid/host density, indicating that intrinsic competition between the two species of parasitoids might seldom occur in the field. The two species of parasitoids could therefore coexist in the same habitat, and any adverse effects on the suppression of EAB populations caused by competitive behaviour between the two species of parasitoids would likely be negligible. Synthesis and applications. Our findings suggest that introducing multiple species of parasitic natural enemies could be feasible for management of invasive species, but it is important to examine multiple extrinsic factors simultaneously when evaluating interspecific competition between them. Among these different extrinsic factors, we found that coexistence between parasitoids can be mediated by trade‐offs in their parasitism efficiency and brood sizes. Thus, the differences in life‐history traits of natural enemies could be used to select among biological control agents being considered for releases.

Electronic transport in two-dimensional high dielectric constant nanosystems.

There has been remarkable recent progress in engineering high-dielectric constant two dimensional (2D) materials, which are being actively pursued for applications in nanoelectronics in capacitor and memory devices, energy storage, and high-frequency modulation in communication devices. Yet many of the unique properties of these systems are poorly understood and remain unexplored. Here we report a numerical study of hopping conductivity of the lateral network of capacitors, which models two-dimensional insulators, and demonstrate that 2D long-range Coulomb interactions lead to peculiar size effects. We find that the characteristic energy governing electronic transport scales logarithmically with either system size or electrostatic screening length depending on which one is shorter. Our results are relevant well beyond their immediate context, explaining, for example, recent experimental observations of logarithmic size dependence of electric conductivity of thin superconducting films in the critical vicinity of superconductor-insulator transition where a giant dielectric constant develops. Our findings mark a radical departure from the orthodox view of conductivity in 2D systems as a local characteristic of materials and establish its macroscopic global character as a generic property of high-dielectric constant 2D nanomaterials.

SG-WSTD: A framework for scalable geographic web search topic discovery

Search engine query logs are recognized as an important information source that contains millions of users’ web search needs. Discovering Geographic Web Search Topics (G-WSTs) from a query log can support a variety of downstream web applications such as finding commonality between locations and profiling search engine users. However, the task of discovering G-WSTs is nontrivial, not only because of the diversity of the information in web search but also due to the sheer size of query log. In this paper, we propose a new framework, Scalable Geographic Web Search Topic Discovery (SG-WSTD), which contains highly scalable functionalities such as search session derivation, geographic information extraction and geographic web search topic discovery to discover G-WSTs from query log. Within SG-WSTD, two probabilistic topic models are proposed to discover G-WSTs from two complementary perspectives. The first one is the Discrete Search Topic Model (DSTM), which discovers G-WSTs that capture the commonalities between discrete locations. The second is the Regional Search Topic Model (RSTM), which focuses on a specific geographic region on the map and discovers G-WSTs that demonstrate geographic locality. Since query log is typically voluminous, we implement the functionalities in SG-WSTD based on the MapReduce paradigm to solve the efficiency bottleneck. We evaluate SG-WSTD against several strong baselines on a real-life query log from AOL. The proposed framework demonstrates significantly improved data interpretability, better prediction performance, higher topic distinctiveness and superior scalability in the experimentation.