scholarly journals The invariances of power law size distributions

F1000Research ◽  
2016 ◽  
Vol 5 ◽  
pp. 2074 ◽  
Author(s):  
Steven A. Frank
Keyword(s):  
Power Law ◽  
Tree Size ◽  
Total Biomass ◽  
Common Pattern ◽  
Simple Interpretation ◽  
Shape Pattern ◽  
Component Processes ◽  
Average Size ◽  
Small Things ◽  
Invariant Properties

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.

scholarly journals The invariances of power law size distributions

F1000Research ◽  
2016 ◽  
Vol 5 ◽  
pp. 2074 ◽  
Author(s):  
Steven A. Frank
Keyword(s):  
Power Law ◽  
Tree Size ◽  
Total Biomass ◽  
Common Pattern ◽  
Simple Interpretation ◽  
Shape Pattern ◽  
Component Processes ◽  
Average Size ◽  
Small Things ◽  
Invariant Properties

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.

scholarly journals The invariances of power law size distributions

F1000Research ◽  
2016 ◽  
Vol 5 ◽  
pp. 2074
Author(s):  
Steven A. Frank
Keyword(s):  
Power Law ◽  
Tree Size ◽  
Total Biomass ◽  
Common Pattern ◽  
Simple Interpretation ◽  
Shape Pattern ◽  
Component Processes ◽  
Average Size ◽  
Small Things ◽  
Invariant Properties

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.

Acceleration of the growth of populations and of the multiplication of tetrathyridia of Mesocestoides corti Hoeppli, 1925 (Cestoda: Cyclophyllidea) by some cytostatic agents

1973 ◽  
Vol 51 (1) ◽  
pp. 83-90 ◽  
Author(s):  
Marie Novak ◽  
George Lubinsky
Keyword(s):  
Echinococcus Multilocularis ◽  
Considerable Increase ◽  
Single Injection ◽  
Total Biomass ◽  
Cytostatic Agents ◽  
Average Size

Experiments with tetrathyridia of Mesocestoides corti implanted intraperitoneally into LDF1, SEC, and SWR mice showed that a single injection of cyclophosphamide, 200 mg/kg 1 day after infection, increased the total biomass of tetrathyridial populations in mice dissected 50 days later by 50 to 200%. Similar, though less pronounced, increases in the total biomass of populations were produced by dactinomycin, 0.35 mg/kg once a week, for 4 to 6 weeks. The average size of individual tetrathyridia decreased despite a considerable increase in the total biomass of their populations.The parasiticides lucanthone, which inhibits the growth of Echinococcus multilocularis cysts, and quinacrine, which is inactive in this respect, accelerate the growth of the biomass of tetrathyridial populations much less than the cytostatic agents cyclophosphamide and dactinomycin.

Growth and allocation of Picea rubens, Picea mariana, and their hybrids under ambient and elevated CO2

2015 ◽  
Vol 45 (7) ◽  
pp. 877-887 ◽  
Author(s):  
John E. Major ◽  
Alex Mosseler ◽  
Kurt H. Johnsen ◽  
Moira Campbell ◽  
John Malcolm
Keyword(s):  
Picea Mariana ◽  
Black Spruce ◽  
Negative Relationship ◽  
Growth Efficiency ◽  
Picea Rubens ◽  
Tree Size ◽  
Total Biomass ◽  
Hybrid Index ◽  
Shoot To Root Ratio ◽  
Size Interaction

Red spruce (RS; Picea rubens Sarg.) – black spruce (BS; Picea mariana (Mill.) B.S.P.) controlled crosses (100%, 75%, 50%, 25%, and 0% RS, balance BS) showed increasingly greater height with increasing proportion of BS in each successive year. Height growth of 4-year-old ambient CO2 (aCO2) grown trees was highly correlated with height of 22-year-old field-grown trees of the same or similar crosses. Bud flush was earliest in BS and declined linearly with increasing proportion of RS with no significant CO2 effect. Percent stem (stem + branches) mass increased under elevated CO2 (eCO2), a quarter of which was due to ontogeny. Conversely, percent needle mass had a significant negative relationship with increasing tree size, and there was a CO2 × tree size interaction. Shoot-to-root ratio was greatest for BS, whereas RS had among the lowest. Hybrid index (HI) 50 had the greatest root mass allocation, lowest shoot-to-root ratio, and among the greatest total mass under eCO2. Growth efficiency increased with tree size and eCO2 but decreased with HI. Percent total biomass stimulation under eCO2 was lowest for BS at 6.5%, greatest for HI 50 at 20.3%, and RS had 17.5%.

CHAIN ROTATIONAL DYNAMICS IN MR SUSPENSIONS

2002 ◽  
Vol 16 (17n18) ◽  
pp. 2293-2299 ◽  
Author(s):  
SONIA MELLE ◽  
OSCAR G. CALDERÓN ◽  
MIGUEL A. RUBIO ◽  
GERALD G. FULLER
Keyword(s):  
Power Law ◽  
Rotating Magnetic Fields ◽  
Hydrodynamic Friction ◽  
Friction Forces ◽  
Number Ratio ◽  
Mason Number ◽  
Dynamics Simulations ◽  
Average Size ◽  
The Magnetic Field ◽  
Good Agreement

The dynamics of induced dipolar chains in magnetorhelogical suspensions subject to rotating magnetic fields has been experimentally studied combining scattering dichroism and video microscopy experiments. When a rotating field is imposed the chainlike aggregates rotate synchronously with the magnetic field. We found that the average size of the aggregates decreases with Mason number (ratio of viscous to magnetic forces) following a power law with exponent -0.5 being the hydrodynamic friction forces the cause of the chains break up. However the total number of aggregated particles shows two different behaviors depending on Mason number. For low Mason numbers, the total number of aggregated particles remains almost constant and above a critical Mason number, the rotation of the field prevents the particle aggregation process from taking place so the number of aggregated particles decreases with Mason number following a power law behavior with exponent -1. Athermal molecular dynamics simulations are also reported, showing good agreement with the experiments.

scholarly journals Invariance in ecological pattern

F1000Research ◽  
2019 ◽  
Vol 8 ◽  
pp. 2093 ◽  
Author(s):  
Steven A. Frank ◽  
Jordi Bascompte
Keyword(s):  
Maximum Entropy ◽  
Individual Component ◽  
Local Community ◽  
Neutral Theory ◽  
Simple Derivation ◽  
Shape Pattern ◽  
Ecological Patterns ◽  
Component Processes ◽  
General Answer ◽  
The Individual

Background: The abundance of different species in a community often follows the log series distribution. Other ecological patterns also have simple forms. Why does the complexity and variability of ecological systems reduce to such simplicity? Common answers include maximum entropy, neutrality, and convergent outcome from different underlying biological processes.  Methods: This article proposes a more general answer based on the concept of invariance, the property by which a pattern remains the same after transformation. Invariance has a long tradition in physics. For example, general relativity emphasizes the need for the equations describing the laws of physics to have the same form in all frames of reference.  Results: By bringing this unifying invariance approach into ecology, we show that the log series pattern dominates when the consequences of processes acting on abundance are invariant to the addition or multiplication of abundance by a constant. The lognormal pattern dominates when the processes acting on net species growth rate obey rotational invariance (symmetry) with respect to the summing up of the individual component processes. Conclusions: Recognizing how these invariances connect pattern to process leads to a synthesis of previous approaches. First, invariance provides a simpler and more fundamental maximum entropy derivation of the log series distribution. Second, invariance provides a simple derivation of the key result from neutral theory: the log series at the metacommunity scale and a clearer form of the skewed lognormal at the local community scale. The invariance expressions are easy to understand because they uniquely describe the basic underlying components that shape pattern.

scholarly journals Effects of Probiotics on Growth and Production of Monosex Tilapia (Oreochromis Niloticus) in Nylon Net Cages at Dekar Haor, Sunamganj, Bangladesh

2018 ◽  
Vol 44 (1) ◽  
pp. 69-78
Author(s):  
P Das ◽  
MS Islam ◽  
M Biswas ◽  
PR Das ◽  
ASM Arif
Keyword(s):  
Survival Rate ◽  
Oreochromis Niloticus ◽  
Conversion Ratio ◽  
Production Performance ◽  
Total Biomass ◽  
Fish Production ◽  
Food Conversion ◽  
Net Profit ◽  
Average Size ◽  
Net Cages

To assess the effect of probiotics on growth, survival rate and production performance of all monosex tilapia (Oreochromis niloticus) for a period of 120 days in 2016 in nylon net cages placed in Dekar haor of Sunamganj district. The study was categorized into four treatments as T1 (brand a), T2 (brand b), T3 (brand c) and T4 (control) based on probiotics and each having three replicates. Cages were stocked with nursed male tilapia fry at a density of 35 nos./m3 with average size of 14.33 ± 6.41 - 16.33 ± 3.15 g. Tilapia of all the cages were fed with commercial mega floating feed at a decreasing rate of 10 - 5% of total biomass thrice daily. Feed was supplemented with probiotics at a rate of 0.5 g/kg. Comparatively higher growth (307.33 ± 33.92 g), survival rate (97.6 ± 4.90%), yield (10.5 ± 1.15 kg/m3), net profit (Tk.798.96 ± 90.85/m3) and lower food conversion ratio (1.16) were secured in T3 than that of other treatments, which were manifolds higher than the earthen freshwater and brackish waterbodies. Therefore, results of the study reveal that probiotics may be used in aquaculture for increasing fish production. Asiat. Soc. Bangladesh, Sci. 44(1): 69-78, June 2018

EXTREME FLUCTUATIONS IN SMALL-WORLD-COUPLED AUTONOMOUS SYSTEMS WITH RELAXATIONAL DYNAMICS

2005 ◽  
Vol 05 (01) ◽  
pp. L43-L62 ◽  
Author(s):  
H. GUCLU ◽  
G. KORNISS
Keyword(s):  
Power Law ◽  
Fundamental Problem ◽  
Discrete Event ◽  
Autonomous Systems ◽  
Small World ◽  
System Size ◽  
Discrete Event Simulations ◽  
Synchronization Problem ◽  
Parallel Discrete Event ◽  
Average Size

Synchronization is a fundamental problem in natural and artificial coupled multi-component systems. We investigate to what extent small-world couplings (extending the original local relaxational dynamics through the random links) lead to the suppression of extreme fluctuations in the synchronization landscape of such systems. In the absence of the random links, the steady-state landscape is "rough" (strongly de-synchronized state) and the average and the extreme height fluctuations diverge in the same power-law fashion with the system size (number of nodes). With small-world links present, the average size of the fluctuations becomes finite (synchronized state). For exponential-like noise the extreme heights diverge only logarithmically with the number of nodes, while for power-law noise they diverge in a power-law fashion. The statistics of the extreme heights are governed by the Fisher–Tippett–Gumbel and the Fréchet distribution, respectively. We illustrate our findings through an actual synchronization problem in parallel discrete-event simulations.

scholarly journals SIMPLE MODELS FOR SCALING IN PHYLOGENETIC TREES

2010 ◽  
Vol 20 (03) ◽  
pp. 805-811 ◽  
Author(s):  
EMILIO HERNÁNDEZ-GARCÍA ◽  
MURAT TUĞRUL ◽  
E. ALEJANDRO HERRADA ◽  
VÍCTOR M. EGUÍLUZ ◽  
KONSTANTIN KLEMM
Keyword(s):  
Power Law ◽  
Phylogenetic Trees ◽  
Critical Parameter ◽  
Biological Species ◽  
Tree Size ◽  
Evolutionary Relationships ◽  
Asymptotic Regime ◽  
New Model ◽  
Large Tree ◽  
Number Of Leaves

Many processes and models — in biological, physical, social, and other contexts — produce trees whose depth scales logarithmically with the number of leaves. Phylogenetic trees, describing the evolutionary relationships between biological species, are examples of trees for which such scaling is not observed. With this goal, we analyze numerically two branching models leading to nonlogarithmic scaling of the depth with the number of leaves. For Ford's alpha model, although a power-law scaling of the depth with tree size was established analytically, our numerical results illustrate that the asymptotic regime is approached only at very large tree sizes. We introduce here a new model, the activity model, showing analytically and numerically that it also displays a power-law scaling of the depth with tree size at a critical parameter value.

Sign in / Sign up

Export Citation Format

Share Document