Universal scaling laws for hierarchical complexity in languages, organisms, behaviors and other combinatorial systems.

There are many complex systems in nature where components, or "words", are combined together to make expressions, or "sentences". Such combinatorial systems include: (1) human language, where sentences are composed of words; (2) bird vocalization, where songs are built from syllables; (3) organisms, where organism-expressions (e.g. the tonsil) are made out of cells; (4) behavioral repertoire, where mammalian behavior consists of a temporal arrangement of muscle contractions; (5) universities, where student academic degrees are comprised of departmental concentrations; and (6) electronic devices, where the device's actions are implemented via strings of button-presses. My central aim here is to discover how combinatorial systems accommodate greater numbers of expressions; that is, what changes do combinatorial systems undergo when they "say more things?" Are there general laws characterizing the properties of combinatorial systems as the number of expressions increases? If so, what are they? My main result is that, in all the kinds of combinatorial system mentioned above, there appear to be general laws describing how combinatorial systems change as they become more expressive. In particular, in each of these cases, increase in expression complexity (i.e. number of expressions the combinatorial system allows) is achieved, at least in part, by increasing the number of component types. Each kind of system follows one of two kinds of scaling law. In the first kind of scaling law, expression complexity increase is carried out exclusively by increasing the number of component types; the number of components per expression (i.e. the expression length) remains invariant. This applies to human language over history, bird vocalization, organisms in phylogeny and ontogeny, and universities. In the second kind of scaling law, expression complexity is accomplished by increasing in a law-like manner both the number of component types and the expression length. This applies to two cases of the ontogeny of language-the development of words and sentences, and the development of phonemes and morphemes-and to mammalian behavior. By treating these diverse systems as combinatorial systems we, in addition to elucidating general principles underlying such systems, gain insight into each kind of system mentioned.     

The economy of the shape of limbed animals

A simple, high-level wire-minimization model appears to drive the relationship between animal limb number and body-to-limb proportion in some animals across at least seven phyla: annelids, arthropods, cnidarians, echinoderms, molluscs, tardigrades and vertebrates. Given an animal's body-to-limb proportion, the model enables one to estimate the animal's number of limbs, and vice versa. Informally, the model states that a limbed animal's large-scale morphology is set so as to maximize its number of limbs subject to the constraint that there is not a more economical shape which reaches out to the same places. A consequence of animals conforming to the model is that their large-scale morphology is “minimally wired.” Just as wire minimization is important in artificial information processing devices, it is hypothesized that one reason why animals' large-scale morphologies conform to a save-wire principle is to minimize the system-wide information processing times. Received: 10 November 1999 / Accepted in revised form: 9 June 2000     

The Optimal Human Ventral Stream from Estimates of the Complexity of Visual Objects

The part of the primate visual cortex responsible for the recognition of objects is parcelled into about a dozen areas organized somewhat hierarchically (the region is called the ventral stream). Why are there approximately this many hierarchical levels? Here I put forth a generic information-processing hierarchical model, and show how the total number of neurons required depends on the number of hierarchical levels and on the complexity of visual objects that must be recognized. Because the recognition of written words appears to occur in a similar part of inferotemporal cortex as other visual objects, the complexity of written words may be similar to that of other visual objects for humans; for this reason, I measure the complexity of written words, and use it as an approximate estimate of the complexity more generally of visual objects. I then show that the information-processing hierarchy that accommodates visual objects of that complexity possesses the minimum number of neurons when the number of hierarchical levels is approximately 15.     

Effect of Nano-Fe as Feed Supplement on Growth Performance,Survival Rate,Blood Parameters and Immune Functions of the Stellate Sturgeon (Acipenser stellatus)

Russian Journal of Marine Biology - The present study is aimed to investigate the effects of iron nanoparticles (Fe-NPs) on growth performance, liver histopathology and some blood parameters of the...     

Sympatric morphotypes of the restricted-range Tashan Cave Garra: distinct species or a case of phenotypic plasticity?

Environmental Biology of Fishes - Among Tashan cave barb Garra tashanensis inhabiting a small cave in southwest Iran, two mental disc (sucking mouth disc) forms were observed. To assess their...     

Principles underlying mammalian neocortical scaling

 The neocortex undergoes a complex transformation from mouse to whale. Whereas synapse density remains the same, neuron density decreases as a function of gray matter volume to the power of around −1/3, total convoluted surface area increases as a function of gray matter volume to the power of around 8/9, and white matter volume disproportionately increases as a function of gray matter volume to the power of around 4/3. These phylogenetic scaling relationships (including others such as neuron number, neocortex thickness, soma radius, and number of cortical areas) are clues to understanding the principles driving neocortex organization, but there is currently no theory that can explain why these neocortical quantities scale as they do. Here I present a two-part model that explains these neocortical allometric scaling laws. The first part of the model is a special case of the physico-mathematical model recently put forward to explain the quarter power scaling laws in biology. It states that the neocortex is a space-filling neural network through which materials are efficiently transported, and that synapse sizes do not vary as a function of gray matter volume. The second part of the model states that the neocortex is economically organized into functionally specialized areas whose extent of area-interconnectedness does not vary as a function of gray matter volume. The model predicts, among other things, that the number of areas and the soma radius increase as a function of gray matter volume to the power of 1/3 and 1/9, respectively, and empirical support is demonstrated for each. Also, the scaling relationships imply that, although the percentage of the total number of neurons to which a neuron connects falls as a function of gray matter volume with exponent −1/3, the network diameter of the neocortex is invariant at around two. Finally, I discuss how a similar approach may have promise in explaining the scaling relationships for the brain and other organs as a function of body mass. Received: 23 December 1999 / Accepted in revised form: 2 August 2000     

Relationship between number of muscles,behavioral repertoire size,and encephalization in mammals

Behavior for mammals is built out of multiple muscles acting in a coordinated fashion. Prima facie, there are three principal ways to increase an animal's behavioral repertoire size. The first is to, for each new behavior type, create a set of new muscle types (e.g. triceps, sartorius, etc.) with new functions specifically devoted to the implementation of that behavior type. If this were the case, then although each behavior is built out of many muscles, behavior is not built in a combinatorial fashion out of muscles. The second is similar to the first in that new behavior types are implemented via new muscle types, but, instead, muscles are used in a combinatorial fashion, so that it is the combination of the new muscle type with existing muscle types that makes the new behavior type possible. This is analogous to the addition of new words in a language. The third way behavioral complexity may be scaled up is to increase the complexity of behavioral expressions themselves (rather than increasing the number of muscles types), namely by having more muscles involved in an average behavior. This is analogous to uttering longer sentences in a language. My main task in this paper is to examine which of these ways underlies the increase of behavioral complexity among mammals. Behavioral repertoire sizes from the ethology literature were accumulated for mammals from two dozen species across eight orders, and the number of muscle types was estimated from atlases of anatomy across eight mammalian orders. The manner in which behavioral complexity actually increases among mammals appears to favor the second possibility mentioned above: greater behavioral complexity is achieved primarily by increasing the number of muscle types, and by using muscles in a combinatorial fashion. The theoretical framework I describe allows us to interpret the manner in which the number of muscle types scales with behavioral repertoire size, and I conclude that the number of degrees of freedom in the construction of behavioral expressions is on the order of three, which is probably due to neurobiological limitations in forming behaviors. The ontogeny of behavior in rat is also discussed within this framework. Finally, I show that there is a strong positive relationship between behavioral repertoire size and encephalization among mammals.     

Investigating key cell types and molecules dynamics in PyMT mice model of breast cancer through a mathematical model

The most common kind of cancer among women is breast cancer. Understanding the tumor microenvironment and the interactions between individual cells and cytokines assists us in arriving at more effective treatments. Here, we develop a data-driven mathematical model to investigate the dynamics of key cell types and cytokines involved in breast cancer development. We use time-course gene expression profiles of a mouse model to estimate the relative abundance of cells and cytokines. We then employ a least-squares optimization method to evaluate the model’s parameters based on the mice data. The resulting dynamics of the cells and cytokines obtained from the optimal set of parameters exhibit a decent agreement between the data and predictions. We perform a sensitivity analysis to identify the crucial parameters of the model and then perform a local bifurcation on them. The results reveal a strong connection between adipocytes, IL6, and the cancer population, suggesting them as potential targets for therapies.     

Feasibility of Breast Cancer Screening by PIXE Analysis of Hair

To reveal the role of key elements present in the hair of breast cancer patients on cancer development, the levels of a number of elements in scalp hair samples of 82 people including healthy individuals, people suffering from benign breast disease, and breast cancer patients were measured by PIXE analysis. Pellets of hair samples were prepared and bombarded by 2.2 MeV proton beam of a 3-MV Van de Graaff accelerator. The number of incident ions hitting the sample was indirectly measured using the RBS spectrum of a thin Ag film placed in the beam path. The concentrations of S, Cl, K, Ca, Fe, and Cu in the hair of healthy individuals were in agreement with those observed in the hair of hyperplasia and cancer patients within standard deviations. However, a lower average level of zinc was found in samples from hyperplasia and breast cancer patients. Strong positive correlations were found between iron and potassium as well as between calcium and potassium in the cancer patients. These results could be of significance in the screening for breast cancer.     

The structures of letters and symbols throughout human history are selected to match those found in objects in natural scenes

Are there empirical regularities in the shapes of letters and other human visual signs, and if so, what are the selection pressures underlying these regularities? To examine this, we determined a wide variety of topologically distinct contour configurations and examined the relative frequency of these configuration types across writing systems, Chinese writing, and nonlinguistic symbols. Our first result is that these three classes of human visual sign possess a similar signature in their configuration distribution, suggesting that there are underlying principles governing the shapes of human visual signs. Second, we provide evidence that the shapes of visual signs are selected to be easily seen at the expense of the motor system. Finally, we provide evidence to support an ecological hypothesis that visual signs have been culturally selected to match the kinds of conglomeration of contours found in natural scenes because that is what we have evolved to be good at visually processing.