Geometrical structures determined by the functional order in nervous nets

The functional order of a collection of neural elements may be defined as the order induced through the total of covariances of signals carried by the members of the collection. Thus functional order differs from geometrical order (e.g. somatotopy) in that geometrical order is only available to external observers, whereas functional order is available to the system itself. It has been shown before that the covariances can be used to construct a partially ordered set that explicitely represents the functional order. It is demonstrated that certain constraints, if satisfied, make this set isomorphic with certain geometrical entities such as triangulations. For instance there may exist a set of hyperspheres in a n-dimensional space with overlap relations that are described with the same partially ordered set as that which describes the simultaneous/successive order of signals in a nerve. Thus it is logically possible that the optic nerve carries (functionally) two-dimensional signals, quite apart from anatomical considerations (e.g. the geometrically two-dimensional structure of the retina which exists only to external observers). The dimension of the modality defined by a collection of nervous elements can in principle be obtained from a cross-correlation analysis of multi-unit recordings without any resort to geometrical data such as somatotopic mappings.     

The construction of a simultaneous functional order in nervous systems

In a previous paper (Part I) we introduced a model that constructs a simultaneous functional order in a set of neuronal elements by monitoring the coincidences in their signal activities (the so-called coincidence-model). The simultaneous signal activity in a neural net will be constrained both by its physical restrictions and by environmental constraints. In this paper we present the results of simulation experiments that were performed to study the influence of environmental constraits on the resulting functional order in a set of neural elements corresponding to a onedimensional detector array. We show that the coincidence-model produces a functional order that encodes the physical constraints of the environment. Moreover, we demonstrate that the signal activity in the neural net (the perceptions) can be related to events in the outer world. We provide some examples to demonstrate that our model may prove useful to gain insight into certain developmental disorders.     

The construction of a simultaneous functional order in nervous systems

The functional order of a collection of nervous elements is available to the system itself, as opposed to the anatomical geometrical order which exists only for external observers. It has been shown before (Part I) that covariances or coincidences in the signal activity of a neural net can be used in the construction of a simultaneous functional order in which a modality is represented as a concatenation of districts with a lattice structure. In this paper we will show how the resulting functional order in a nervous net can be related to the geometry of the underlying detector array. In particular, we will present an algorithm to construct an abstract geometrical complex from this functional order. The algebraic structure of this complex reflects the topological and geometrical structure of the underlying detector array. We will show how the activated subcomplexes of a complex can be related to segments of the detector array that are activated by the projection of a stimulus pattern. The homology of an abstract complex (and therefore of all of its subcomplexes) can be obtained from simple combinatorial operations on its coincidence scheme. Thus, both the geometry of a detector array and the topology of projections of stimulus patterns may have an objective existence for the neural system itself.     

The construction of a simultaneous functional order in nervous systems

The signal activity in a neural net will be constrained both by its physical structure and by environmental constraints. By monitoring its signal activity a neural system can build up a simultaneous functional order that encodes these constraints. We have previously (Part I) presented two models that construct a simultaneous functional order in a collection of neural elements using either signal-covariances or signal-coincides. In this paper we present the results of simulation experiments that were performed to study the influence of the physical constraints of a neural system on the simultaneous functional order produced by both models. In the simulation experiments we used a one-dimensional detector array. We delineate the physical constraints such an array has to satisfy in order to induce a functional order relation that allows an isomorphism with a geometrical order. We show that for an appropriate choice of the system parameters both models can produce a simultaneous functional order with sufficient internal coherence to allow isomorphisms with a triangulation. In this case the dimensionality and the coherence of the detector array are objectively available to the system itself.     

The construction of a simultaneous functional order in nervous systems

We have developed two algorithms that construct a simultaneous functional order in a collection of neural elements using purely functional relations. The input of the first algorithm is a matrix describing the total of covariances of signals carried by the members of the neural collection. The second algorithm proceeds from a matrix describing a primitive inclusion relation among the members of the neural collection that can be determined from coincidences in their signal activity. From this information both algorithms compute a partial functional order in the collection of neural elements. Such an order has an objective existence for the system itself and not only for an external observer. By either merging individual neurons or recruiting previously unspecified ones the partial order is locally transformed into a lattice order. Thus, the simultaneous functional order in a nervous net may become isomorphic with a geometrical order if the system has eneough internal coherence. Simulation experiments were done, both for the neuron-merging and the neuron-recruitment routines, to study the number of individuals in the resulting lattice order as a function of the number of individuals in the underlying partially ordered set.     

Looking at physiological anthropology from a historical standpoint

As one way of thinking about physiological anthropology, let us survey it from a historical viewpoint. At the beginning of the 19th century, Blumenbach, considered the father of Physical Anthropology, wrote his "Handbook of Comparative Anatomy and Physiology." The subsequent research conducted and papers written by researchers such as Broca and Martin pointed in the direction of physiological anthropology; furthermore, the research carried out by the American researchers Demon and Baker had a physiological anthropology "feel." The courses in Physiological Anthropology taught by Tokizane exerted a major influence on physiological anthropology in Japan. The precursor of the Japan Society of Physiological Anthropology, organized by Sato in 1978, was extremely significant in the effect that it had on the subsequent development of physiological anthropology. The holding of the biennial International Congress of Physiological Anthropology, along with the allocation of the Research sub-field of Physiological Anthropology in the Grant-in-Aid for Scientific Research, would seem to suggest that the field of physiological anthropology is set to increasingly grow and evolve.     

Cholesterol crystallite nucleation in supersaturated model biles from a thermodynamic standpoint

A rapid, silicone polymer film uptake method was used to determine the cholesterol (Ch) thermodynamic activity (A(T)) in taurocholate (TC)-lecithin (L) and taurochenodeoxycholate (TCDC)-L model biles supersaturated with Ch. Also, time-dependent quasielastic light scattering (QLS) measurements and microscopic observations were made to determine the nature of particle species and the Ch nucleation times. In all cases in which Ch-L vesicles were present, a linear relationship between the logarithm of Ch nucleation times and Ch A(T) was found. These findings support that Ch A(T) is the appropriate parameter that represents the Ch nucleation tendency and that vesicles are catalytic sites in the Ch nucleation process. When Ca2+, a nucleation promoter ion, was present in the supersaturated model biles, the increased values of Ch A(T) quantitatively correlated with shorter Ch nucleation times. These latter findings further demonstrate that Ch A(T) is the dominant factor in explaining the Ch nucleation tendencies in supersaturated model biles.     

A statistical consequence of the logical calculus of nervous nets

A formal method is derived for converting logical relations among the actions of neurons in a net into statistical relations among the frequencies of their impulses.     

Some remarks on the boolean algebra of nervous nets in mathematical biophysics

Recent demonstration by the author has shown that the fundamental equations of the mathematical biophysics of the central nervous system can be considered as describing the behavior of very large numbers of neurons, of which each one follows discontinuous laws, such as discussed by W. S. McCulloch and W. Pitts. In that light some of the old problems are discussed. The comparative merits of the “microscopic” and “macroscopic” approaches are discussed for the problem of the point to point correspondence between the retina and the cortex, with the number of connecting fibers much less than the number of cells. Some aspects of discrimination of intensities are also discussed. Finally, a few generalizations of the McCulloch-Pitts treatment are suggested, and a nervous network is constructed which illustrates some aspects of the perception of numbers.     

Factors affecting plasmid production in Escherichia coli from a resource allocation standpoint

Background  

Plasmids are being reconsidered as viable vector alternatives to viruses for gene therapies and vaccines because they are safer, non-toxic, and simpler to produce. Accordingly, there has been renewed interest in the production of plasmid DNA itself as the therapeutic end-product of a bioprocess. Improvement to the best current yields and productivities of such emerging processes would help ensure economic feasibility on the industrial scale. Our goal, therefore, was to develop a stoichiometric model of Escherichia coli metabolism in order to (1) determine its maximum theoretical plasmid-producing capacity, and to (2) identify factors that significantly impact plasmid production.     

Constructing biological pathway models with hybrid functional Petri nets

In many research projects on modeling and analyzing biological pathways, the Petri net has been recognized as a promising method for representing biological pathways. From the pioneering works by Reddy et al., 1993, and Hofest?dt, 1994, that model metabolic pathways by traditional Petri net, several enhanced Petri nets such as colored Petri net, stochastic Petri net, and hybrid Petri net have been used for modeling biological phenomena. Recently, Matsuno et al., 2003b, introduced the hybrid functional Petri net (HFPN) in order to give a more intuitive and natural modeling method for biological pathways than these existing Petri nets. Although the paper demonstrates the effectiveness of HFPN with two examples of gene regulation mechanism for circadian rhythms and apoptosis signaling pathway, there has been no detailed explanation about the method of HFPN construction for these examples. The purpose of this paper is to describe method to construct biological pathways with the HFPN step-by-step. The method is demonstrated by the well-known glycolytic pathway controlled by the lac operon gene regulatory mechanism.     

A heterarchy of values determined by the topology of nervous nets

Because of the dromic character of purposive activities, the closed circuits sustaining them and their interaction can be treated topologically. It is found that to the value anomaly, whenA is preferred toB,B toC, butC toA, there corresponds a diadrome, or circularity in the net which is not the path of any drome and which cannot be mapped without a diallel on a surface sufficient to map the dromes. Thus the apparent inconsistency of preference is shown to indicate consistency of an order too high to permit construction of a scale of values, but submitting to finite topological analysis based on the finite number of nervous cells and their possible connections.     

Exophthalmos from the standpoint of the otolaryngologist

Exophthalmos may be due to an inflammatory process or to tumor formation. Inflammatory processes are most likely to occur in children and young adults. Tumors are the most common cause of exophthalmos in adults.Since the advent of chemotherapy and the antibiotics, rarely does orbital cellulitis develop from sinal infection. Tumors causing exophthalmos are likely to be benign if they arise from the frontal sinus and malignant if they arise from the maxillary and ethmoid sinuses.     

Exophthalmos from the standpoint of the ophthalmologist

There are many causes of abnormal protrusion of one or both eyes, the most common of which is imbalance of the glands of internal secretion. Among other causes are a variety of tumors that originate behind the eye or that extend to that location from other parts in the body. Infections can extend to the orbit behind the eye from the neighboring structures such as the paranasal sinuses. Infection may also extend to the orbit from distant areas by way of the blood and cause exophthalmos.