Linear analysis of switching nets

Summary The switching net that has been used as a model of several biological systems is studied using the mathematical concept of finite field. Since every function over a finite field can be represented as a terminating series, all switching nets can be linearized and thus represented by a matrix. In fact two matrices—the function matrix and the transition matrix—both represent the net. These matrices are related by an orthogonal transformation. The autonomous behavior of switching nets is obtained from a consideration of the characteristic equation and eigenvectors of either of the matrices. A simple criterion for the invertibility of a set of switching functions is obtained from this formalism. A test for invertibility proposed by Huffman is discussed, and it is show that the Jacobian test is invalid for finite fields.This paper is based on a thesis submitted to The University of Chicago in partial fulfillment of the requirements for the Doctor of Philosophy in Mathematical Biology. The research was supported by USPHS Training Grant 1-TO1 GM-2037.     

A method of statistical neurodynamics

A method of statistical neurodynamics is presented for treating ensembles of nets of randomly connected neuron-like elements. The concept of a macrostate plays a fundamental role in statistical neurodynamics and a criterion is given for ascertaining that given macroscopic quantities together constitute a macrostate. The activity of a nerve net is shown to be a macrostate and the equation of the dynamics of the activity is elucidated for various ensembles of random nerve nets. It is shown that the distance between two microstates can also be treated as a macrostate in a generalized sense. The equation of its dynamics represents how the distance between two states changes in the course of state transitions. The dynamics of distance reveals interesting microscopic properties of random nerve nets, such as the stability of state-transition, the transient lengths, etc.     

A statistical approach to the theory of the central nervous system

A “probabilistic” rather than a “deterministic” approach to the theory of neural nets is developed. Neural nets are characterized by certain parameters which give the probability distributions of different kinds of synaptic connections throughout the net. Given a “state” of the net (i.e., the distribution of firing neurons) at a given moment, an equation for the state at the next moment of quantized time is deduced. Certain very special cases involving constant distributions are solved. A necessary condition for a steady state is deduced in terms of an integral equation, in general non-linear.     

Evaluating catches of salmonids taken by gillnets

Data from 10 185 gillnetted brown trout ( Salmo trutta L.) and 5777 Arctic charr [ Salvelinus alpinus (L.)] were analysed. Relative to mesh size, the most efficiently caught fish length (the modal length) was somewhat larger with floated nets than with smaller nets placed on the bottom. There were no such consistent differences between the two species. Fish that exceeded the modal lengths were caught more efficiently than smaller fish. The relationship of most efficient mesh size to fish length and condition factor fitted excellently to a linear equation. Based on this equation, the selectivity curve for Arctic charr gillnetted in the Nesjø reservoir, the different efficiency of nets of 0.1 and 0.17mm twine and an equation expressing the increasing height of the selectivity curve with increasing mesh size, a model is presented to compare length frequencies and total numbers of gillnet catches taken with any combination of mesh sizes.     

Contribution to the theory of random and biased nets

The probabilistic theory of random and biased nets is further developed by the “tracing” method treated previously. A number of biases expected to be operating in nets, particularly in sociograms, is described. Distribution of closed chain lengths is derived for random nets and for nets with a simple “reflexive” bias. The “island model” bias is treated for the case of two islands and a single axon tracing, resulting in a pair of linear difference equations with two indices. The reflexive bias is extended to multiple-axon tracing by an approximate method resulting in a modification of the random net recursion formula. Results previously obtained are compared with empirical findings and attempts are made to account for observed discrepancies.     

Control of switching nets

Switching nets have long been used as models of biological phenomena. In this paper, control properties of switching nets are discussed. Bounds on control parameters for general nets, linear nets and nets with linear inputs are obtained. In particular, bounds are obtained on the maximum distance between two states and on the length of input sequences needed to synchronize two copies of the same net. Bounds on the number of input lines that must be added to an autonomous net to make it controllable are obtained in terms of the number of cycles and transient chains of the net.     

Do Size and Insecticide Treatment Matter? Evaluation of Different Nets against Phlebotomus argentipes,the Vector of Visceral Leishmaniasis in Nepal

In the Indian subcontinent, Leishmania donovani, the parasite causing visceral leishmaniasis (VL) is transmitted by the sand fly vector Phlebotomus argentipes. Long lasting insecticide treated nets (LN) have been postulated as alternative or complement to Indoor Residual Spraying but there are few field studies evaluating the entomological efficacy of different nets against this vector. We conducted two crossover trials in a VL endemic area in Nepal to compare the barrier effect of (1) LN with different mesh sizes (156 holes/inch² vs 625 holes/inch²) and (2) alpha-cypermethrin treated LN and untreated nets having the same mesh size (156 holes/inch²). Each crossover trial had two arms consisting of a sequence of two different nets for 8 nights. We used 10 cattle sheds per trial. A cow placed under the net was used as bait. CDC light traps placed inside the nets were used to evaluate the number of P. argentipes crossing the net barrier. Negative binomial generalized estimating equation (GEE) population-averaged models adjusted by night and sequence were used to estimate the barrier effect of the different nets. The crossover trials conducted in a rural village in Morang district (South-eastern Nepal) demonstrated that reducing the size of the holes in treated nets (625 holes/inch²) increased the barrier effect of LN by 77% (95% confidence interval (CI): 56%–88%) compared with treated nets with larger holes (156 holes/inch²). Treating nets with alpha-cypermethrin reduced the number of P. argentipes captured inside the nets by 77% (95% CI: 27%–93%) compared with untreated nets. The effectiveness and acceptability of finer mesh pyrethroid treated LN should be tested for VL prevention in a randomized controlled trial.     

ACOUSTIC REFLECTIVITY OF NETS: IMPLICATIONS CONCERNING INCIDENTAL TAKE OF DOLPHINS

Sonar target strength measurements of several types of nets and associated gear were made using simulated dolphin echolocation signals. The different types of nets included (a) standard commercial monofilament gillnet used in the salmon mothership fishery, (b) prototype hollow core monofilament net, (c) Macah tribal cord setnet, and (d) multifilament nets. Target strength measurements were made at four angles of incidence, 0° (normal to net), 15°, 30°, and 45°. The standard gillnet had the smallest target strength which was relatively independent of the angle of incidence. The target strength based on the peak-to-peak values of the echoes varied from –59 to – 62 dB. Using echo energy within the integration time of Tursiops truncatus , the target strength was found to be between – 54 and –59 dB. Biosonar detection ranges for different sea state conditions were estimated using the noise-limited form of the sonar equation and target detection data obtained for Tursiops truncatus in Kaneohe Bay, Oahu, Hawaii. The results suggest that an echolocating dolphin should be able to detect a gillnet at ranges long enough to avoid entanglement, even in sea state 6 conditions. Several possibilities for the seeming inability of dolphins to detect gillnets are discussed.     

A community model of mutually learning neuronal nets

A model of a community is suggested whose members are formal neuron nets interacting by signals exchange. As a signal each net can emit an image formed by it when recognising the preceding signal. The emitted signal comes to the inputs of other nets and is used as their initial state for the recognition process. The collective dynamics of such model is discussed for the case of non-learning nets. Possible algorithm of mutual learning of the nets in them course of signals exchange is considered.     

Induction of Nematode-Trapping Organs in the Predacious Fungus Arthrobotrys oligospora (Hyphomycetales) by Infective Larvae of Ostertagia ostertagi (Trichostrongylidae)

Laboratory experiments were designed to study the influence of temperature, concentrations of nematodes, oxygen tension, light, and nutrient levels, on the induction of nematode-trapping hyphal nets in the predacious fungus Arthrobotrys oligospora. When induced by infective Ostertagia ostertagi larvae, a maximum number of nets was produced at 20°C, at which temperature nets in surplus were produced at larval concentrations up to 1,000 larvae per cm2. A. oligospora did not produce nets in an anaerobic atmosphere containing 21 % CO2 (v/v), and net induction was suppressed to a certain degree by exposure to light. The composition of the medium had an important influence on the saprophytic growth and the net-forming capability of A. oligospora as a maximum number of nets was induced at a relatively low concentration of corn meal supporting the relatively sparse mycelium. It was shown that a proportion of trapping nets in A. oligospora maintained their trapping potential for more than 7 weeks when the temperature was below 25°C. Induction of nematodetrapping organs in A. oligospora is discussed in relation to control of infective nematode parasite larvae in cow pats.     

Un modéle mathématique de l'évitement d'un filet à plancton,son application pratique,et sa vérification indirecte en recourant au parasitisme de l'amphipode hypéride Vibilia armata Bovallius

An index of avoidance of a net by a pelagic organism, ranging from 0 to 1, is defined and an equation relating it to the diameter and the speed of the net is found. A set of derived equations allow calculation of the proportion of individuals of a given organism avoiding a net, based on comparison of pairs of tows made with nets of two different diameters, or at two different speeds.The model is tested in an indirect way using the peculiarities of the parasitism of the pelagic amphipod Vibilia armata Bovallius. During the night, females of this species hang on their weakly swimming hosts (salps) which cannot avoid the net, while males of the species are free-living and thus capable of avoidance. The proportion of sexes in catches varies with the net diameter and allows one to estimate avoidance values. Data from plankton catches show a good fit with the model predictions.Data selected from the literature are used to show the application of the equations. High indexes of avoidance for the smaller nets were found for the copepod species tested.     

Communication in a hierarchical network

An analogy is drawn between a hierarchical communication network and a pyramidal election system. An equation is derived relating the probability that a given person will vote for an issue to the probability that the elected officer will also vote for that issue. The equation contains the size of the population, the required majority ratio, and the number of stages in the election system as parameters. Such an election system is compared to the simple majority vote without a hierarchy. The absence of a hierarchy appears to favor the minority voice. All of the results are translatable into the language of neural nets.     

Insecticide mixtures for mosquito net impregnation against malaria vectors

Insecticides belonging to the pyrethroid family are the only compounds currently available for the treatment of mosquito nets. Unfortunately, some malaria vector species have developed resistance to pyrethroids and the lack of alternative chemical categories is a great concern. One strategy for resistance management would be to treat mosquito nets with a mixture associating two insecticides having different modes of action. This study presents the results obtained with insecticide mixtures containing several proportions of bifenthrin (a pyrethroid insecticide) and carbosulfan (a carbamate insecticide). The mixtures were sprayed on mosquito net samples and their efficacy were tested against a susceptible strain of Anopheles gambiae, the major malaria vector in Africa. A significant synergism was observed with a mixture containing 25 mg/m2 of bifenthrin (half the recommended dosage for treated nets) and 6.25 mg/m2 of carbosulfan (about 2% of the recommended dosage). The observed mortality was significantly more than expected in the absence of any interaction (80% vs 41%) and the knock-down effect was maintained, providing an effective barrier against susceptible mosquitoes.     

Length‐weight relationships of three freshwater fishes from Hoiya River in South Korea

The length‐weight relationships (LWRs) for three freshwater fish species in catchment area of Hoiya River, Republic of Korea, were analyzed. Fish samples were collected quarterly using scoop‐nets (5 mm mesh size), casting nets (7 mm mesh size) from 2017 to 2018. For LWRs using the general equation from Froese (2006), the parameter b ranges from 3.14 (Oryzias latipes) to 3.37 (Iksookimia longicorpa). LWRs data of these two species have not yet been listed in FishBase.     

Characterization of proteoglycan-containing perineuronal nets by enzymatic treatments of rat brain sections

Proteoglycans are among the major extracellular matrix components of the central nervous system. In the cerebral cortex and many subcortical regions, chondroitin sulphate proteoglycans, which are related to the aggrecan-versican- neurocan family, have been detected immunocytochemically in perineuronal nets that surround various types of neurons. This indicates that, in the brain, there is a nonhomogeneous but defined distribution of extracellular matrix components. The present study is a further attempt to characterize the perineuronal nets in the cerebral cortex. Sections obtained from fixed and unfixed rat brains were subjected to different enzymatic treatments prior to the visualization of perineuronal nets using N-acetylgal actosamine-binding Wisteria floribunda agglutinin, antibodies against chondroitin sulphate proteoglycans or hyaluronectin, and biotinylated hyaluronectin which detects hyaluronan. In all perineuronal nets the binding of the Wisteria floribunda agglutinin was abolished after the incubation of sections with chondroitinase ABC. The protein components of the proteoglycan complexes became easier to digest after removal of chondroitin sulphate chains or hyaluronan. Since only quantitative, and not qualitative, differences in the labelling properties and the structural appearance of cortical perineuronal nets were observed after the various treatments, it is concluded that, with regard to their proteoglycan composition, these structures have common basic properties     

Effect of Structure on Function in Model Nerve Nets

A theoretical analysis has been made on the effect of the pattern of interneuronal connectivity in model nerve nets on the activity of these nets. Two types of nets have been investigated: one in which the likelihood of a connection between a given neuron and any other element in the net is given by a Poisson probability distribution, and a second type in which the pattern of interconnection follows a Gaussian distribution. An analytical treatment is presented of the equations for noiseless nets in these two conditions. The principal result is that nets with Poisson connectivity law are activated by extraneous firing of a single neuron and continue in spontaneous activity indefinitely. On the other hand, similar nets in which the connections are, however, distributed according to a normal connectivity law, exhibit a definite threshold and produce spontaneous activity only subsequent to extraneous activation of a substantial fraction of the population. Moreover, spontaneous activity in Gaussian nets, but not in Poisson nets, becomes extinguished if the number of active neurons falls below the critical threshold. Some neuroanatomical implications are discussed which suggest that the pyramidal system of the cerebral cortex and other neuronal systems histologically characterized by large numbers of synapses per neuron may incorporate a Gaussian connectivity law, whereas a Poisson law may be characteristic of these cortical layers and nuclei primarily containing granule cells.     

A comparison of Antarctic petrel (Thalassoica antarctica) diets with net samples of Antarctic krill (Euphausia superba) taken from the Prydz Bay region

Samples of the stomach contents of Antarctic petrels (Thalassoica antarctica) were obtained on board ship in the Prydz Bay region of Antarctica from birds which had spontaneously regurgitated. The weight of food and the species composition of the stomach contents were measured. Antarctic krill,Euphausia superba, the sole prey item taken, were compared to krill obtained by nets in the same region as part of a large-scale krill survey. Krill from petrel stomach samples were larger in mean size than those sampled by nets. This may be attributed to selection of the larger sized krill by the petrels, it may be caused by the nets sampling different populations of krill or it may be due to net avoidance by the larger krill.     

A moorable,automated plankton sampler

A moorable, automated plankton sampler is described, designed to obtain series of plankton samples over extended time periods in the absence of a surface vessel. The sampler consists of one or more net-containing boxes, a unit for generating as well as measuring water flow through the net boxes, a programmeable control unit, and a frame. Each net box contains several nets on a vinyl strip, used to move the nets from the storage chamber into the fishing position and then into the preservative chamber. Preservation of samples is in a formalin-brine mixture.Net boxes can be added and the number of nets per box changed; the prototype is described with 1 net box with 10 nets. Volume of water to be filtered, time between sample collections, number of net boxes and the number of nets in each box is programmed into the control unit before sampler deployment. Collections made with the sampler are compared with those made with a SCOR net and a pump.