Bits and q-bits in a psychiatric ward.

The present study is a trial on expressing the whole state of a psychiatric ward as a linear combination of base states in a Hilbert space. Real data were collected by observing the behavior of the patients from the psychiatric ward of the Clinical Hospital from Faculdade de Medicina de Ribeirão Preto for 12 days and, according to standard procedures, 18 behavioral parameters were daily measured for each patient. The whole data set was analyzed and, by taking the standard grades as eigenstates, the state of the ward was daily expressed by a linear combination of them, allowing the estimation of state transition matrices and of the quantum variability measure. Coefficients of the linear combination can be interpreted as square roots of probabilities and informational entropy is associated to each state resulting in the classical variability measure. Temporal evolutions of the classical and quantum variability measures are plotted trying to relate them to the behavioral state of the whole ward.

Biological models: measuring variability with classical and quantum information.

This essay proposes methods to analyse the variability of biological data. The idea is to express the state of a biological system as a linear combination of base states in a Hilbert space. Coefficients of the linear combination can be interpreted as probabilities and informational entropy is associated to each state allowing the definition of a classical variability measure. Besides, state transition matrices can also be calculated and their norms express the dynamics of the system organization and a quantum variability measure. As the examples show, the classical measure expresses a structural variability and the quantum measure expresses a functional variability.

Fluorescent and dispersion experiments on biological membranes under micro-gravity.

Almost all biological processes, especially those involved in signal reception and signal transduction, depend on the physical and physiological properties of biological membranes. It has been shown, that neuronal tissue and the speed of the action potential (AP) which is the basic neuronal unit of all nervous activity, is sensitive to changes in gravity as well as to other weak external forces. We strongly suppose the membrane to be the most important factor in gravitational responses although it is very difficult to observe the effects of gravity changes on these fragile thermodynamic systems. Therefore we developed two different experiments to measure the structural changes and the lateral membrane tension of spheroid cells under microgravity.

Coupled biological oscillators in a cave insect.

Insects that live in the interior of caves show the basic internal temporal organization of coupled oscillators. An analysis is made of the coupled moulting and oviposition cycles of Folsomia candida, a cave-dwelling Collembolan, with regard to their oscillatory nature, their phase dependent responses to external perturbations, the effect of coupling on these responses, and conjecture about the link of these cycles with circadian clocks in other organisms.

Using Shannon entropy on measuring the individual variability in the Rufous-bellied thrush Turdus rufiventris vocal communication.

We applied the information theory concepts to notes repertoire characteristics combined with temporal parameters of the Rufous-bellied thrush Turdus rufiventris song, using this particular case to test a new method of analysing quantitatively complex animal communication systems. Like most Turdus thrushes, Rufous-bellied thrushes are remarkable for their long, varied and melodious songs. For the analysis of the species repertoire, we used recordings of 44 individuals from 24 localities covering its full geographical range. We measured the repertoire size, note duration and rhythm (frequency of note utterance), and combined these parameters with the Shannon entropy values calculated for each individual. Although individuals maintain species-specific recognition capacity, we find a large variation between their song parameters and show that the information theory can be useful to analyse large and varied animal vocal repertoires. We are introducing two new parameters, temporal average entropy (E(t)) and utterance frequency average entropy (E(f)), for measuring such communication systems.

A condition for successful escape of a mutant after primary HIV infection.

Cytotoxic T lymphocytes (CTLs) vigorously restrict primary human immunodeficiency virus (HIV) infection. However, the frequently erroneous process of viral replication favors the creation of mutants not recognizable by primary CTLs. Variants that tolerate the mutations may have selective advantage and may increase in abundance, until the immune system reacts against them. Therefore, such variants represent a way of propagating the viremia. With the aid of a simple mathematical model, here we estimate the intensity of CTL cross-reactivity against different strains of HIV in a typical progressor. We show that below a critical intensity of cross-reactivity, the concentration of a mutant created at primary peak grows and causes a secondary peak in viremia. Above this critical intensity, such a mutant strain is prevented from reaching a detectable level. We speculate about how this result may contribute to the design of an anti-HIV vaccine.

Zipf's law organizes a psychiatric ward.

We developed a simple mathematical model based on power law fitting for describing the interactions among patients from a psychiatric ward. First we defined a protocol in order to evaluate in a quantative way the state of the patient, measuring sociability/restlessness through a daily analysis of the behavior and attributing a grade for both parameters, per patient. The grades were checked by two different specialists and a table of incidence was constructed. This table generated power laws for the grades and their variations. We concluded that power laws, like Zipf's law, may be good to explain the data, showing a self-organizing process that indicates a strong interaction component determining the whole behavior. We would like to see more data being collected, in other centers and among normal populations, trying to quantify complex collective behavioral phenomena using self-organizing criticality laws.

Modeling homopolymer self-replication: implications for early competition.

We start showing that the rate equation for a homopolymer self-replication may be written as being proportional to mbetapGamma with beta=1 and Gamma=1/2, where m is the monomer concentration and p is the homopolymer total concentration (double helices plus isolated strands). With such values for the exponents beta and Gamma, we examine analytically the asymptotic behavior of our model previously proposed for studying the early polymer evolution. In this model, polymers compete for activated monomers carried into the system under a constant flux. Time changes on their concentrations are determined by the reactions of: spontaneous generation of dimers through non-instructed junction of two monomers; ligation among free monomers and polymers at the end of their chains, so that they can extend their sizes; template-instructed synthesis by which polymers with lengths above a length threshold can catalyse the formation of other polymers; and decomposition of all species. We find out that if the monomer flux intensity is "low" (lesser than the decomposition rate constants), dimer is the dominant species. Under a "high" flux (greater than the template-instructed synthesis rate constant), the longest self-replicating species prevails. For a "middle" flux (between "low" and "high"), the shortest self-replicating polymer is the winner. Whatever the flux intensity, all polymer species ever coexist.