Maximal reproduction number estimation and identification of transmission rate from the first inflection point of new infectious cases waves: COVID-19 outbreak example

The dynamics of COVID-19 pandemic varies across countries and it is important for​ researchers to study different kind of phenomena observed at different stages of the waves during the epidemic period. Our interest in this paper is not to model what happened during the endemic state but during the epidemic state. We proposed a continuous formulation of a unique maximum reproduction number estimate with an assumption that the epidemic curve is in form of the Gaussian curve and then compare the model with the discrete form and the observed basic reproduction number during the contagiousness period considered. Furthermore, we estimated the transmission rate from identification of the first inflection point of a wave of the curve of daily new infectious cases using the Bernoulli S-I (Susceptible-Infected) equation. We applied this new method to the real data from Cameroon COVID-19 outbreak both at national and regional levels. High correlation was observed between the socio-economic parameters and epidemiology parameters at regional level in Cameroon. Also, the method was applied to the second wave COVID-19 outbreak for the world data which is a period the phenomena we are considering were observed. Lastly, it was observed that the models presented results correspond with the epidemic dynamics in Cameroon and World data. We recommend that it is important to study what happened during the growth inflection point as some countries data did not climax.

SI epidemic model applied to COVID-19 data in mainland China

The article is devoted to the parameters identification in the SI model. We consider several methods, starting with an exponential fit to the early cumulative data of SARS-CoV2 in mainland China. The present methodology provides a way to compute the parameters at the early stage of the epidemic. Next, we establish an identifiability result. Then we use the Bernoulli-Verhulst model as a phenomenological model to fit the data and derive some results on the parameters identification. The last part of the paper is devoted to some numerical algorithms to fit a daily piecewise constant rate of transmission.

Reduction of Prolonged Excessive Pressure in Seated Persons With Paraplegia Using Wireless Lingual Tactile Feedback: A Randomized Controlled Trial

Pressure ulcers (PU) are known to be a high-cost disease with a risk of severe morbidity. This paper evaluates a new clinical strategy based on an innovative medical device [Tongue Display Unit (TDU)] that implements perceptive supplementation in order to reduce prolonged excessive pressure, recognized as one of the main causes of PU. A randomized, controlled, and parallel-group trial was carried out with 12 subjects with spinal cord injuries (SCI). Subjects were assigned to the control (without TDU, [Formula: see text]) or intervention (with TDU, [Formula: see text]) group. Each subject took part in two sessions, during which the subject, seated on a pressure map sensor, watched a movie for one hour. The TDU was activated during the second session of the intervention group. Intention-to-treat analysis showed that the improvement in adequate weight shifting between the two sessions was higher in the intervention group (0.84 [0.24; 0.89]) than in the control group (0.01 [-0.01; 0.09]; [Formula: see text]) and that the ratio of prolonged excessive pressure between the two sessions was lower in the intervention group (0.74 [0.37; 1.92]) than in the control group (1.72 [1.32; 2.56]; [Formula: see text]). The pressure map sensor was evaluated as being convenient for use in daily life; however, this was not the case for the TDU. This paper shows that persons with SCI could benefit from a system based on perceptive supplementation that alerts and guides the user on how to adapt their posture in order to reduce prolonged excessive pressure, one of the main causes of PU.

Estimation of life expectancy of patients diagnosed with the most common cancers in the Valparaiso Region, Chile

Background

The 1000s of people who die from cancer each year have become one of the leading causes of death among the Chilean population, placing it as the second cause of death in the region of Valparaiso between 1997 and 2003. Statistics have provided different measures regarding the life expectancy of cancer patients which have resulted in being useful to establish courses of action for prevention and treatment plans to follow.

Methods

Data was extracted from the cancer module of the Epidemiology Assistance System (SADEPI for its initials in Spanish) which stores information about cancer cases in the provinces of Valparaiso and Petorca. The survival period is defined as the difference in days between the date of occurrence and the date of death of the patient by separating the data into quartiles.

Results

The more frequent cancers in the region of Valparaiso behave similarly to global behaviours of the disease. The majority of affected patients are around 65 years of age which progressively lowers its occurrence in younger adults under the age of 45.

Conclusions

Further efforts are required for early detection and timely access to treatment for cancer patients. Statistics are an important support in achieving this.

Wound Healing and Scale Modelling in Zebrafish

We propose to study the wound healing in Zebrafish by using firstly a differential approach for modelling morphogens diffusion and cell chemotactic motion, and secondly a hybrid model of tissue regeneration, where cells are considered as individual objects and molecular concentrations are described by partial differential equations.

Discrete dynamics of contagious social diseases: Example of obesity

Modeling contagious diseases needs to incorporate information about social networks through which the disease spreads as well as data about demographic and genetic changes in the susceptible population. In this paper, we propose a theoretical framework (conceptualization and formalization) which seeks to model obesity as a process of transformation of one's own body determined by individual (physical and psychological), inter-individual (relational, i.e., relative to the relationship between the individual and others) and socio-cultural (environmental, i.e., relative to the relationship between the individual and his milieu) factors. Individual and inter-individual factors are tied to each other in a socio-cultural context whose impact is notably related to the visibility of anybody being exposed on the public stage in a non-contingent way. The question we are dealing with in this article is whether such kind of social diseases, i.e., depending upon socio-environmental exposure, can be considered as "contagious". In other words, can obesity be propagated from individual to individual or from environmental sources throughout an entire population?

Evaluation of a Smartphone-based audio-biofeedback system for improving balance in older adults--a pilot study

This study was designed to assess the effectiveness of a Smartphone-based audio-biofeedback (ABF) system for improving balance in older adults. This so-called "iBalance-ABF" system that we recetly developed is "all-inclusive" in the sense that its three main components of a balance prosthesis, (i) the sensory input unit, (ii) the processing unit, and (iii) the sensory output unit, are entirely embedded into the Smartphone. The underlying principle of this system is to supply the user with supplementary information about the medial-lateral (ML) trunk tilt relative to a predetermined adjustable "dead zone" through sound generation in earphones. Six healthy older adults voluntarily participated in this pilot study. Eyes closed, they were asked to stand upright and to sway as little as possible in two (parallel and tandem) stance conditions executed without and with the use of the iBalance-ABF system. Results showed that, without any visual information, the use of the Smartphone-based ABF allowed the older healthy adults to significantly decrease their ML trunk sway in the tandem stance posture and to mitigate the destabilizing effect induced by this particular stance. Although an extended study including a larger number of participants is needed to confirm these data, the present results are encouraging. They do suggest that Smartphone-based ABF system could be used for balance training and rehabilitation therapy in older adults.

A protocol for testing expert-system reliability

We set out a protocol for giving a computerised medical decision system the label of expert-system meaning that its responses are of the same standard as those of an expert. We apply it to the validation of an expert-system, MENINGE, which is applied to diagnosis of meningitis in children. The proposed protocol can be widely used since it doesn't refer to the existence of correct responses for therapy or diagnosis, and since it involves simple statistical computations. First this validation rests on a comparison of agreement among experts and among physicians new to medical practice. Secondly, the agreement of the system with the experts is compared to the agreement of the system with physicians new to medical practice. In order to perform this comparison we recommend a standard agreement measure, the choice of which is an important issue in this paper.

MitomiRs delineating the intracellular localization of microRNAs at mitochondria

Mitochondria play a crucial role in energetic metabolism, signaling pathways, and overall cell viability. Mitochondrial dysfunctions are known to cause a wide range of human diseases that affect tissues especially those with high energetic requirements, such as skeletal muscle, heart, kidney, and central nervous system, while being involved in cancer, aging, and metabolic processes. At the same time, the microRNA (miRNA) gene family has been demonstrated to be involved in most cellular processes through modulation of proteins critical for cellular homeostasis. Given the broad scope of reactivity profiles and the ability of miRNAs to modify numerous proteomic and genomic processes, new emphasis is being placed on the influence of miRNAs at the mitochondrial level. Recently, the localization of miRNAs in mitochondria was characterized in different species. This raises the idea that those miRNAs, noted "mitomiRs," could act as "vectors" that sense and respond dynamically to the changing microenvironment of mitochondria at the cellular level. Reciprocally, we present the involvement of mitochondria in small RNA biogenesis. With the aim of deciphering the significance of this localization, we discuss the putative mechanism of import of miRNAs at mitochondria, their origin, and their hypothetical roles within the organelle.

MitomiRs, chloromiRs and modelling of the microRNA inhibition

MicroRNAs are non-coding parts of nuclear and mitochondrial genomes, preventing the weakest part of the genetic regulatory networks from being expressed and preventing the appearance of a too many attractors in these networks. They have also a great influence on the chromatin clock, which ensures the updating of the genetic regulatory networks. The post-transcriptional inhibitory activity by the microRNAs, which is partly unspecific, is due firstly to their possibly direct negative action during translation by hybridizing tRNAs, especially those inside the mitochondrion, hence slowing mitochondrial respiration, and secondly to their action on a large number of putative m-RNA targets like those involved in immunetworks; We show that the circuits in the core of the interaction graphs are responsible for the small number of dedicated attractors that correspond to genetically controlled functions, partly due to a general filtering by the microRNAs. We analyze this influence as well as their impact on important functions like the control by the p53 network over the apoptosis/proliferation system and the homeostasis of the energy metabolism. In this last case, we show the role of two kinds of microRNAs, both involved in the control of the mitochondrial genome: (1) nuclear microRNAs, called mitoMirs, inhibiting mitochondrial genes and (2) putative mitochondrial microRNAs inhibiting the tRNAs functioning.

Random modelling of contagious diseases

Modelling contagious diseases needs to include a mechanistic knowledge about contacts between hosts and pathogens as specific as possible, e.g., by incorporating in the model information about social networks through which the disease spreads. The unknown part concerning the contact mechanism can be modelled using a stochastic approach. For that purpose, we revisit SIR models by introducing first a microscopic stochastic version of the contacts between individuals of different populations (namely Susceptible, Infective and Recovering), then by adding a random perturbation in the vicinity of the endemic fixed point of the SIR model and eventually by introducing the definition of various types of random social networks. We propose as example of application to contagious diseases the HIV, and we show that a micro-simulation of individual based modelling (IBM) type can reproduce the current stable incidence of the HIV epidemic in a population of HIV-positive men having sex with men (MSM).

iBalance-ABF: a smartphone-based audio-biofeedback balance system

This paper proposes an implementation of a Kalman filter, using inertial sensors of a smartphone, to estimate 3-D angulation of the trunk. The developed system monitors the trunk angular evolution during bipedal stance and helps the user to improve balance through a configurable and integrated auditory-biofeedback (ABF) loop. A proof-of-concept study was performed to assess the effectiveness of this so-called iBalance-ABF--smartphone-based audio-biofeedback system--in improving balance during bipedal standing. Results showed that young healthy individuals were able to efficiently use ABF on sagittal trunk tilt to improve their balance in the medial-lateral direction. These findings suggest that the iBalance-ABF system as a telerehabilitation system could represent a suitable solution for ambient assisted living technologies.

Can an electro-tactile vestibular substitution system improve balance in patients with unilateral vestibular loss under altered somatosensory conditions from the foot and ankle?

This pilot study aimed at assessing the feasibility and the effectiveness of an electro Electro-tactile Vestibular Substitution System (EVSS) in patients with unilateral vestibular loss under normal and altered somatosensory conditions from the foot and ankle. Four unilateral vestibular-defective patients voluntarily participated in the experiment. They were asked to stand upright as still as possible with their eyes closed in two Normal and Altered foot and ankle sensory conditions. In the Normal condition, the postural task was executed on a firm support surface constituted by the force platform. In the Altered condition, a 2-cm thick foam support surface was placed under the participants' feet. These two foot and ankle sensory conditions were executed under two No EVSS and EVSS experimental conditions. The No EVSS condition served as a control condition. In the EVSS condition, participants executed the postural task using a biofeedback system whose underlying principle consisted of supplying them with additional information about their head orientation/motion with respect to gravitational vertical through electro-tactile stimulation of their tongue. Centre of foot pressure displacements (CoP) were recorded using the force platform. Results showed that, relative to the No EVSS condition, the EVSS condition decreased CoP displacements in both the Normal and the Altered foot and ankle sensory conditions. Interestingly, the stabilizing effect was more pronounced in the Altered than in the Normal foot and ankle sensory condition. These preliminary results suggest that patients with unilateral vestibular loss were able to take advantage to a head position-based electro-tactile tongue biofeedback to mitigate the postural perturbation induced by alteration of somatosensory input from the foot and the ankle.

Predictive power of "a minima" models in biology

Many apparently complex mechanisms in biology, especially in embryology and molecular biology, can be explained easily by reasoning at the level of the "efficient cause" of the observed phenomenology: the mechanism can then be explained by a simple geometrical argument or a variational principle, leading to the solution of an optimization problem, for example, via the co-existence of a minimization and a maximization problem (a min-max principle). Passing from a microscopic (or cellular) level (optimal min-max solution of the simple mechanistic system) to the macroscopic level often involves an averaging effect (linked to the repetition of a large number of such microscopic systems with possible random choice of the parameters of each of them) that gives birth to a global functional feature (e.g. at the tissue level). We will illustrate these general principles by building in four different domains of application "a minima" models and showing the main properties of their solutions: (1) extraction of a minimal RNA structure functioning as the first "peptidic machine," a kind of ancestral ribosome; (2) study of a genetic regulatory network of Drosophila centred on Engrailed gene and expressing successively two genes inside a limit cycle; (3) study of a genetic network regulating neural activity and proliferation in mammals; and (4) study of a simple geometric model of epiboly in zebrafish.

Demography and diffusion in epidemics: malaria and black death spread

The classical models of epidemics dynamics by Ross and McKendrick have to be revisited in order to incorporate elements coming from the demography (fecundity, mortality and migration) both of host and vector populations and from the diffusion and mutation of infectious agents. The classical approach is indeed dealing with populations supposed to be constant during the epidemic wave, but the presently observed pandemics show duration of their spread during years imposing to take into account the host and vector population changes as well as the transient or permanent migration and diffusion of hosts (susceptible or infected), as well as vectors and infectious agents. Two examples are presented, one concerning the malaria in Mali and the other the plague at the middle-age.

Optimizing the use of an artificial tongue-placed tactile biofeedback for improving ankle joint position sense in humans

The performance of an artificial tongue-placed tactile biofeedback device for improving ankle joint position sense was assessed in 12 young healthy adults using an active matching task. The underlying principle of this system consisted of supplying individuals with supplementary information about the position of the matching ankle relative to the reference ankle position through a tongue-placed tactile output device generating electrotactile stimulation on a 36- point (6 x 6) matrix held against the surface of the tongue dorsum. Precisely, (1) no electrodes were activated when both ankles were in a similar angular position within predetermined "angular dead zone" (ADZ); (2) 12 electrodes (2 x 6) of the anterior and posterior zones of the matrix were activated (corresponding to the stimulation of the front and rear portion of the tongue) when the matching ankle was in too plantar and dorsiflexed position relative to the reference ankle, respectively. The effects of two ADZ values of 0.5 degrees and 1.5 degrees were evaluated. Results showed (1) more accurate and more consistent matching performances with than without biofeedback and (2) more accurate and more consistent ankle joint matching performances when using the biofeedback device with the smaller ADZ value. These findings suggest that (1) electrotactile stimulation of the tongue can be used to improve ankle joint proprioception and (2) this improvement can be increased through an appropriate specification of the ADZ parameter provided by the biofeedback system. Further investigations are needed to strengthen the potential clinical value of this device.

Pressure sensor-based tongue-placed electrotactile biofeedback for balance improvement--biomedical application to prevent pressure sores formation and falls

We introduce the innovative technologies, based on the concept of "sensory substitution", we are developing in the fields of biomedical engineering and human disability. Precisely, our goal is to design, develop and validate practical assistive biomedical and/or technical devices and/or rehabilitating procedures for persons with disabilities, using artificial tongue-placed tactile biofeedback systems. Proposed applications are dealing with: (1) pressure sores prevention in case of spinal cord injuries (persons with paraplegia, or tetraplegia); and (2) balance control improvement to prevent fall in older and/or disabled adults. This paper describes the architecture and the functioning principle of these biofeedback systems and presents preliminary results of two feasibility studies performed on young healthy adults.

[Spatial cluster detection without point source specification: the use of five methods and comparison of their results]

BACKGROUND

Various statistical methods have been developed to describe spatial heterogeneity, in terms of high risk zones. If no source can be determined, this heterogeneity can be globally or locally described. Global methods test a statistic estimated over the whole studied geographical area, whereas local methods estimate a statistic on each spatial unit (or regrouping unit). This paper aimed to present, and to compare results of an epidemiological application, of five methods of spatial cluster detection.

METHODS

The two global detection methods were: 1) Moran's coefficient, a classically used autocorrelation coefficient; 2) Tango's statistic, a spatial generalization of the Chi(2) statistic. The three local methods were: 1) the local application of Moran's coefficient, proposed by Anselin; 2) the scan statistic, which searches for grouping of spatial units; 3) the oblique regression tree, which splits the studied zone into sub-zones of different risks. These five methods were applied to the description of the spatial heterogeneity of the malaria risk over a hyperendemic village, in Mali.

RESULTS

All the methods highlighted a significant spatial heterogeneity. Both global methods (Moran's coefficient and Tango's statistic) showed weak spatial correlations. Local Moran's coefficient (with Bonferronis' adjustment) highlighted five spatial units. The scan statistic identified a single high risk cluster. The regression oblique tree split the study area into six sub-zones; the sub-zone with the higher risk was consistent with the cluster identified by the scan statistic.

CONCLUSION

These presented methods do not require any previous knowledge of a source. They allow evaluating spatial risk heterogeneity over the entire geographical area under study. It is noteworthy that shape, size, and spatial heterogeneity characteristics (either global or local) of the study area, as well as the definition of the proximity, significantly influence the spatial risk analysis' outcome. Although their results should be cautiously interpreted, these methods are useful for preliminary field studies or epidemiological surveys.

What is the biological basis of pattern formation of skin lesions?

Pattern recognition is at the heart of clinical dermatology and dermatopathology. Yet, while every practitioner of the art of dermatological diagnosis recognizes the supreme value of diagnostic cues provided by defined patterns of 'efflorescences', few contemplate on the biological basis of pattern formation in and of skin lesions. Vice versa, developmental and theoretical biologists, who would be best prepared to study skin lesion patterns, are lamentably slow to discover this field as a uniquely instructive testing ground for probing theoretical concepts on pattern generation in the human system. As a result, we have at best scraped the surface of understanding the biological basis of pattern formation of skin lesions, and widely open questions dominate over definitive answer. As a symmetry-breaking force, pattern formation represents one of the most fundamental principles that nature enlists for system organization. Thus, the peculiar and often characteristic arrangements that skin lesions display provide a unique opportunity to reflect upon--and to experimentally dissect--the powerful organizing principles at the crossroads of developmental, skin and theoretical biology, genetics, and clinical dermatology that underlie these--increasingly less enigmatic--phenomena. The current 'Controversies' feature offers a range of different perspectives on how pattern formation of skin lesions can be approached. With this, we hope to encourage more systematic interdisciplinary research efforts geared at unraveling the many unsolved, yet utterly fascinating mysteries of dermatological pattern formation. In short: never a dull pattern!

A logical (discrete) formulation for the storage and recall of environmental signals in plants

When subjected to an appropriate asymmetric stimulus, seedlings of Bidens pilosa L. "store" a symmetry-breaking instruction that will finally take effect (in the form of a differential growth of the cotyledonary buds) only if the plants are in a state in which they can "recall" this information. The ability of the plants to recall the stored symmetry-breaking instruction may be switched "on" or "off" by the application of a variety of stimuli. Although its detailed phenomenology is rather complicated, the overall behaviour of the plant storage/recall system can be modelled by use of an asynchronous, logical (discrete) description involving positive and negative feedback circuits, which are required for the existence of multi-stationarity and stability, respectively. The state tables, as used in this formalism, give a concise and easy-to-handle description of the evolution of the system and make it particularly easy to determine its stable states. This modelling approach may be extended to the formulation of many other experimental systems.

Mathematical Methods for Inferring Regulatory Networks Interactions: Application to Genetic Regulation

This paper deals with the problem of reconstruction of the intergenic interaction graph from the raw data of genetic co-expression coming with new technologies of bio-arrays (DMA-arrays, protein-arrays, etc.). These new imaging devices in general only give information about the asymptotical part (fixed configurations of co-expression or limit cycles of such configurations) of the dynamical evolution of the regulatory networks (genetic and/or proteic) underlying the functioning of living systems. Extracting the casual structure and interaction coefficients of a gene interaction network from the observed configurations is a complex problem. But if all the fixed configurations are supposedly observed and if they are factorizable into two or more subsets of values, then the interaction graph possesses as many connected components as the number of factors and the solution is obtained in polynomial time. This new result allows us for example to partly solve the topology of the genetic regulatory network ruling the flowering in Arabidopsis thaliana .

HC Forum: a web site based on an international human cytogenetic database

Familial structural rearrangements of chromosomes represent a factor of malformation risk that could vary over a large range, making genetic counseling difficult. However, they also represent a powerful tool for increasing knowledge of the genome, particularly by studying breakpoints and viable imbalances of the genome. We have developed a collaborative database that now includes data on more than 4100 families, from which we have developed a web site called HC Forum (http://HCForum.imag.fr). It offers geneticists assistance in diagnosis and in genetic counseling by assessing the malformation risk with statistical models. For researchers, interactive interfaces exhibit the distribution of chromosomal breakpoints and of the genome regions observed at birth in trisomy or in monosomy. Dedicated tools including an interactive pedigree allow electronic submission of data, which will be anonymously shown in a forum for discussions. After validation, data are definitively registered in the database with the email of the sender, allowing direct location of biological material. Thus HC Forum constitutes a link between diagnosis laboratories and genome research centers, and after 1 year, more than 700 users from about 40 different countries already exist.

Cooperation of selection and meiotic mechanisms in the production of imbalances in reciprocal translocations

We have used data from chromosomally unbalanced offspring observed at birth, as well as data from sperm chromosome analysis, to study the meiotic segregation of reciprocal translocations. Using data from a total of 1,597 unbalanced children, we have observed an excess in maternal origin for all modes of imbalance. This excess is particularly marked for the 3:1 unbalanced mode, for which we have also observed a maternal age effect, indicating a close relationship with autosomal trisomies. In addition, a statistical analysis of data from 34 different published studies using sperm chromosome analysis has demonstrated that factors which, for reasons of viability, produce a predisposition for a particular mode of imbalance at birth also appear to favor meiotic production of this type of imbalance. Thus the production of unbalanced gametes of a particular type is influenced by the size of the imbalance.

A mathematical model for storage and recall functions in plants

In plantlets of Bidens pilosa L., under severely limiting environmental conditions the growth of the buds at the axil of the cotyledons (cotyledonary buds) is asymmetric (i.e. one of the buds starts growing before the other one), this asymmetry being oriented by the pricking of one of the cotyledons (i.e. pricking one cotyledon increases the probability that the bud at the axil of the other cotyledon be the first to start to grow). As long as the plant apex (i.e. the terminal bud) is present, the growth of the cotyledonary buds is inhibited (apical dominance), but the souvenir of the asymmetric message caused by sub-optimal environmental conditions and the orientation given by the cotyledon pricking is always present in the plant and can be revealed by removing the apex. Depending on the conditions for removing the plant apex and/or on the application of a variety of symmetrical treatments (e.g. thermal treatment, symmetrical pricking treatments, etc.) the stored asymmetry will either take effect (the bud at the axil of the non-pricked cotyledon will be the first to start to grow more often than the other one) or not (both buds will have equal chance to be the first to start to grow). This has been termed 'recalling' the stored asymmetry. By combining several successive symmetrical treatments, it is possible to reversibly switch on and off the recall function several times. This recall of the stored plant-asymmetry is analogous to the evocation function of a memory system. In this paper, we will present first a discrete logical version of the observed interaction structure between the main components of the bud growth system, then a continuous differential version, taking into account the main features of the observed experimental reality and trying to explain this phenomenology. The interaction structure of both the discrete and the continuous models presents similar positive and negative feedback circuits, necessary condition for observing multistationarity and stability.

Positive feedback circuits and memory

The concept of regulatory feedback circuit refers to oriented cyclic interactions between elements of a system. There are two classes of circuits, positive and negative, whose properties are in striking contrast. Positive circuits are a prerequisite for the occurrence of multiple steady states (multistationarity), and hence, they are involved in all processes showing hysteresis or memory. Endogenous or exogenous perturbations can lead the system to exhibit or to evoke one particular stable regime. The role of positive circuits in cell differentiation and in immunology is well documented. Negative circuits are involved in homeostatic regulation, with or without oscillations. The aim of this paper is to show: a) that positive circuits account for many features of memory stricto sensu (i.e., neural memory and mnesic evocation) as well as largo sensu (e.g. differentiation or immunological memory); and b) that simple combinations of positive and negative circuits provide powerful regulatory modules, which can also be associated in batteries. These entities have vast dynamical possibilities in the field of neurobiology, as well as in the fields of differentiation and immunology. Here we consider a universal minimal regulatory module, for which we suggest to adopt the term 'logical regulon', which can be considered as an atom of Jacob's integron. It comprises a positive and a negative circuit in its interaction matrix, and we recall the main results related to the simultaneous presence of these circuits. Finally, we give three applications of this type of interaction matrix. The first two deal with the coexistence of multiple stable steady states and periodicity in differentiation and in an immunological system showing hysteretic properties. The third deals with the dual problems of synchronization and desynchronization of a neural model for hippocampus memory evocation processes.

Synchronization and desynchronization of neural oscillators

We have used continuous and discrete-time versions of a neural oscillator model to analyze how various types of synaptic connections between oscillators affect synchronization and desynchronization phenomena. First, we present a synthesis of the mathematical properties of both neural oscillator versions. Then, we show that the choice of parameters leads to a relationship between the two versions. Finally, we achieve the coupling of two oscillators in order to study how synaptic connections affect the phase lag. With this in mind, we state some of the results for the continuous-time model. The second part of this paper deals with the behavior of neural networks comprising connected oscillators, which involves looking at the conditions for desynchronization of a totally synchronized oscillator net. Such a study has been carried out both for a fully and for a sparsely connected network. This leads to the observation that some architectures enable proper desynchronization when the size of the network is large. While searching for the conditions for desynchronization, we have discovered that a macroscopic description of the network is sometimes possible. To conclude, we discuss the advantages and the limitations of this macroscopic approach.

The genetic code and cyclic codes

We proposed previously a cyclic code made of 22 triplets, which we now call the AB code. It is made up of the following chain: AUGGUGCCAUUCAAGACUAUGA. The letters A, U, C, G represent the classical symbols of the (purine and pyrimidine) bases of the genetic code. This chain presents the following features: (1) when it is in cyclic form, it begins with the initiation codon AUG, ends with the termination codon UGA, and it can be read triplet after triplet by choosing 1 and only 1 representative of each synonymy class in the classical degenerate genetic code made of 64 triplets. The chain, therefore, possesses 1 and only 1 codon for each amino-acid; (2) except for the doublet CG, triplets of the chain begin with the 15 other possible doublets of bases (satisfying the "wobble" hypothesis presented by Crick); (3) it corresponds (except for 1 base) to the "loop" part of the CEnothera mitochondrial Gly-tRNA; (4) it can be modified, without loss of the properties (1) and (2), in such a way as to have 15 bases in common with the loop part of other mitochondrial tRNA's considered as primitive, like Ala-, Pro- and Arg-tRNA; (5) it contains the most frequent triplets, but not the most rare ones, appearing in the genome of numerous species; (6) it exhibits a coherent internal structure with respect to the molecular weight of its triplets. This structure, also found in the loop part of mitochondrial tRNA's, contains an excess of AU bases with respect to GC bases. This fact has no explanation in the classical probabilistic model of the tRNA's. Therefore, we propose the cyclic AB code as a primitive genetic structure with the essential coding properties of the present genetic code.

Cartographic study: breakpoints in 1574 families carrying human reciprocal translocations

Reciprocal translocations (rcp) are among the most common constitutional chromosomal aberrations in man. Using a European database of 1574 families carrying autosomal rcp, a cartographic study was done on the breakpoints involved. The breakpoints are non-randomly distributed along the different chromosomes, indicating "hot spots". Breakpoints of rcp that result in descendants that are unbalanced chromosomally at birth are more frequent in a distal position on chromosomal arms, and 65% of them are localised in R-bands. Among the R-bands, bands rich in GC islands and poor in Alu repetitive sequences are more frequently the site of breakpoints, as well as bands that include a fragile site. This result suggests that the variation in degree of methylation in GC islands could be involved in chromosomal breakage and hence in chromosomal rearrangements. The heterogeneity of the human chromosomal structure has been demonstrable by metaphase banding techniques since 1970. In contrast to G-bands, R-bands are sites of high gene concentration (Korenberg et al. 1978), are relatively rich in cytosine plus guanine (GC), and in Alu repetitive DNA sequences (Korenberg and Rykowski 1988). More recently Holmquist (1992) has proposed four types of R-bands, depending on their relative richness in GC and Alu DNA sequences. R-bands rich in GC correspond almost exactly to T-bands (Dutrillaux 1977). They contain 65% of all genes while they represent only 15% of the genome (Holmquist 1992). The aim of this study is to analyse the distribution of the breakpoints along chromosomes from a European database of autosomal rcp in order to relate it to the specificity of different chromosomal regions.

Dynamic functional and structural analysis of living cells: new tools for vital staining of nuclear DNA and for characterisation of cell motion

Increasing interest has been paid to applications of fluorescence measurements to analyze physiological mechanisms in living cells. However, few studies have taken advantage of DNA quantification by fluorometry for dynamic assessment of chromatin organization as well as cell motion during the cell cycle. This approach involves both optimal conditions for DNA staining and cell tracking methods. In this context, this report describes a stoichiometric method for nuclear DNA specific staining, using the bisbenzimidazole dye Hoechst 33342 associated with verapamil, a calcium membrane channel blocker. This method makes it possible to correlate variations of nuclear DNA content with cell motion in cells that are maintained alive. Motion measurement is the second goal of this paper and it explains the snake-spline method, and the associated cell following method.

Interpretation of multimodal medical images using connectionist and variational methods

Our medical objective is to match multimodal 3D medical images into a coherent model of the patient, from which diagnosis can be assessed and therapeutics guided. 3D image segmentation is absolutely necessary to reach this objective. We investigate two complementary approaches for segmenting 3D medical images. First we present some definitions, basic properties and recent theoretical results about formal neural networks, and show that these results can be applied to brain tumour segmentation. A variational approach (called the 'snake spline' method) is then detailed. We finally show how segmented 3D images can be used for multimodal image matching.

"Dynamical confinement" in neural networks and cell cycle

In this paper randomization of well-known former mathematical models is proposed (i.e., the Hopfield model for neural networks and the Hahn model for the cell cycle) in order to facilitate the study of their asymptotic behavior: in fact, we replace the determination of the stability basins for attractors and boundaries by the study of a unique (or a small number of) invariant measure(s), whose distribution function maxima (or, respectively, percentile contour lines) correspond to the location of the attractors (or, respectively, boundaries of their stability basins). We give the name of "confinement" to this localization of the mass of the invariant measure(s). We intend to show here that the study of the confinement is in certain cases easier than the study of underlying attractors, in particular if these last are numerous and possess small stability basins (for example, for the first time we calculate the invariant measure in the random Hopfield model in a case for which the deterministic version exhibits many attractors, and in a case of phase transition). (c) 1995 American Institute of Physics.

Viability thresholds for partial trisomies and monosomies. A study of 1,159 viable unbalanced reciprocal translocations

From a data base of 1,590 independent families with autosomal reciprocal translocations, 1,159 viable unbalances were studied and the lengths of their trisomy/monosomy segments measured according to the method proposed by Daniel. About 5% of cases were found not to comply with Daniel viability criteria. The thresholds of viability vary with the mode of unbalance and with the sex of the carrier. Thus, new viability criteria are proposed as a guide for genetic counseling and prenatal diagnosis.

Logistic regression model to estimate the risk of unbalanced offspring in reciprocal translocations

The aim of this study was to estimate the risk of viable unbalanced offspring for a parental carrier of reciprocal translocation. On a large computerized database of reciprocal translocations we used logistic regression to model this risk. The status of the progeny is the outcome variable. Explanatory covariates are cytogenetic characteristics of the translocation, age and sex of the parental carrier, and potential viability of the gametes. The results obtained by the logistic model demonstrate the important role of certain variables such as the sex of the parental carrier and the R band length of the translocated segments. Within the group of lower risk (risk of viable unbalanced offspring less than 5%), 97% of the individuals are correctly classified with this model. For this group, the choice prenatal diagnosis can be best discussed by considering both the risk for viable unbalanced offspring and the risk of induced abortion following prenatal diagnosis.

Entrainment of the respiratory rhythm: a new approach

When we periodically perturbed the central respiratory oscillator with a controlled periodic stimulation provided by a mechanical ventilator, an entrainment phenomenon occurred: the actual rhythm of the respiratory centres was phase locked to the periodic stimulation. In some experiments, we observed an intermittence phenomenon: the respiratory rhythm successively seemed entrained, departed from this mode for few cycles, returned to the previous pseudo entrainment and so on. From intermittence data, we were able to plot a phase response curve. From literature data on the effects of a single stimulation applied at various moments in the respiratory cycle, we built up a mathematical model designed to simulate entrainment experiments. This model simulated entrainment phenomenon, but did not satisfactorily accommodate the experimental phase response curve. The section of the simulated phase response curve responsible for discrepancies was the result of the combination of an inspiratory shortening owing to a stimulation occurring during inspiration, and a positive relationship between inspiratory duration TI and expiratory duration TE. We changed the TE-TI relationship, assuming that the expiratory duration is determined not by the inspiratory duration but rather by the lung volume at the end of inspiration. The revised model was then able to exhibit almost all the qualitative properties previously noted in experiments. The significance in biological terms of the new TE-TI relationship, which is apparently incompatible with almost all previous experimental data, is discussed.

Comparative study of human expertise and an expert system: application to the diagnosis of child's meningitis

We present a general method of statistical evaluation for expert systems, applied to a system for the diagnosis of child's meningitis. Fifty difficult clinical cases of child's meningitis were submitted to the system, to seven senior specialists and to seven young physicians. Multidimensional analysis of the diagnosis of the infection category reveals that the two groups of physicians separate naturally and that the system is located among the group of experts. The study of the agreement of the microbiological diagnosis and therapeutic advice shows that the advice of the two groups of physicians is significantly different and that the advice of the system is significantly closer to that of the experts. This result is confirmed by the study of therapeutic errors. This type of study allows one to classify the performance of the system among physicians having different levels of expertise without referring to an objective solution.

Human reciprocal translocations: is the unbalanced mode at birth predictable?

Two methods of prediction for the risk of unbalance at birth were tested on a large data base of reciprocal translocation (1376 families): the pachytene diagram predictive method (PDP method) and the discriminant method (D method). These method succeeded in correctly predicting the segregation mode in 66% of the data for the PDP method and in 80% of the data for the D method. The quality of chromosome material (in particular R bands) must be taken into account for more accurate prediction. Some difficulties still exist in predicting the 3:1 tertiary segregation mode, which can frequently be incorrectly classified as the adjacent 1 mode.

Potential use of robots in endoscopic neurosurgery

A 6-axis stereotactic robot has been designed and linked to a stereotactic frame for routine use. Robot software allows the positioning of a probe holder in order to reach a given target. A calibration step enables the robot to compute the position of the x-ray beam and correct its final position to avoid parallax errors. The co-ordinates of the target are presently taken from anteroposterior and lateral X-rays using a digitizing table. Connection with a digitized angiography system is in progress and will allow direct sampling of numerical data from the x-ray data. Further steps will include connections with a 3D-reconstructed image from MRI and CAT as well as with a resident computerized atlas. Present experience after 14 months of daily practice represents 140 stereotactic procedures which can be extended to any special use, including endoscopic approaches.