Mathematical models of cognitive processes

The research activity carried out during the PhD course was focused on the development of mathematical models of some cognitive processes and their validation by means of data present in literature, with a double aim: i) to achieve a better interpretation and explanation of the great amount of data obtained on these processes from different methodologies (electrophysiological recordings on animals, neuropsychological, psychophysical and neuroimaging studies in humans), ii) to exploit model predictions and results to guide future research and experiments. In particular, the research activity has been focused on two different projects: 1) the first one concerns the development of neural oscillators networks, in order to investigate the mechanisms of synchronization of the neural oscillatory activity during cognitive processes, such as object recognition, memory, language, attention; 2) the second one concerns the mathematical modelling of multisensory integration processes (e.g. visual-acoustic), which occur in several cortical and subcortical regions (in particular in a subcortical structure named Superior Colliculus (SC)), and which are fundamental for orienting motor and attentive responses to external world stimuli. This activity has been realized in collaboration with the Center for Studies and Researches in Cognitive Neuroscience of the University of Bologna (in Cesena) and the Department of Neurobiology and Anatomy of the Wake Forest University School of Medicine (NC, USA). PART 1. Objects representation in a number of cognitive functions, like perception and recognition, foresees distribute processes in different cortical areas. One of the main neurophysiological question concerns how the correlation between these disparate areas is realized, in order to succeed in grouping together the characteristics of the same object (binding problem) and in maintaining segregated the properties belonging to different objects simultaneously present (segmentation problem). Different theories have been proposed to address these questions (Barlow, 1972). One of the most influential theory is the so called “assembly coding”, postulated by Singer (2003), according to which 1) an object is well described by a few fundamental properties, processing in different and distributed cortical areas; 2) the recognition of the object would be realized by means of the simultaneously activation of the cortical areas representing its different features; 3) groups of properties belonging to different objects would be kept separated in the time domain. In Chapter 1.1 and in Chapter 1.2 we present two neural network models for object recognition, based on the “assembly coding” hypothesis. These models are networks of Wilson-Cowan oscillators which exploit: i) two high-level “Gestalt Rules” (the similarity and previous knowledge rules), to realize the functional link between elements of different cortical areas representing properties of the same object (binding problem); 2) the synchronization of the neural oscillatory activity in the γ-band (30-100Hz), to segregate in time the representations of different objects simultaneously present (segmentation problem). These models are able to recognize and reconstruct multiple simultaneous external objects, even in difficult case (some wrong or lacking features, shared features, superimposed noise). In Chapter 1.3 the previous models are extended to realize a semantic memory, in which sensory-motor representations of objects are linked with words. To this aim, the network, previously developed, devoted to the representation of objects as a collection of sensory-motor features, is reciprocally linked with a second network devoted to the representation of words (lexical network) Synapses linking the two networks are trained via a time-dependent Hebbian rule, during a training period in which individual objects are presented together with the corresponding words. Simulation results demonstrate that, during the retrieval phase, the network can deal with the simultaneous presence of objects (from sensory-motor inputs) and words (from linguistic inputs), can correctly associate objects with words and segment objects even in the presence of incomplete information. Moreover, the network can realize some semantic links among words representing objects with some shared features. These results support the idea that semantic memory can be described as an integrated process, whose content is retrieved by the co-activation of different multimodal regions. In perspective, extended versions of this model may be used to test conceptual theories, and to provide a quantitative assessment of existing data (for instance concerning patients with neural deficits). PART 2. The ability of the brain to integrate information from different sensory channels is fundamental to perception of the external world (Stein et al, 1993). It is well documented that a number of extraprimary areas have neurons capable of such a task; one of the best known of these is the superior colliculus (SC). This midbrain structure receives auditory, visual and somatosensory inputs from different subcortical and cortical areas, and is involved in the control of orientation to external events (Wallace et al, 1993). SC neurons respond to each of these sensory inputs separately, but is also capable of integrating them (Stein et al, 1993) so that the response to the combined multisensory stimuli is greater than that to the individual component stimuli (enhancement). This enhancement is proportionately greater if the modality-specific paired stimuli are weaker (the principle of inverse effectiveness). Several studies have shown that the capability of SC neurons to engage in multisensory integration requires inputs from cortex; primarily the anterior ectosylvian sulcus (AES), but also the rostral lateral suprasylvian sulcus (rLS). If these cortical inputs are deactivated the response of SC neurons to cross-modal stimulation is no different from that evoked by the most effective of its individual component stimuli (Jiang et al 2001). This phenomenon can be better understood through mathematical models. The use of mathematical models and neural networks can place the mass of data that has been accumulated about this phenomenon and its underlying circuitry into a coherent theoretical structure. In Chapter 2.1 a simple neural network model of this structure is presented; this model is able to reproduce a large number of SC behaviours like multisensory enhancement, multisensory and unisensory depression, inverse effectiveness. In Chapter 2.2 this model was improved by incorporating more neurophysiological knowledge about the neural circuitry underlying SC multisensory integration, in order to suggest possible physiological mechanisms through which it is effected. This endeavour was realized in collaboration with Professor B.E. Stein and Doctor B. Rowland during the 6 months-period spent at the Department of Neurobiology and Anatomy of the Wake Forest University School of Medicine (NC, USA), within the Marco Polo Project. The model includes four distinct unisensory areas that are devoted to a topological representation of external stimuli. Two of them represent subregions of the AES (i.e., FAES, an auditory area, and AEV, a visual area) and send descending inputs to the ipsilateral SC; the other two represent subcortical areas (one auditory and one visual) projecting ascending inputs to the same SC. Different competitive mechanisms, realized by means of population of interneurons, are used in the model to reproduce the different behaviour of SC neurons in conditions of cortical activation and deactivation. The model, with a single set of parameters, is able to mimic the behaviour of SC multisensory neurons in response to very different stimulus conditions (multisensory enhancement, inverse effectiveness, within- and cross-modal suppression of spatially disparate stimuli), with cortex functional and cortex deactivated, and with a particular type of membrane receptors (NMDA receptors) active or inhibited. All these results agree with the data reported in Jiang et al. (2001) and in Binns and Salt (1996). The model suggests that non-linearities in neural responses and synaptic (excitatory and inhibitory) connections can explain the fundamental aspects of multisensory integration, and provides a biologically plausible hypothesis about the underlying circuitry.

Le reti in Sanità

Il presente lavoro di ricerca intende analizzare l’importanza dei modelli organizzativi a reti per rispondere alla sfida della complessità del momento storico, politico, sociologico, economico; in modo particolare in Sanità per rispondere all’esigenza di mettere al centro la persona nel percorso di cura ed ottenere una migliore integrazione delle cure. Sebbene i vantaggi delle reti siano bene descritti in letteratura sono ancora pochi gli studi nell’ambito della valutazione. Il caso di studio ha riguardato la rete oncologica romagnola così come percepita dagli informatori chiave, dagli operatori (medici, infermieri, amministrativi) e dalle persone con esperienza di tumore. Dall’analisi degli informatori chiave emerge forte che la rete nasce per dare risposte di qualità ai bisogni dei pazienti, mentre per gli operatori quanto sia importante la dimensione delle relazioni umane e avere valori condivisi per raggiungere obiettivi di efficacia e qualità delle cure. Per quanto riguarda invece la percezione delle persone con esperienza di tumore si rileva quanto sia importante l’appropriatezza della traiettoria di cura nonché l’avere continuità in un percorso, già di per sé difficile, oltre all’importanza dell’umanizzazione dei servizi e della corretta comunicazione medico paziente.

Reti di contratti e reti di imprese

Il lavoro di ricerca prende le mosse da una premessa di ordine economico. Il fenomeno delle reti di impresa, infatti, nasce dalla realtà economica dei mercati. In tale contesto non può prescindere dal delineare un quadro della situazione- anche di crisi- congiunturale che ha visto coinvolte specialmente le imprese italiane. In tale prospettiva, si è reso necessario indagare il fenomeno della globalizzazione, con riferimento alle sue origini,caratteristiche e conseguenze. Ci si sofferma poi sulla ricostruzione dogmatica del fenomeno. Si parte dalla ricostruzione dello stesso in termini di contratto plurilaterale- sia esso con comunione di scopo oppure plurilaterale di scambio- per criticare tale impostazione, non del tutto soddisfacente, in quanto ritenuto remissiva di fronte alla attuale vis espansiva del contratto plurilaterale. Più convincente appare lo schema del collegamento contrattuale, che ha il pregio di preservare l’autonomia e l’indipendenza degli imprenditori aderenti, pur inseriti nel contesto di un’operazione economica unitaria, volta a perseguire uno scopo comune, l’“interesse di rete”, considerato meritevole di tutela secondo l’ordinamento giuridico ex art. 1322 2.co. c.c. In effetti il contratto ben si presta a disegnare modelli di rete sia con distribuzione simmetrica del potere decisionale, sia con distribuzione asimmetrica, vale a dire con un elevato livello di gerarchia interna. Non può d’altra parte non ravvisarsi un’affinità con le ipotesi di collegamento contrattuale in fase di produzione, consistente nel delegare ad un terzo parte della produzione, e nella fase distributiva, per cui la distribuzione avviene attraverso reti di contratti. Si affronta la materia della responsabilità della rete, impostando il problema sotto due profili: la responsabilità interna ed esterna. La prima viene risolta sulla base dell’affidamento reciproco maturato da ogni imprenditore. La seconda viene distinta in responsabilità extracontrattuale, ricondotta nella fattispecie all’art. 2050 c.c., e contrattuale.

The Influence of Fractures on Vulnerability to Pollution of a Carbonate Aquifer: Monte Conero (Italy)

The carbonate outcrops of the anticline of Monte Conero (Italy) were studied in order to characterize the geometry of the fractures and to establish their influence on the petrophysical properties (hydraulic conductivity) and on the vulnerability to pollution. The outcrops form an analog for a fractured aquifer and belong to the Maiolica Fm. and the Scaglia Rossa Fm. The geometrical properties of fractures such as orientation, length, spacing and aperture were collected and statistically analyzed. Five types of mechanical fractures were observed: veins, joints, stylolites, breccias and faults. The types of fractures are arranged in different sets and geometric assemblages which form fracture networks. In addition, the fractures were analyzed at the microscale using thin sections. The fracture age-relationships resulted similar to those observed at the outcrop scale, indicating that at least three geological episodes have occurred in Monte Conero. A conceptual model for fault development was based on the observations of veins and stylolites. The fracture sets were modelled by the code FracSim3D to generate fracture network models. The permeability of a breccia zone was estimated at microscale by and point counting and binary image methods, whereas at the outcrop scale with Oda’s method. Microstructure analysis revealed that only faults and breccias are potential pathways for fluid flow since all veins observed are filled with calcite. According this, three scenarios were designed to asses the vulnerability to pollution of the analogue aquifer: the first scenario considers the Monte Conero without fractures, second scenario with all observed systematic fractures and the third scenario with open veins, joints and faults/breccias. The fractures influence the carbonate aquifer by increasing its porosity and hydraulic conductivity. The vulnerability to pollution depends also on the presence of karst zones, detric zones and the material of the vadose zone.

Models for the study of neuronal activity during cognitive tasks

Assessment of brain connectivity among different brain areas during cognitive or motor tasks is a crucial problem in neuroscience today. Aim of this research study is to use neural mass models to assess the effect of various connectivity patterns in cortical EEG power spectral density (PSD), and investigate the possibility to derive connectivity circuits from EEG data. To this end, two different models have been built. In the first model an individual region of interest (ROI) has been built as the parallel arrangement of three populations, each one exhibiting a unimodal spectrum, at low, medium or high frequency. Connectivity among ROIs includes three parameters, which specify the strength of connection in the different frequency bands. Subsequent studies demonstrated that a single population can exhibit many different simultaneous rhythms, provided that some of these come from external sources (for instance, from remote regions). For this reason in the second model an individual ROI is simulated only with a single population. Both models have been validated by comparing the simulated power spectral density with that computed in some cortical regions during cognitive and motor tasks. Another research study is focused on multisensory integration of tactile and visual stimuli in the representation of the near space around the body (peripersonal space). This work describes an original neural network to simulate representation of the peripersonal space around the hands, in basal conditions and after training with a tool used to reach the far space. The model is composed of three areas for each hand, two unimodal areas (visual and tactile) connected to a third bimodal area (visual-tactile), which is activated only when a stimulus falls within the peripersonal space. Results show that the peripersonal space, which includes just a small visual space around the hand in normal conditions, becomes elongated in the direction of the tool after training, thanks to a reinforcement of synapses.

Models and methods for power monolithic microwave integrated circuits

Computer aided design of Monolithic Microwave Integrated Circuits (MMICs) depends critically on active device models that are accurate, computationally efficient, and easily extracted from measurements or device simulators. Empirical models of active electron devices, which are based on actual device measurements, do not provide a detailed description of the electron device physics. However they are numerically efficient and quite accurate. These characteristics make them very suitable for MMIC design in the framework of commercially available CAD tools. In the empirical model formulation it is very important to separate linear memory effects (parasitic effects) from the nonlinear effects (intrinsic effects). Thus an empirical active device model is generally described by an extrinsic linear part which accounts for the parasitic passive structures connecting the nonlinear intrinsic electron device to the external world. An important task circuit designers deal with is evaluating the ultimate potential of a device for specific applications. In fact once the technology has been selected, the designer would choose the best device for the particular application and the best device for the different blocks composing the overall MMIC. Thus in order to accurately reproducing the behaviour of different-in-size devices, good scalability properties of the model are necessarily required. Another important aspect of empirical modelling of electron devices is the mathematical (or equivalent circuit) description of the nonlinearities inherently associated with the intrinsic device. Once the model has been defined, the proper measurements for the characterization of the device are performed in order to identify the model. Hence, the correct measurement of the device nonlinear characteristics (in the device characterization phase) and their reconstruction (in the identification or even simulation phase) are two of the more important aspects of empirical modelling. This thesis presents an original contribution to nonlinear electron device empirical modelling treating the issues of model scalability and reconstruction of the device nonlinear characteristics. The scalability of an empirical model strictly depends on the scalability of the linear extrinsic parasitic network, which should possibly maintain the link between technological process parameters and the corresponding device electrical response. Since lumped parasitic networks, together with simple linear scaling rules, cannot provide accurate scalable models, either complicate technology-dependent scaling rules or computationally inefficient distributed models are available in literature. This thesis shows how the above mentioned problems can be avoided through the use of commercially available electromagnetic (EM) simulators. They enable the actual device geometry and material stratification, as well as losses in the dielectrics and electrodes, to be taken into account for any given device structure and size, providing an accurate description of the parasitic effects which occur in the device passive structure. It is shown how the electron device behaviour can be described as an equivalent two-port intrinsic nonlinear block connected to a linear distributed four-port passive parasitic network, which is identified by means of the EM simulation of the device layout, allowing for better frequency extrapolation and scalability properties than conventional empirical models. Concerning the issue of the reconstruction of the nonlinear electron device characteristics, a data approximation algorithm has been developed for the exploitation in the framework of empirical table look-up nonlinear models. Such an approach is based on the strong analogy between timedomain signal reconstruction from a set of samples and the continuous approximation of device nonlinear characteristics on the basis of a finite grid of measurements. According to this criterion, nonlinear empirical device modelling can be carried out by using, in the sampled voltage domain, typical methods of the time-domain sampling theory.

Multi-level models and infrastructures for simulating biological system development

The hierarchical organisation of biological systems plays a crucial role in the pattern formation of gene expression resulting from the morphogenetic processes, where autonomous internal dynamics of cells, as well as cell-to-cell interactions through membranes, are responsible for the emergent peculiar structures of the individual phenotype. Being able to reproduce the systems dynamics at different levels of such a hierarchy might be very useful for studying such a complex phenomenon of self-organisation. The idea is to model the phenomenon in terms of a large and dynamic network of compartments, where the interplay between inter-compartment and intra-compartment events determines the emergent behaviour resulting in the formation of spatial patterns. According to these premises the thesis proposes a review of the different approaches already developed in modelling developmental biology problems, as well as the main models and infrastructures available in literature for modelling biological systems, analysing their capabilities in tackling multi-compartment / multi-level models. The thesis then introduces a practical framework, MS-BioNET, for modelling and simulating these scenarios exploiting the potential of multi-level dynamics. This is based on (i) a computational model featuring networks of compartments and an enhanced model of chemical reaction addressing molecule transfer, (ii) a logic-oriented language to flexibly specify complex simulation scenarios, and (iii) a simulation engine based on the many-species/many-channels optimised version of Gillespie’s direct method. The thesis finally proposes the adoption of the agent-based model as an approach capable of capture multi-level dynamics. To overcome the problem of parameter tuning in the model, the simulators are supplied with a module for parameter optimisation. The task is defined as an optimisation problem over the parameter space in which the objective function to be minimised is the distance between the output of the simulator and a target one. The problem is tackled with a metaheuristic algorithm. As an example of application of the MS-BioNET framework and of the agent-based model, a model of the first stages of Drosophila Melanogaster development is realised. The model goal is to generate the early spatial pattern of gap gene expression. The correctness of the models is shown comparing the simulation results with real data of gene expression with spatial and temporal resolution, acquired in free on-line sources.

An Input-Process-Output Approach to Interorganizational Teams: The Influence of Work Group Diversity, Trust and Shared Leadership on Communication Network and Team Outputs.

The market’s challenges bring firms to collaborate with other organizations in order to create Joint Ventures, Alliances and Consortia that are defined as “Interorganizational Networks” (IONs) (Provan, Fish and Sydow; 2007). Some of these IONs are managed through a shared partecipant governance (Provan and Kenis, 2008): a team composed by entrepreneurs and/or directors of each firm of an ION. The research is focused on these kind of management teams and it is based on an input-process-output model: some input variables (work group’s diversity, intra-team's friendship network density) have a direct influence on the process (team identification, shared leadership, interorganizational trust, team trust and intra-team's communication network density), which influence some team outputs, individual innovation behaviors and team effectiveness (team performance, work group satisfaction and ION affective commitment). Data was collected on a sample of 101 entrepreneurs grouped in 28 ION’s government teams and the research hypotheses are tested trough the path analysis and the multilevel models. As expected trust in team and shared leadership are positively and directly related to team effectiveness while team identification and interorganizational trust are indirectly related to the team outputs. The friendship network density among the team’s members has got positive effects on the trust in team and on the communication network density, and also, through the communication network density it improves the level of the teammates ION affective commitment. The shared leadership and its effects on the team effectiveness are fostered from higher level of team identification and weakened from higher level of work group diversity, specifically gender diversity. Finally, the communication network density and shared leadership at the individual level are related to the frequency of individual innovative behaviors. The dissertation’s results give a wider and more precise indication about the management of interfirm network through “shared” form of governance.