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.

Using P-GENESIS for Parallel Simulation of GENESIS Models

P-GENESIS is an extension to the GENESIS neural simulator that allows users to take advantage of parallel machines to speed up the simulation of their network models or concurrently simulate multiple models. P-GENESIS adds several commands to the GENESIS script language that let a script running on one processor execute remote procedure calls on other processors, and that let a script synchronize its execution with the scripts running on other processors. We present here some brief comments on the mechanisms underlying parallel script execution. We also offer advice on parallelizing parameter searches, partitioning network models, and selecting suitable parallel hardware on which to run P-GENESIS.

Code-switching: a touchstone of models of bilingual language production

The goal of the present thesis was to investigate the production of code-switched utterances in bilinguals’ speech production. This study investigates the availability of grammatical-category information during bilingual language processing. The specific aim is to examine the processes involved in the production of Persian-English bilingual compound verbs (BCVs). A bilingual compound verb is formed when the nominal constituent of a compound verb is replaced by an item from the other language. In the present cases of BCVs the nominal constituents are replaced by a verb from the other language. The main question addressed is how a lexical element corresponding to a verb node can be placed in a slot that corresponds to a noun lemma. This study also investigates how the production of BCVs might be captured within a model of BCVs and how such a model may be integrated within incremental network models of speech production. In the present study, both naturalistic and experimental data were used to investigate the processes involved in the production of BCVs. In the first part of the present study, I collected 2298 minutes of a popular Iranian TV program and found 962 code-switched utterances. In 83 (8%) of the switched cases, insertions occurred within the Persian compound verb structure, hence, resulting in BCVs. As to the second part of my work, a picture-word interference experiment was conducted. This study addressed whether in the case of the production of Persian-English BCVs, English verbs compete with the corresponding Persian compound verbs as a whole, or whether English verbs compete with the nominal constituents of Persian compound verbs only. Persian-English bilinguals named pictures depicting actions in 4 conditions in Persian (L1). In condition 1, participants named pictures of action using the whole Persian compound verb in the context of its English equivalent distractor verb. In condition 2, only the nominal constituent was produced in the presence of the light verb of the target Persian compound verb and in the context of a semantically closely related English distractor verb. In condition 3, the whole Persian compound verb was produced in the context of a semantically unrelated English distractor verb. In condition 4, only the nominal constituent was produced in the presence of the light verb of the target Persian compound verb and in the context of a semantically unrelated English distractor verb. The main effect of linguistic unit was significant by participants and items. Naming latencies were longer in the nominal linguistic unit compared to the compound verb (CV) linguistic unit. That is, participants were slower to produce the nominal constituent of compound verbs in the context of a semantically closely related English distractor verb compared to producing the whole compound verbs in the context of a semantically closely related English distractor verb. The three-way interaction between version of the experiment (CV and nominal versions), linguistic unit (nominal and CV linguistic units), and relation (semantically related and unrelated distractor words) was significant by participants. In both versions, naming latencies were longer in the semantically related nominal linguistic unit compared to the response latencies in the semantically related CV linguistic unit. In both versions, naming latencies were longer in the semantically related nominal linguistic unit compared to response latencies in the semantically unrelated nominal linguistic unit. Both the analysis of the naturalistic data and the results of the experiment revealed that in the case of the production of the nominal constituent of BCVs, a verb from the other language may compete with a noun from the base language, suggesting that grammatical category does not necessarily provide a constraint on lexical access during the production of the nominal constituent of BCVs. There was a minimal context in condition 2 (the nominal linguistic unit) in which the nominal constituent was produced in the presence of its corresponding light verb. The results suggest that generating words within a context may not guarantee that the effect of grammatical class becomes available. A model is proposed in order to characterize the processes involved in the production of BCVs. Implications for models of bilingual language production are discussed.

Forecasting exchange rates with linear and nonlinear models

In this paper, the exchange rate forecasting performance of neural network models are evaluated against the random walk, autoregressive moving average and generalised autoregressive conditional heteroskedasticity models. There are no guidelines available that can be used to choose the parameters of neural network models and therefore, the parameters are chosen according to what the researcher considers to be the best. Such an approach, however,implies that the risk of making bad decisions is extremely high, which could explain why in many studies, neural network models do not consistently perform better than their time series counterparts. In this paper, through extensive experimentation, the level of subjectivity in building neural network models is considerably reduced and therefore giving them a better chance of Forecasting exchange rates with linear and nonlinear models 415 performing well. The results show that in general, neural network models perform better than the traditionally used time series models in forecasting exchange rates.

Forecasting exchange rates with linear and nonlinear models

In this paper the exchange rate forecasting performance of neural network models are evaluated against random walk and a range of time series models. There are no guidelines available that can be used to choose the parameters of neural network models and therefore the parameters are chosen according to what the researcher considers to be the best. Such an approach, however, implies that the risk of making bad decisions is extremely high which could explain why in many studies neural network models do not consistently perform better than their time series counterparts. In this paper through extensive experimentation the level of subjectivity in building neural network models is considerably reduced and therefore giving them a better chance of performing well. Our results show that in general neural network models perform better than traditionally used time series models in forecasting exchange rates.

Structural damage detection using frequency response functions and neural networks

This paper illustrates the damage identification and condition assessment of a three story bookshelf structure using a new frequency response functions (FRFs) based damage index and Artificial Neural Networks (ANNs). A major obstacle of using measured frequency response function data is a large size input variables to ANNs. This problem is overcome by applying a data reduction technique called principal component analysis (PCA). In the proposed procedure, ANNs with their powerful pattern recognition and classification ability were used to extract damage information such as damage locations and severities from measured FRFs. Therefore, simple neural network models are developed, trained by Back Propagation (BP), to associate the FRFs with the damage or undamaged locations and severity of the damage of the structure. Finally, the effectiveness of the proposed method is illustrated and validated by using the real data provided by the Los Alamos National Laboratory, USA. The illustrated results show that the PCA based artificial Neural Network method is suitable and effective for damage identification and condition assessment of building structures. In addition, it is clearly demonstrated that the accuracy of proposed damage detection method can also be improved by increasing number of baseline datasets and number of principal components of the baseline dataset.

Enhancing human action recognition with region proposals

Deep convolutional network models have dominated recent work in human action recognition as well as image classification. However, these methods are often unduly influenced by the image background, learning and exploiting the presence of cues in typical computer vision datasets. For unbiased robotics applications, the degree of variation and novelty in action backgrounds is far greater than in computer vision datasets. To address this challenge, we propose an “action region proposal” method that, informed by optical flow, extracts image regions likely to contain actions for input into the network both during training and testing. In a range of experiments, we demonstrate that manually segmenting the background is not enough; but through active action region proposals during training and testing, state-of-the-art or better performance can be achieved on individual spatial and temporal video components. Finally, we show by focusing attention through action region proposals, we can further improve upon the existing state-of-the-art in spatio-temporally fused action recognition performance.

Understanding Protein Structure from a Percolation Perspective

Underlying the unique structures and diverse functions of proteins area vast range of amino-acid sequences and a highly limited number of folds taken up by the polypeptide backbone. By investigating the role of noncovalent connections at the backbone level and at the detailed side-chain level, we show that these unique structures emerge from interplay between random and selected features. Primarily, the protein structure network formed by these connections shows simple (bond) and higher order (clique) percolation behavior distinctly reminiscent of random network models. However, the clique percolation specific to the side-chain interaction network bears signatures unique to proteins characterized by a larger degree of connectivity than in random networks. These studies reflect some salient features of the manner in which amino acid sequences select the unique structure of proteins from the pool of a limited number of available folds.

Analyzing information flow in brain networks with nonparametric Granger causality

Multielectrode neurophysiological recording and high-resolution neuroimaging generate multivariate data that are the basis for understanding the patterns of neural interactions. How to extract directions of information flow in brain networks from these data remains a key challenge. Research over the last few years has identified Granger causality as a statistically principled technique to furnish this capability. The estimation of Granger causality currently requires autoregressive modeling of neural data. Here, we propose a nonparametric approach based on widely used Fourier and wavelet transforms to estimate both pairwise and conditional measures of Granger causality, eliminating the need of explicit autoregressive data modeling. We demonstrate the effectiveness of this approach by applying it to synthetic data generated by network models with known connectivity and to local field potentials recorded from monkeys performing a sensorimotor task.

Uplink Power Control and Base Station Association in Multichannel Cellular Networks

A combined base station association and power control problem is studied for the uplink of multichannel multicell cellular networks, in which each channel is used by exactly one cell (i.e., base station). A distributed association and power update algorithm is proposed and shown to converge to a Nash equilibrium of a noncooperative game. We consider network models with discrete mobiles (yielding an atomic congestion game), as well as a continuum of mobiles (yielding a population game). We find that the equilibria need not be Pareto efficient, nor need they be system optimal. To address the lack of system optimality, we propose pricing mechanisms. It is shown that these mechanisms can be implemented in a distributed fashion.

Designing a blended learning model for primary school language learning

In Finland, there is a desperate need for flexible, reliable and functional multi-e-learning settings for pupils aged 11-13. Southern Finland has several ongoing e-learning projects, but none that develop a multiple setting, with learning and teaching occurring between more than two schools. In 2006, internet connections were not broadband and data transfer was mainly audio data. Connections and technical problems occurred, which were an obstacle to multi-e-learning. Internet connections today enable web-based learning in major parts of
Lapland and by 2015, broadband will reach even the remotest villages up north. Therefore, it is important to research the possibilities of multi-e-learning and to build collaborative, learner-centred, versatile network models for primary school-aged pupils. The resulting model will facilitate distance learning to extend education to rural, sparsely populated areas, and it will give a model of using mobile devices in language portfolios. This will promote regional equality and prevent exclusion. Working with portfolios provides the opportunity to develop mobility from a pedagogical point of view. It is important to study the pros and cons of mobile devices in producing artefacts on portfolios in e-learning and language learning settings.
The current study represents a design-based research approach. The design research approach includes two important aspects concerning the current research: ‘a teacher as researcher’ aspect, which means there is the possibility to be strongly involved in developing processes and an obstacle-aspect, which means that problems while developing, are seen as a
promoter in evolving the designed model, as apposed to negative results.

Designing a blended learning model for primary school language learning

In Finland, there is a desperate need for flexible, reliable and functional multi-e-learning settings for pupils aged 11-13. Southern Finland has several ongoing e-learning projects, but none that develop a multiple setting, with learning and teaching occurring between more than two schools. In 2006, internet connections were not broadband and data transfer was mainly audio data. Connections and technical problems occurred, which were an obstacle to multi-e-learning. Internet connections today enable web-based learning in major parts of Lapland and by 2015, broadband will reach even the remotest villages up north. Therefore, it is important to research the possibilities of multi-e-learning and to build collaborative, learner-centred, versatile network models for primary school-aged pupils. The resulting model will facilitate distance learning to extend education to rural, sparsely populated areas, and it will give a model of using mobile devices in language portfolios. This will promote regional equality and prevent exclusion. Working with portfolios provides the opportunity to develop mobility from a pedagogical point of view. It is important to study the pros and cons of mobile devices in producing artefacts on portfolios in e-learning and language learning settings. The current study represents a design-based research approach. The design research approach includes two important aspects concerning the current research: ‘a teacher as researcher’ aspect, which means there is the possibility to be strongly involved in developing processes and an obstacle-aspect, which means that problems while developing, are seen as a promoter in evolving the designed model, as apposed to negative results.

An Eigen Approach to Transmit Beamforming in Wireless Networks With Single Antenna Receivers

In this paper, we propose an eigen framework for transmit beamforming for single-hop and dual-hop network models with single antenna receivers. In cases where number of receivers is not more than three, the proposed Eigen approach is vastly superior in terms of ease of implementation and computational complexity compared with the existing convex-relaxation-based approaches. The essential premise is that the precoding problems can be posed as equivalent optimization problems of searching for an optimal vector in the joint numerical range of Hermitian matrices. We show that the latter problem has two convex approximations: the first one is a semi-definite program that yields a lower bound on the solution, and the second one is a linear matrix inequality that yields an upper bound on the solution. We study the performance of the proposed and existing techniques using numerical simulations.

A Comparison of Machine Learning Techniques for Modeling River Flow Time Series: The Case of Upper Cauvery River Basin

Models of river flow time series are essential in efficient management of a river basin. It helps policy makers in developing efficient water utilization strategies to maximize the utility of scarce water resource. Time series analysis has been used extensively for modeling river flow data. The use of machine learning techniques such as support-vector regression and neural network models is gaining increasing popularity. In this paper we compare the performance of these techniques by applying it to a long-term time-series data of the inflows into the Krishnaraja Sagar reservoir (KRS) from three tributaries of the river Cauvery. In this study flow data over a period of 30 years from three different observation points established in upper Cauvery river sub-basin is analyzed to estimate their contribution to KRS. Specifically, ANN model uses a multi-layer feed forward network trained with a back-propagation algorithm and support vector regression with epsilon intensive-loss function is used. Auto-regressive moving average models are also applied to the same data. The performance of different techniques is compared using performance metrics such as root mean squared error (RMSE), correlation, normalized root mean squared error (NRMSE) and Nash-Sutcliffe Efficiency (NSE).

Correlation equations for average deposition rate coefficients of nanoparticles in a cylindrical pore

Nanoparticle deposition behavior observed at the Darcy scale represents an average of the processes occurring at the pore scale. Hence, the effect of various pore-scale parameters on nanoparticle deposition can be understood by studying nanoparticle transport at pore scale and upscaling the results to the Darcy scale. In this work, correlation equations for the deposition rate coefficients of nanoparticles in a cylindrical pore are developed as a function of nine pore-scale parameters: the pore radius, nanoparticle radius, mean flow velocity, solution ionic strength, viscosity, temperature, solution dielectric constant, and nanoparticle and collector surface potentials. Based on dominant processes, the pore space is divided into three different regions, namely, bulk, diffusion, and potential regions. Advection-diffusion equations for nanoparticle transport are prescribed for the bulk and diffusion regions, while the interaction between the diffusion and potential regions is included as a boundary condition. This interaction is modeled as a first-order reversible kinetic adsorption. The expressions for the mass transfer rate coefficients between the diffusion and the potential regions are derived in terms of the interaction energy profile. Among other effects, we account for nanoparticle-collector interaction forces on nanoparticle deposition. The resulting equations are solved numerically for a range of values of pore-scale parameters. The nanoparticle concentration profile obtained for the cylindrical pore is averaged over a moving averaging volume within the pore in order to get the 1-D concentration field. The latter is fitted to the 1-D advection-dispersion equation with an equilibrium or kinetic adsorption model to determine the values of the average deposition rate coefficients. In this study, pore-scale simulations are performed for three values of Peclet number, Pe = 0.05, 5, and 50. We find that under unfavorable conditions, the nanoparticle deposition at pore scale is best described by an equilibrium model at low Peclet numbers (Pe = 0.05) and by a kinetic model at high Peclet numbers (Pe = 50). But, at an intermediate Pe (e.g., near Pe = 5), both equilibrium and kinetic models fit the 1-D concentration field. Correlation equations for the pore-averaged nanoparticle deposition rate coefficients under unfavorable conditions are derived by performing a multiple-linear regression analysis between the estimated deposition rate coefficients for a single pore and various pore-scale parameters. The correlation equations, which follow a power law relation with nine pore-scale parameters, are found to be consistent with the column-scale and pore-scale experimental results, and qualitatively agree with the colloid filtration theory. These equations can be incorporated into pore network models to study the effect of pore-scale parameters on nanoparticle deposition at larger length scales such as Darcy scale.