Giorgio Koch

Bilinear systems: An appealing class of "nearly linear" systems in theory and applications

Recently, attention has been focused on the class of bilinear systems, both for its applicative interest and intrinsic simplicity. In fact, it appears that many important processes, not only in engineering, but also in biology, socio-economics, and ecology, may be modeled by bilinear systems. Moreover, since their nonlinearity is due to products between input and state variables, this class frequently may be studied by techniques similar to those employed for linear systems. This work is intended to motivate the interest of bilinear systems and to present the current state of research in its various aspects. After an introductory section, in which theoretical and applicative aspects of bilinear systems are enlightened, four other sections follow, respectively, devoted to structural properties, mathematical models, identification and optimization. In a final section, some concluding remarks are made on still open problems and possible trends for future research.

Derivation of antibody distribution from experimental binding data

Abstract It can be demonstrated that antibody populations cannot be suitably described in terms of a Sips distribution. Use of the Stieltjes transform allows instead derivation, from experimental binding data, of the most probable distribution of the association constants. From graphical interpolation of the experimental data four parameters can be obtained, which characterize a satisfactory bimodal distribution. By this procedure, analysis of data taken at different times of a humoral immune response, indicates that the relative abundance of the two sub-populations, rather than their mean association constant, is mainly affected by time or by variations of antigen dose. By use of the same procedure it is also possible to show that, at least as far as haptens are concerned, the slope of the 50% antigen-binding plot, often taken as a measure of the “avidity” of antibodies, is instead a function of the relative weight of the two sub-populations and of the spread of each of them.

Statistics of Optical Coherence Tomography Data From Human Retina

Optical coherence tomography (OCT) has recently become one of the primary methods for noninvasive probing of the human retina. The pseudoimage formed by OCT (the so-called B-scan) varies probabilistically across pixels due to complexities in the measurement technique. Hence, sensitive automatic procedures of diagnosis using OCT may exploit statistical analysis of the spatial distribution of reflectance. In this paper, we perform a statistical study of retinal OCT data. We find that the stretched exponential probability density function can model well the distribution of intensities in OCT pseudoimages. Moreover, we show a small, but significant correlation between neighbor pixels when measuring OCT intensities with pixels of about 5 ¿m. We then develop a simple joint probability model for the OCT data consistent with known retinal features. This model fits well the stretched exponential distribution of intensities and their spatial correlation. In normal retinas, fit parameters of this model are relatively constant along retinal layers, but varies across layers. However, in retinas with diabetic retinopathy, large spikes of parameter modulation interrupt the constancy within layers, exactly where pathologies are visible. We argue that these results give hope for improvement in statistical pathology-detection methods even when the disease is in its early stages.

Modeling for edge detection problems in blurred noisy images

The aim of this paper is to provide a theoretical set up and a mathematical model for the problem of image reconstruction. The original image belongs to a family of two-dimensional (2-D) possibly discontinuous functions, but is blurred by a Gaussian point spread function introduced by the measurement device. In addition, the blurred image is corrupted by an additive noise. We propose a preprocessing of data which enhances the contribution of the signal discontinuous component over that one of the regular part, while damping down the effect of noise. In particular we suggest to convolute data with a kernel defined as the second order derivative of a Gaussian spread function. Finally, the image reconstruction is embedded in an optimal problem framework. Now convexity and compactness properties for the admissible set play a fundamental role. We provide an instance of a class of admissible sets which is relevant from an application point of view while featuring the desired properties.

Resource management in network dynamics: An optimal approach to the admission control problem

This paper presents an innovative procedure to solve the Connection Admission Control Problem for a telecommunication network. Here, this important problem in the context of Communication Theory and Network Dynamics is dealt with by imbedding it in the framework of System and Control Theory. Highlights of the procedure are technology independence, coordinated and coherent decoupling, optimality and feedback properties, stochastic dynamic control.

Quality of Experience Provision in the Future Internet

This work deals with the satisfaction of the quality of experience (QoE) requirements in the perspective of the emerging future Internet framework. The evolution of the Internet is pointing out its limitations, which are likely to hinder its potential. In this respect, this paper introduces an innovative approach to cope with some key limitations of the present communication networks. In particular, the need of efficiently utilizing the available network resources and of guaranteeing the user expectations in terms of QoE requires a full cognitive approach, which is realized by the introduction of a novel architecture design, the so-called future Internet core platform. The future Internet core platform aims at bringing together the applications world with the network world, hence introducing a further cognitive level while enabling a new generation of applications: network-aware applications. This paper is concerned with an important aspect of the intelligent connectivity between applications and network: the service class association, which, if performed with a cognitive approach, can yield some important improvements and advantages in the emerging information era. The key idea presented in this paper is a real-time dynamic control procedure for the selection of the optimal service class. The approach is based on theoretical considerations validated by a proof-of-concept simulation.

An optimal approach to the connection admission control problem

The paper considers the connection admission control (CAC), which is a key resource management procedure, and proposes a solution to the problem based on modelling and control methodologies. The CAC problem will be formulated as an optimal control problem subject to a set of constraints. As a matter of fact, the proposed controller, modelling the CAC mechanism, computes the above-mentioned control variables so that (i) a set of proper constraints, which model the quality of service (QoS) requirements (link availability, blocking probability and dropping probability), are respected and (ii) a proper performance index, which models the exploitation degree of the available bandwidth, is maximized. The proposed CAC successfully compares with other CACs proposed in the literature, and in particular significantly extends the upper limit of the accepted traffic rate.

Filtering and forecasting problems for aggregate traffic in internet links

An important problem in bandwidth allocation and reservation over a communication link is to estimate the traffic bit rate in that link. This can be done by using specific tools for measurements of the traffic bit rate. However, the obtained measures are affected by some noise. Moreover, one might be interested in future traffic forecasting, when a prediction is needed. In this paper, an iterative filtering procedure is proposed for updating the traffic estimate upon the arrival of a new measurement. A birth and death stochastic model is assumed for the traffic bit rate to provide dynamical equations for the average behavior in the absence of information carried by measurements. Approximate solutions of the same updating problem are also given under the assumption that the posterior distribution of the traffic bit rate belongs to a specific class (beta or Gaussian distribution). This leads to approximate filtering procedures, which are expected to provide significant computational advantages. Finally, results obtained by processing simulated and real data are presented; stressing that the practical behavior of the approximate filters is quite satisfactory.

Global optimal image reconstruction from blurred noisy data by a Bayesian approach

In this paper, a procedure is presented which allows the optimal reconstruction of images from blurred noisy data. The procedure relies on a general Bayesian approach, which makes proper use of all the available information. Special attention is devoted to the informative content of the edges; thus, a preprocessing phase is included, with the aim of estimating the jump sizes in the gray level. The optimization phase follows; existence and uniqueness of the solution is secured. The procedure is tested against simple simulated data and real data.

Automatic analysis of flow cytometrically determined dna distributions in the presence of abnormal stemlines

Abstract In this paper the problem of FC histogram processing in the presence of an abnormal stemline, which appears of paramount importance in diagnosis and prognosis of cancer diseases, is considered. An automatic procedure is proposed to estimate the unknown parameters which describe the normal and the abnormal subpopulations. The procedure is extensively tested against simulated data and some preliminary inverstigation is also performed on its behavior and potentialities against real data.