Sandro Bosio

Set-base dynamical parameter estimation and model invalidation for biochemical reaction networks

BackgroundMathematical modeling and analysis have become, for the study of biological and cellular processes, an important complement to experimental research. However, the structural and quantitative knowledge available for such processes is frequently limited, and measurements are often subject to inherent and possibly large uncertainties. This results in competing model hypotheses, whose kinetic parameters may not be experimentally determinable. Discriminating among these alternatives and estimating their kinetic parameters is crucial to improve the understanding of the considered process, and to benefit from the analytical tools at hand.ResultsIn this work we present a set-based framework that allows to discriminate between competing model hypotheses and to provide guaranteed outer estimates on the model parameters that are consistent with the (possibly sparse and uncertain) experimental measurements. This is obtained by means of exact proofs of model invalidity that exploit the polynomial/rational structure of biochemical reaction networks, and by making use of an efficient strategy to balance solution accuracy and computational effort.ConclusionsThe practicability of our approach is illustrated with two case studies. The first study shows that our approach allows to conclusively rule out wrong model hypotheses. The second study focuses on parameter estimation, and shows that the proposed method allows to evaluate the global influence of measurement sparsity, uncertainty, and prior knowledge on the parameter estimates. This can help in designing further experiments leading to improved parameter estimates.

A set-based framework for coherent model invalidation and parameter estimation of discrete time nonlinear systems

This work introduces a unified framework for model invalidation and parameter estimation for nonlinear systems. We consider a model given by implicit nonlinear difference equations that are polynomial in the variables. Experimental data is assumed to be available as possibly sparse, uncertain, but (set-)bounded measurements. The derived approach is based on the reformulation of the invalidation and parameter/state estimation tasks into a set-based feasibility problem. Exploiting the polynomial structure of the considered model class, the resulting non-convex feasibility problem is relaxed into a convex semi-definite one, for which infeasibility can be efficiently checked. The parameter/state estimation task is then reformulated as an outer-bounding problem. In comparison to other methods, we check for feasibility of whole parameter/state regions. The practicability of the proposed approach is demonstrated with two simple biological example systems.

Minimizing the number of switch instances on a flexible machine in polynomial time

We revisit the tool switching problem on a flexible manufacturing machine. We present a polynomial algorithm for the problem of finding a switching plan that minimizes the number of tool switch instances on the machine, given a fixed job sequence. We prove tight hardness results for the variable sequence case with the same objective function, as well as a new objective function naturally arising in multi-feeder mailroom inserting systems.

Solving Nonlinear Covering Problems Arising in WLAN Design

Wireless local area networks (WLANs) are widely used for cable replacement and wireless Internet access. Because the medium access control (MAC) scheme of WLANs has a strong influence on network performance, it should be accounted for in WLAN design. This paper presents AP location models that optimize a network performance measure specifically for the MAC scheme of WLANs that represents the efficiency in sharing the wireless medium. For these models, we propose a solution framework based on an effective integer-linear programming Dantzig--Wolfe reformulation. This framework is applicable to any nonlinear covering problem where the objective function is a sum of contributions over the groundset elements (users in WLANs). Extensive computational results show that our solution strategy quickly yields optimal or near-optimal solutions for WLAN design instances of realistic size.

Model discrimination and parameter estimation via infeasibility certificates for dynamical biochemical reaction networks

Abstract Current approaches to parameter estimation and model invalidation are often inappropriate for biochemical reaction networks. This is because often only noisy measurements and sparse experimental data is available, and since they do not take the special structure of biochemical reaction networks into account. In this work a new method to prove model invalidity and to estimate parameters is introduced. It is based on a certificate of non-existence of feasible parameterizations for a given models. This is done by reformulating the model invalidation task into a set-based feasibility problem. As shown, due to the polynomial structure of many biochemical reaction systems, it is possible to relax the non-convex feasibility problem into a semidefinite program and thus to obtain conclusive results on model invalidity and parameter estimation. Our framework allows us to consider the arising difficulties posed by biochemical reaction networks by taking the specific structure of the dynamics and model outputs into account. It also enables us to discard large parameter regions as infeasible. We also show on a well-known biological example, namely the Michaelis-Menten and the Henri kinetics, how with this method it is possible to discriminate between model hypotheses and how to estimate parameters.

Hyperbolic set covering problems with competing ground-set elements

Motivated by a challenging problem arising in wireless network design, we investigate a new nonlinear variant of the set covering problem with hyperbolic objective function. Each ground-set element (user) competes with all its neighbors (interfering users) for a shared resource (the network access time), and the goal is to maximize the sum of the resource share assigned to each ground-set element (the network efficiency) while covering all of them. The hyperbolic objective function privileges covers with limited overlaps among selected subsets. In a sense, this variant lies in between the set partitioning problem, where overlaps are forbidden, and the standard set covering problem, where overlaps are not an issue at all. We study the complexity and approximability of generic and Euclidean versions of the problem, present an efficient Lagrangean relaxation approach to tackle medium-to-large-scale instances, and compare the computational results with those obtained by linearizations.

Mathematical Optimization Models for WLAN Planning

Wireless Local Area Networks (WLANs) based on the Ieee 802.11 standard family are used widely for wireless broadband Internet access. The performance aspects of WLANs range from deployment cost, coverage, capacity, interference, and data throughput to efficiency of radio resource utilization. In this chapter, we summarize some recent advances in applying mathematical optimization models for solving planning problems arising in placing access points (APs) and assigning channels in WLANs. For AP location, we present an optimization model aimed at maximizing the average user throughput. For channel assignment, we present two modeling approaches that use different performance metrics. We also discuss integrated models for joint optimization of AP location and channel assignment. We report computational experiments with real-life data, and show the advantages of mathematical optimization in WLAN planning.

Exact and Approximation Algorithms for Optimal Equipment Selection in Deploying In-Building Distributed Antenna Systems

We consider a combinatorial optimization problem in passive In-Building Distributed Antenna Systems (IB-DAS) deployment for indoor mobile broadband service. These systems have a tree topology, in which a central base station is connected to a number of antennas located at tree leaves via cables represented by the tree edges. Each inner node corresponds to a power equipment, of which the available types differ in the number of output ports and/or by power gain at the ports. This paper focuses on the equipment selection problem that amounts to, for a given passive DAS tree topology, selecting a power equipment type for each inner node and assigning the outgoing edges of the node to the equipment ports. The performance metric is the power deviation at the antennas from the target values. We consider as objective function the minimization of either the total or the largest power deviation over all antennas. Our contributions are the development of exact pseudo-polynomial time algorithms and (additive) fully-polynomial time approximation schemes for both objectives. Numerical results are provided to illustrate the algorithms. We also extend some results to account for equipment cost.

Graph problems arising from parameter identification of discrete dynamical systems

This paper focuses on combinatorial feasibility and optimization problems that arise in the context of parameter identification of discrete dynamical systems. Given a candidate parametric model for a physical system and a set of experimental observations, the objective of parameter identification is to provide estimates of the parameter values for which the model can reproduce the experiments. To this end, we define a finite graph corresponding to the model, to each arc of which a set of parameters is associated. Paths in this graph are regarded as feasible only if the sets of parameters corresponding to the arcs of the path have nonempty intersection. We study feasibility and optimization problems on such feasible paths, focusing on computational complexity. We show that, under certain restrictions on the sets of parameters, some of the problems become tractable, whereas others are NP-hard. In a similar vein, we define and study some graph problems for experimental design, whose goal is to support the scientist in optimally designing new experiments.

Time-Expanded Packings

We introduce a general model for time-expanded versions of packing problems with a variety of applications. Our notion for time-expanded packings, which we introduce in two natural variations, requires elements to be part of the solution for several consecutive time steps. Despite the fact that the time-expanded counterparts of most combinatorial optimization problems become computationally hard to solve, we present strong approximation algorithms for general dependence systems and matroids, respectively, depending on the considered variant. More precisely, for both notions of time-expanded packings that we introduce, the approximation guarantees we obtain are at most a small constant-factor worse than the best approximation algorithms for the underlying problem in its non-time-expanded version.