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## Über dieses Buch

This volume explores the emerging and current, cutting-edge theories and methods of modeling, optimization, dynamics and bio economy. It provides an overview of the main issues, results and open questions in these fields as well as covers applications to biology, economy, energy, industry, physics, psychology and finance.

The majority of the contributed papers for this volume come from the participants of the International Conference on Modeling, Optimization and Dynamics (ICMOD 2010), a satellite conference of EURO XXIV Lisbon 2010, which took place at Faculty of Sciences of University of Porto, Portugal and from the Berkeley Bio economy Conference 2012, at the University of California, Berkeley, USA.

## Inhaltsverzeichnis

### Chapter 1. Dynamic Management of Fossil Fuel, Biofuel, and Solar Energy

Cheap energy has been key to the modern economy. The use of electricity and the internal combustion engine have been crucial for current patterns of civilization, and reduction in availability or increases in the cost of energy have serious consequences for current activities of society. Concerns about climate change, depletion of fossil fuel, and exchange rates are causing societies to transition from fossil to renewable fuel. The transition is challenging both in terms of modeling and policy design. There is an emerging portfolio of alternative technologies, but the extent and order in which they will be introduced is uncertain and presents a major challenge.

Scott Kaplan, Charles Séguin, Karl W. Steininger, David Zilberman

### Chapter 2. Optimal Localization of Firms in Hotelling Networks

This paper develops a theoretical framework to study price competition in a Hotelling-type network game, extending the Hotelling’s model of price competition with linear transportation costs from a line to a network. Under explicit conditions on the production costs and road lengths, we exhibit the existence of a pure Nash equilibrium strategy. We study the effect of small perturbations on the localizations of firms and we conclude that, for networks with all degrees above two, the node localization is optimal.

### Chapter 3. On the Dynamics and Effects of Corruption on Environmental Protection

This paper studies the joint dynamics of corruption and pollution in a model of evolutionary game theory, where firms face a given pollution standard and the government must check the compliance to this standard by means of public officials who can be honest or not. A novelty of our paper is that officials decide to be honest or not by imitation, while firms are assumed to be inter-temporal profit maximizers. One of the main findings of the paper is that one possible “bad” outcome characterized by a whole society of polluting firms and corrupt officers can be sustained by rational agents who learn by imitation, despite the existence of multiplicity of equilibria of a perfectly honest population and a more realistic simultaneous presence of honest and dishonest agents. Moreover, we show that the firm’s discount rate is an important decision factor that influences the environmental pollution.

Elvio Accinelli, Laura Policardo, Edgar J. Sánchez Carrera

### Chapter 4. A Bayesian Pricing Model for CAT Bonds

This paper examines the impact of the 2005 hurricane season, particularly Hurricane Katrina, on the pricing of CAT bonds. We examine whether highly rated CAT bonds demonstrate a different relationship than subinvestment bonds between objective risk measures and the spread. The theoretical framework for this relationship is based on the Lance Financial (LFC) model, introduced by Lane (Rationale and results with the LFC cat bond pricing model, Discussion paper, Lane Financial LLC, Wilmette, 2003). The empirical results of treed Bayesian estimation confirm that the severity component of the spread has an increased impact, indicating a shift in investor perception during the pricing process. The impact of the conditional expected loss also significantly increases, but it contributes through its interaction with the attachment probability rather than through its variance. Finally, we show that the influence of conditional expected loss is also increased by investment-grade ratings, because investors who demand highly rated bonds may be more concerned about possible losses than junk bond investors.

Frieder Ahrens, Roland Füss, A. Sevtap Selcuk-Kestel

### Chapter 5. Properties and Comparative-Static Effects in Models of Decision Under Uncertainty: Applications to the Theory of the Firm

We consider a simple model of decision under uncertainty, in which a representative risk-averse agent maximizes the expected utility of a random wealth. The wealth is postulated in a quite general form, especially concerning the effect of the decision variable, so that other decision problems under uncertainty can be considered as particular cases of this model. In this general framework, we propose a new method to easily obtain both properties of the optimal solution and comparative-static effects. We illustrate the usefulness of this formulation by applying it to some models from the theory of the firm under uncertainty. In these models we are able to easily derive their key properties, and also new results.

Alberto A. Álvarez-López, Inmaculada Rodríguez-Puerta, Francisco Sebastiá-Costa, Mónica Buendía

### Chapter 6. On Sensitive Dependence on Initial Conditions and Existence of Physical Measure for 3-Flows

After reviewing known results on sensitiveness and also on robustness of attractors together with observations on their proofs, we show that for attractors of three-dimensional flows, robust chaotic behavior (meaning sensitiveness to initial conditions for the past as well for the future for all nearby flows) is equivalent to the existence of certain hyperbolic structures. These structures, in turn, are associated to the existence of physical measures. In short

in low dimensions, robust chaotic behavior for smooth flows ensures the existence of a physical measure

.

Vítor Araújo

### Chapter 7. Thermodynamic Formalism for the General One-Dimensional XY Model: Positive and Zero Temperature

This is a survey paper on the general one-dimensional

XY

model. The proofs of the results presented here appear in two papers which are [2] and [18]. In the last mentioned work it is consider a more general setting where the state space is a compact metric space and the a-priory probability is any fixed probability on the metric space.

A. T. Baraviera, L. Ciolleti, A. O. Lopes, J. Mengue, J. Mohr, R. R. Souza

### Chapter 8. Impact of Political Economy and Logistical Constraints on Assessments of Biomass Energy Potential: New Jersey as a Case Study

Much of the analysis on the viability of biomass to energy focuses on the implications of utilizing biomass feedstocks on energy and food pathways, land use and the environment. However, to more accurately assess biomass energy potential, analysis also needs to include political economy and logistical constraints, such as institutional barriers, existing policies, and collection and delivery infrastructure. To demonstrate the importance of introducing such constraints into an assessment model, a biomass analysis conducted for New Jersey in 2007 is used as a case study. In this assessment, biomass potential for the state was calculated with and without political economy and logistical constraints. The case study shows that introducing political economy and logistical constraints have a significant impact on the estimated quantities of Class 1 biomass feedstocks available for energy production. In the New Jersey case, 35 % of total estimated biomass resources were unavailable for bioenergy generation when considering political economy and logistical constraints in the assessment model.

Margaret Brennan-Tonetta, Gal Hochman, Brian Schilling

### Chapter 9. Modelling Decentralized Interaction in a Monopolistic Competitive Market

This paper models the interaction of consumers’ and firms’ optimal choices with imperfect information in a monopolistic competitive market institution. The decisions of the agents are modeled with stochastic utility and profit functions. We show that using Markov mean field and an agent based model specification the agents stays most of the time within a subset of the space of states. We explore how our results depends on the exogenously established price rule and we make specific interpretation of the transition rate parameters in the context of the economic problem.

Juan Gabriel Brida, Nicolás Garrido

### Chapter 10. Measuring the Effectiveness of an E-Commerce Site Through Web and Sales Activity

An electronic commerce Website is successful if it achieves the purpose for which it has been created. In this chapter we objectively assess the success of a real Website in terms of its pages’ ability to attract customers. The analysis is conducted using web access logs and sales data. Existing measures of the success of different pages on a site are employed with respect to the aims of the site owner. The pages of different products are also compared in terms of their success on the site and sales figures. A segmentation of the customers was performed according to usage and sales profile. Finally, the success of product pages in the different segments was analyzed.

Ana Ribeiro Carneiro, Alípio Mário Jorge, Pedro Quelhas Brito, Marcos Aurélio Domingues

### Chapter 11. Worldwide Survey of Biodegradable Feedstocks, Waste-to-Energy Technologies, and Adoption of Technologies

The current chapter survey categories of biodegradable waste, including manure and animal waste, food waste, crop residues, and sewage waste. The chapter then identify and analyze several major types of waste management technologies, such as anaerobic digestion, landfilling, composting, and incineration. It concludes with a brief discussion on the different patterns of adoption among regions.

Mike Centore, Gal Hochman, David Zilberman

### Chapter 12. Ergodic Transport Theory, Periodic Maximizing Probabilities and the Twist Condition

Consider the shift

T

acting on the Bernoulli space

$$\varSigma =\{ 1,2,3,..,d\}^{\mathbb{N}}$$

and

$$A:\varSigma \rightarrow \mathbb{R}$$

a Hölder potential. Denote

$$\displaystyle{m(A) =\max _{\nu \mbox{ an invariant probability for T}}\int A(x)\;d\nu (x),}$$

and,

μ

,

A

, any probability which attains the maximum value. We will assume that the maximizing probability

μ

is unique and has support in a periodic orbit. We denote by

$$\mathbb{T}$$

the left-shift acting on the space of points

$$(w,x) \in \{ 1,2,3,..,d\}^{\mathbb{Z}} =\varSigma \times \varSigma =\hat{\varSigma }$$

. For a given potential Hölder

$$A:\varSigma \rightarrow \mathbb{R}$$

, where

A

acts on the variable

x

, we say that a Hölder continuous function

$$W:\hat{\varSigma }\rightarrow \mathbb{R}$$

is a involution kernel for

A

(where

A

acts on the variable

w

), if there is a Hölder function

$$A^{{\ast}}:\varSigma \rightarrow \mathbb{R}$$

, such that,

$$\displaystyle{A^{{\ast}}(w) = A \circ \mathbb{T}^{-1}(w,x) + W \circ \mathbb{T}^{-1}(w,x) - W(w,x).}$$

One can also consider

V

the calibrated subaction for

A

, and, the maximizing probability

$$\mu _{\infty,A^{{\ast}}}$$

for

A

. The following result was obtained on a paper by Lopes et al.: for any given

x

Σ

, it is true the relation

$$\displaystyle{V (x) =\sup _{w\in \varSigma }\,[\,(W(w,x) - I^{{\ast}}(w)) - V ^{{\ast}}(w)\,],}$$

where

I

is non-negative lower semicontinuous function (it can attain the value

in some points). In this way

V

and

V

form a dual pair. For each

x

one can get one (or, more than one)

w

x

such attains the supremum above. That is, solutions of

$$\displaystyle{V (x) = W(w_{x},x) - V ^{{\ast}}(w_{ x}) - I^{{\ast}}(w_{ x})\,.}$$

A pair of the form (

x

,

w

x

) is called an optimal pair. Under some technical assumptions, we show that generically on the potential

A

, the set of possible optimal

w

x

, when

x

covers the all range of possible elements

x

in ∈

Σ

, is finite.

G. Contreras, A. O. Lopes, E. R. Oliveira

### Chapter 13. Measuring the Welfare Impact of Biofuel Policies: A Review of Methods and Findings from Numerical Models

The welfare impact of biofuel policies in the US has received considerable attention in the past several years due to the cost of these policies as well as their possible contribution to rising food prices and deforestation. This chapter discusses the various modeling approaches used to measure the welfare impact of biofuel policies and summarizes findings of the literature on the subject. Welfare analyses of biofuel policies have evolved with changing regulation and new findings about the economic and environmental impacts of biofuel policies. Future research is needed to address the long-term welfare implications of biofuel policies on energy security.

Christine L. Crago

### Chapter 14. Advanced Mathematical and Statistical Tools in the Dynamic Modeling and Simulation of Gene-Environment Regulatory Networks

In this study, some methodologies and a review of the recently obtained new results are presented for the problem of modeling, anticipation and forecasting of genetic regulatory systems, as complex systems. In this respect, such kind of complex systems are modeled in the dynamical sense into the two different ways, namely, by a system of ordinary differential equations (ODEs) and Gaussian graphical methods (GGM). An artificial time-course microarray dataset of a gene-network is modeled as an example by using both ODE method and GGM. In this analysis, since the actual interactions of the nodes, i.e., genes, are assumed to be unknown, the discrete time measurements are initially used for the inference of the system’s interactions, i.e., the edges between nodes, by the underlying two methods. Then, the results of inference from ordinary differential equation based model are applied to a class of previously developed new numerical schemes for the generation of further states of the system. In this simulation, we present the recent results of a set of explicit Runge-Kutta methods that are implemented.

Özlem Defterli, Vilda Purutçuoğlu, Gerhard-Wilhelm Weber

### Chapter 15. BHP Universality in Energy Sources

We consider the

α

re-scaled energy source (ES) daily positive returns

r

(

t

)

α

and negative returns (−

r

(

t

))

α

that we call, after normalization, the

α

positive fluctuations and

α

negative fluctuations, respectively. We use the Kolmogorov-Smirnov statistical test as a method to find the values of

α

that optimize the data collapse of the histogram of the

α

fluctuations with the truncated Bramwell-Holdsworth-Pinton (BHP) probability density function. Using the optimal

α

s

we compute analytical approximations of the probability distributions of the normalized positive and negative energy source (ES) daily returns

r

(

t

). Since the BHP probability density function appears in several other dissimilar phenomena, our results reveal a universal feature of energy source prices and a new measure that allows the comparison between the intensity of gains and losses of market activity in different energy sources prices.

Helena Ferreira, Rui Gonçalves, Alberto Adrego Pinto

### Chapter 16. Dynamical Phase Transition in Slowed Exclusion Processes

In this work, we present symmetric simple exclusion processes with a finite number of bonds whose dynamics is slowed down in order to difficult the passage of particles at those bonds. We study the influence of the rate of passage of mass at those bonds in the macroscopic hydrodynamic equation. As a consequence, we exhibit a dynamical phase transition that goes from smooth profiles to the development of discontinuities.

Tertuliano Franco, Patrícia Gonçalves, Adriana Neumann

### Chapter 17. Cooperative Ellipsoidal Games: A Survey

Involving of uncertainty into cooperative games is motivated by the real world where noise in observation and experimental design, incomplete information and further vagueness in preference structures and decision making play an important role. The theory of cooperative ellipsoidal games provides a new game theoretical understanding and suitable tools for to solve this question. This survey aims to briefly present the state-of-the-art in this young field of research, discusses how the model of cooperative ellipsoidal games extends the cooperative game theory literature, and reviews its existing and potential applications in economic situations.

S. Z. Alparslan Gök, G.-W. Weber

### Chapter 18. Zeta Functions and Continuous Time Dynamics

The purpose of this survey is to introduce the reader to the relation between continuous time hyperbolic systems and zeta functions, focusing on Anosov flows and billiards as seen through the lenses of transfer operators.

Paolo Giulietti

### Chapter 19. Diffusion Dynamics in Economics: An Application to the Effects of Fiscal Policy

This study addresses diffusion dynamics in an economic environment in which fiscal policy changes take place. The discussion, based upon a conventional intertemporal optimization setup, involves the consideration of a peculiar form of bounded rationality: it is assumed that only a small share of households is able to instantly recompute the optimal solution once the value of a tax rate is disturbed; all the other agents will then, gradually, follow the behavior of the first group (this can occur through contagion, social influence or social learning). As a result, the convergence towards the post-perturbation steady-state tends to follow a diffusion process and, consequently, policy measures may take time in affecting pervasively labor-leisure and consumption-savings choices.

Orlando Gomes

### Chapter 20. Occupation Times of Exclusion Processes

In this paper we consider exclusion processes {

η

t

:

t

≥ 0} evolving on the one-dimensional lattice

$$\mathbb{Z}$$

, under the diffusive time scale

tn

2

and starting from the invariant state

ν

ρ

—the Bernoulli product measure of parameter

ρ

∈ [0, 1]. Our goal consists in establishing the scaling limits of the additive functional

$$\varGamma _{t}:=\int _{ 0}^{tn^{2} }\eta _{s}(0)\, ds$$

the occupation time of the origin

. We present a method, recently introduced in Gonçalves and Jara (Universality of KPZ equation, Available online at arXiv:1003.4478, 2011), from which a

local Boltzmann-Gibbs Principle

can be derived for a general class of exclusion processes. In this case, this principle says that

Γ

t

is very well approximated to the additive functional of the density of particles. As a consequence, the scaling limits of

Γ

t

follow from the scaling limits of the density of particles. As examples we present the mean-zero exclusion, the symmetric simple exclusion and the weakly asymmetric simple exclusion. For the latter under a strong asymmetry regime, the limit of

Γ

t

is given in terms of the solution of the KPZ equation.

Patrícia Gonçalves

### Chapter 21. Error Estimates for a Coupled Continuous-Discontinuous FEM for the Two-Layer Shallow Water Equations

We present a coupled continuous-discontinuous finite element method for solving multi-layer shallow-water equations in their primitive form. The method is based on a continuous approximation of the horizontal velocities together with a discontinuous approximation of the surface and interface elevations. A priori estimates are derived for the semi-discrete problem.

Pedro S. Gonçalves, Bruno M. Pereira, Juha H. Videman

### Chapter 22. Bankruptcy Triggering Asset Value: Continuous Time Finance Approach

This paper utilizes means of game theory and option pricing to compute a bankruptcy triggering asset value. Combination of these two fields of economic study serves to separating the given problem into valuation of the payoffs, where we use option pricing and the analysis of strategic interactions between parties of a contract which could be designed and solved with the use of game theory. First of all, we design a contract between three parties each having a stake in the company, but with different rights reflected in the boundary conditions of the Black-Scholes equation. Then we will compute the values of debts and the whole value of the company. From here we directly compute the value of the firm’s equity and optimize it from the point of view of managing shareholders. The theoretically computed bankruptcy triggering asset value is then compared to the actual stock price. Depending on this relation, we may say whether the company is likely to go under or not. Such knowledge is an example of the use of computational methods in sell-side analysis. In addition, this article also provides reader with a real-life case study of the investment bank Bear Stearns and the optimal bankruptcy strategy in this particular case. As we will observe, the bankruptcy trigger computed in this example could have served as a good guide for predicting fall of this investment bank.

Karel Janda, Jakub Rojcek

### Chapter 23. Economic Impact Analysis of Potential Trade Restrictions on Biotech Maize in Latin American Countries

The production and trade of biotech maize across major North and South America exporters has increased dramatically in the last 15 years. However, as new biotech maize traits are being deregulated by national regulatory authorities at increasingly different speeds, the chances that some biotech maize traits may be approved for commercialization and production in some exporting country but not for use in an importing country, have been growing. So has the risk of costly trade disruptions. In this paper we use a spatial equilibrium model of the global maize trade to evaluate the potential economic impacts of such trade disruptions in the Americas. We find that potential trade disruptions for import dependent Latin American countries can have significant negative economic impacts. The results suggest that the development of adequate regulatory capacity and pooling regulatory resources at a regional level as well as adopting national policies for dealing with unapproved biotech crops (e.g. adoption of CODEX Annex) will likely be important in the future in Latin America.

Nicholas Kalaitzandonakes, James Kaufman, Douglas Miller

### Chapter 24. How Venture Capital Creates Externalities in the Bioeconomy: A Geographical Perspective

A stream of literature has demonstrated that venture capital generates externalities that enhance the knowledge base of a given region and accordingly assist high technology firms to improve their innovative performance. What has gone largely unexamined in this literature is the geographic extent of such externality impact. In this research we address the issue at hand. We do so by analyzing the association between the patenting rate of all life sciences firms that have won Small Business Innovation Research grants from 1983 to 2006 and the venture capital investments that have occurred at increasingly distant spatial units from those firms. Controlling for firm-specific and environmental factors as well as for endogeneity concerns, we document that life sciences firms tend to produce more patents whenever they are situated in very close proximity to where venture capital investments occur. Further, we find that improvements of the patenting rate of focal firms largely emanate from investments that reflect the expertise of venture capitalists on advancing existing prototypes closer to commercialization. We conclude the paper with a discussion on research and policy implications of our findings.

Christos Kolympiris, Nicholas Kalaitzandonakes

### Chapter 25. Inverse Problems in Complex Multi-Modal Regulatory Networks Based on Uncertain Clustered Data

Complex regulatory networks effected by noise and data uncertainty occur in many OR applications. The complexity is compounded by the unknown interactions between the system variables that have to be revealed from unprecise measurement data. The concept of target-environment networks provides a generic framework for the analysis of complex regulatory systems under uncertainty. Data mining methods like clustering and classification can be applied for an identification of functionally related groups of targets and environmental factors. The effects of the intricate connections between target and environmental clusters on single entities are determined by a parameterized time-discrete model. A crisp regression problem is introduced for parameter estimation and in case of uncertain data, ellipsoids are used to describe the clusters and error sets what refers to particular robust counterpart programs.

Erik Kropat, Gerhard-Wilhelm Weber, Sırma Zeynep Alparslan-Gök, Ayşe Özmen

### Chapter 26. Financial Bubbles

We study on speculative financial bubbles whose characteristic can be modeled by Log Periodic Power Law (LPPL) which is represented by

Anders Johansen

,

Olivier Ledoit

and

Didier Sornette

. The most probable time of the crash is estimated by a parameter in the equation. All parameters used in the equation, are forecasted by optimization through a genetic algorithm. Analysis of a time series by S&P 500 from 1987 shows the signals of the LPPL before the financial crisis of October 1987. In addition to the speculative bubbles, we also present and investigate antibubbles. They, likewise speculative bubbles, also follow log-periodic power law but, of course, with decelerating oscillations and, generally, in a bearish way inclined instead of a bullish way. We also introduce an alternative method which approaches the bubble concept geometrically and benefits from the advantages of optimization and machine learning.

Efsun Kürüm, Gerhard-Wilhelm Weber, Cem İyigün

### Chapter 27. Modern Applied Mathematics for Alternative Modeling of the Atmospheric Effects on Satellite Images

Nonparametric regression and classification techniques are mostly the key data mining tools in explaining real life problems and natural phenomena where many effects often exhibit nonlinear behavior. The remotely sensed earth data collected by earth-observing satellites is degraded due to the absorption and scattering of solar radiation by atmospheric gases and aerosols. In order to use these data for information extraction, they must first be corrected for the atmospheric effects. Recent methods based on radiative transfer modelling still have many challenges including achieving high accuracy and developing real-time processing capability of large numbers of satellite images acquired with high temporal resolution and Large Field of View instruments. In this chapter, two state-of-the-art nonparametric tools, Multivariate Adaptive Regression Splines (MARS) and its successor Conic Multivariate Adaptive Regression Splines (CMARS), are reviewed within the frame of an earth science example. Both methods are utilized for the atmospheric correction of five sets of MODIS images taken over European Alps. The Simplified Method for Atmospheric Correction (SMAC), a simplified version of 6S radiative transfer model, is also applied on the image data sets for the removal of atmospheric effects. The performance of the models was evaluated by comparing their results with the MODIS atmospherically corrected surface reflectance product in terms of RMSE. Although MARS and CMARS approaches produce similar results on the data sets, they both outperform SMAC.

Semih Kuter, Gerhard Wilhelm Weber, Ayşe Özmen, Zuhal Akyürek

### Chapter 28. Modeling Ethanol Investment Decisions

This article reviews some of the papers my co-authors and I have written analyzing what factors affect the decision to invest in building new ethanol plants using a dynamic structural econometric model of the investment timing game. The results of our research will help determine which policies and factors can promote fuel-ethanol industry development. In Lin and Thome (Investment in corn-ethanol plants in the Midwestern United States: an analysis using reduced-form and structural models, Working paper, University of California at Davis, 2013), we estimate a model of the investment timing game in corn ethanol plants in the United States. This model follows my previous work estimating a structural econometric model of the multi-stage dynamic investment timing game in offshore petroleum production (Lin, 2013). In Lin and Yi (Ethanol plant investment in Canada: a structural model, Working paper, University of California at Davis, 2013; What factors affect the decision to invest in a fuel ethanol plant? a structural model of the ethanol investment timing game, Working paper, University of California at Davis, 2013), we estimate a model of the investment timing game in ethanol plants worldwide that allows for the choice among different feedstocks.

C.-Y. Cynthia Lin

### Chapter 29. Ethanol and Distiller’s Grain: Implications of the Multiproduct Firm on United States Bioenergy Policy

The use of corn for ethanol production has spawned considerable debate. There is little agreement among economists as to whether U.S. ethanol policy generates a welfare net loss or welfare net gain to society [16]. In modeling the impact of ethanol policy, there are several key components, including, for example, the impact of increased ethanol output on gasoline prices. If the impact is positive, the benefits from ethanol policy exceed the costs, but the reverse can be true if the impact is small or nonexistent [15]. More recently, the potential effect of an ethanol byproduct (distiller’s grain) has become increasingly important. According to Dennis Conley “We’re set on ethanol as the product and distiller’s grain as the byproduct, but that could shift. Distiller’s grain may become the product and ethanol the byproduct” [2]. Given that the ethanol process removes nutritional content from the corn in the process of creating ethanol, the primary profit center for distillers will likely continue to be ethanol. However, the potential value of distiller’s grain undoubtedly affects the profitability of ethanol producers. This chapter incorporates some of the effects of distiller’s grain into the benefit-cost of ethanol policy. It is possible that some of these considerations may yield a benefit-cost ratio greater than one if that is not already the case in the absence of distiller’s grain.

Charles B. Moss, Andrew Schmitz, Troy G. Schmitz

### Chapter 30. A Review on Protein-Protein Interaction Network Databases

Protein-protein interaction networks (PPI) are one of the vital resources that are available for understanding the processes in a living cell. Protein associations are studied in different perspectives, including biochemistry, quantum chemistry, molecular dynamics, metabolic or genetic/epigenetic networks and so on. There are several experimental methods designed to probe these interactions, such as co-immunoprecipitation or affinity chromatography, mass spectrometry, yeast to hybrid and so on. These experimental techniques can be further categorized into low-throughput and high-throughput methods. All these techniques are labor-intensive methods. However, there are several computational tools developed to predict the protein-protein interaction network from experiment verified protein-protein interactions. There are several complementing efforts made to centralize protein-protein interaction data through the construction of databases which play a vital role in the prediction of protein-protein interactions from sequence and structural features. These PPI databases can be grouped under general databases (contains wide variety of organisms) and specialized databases (meant for specific organism). In this paper, we attempt to provide a summary of these recent and most widely used protein-protein interactions databases. However, computational approaches developed for PPI and their performance is out of the scope of this paper.

Chandra Sekhar Pedamallu, Linet Ozdamar

### Chapter 31. On the Use of Cross Impact Analysis for Enhancing Performance in Primary School Education

The system dynamics approach is a holistic way of solving problems in real-time scenarios. The Cross Impact Analysis (CIA) is a system dynamics method that enables the construction of a model relating entities and attributes relevant to a system. Then, the CIA simulates the model construct and observes the changing system status. The CIA permits the integration of policies into the model construct and enables the comparison of the simulated system with the one that is augmented by policies. Thereby, it is possible to observe policy effects on future system status. Here, we describe how CIA is utilized to enhance student enrolment and performance with simulated government policies in two developing countries.

Chandra Sekhar Pedamallu, Linet Ozdamar, Gerhard-Wilhelm Weber

### Chapter 32. The Bioeconomics of Migration: A Selective Review Towards a Modelling Perspective

We present a selective review of migration and its connection with the economy, focusing on issues leading towards a modelling perspective. We introduce a class of models based on difference equations on directed graphs that may provide a quantitative and qualitative description of human migration and present some of their bioeconomic, mathematical and simulation challenges.

E. V. Petracou, A. Xepapadeas, A. N. Yannacopoulos

### Chapter 33. Complete versus Incomplete Information in the Hotelling Model

For the linear Hotelling model with firms located at the boundaries of the segment line, we study the price competition in a scenario of complete and incomplete information in the production costs of both firms. We compute explicitly the Nash price strategy in the cases of complete and incomplete information. We explicitly determine for the profit, consumer surplus and welfare, the quantitative economical advantages and disadvantages between having complete or incomplete information in the production costs. We prove that, in expected value, the consumer surplus and the welfare are greater with incomplete information than with the complete information and the difference is determined by the variances of the probability distributions. In expected value, the profit it is greater for the firm with higher variance for the probability distribution of its productions costs with incomplete information than with the complete information. However, in expected value, the profit can be smaller for the firm with lower variance for the probability distribution of its productions costs with incomplete information than with the complete information.

### Chapter 34. Maximal Differentiation in the Hotelling Model with Uncertainty

For the quadratic Hotelling model, we study the optimal localization and price strategies under incomplete information on the production costs of the firms. We compute explicitly the pure Nash-Bayesian price duopoly equilibrium and we prove that it does not depend upon the distributions of the production costs of the firms, except on their first moments. We find when the maximal differentiation is a local optimum for the localization strategy of both firms.

### Chapter 35. A Cost Sharing Mechanism for Job Scheduling Problems

In this chapter we propose a cost sharing mechanism for job scheduling problems by means of a modification to the concept of the potential of Hart and Mas-Colell for cooperative games. We obtain explicit formulas for the potential of job scheduling problems and for its corresponding cost sharing mechanism. Also, we establish a relation between this mechanism and the Shapley value of an specific cooperative game.

Joss Sánchez-Pérez

### Chapter 36. Welfare Assessment of the Renewable Fuel Standard: Economic Efficiency, Rebound Effect, and Policy Interactions in a General Equilibrium Framework

In this paper, we have shown that partial equilibrium evaluations of biofuels policies can lead to misleading results. We develop a stylized theoretical model to show how a general equilibrium setup can improve the analysis of price, welfare, rebound, and other impacts. We then implement an empirical analysis of the US corn ethanol mandate and show that inclusion of agricultural subsidies and income tax impacts are very important. Previous work has seriously underestimated the price impacts on coarse grains because the financing of the implicit subsidy did not consider the reduction of agricultural subsidies. Also, other studies in the literature have estimated huge gasoline price decreases due to the US ethanol program. We show that the gasoline price impact is essentially negligible. These other studies did not include all the economy wide impacts. We also show the rebound, trade, and welfare impacts of the policy cases. The land use impact varies significantly with implemented ethanol policy, but the welfare impacts do not differ meaningfully across the cases.

### Chapter 37. New Uncertainties in Land Use Changes Caused by the Production of Biofuels

The environmental benefits of biofuels continue to be debated. Recent attention focuses on biofuel-induced land use changes and their impact on greenhouse gas emissions. We develop an international, multi-commodity, partial equilibrium model and measure the impact of US and EU biofuel production on land use as well as the associated greenhouse gas emissions. We find these measures to be sensitive to changes in assumptions, specifically relating to yields. We note the possibility of offsetting cross-commodity effects. We identify the context and time path as previously unrecognized sources of variation and potential error in greenhouse gas calculations.

Wyatt Thompson, Nicholas Kalaitzandonakes, James Kaufman, Seth Meyer

### Chapter 38. Inequalities on the Parameters of a Strongly Regular Graph

In this paper we establish inequalities over the parameters and over the spectra of strongly regular graphs in the environment of Euclidean Jordan algebras. We consider a strongly regular graph,

G

A

has three distinct eigenvalues, and the Euclidean Jordan algebra of real symmetric matrices of order

n

,

$$\text{Sym}(n, \mathbb{R})$$

with the vector product and the inner product being the Jordan product and the usual trace of matrices, respectively. We associate a three dimensional real Euclidean Jordan subalgebra

$$\mathcal{A}$$

of

$$\text{Sym}(n, \mathbb{R})$$

to

A

, spanned by the identity matrix and the natural powers of

A

. Next, we compute the unique complete system of orthogonal idempotents

$$\mathcal{B}$$

associated to

A

and we consider particular convergent Hadamard series constructed from the idempotents of

$$\mathcal{B}$$

. Finally, by the analysis of the spectra of the sums of these Hadamard series we establish new conditions for the existence of a strongly regular graph.

Vasco Moço Mano, Enide Andrade Martins, Luís Almeida Vieira

### Chapter 39. Financial, Real, and Quasi Options: Similarities and Differences

Flexibility, uncertainty, and irreversibility provide gains from waiting. These gains have been elaborated in the context of finance (financial option), investment (real option), and environmental policy (quasi option). While the financial and real option values are closely linked as the real option value theory has been developed from the financial option value theory the quasi option value originated from environmental economics and the link with financial and real option value theory is less obvious. A comparison between the three option theories shows similarities as well as differences. Knowing in particular the cause of differences will be important for understanding why either of the approach may yield a different result, for the interpretation of the results, and for the choice of approach.

Justus Wesseler

### Chapter 40. A Review and New Contribution on Conic Multivariate Adaptive Regression Splines (CMARS): A Powerful Tool for Predictive Data Mining

This study aims at critically reviewing the research that has been conducted to improve the backward part of the Multivariate Adaptive Regression Splines (MARS) method that leads to the development of Conic MARS (CMARS) method. Several studies have been carried out to apply the method to various fields of study including life, finance, industry, business, energy, and environment. Moreover, the performance of CMARS method is empirically compared to that of Classification and Regression Trees, Generalized Additive Models and Infinite Kernal Learning for classification, and to that of Multiple Linear Regression and MARS for prediction. For this purpose, real-life and simulation data sets with different characteristics such as size, the number and type of predictors, application areas are used. Comparative studies indicate that the CMARS method is a very promising tool for establishing computational models between variables of complex data sets. Yet, in other studies, CMARS have been improved and extended further. The improvement leads to the development of Bootstrapping CMARS method to build less complex CMARS models while the extension robustifies CMARS to enable modeling random input and output variables more precisely. To sum up, this review indicates that currently the CMARS method is a powerful alternative to the MARS algorithm as well as the other predictive data mining tools, and thus, deserves more attention to evaluate and develop it even further.

Fatma Yerlikaya-Özkurt, İnci Batmaz, Gerhard-Wilhelm Weber

### Chapter 41. Survey and Evaluation on Modelling of Next-Day Electricity Prices

Existing energy markets are evolving into competitive structures. Competitive structures dictate precise forecasting of next-day prices. Hence, next-day electricity price forecasting models are presented in this survey. Studies on next day electricity price forecasting are categorized as time-series methods, simulation and game-theory based methods. Considering the existence of explanatory variables and domain (time or frequency) of models, a new taxonomy is defined. Applications and theoretical improvements on forecasting of next day’s electricity price are presented. Different approaches are also highlighted to show their effects on tackling the forecasting issues and suppressing the disadvantages of classical methods.

Miray Hanım Yıldırım, Özlem Türker Bayrak, Gerhard-Wilhelm Weber

### Chapter 42. Calculus and “Digitalization” in Finance: Change of Time Method and Stochastic Taylor Expansion with Computation of Expectation

In this chapter, we give a review and new interpretations on the solution of stochastic differential equation by using the change of time method and the numerical solution with stochastic Taylor expansion. Firstly, a random time change is analyzed. Time change is one of the standard tools for building financial models. The process can be done by a subordinator or an absolutely continuous time change (CTM). The main results of CTM are covered in this chapter. It is applied on one of the important financial problems: Heston model, and to variance and volatility swap as well. In the second part, we focus on numerical simulation of stochastic differential equations arising from the stochastic Taylor series expansion. In order to get more accurate discrete schemes, more terms are added to the Taylor expansion. Application of Itô formula iteratively gives rise to multiple Itô integrals. As for the order of the numerical scheme, the expectations of the product of multiple Itô integrals are to be computed. We discuss the formula for the expectations of the products of Itô integrals. Throughout the chapter, we pay extra attention to the interplay between states and time, and to a “digitalization” of algebraic operations.

Fikriye Yılmaz, Hacer Öz, Gerhard-Wilhelm Weber
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