A geometric chracterization of the nucleolus of the assignment game

Maschler et al. (1979) caracteritzen geomètricament la intersecció del kernel i del core en els jocs cooperatius, demostrant que les distribucions que pertanyen a ambdós conjunts es troben en el punt mig d’un cert rang de negociació entre parelles de jugadors. En el cas dels jocs d’assignació, aquesta caracterització vol dir que el kernel només conté aquells elements del core on el màxim que un jugador pot transferir a una parella òptima és igual al màxim que aquesta parella li pot transferir, sense sortir-se’n del core. En aquest treball demostrem que el nucleolus d’un joc d’assignació queda caracteritzat si requerim que aquesta propietat de bisecció es compleixi no només per parelles, sinó també per coalicions entre sectors aparellades òptimament.

A geometric chracterization of the nucleolus of the assignment game

Maschler et al. (1979) caracteritzen geomètricament la intersecció del kernel i del core en els jocs cooperatius, demostrant que les distribucions que pertanyen a ambdós conjunts es troben en el punt mig d’un cert rang de negociació entre parelles de jugadors. En el cas dels jocs d’assignació, aquesta caracterització vol dir que el kernel només conté aquells elements del core on el màxim que un jugador pot transferir a una parella òptima és igual al màxim que aquesta parella li pot transferir, sense sortir-se’n del core. En aquest treball demostrem que el nucleolus d’un joc d’assignació queda caracteritzat si requerim que aquesta propietat de bisecció es compleixi no només per parelles, sinó també per coalicions entre sectors aparellades òptimament.

Coopetitive advantage – How firms create and appropriate value by collaborating with their competitors

Collaboration between competing firms (coopetition) has emerged as an important issue forn business practice in many industries. Extant literature has examined coopetition on many levels of analysis, but lacks clarity in distinguishing it explicitly from cooperation between noncompeting organizations. Because of this, the performance implications of coopetition from the perspective of an individual firm are still ambiguous – some research suggests positive results whereas other studies suggest detrimental outcomes. The aim in this dissertation is to narrow these gaps by exploring how firms create and appropriate value through collaboration with their competitors. The dissertation is divided into two parts. The first part comprises an overview of the relevant literature, as well as the conclusions of the whole study, and the second part includes six research publications. Both qualitative and quantitative methodologies are utilized. The results suggest that coopetition embodies the distinctive logic of value creation and appropriation from the perspective of an individual firm, and thus differs in terms of performance implications from cooperation between non-competitors. The distinction comes from the fact that competitors have somewhat similar understanding, capabilities and interest related to certain markets, which is potentially both challenging and beneficial in terms of the individual firm’s competitiveness. It appears from the findings that there are distinctive firm-external and firm-specific factors affecting the success of a coopetition strategy. This study makes three main contributions. First, on the conceptual level it shows the distinction between coopetition and cooperation between non-rivals as a collaborative inter-organizational relationship. Secondly, it sets out a framework and propositions that enhance understanding of how value is created and appropriated in coopetition from the perspective of an individual firm. Thirdly, it offers empirical evidence of how coopetition affects firms’ innovation and market performance, and identifies the focal internal and external factors involved. In general terms, the thesis adds to our knowledge of how a firm can successfully utilize a coopetition strategy in its pursuit of improved performance.

Spontaneous Focusing on Quantitative Relations and the Development of Rational Number Conceptual Knowledge

The aim of the present set of studies was to explore primary school children’s Spontaneous Focusing On quantitative Relations (SFOR) and its role in the development of rational number conceptual knowledge. The specific goals were to determine if it was possible to identify a spontaneous quantitative focusing tendency that indexes children’s tendency to recognize and utilize quantitative relations in non-explicitly mathematical situations and to determine if this tendency has an impact on the development of rational number conceptual knowledge in late primary school. To this end, we report on six original empirical studies that measure SFOR in children ages five to thirteen years and the development of rational number conceptual knowledge in ten- to thirteen-year-olds. SFOR measures were developed to determine if there are substantial differences in SFOR that are not explained by the ability to use quantitative relations. A measure of children’s conceptual knowledge of the magnitude representations of rational numbers and the density of rational numbers is utilized to capture the process of conceptual change with rational numbers in late primary school students. Finally, SFOR tendency was examined in relation to the development of rational number conceptual knowledge in these students. Study I concerned the first attempts to measure individual differences in children’s spontaneous recognition and use of quantitative relations in 86 Finnish children from the ages of five to seven years. Results revealed that there were substantial inter-individual differences in the spontaneous recognition and use of quantitative relations in these tasks. This was particularly true for the oldest group of participants, who were in grade one (roughly seven years old). However, the study did not control for ability to solve the tasks using quantitative relations, so it was not clear if these differences were due to ability or SFOR. Study II more deeply investigated the nature of the two tasks reported in Study I, through the use of a stimulated-recall procedure examining children’s verbalizations of how they interpreted the tasks. Results reveal that participants were able to verbalize reasoning about their quantitative relational responses, but not their responses based on exact number. Furthermore, participants’ non-mathematical responses revealed a variety of other aspects, beyond quantitative relations and exact number, which participants focused on in completing the tasks. These results suggest that exact number may be more easily perceived than quantitative relations. As well, these tasks were revealed to contain both mathematical and non-mathematical aspects which were interpreted by the participants as relevant. Study III investigated individual differences in SFOR 84 children, ages five to nine, from the US and is the first to report on the connection between SFOR and other mathematical abilities. The cross-sectional data revealed that there were individual differences in SFOR. Importantly, these differences were not entirely explained by the ability to solve the tasks using quantitative relations, suggesting that SFOR is partially independent from the ability to use quantitative relations. In other words, the lack of use of quantitative relations on the SFOR tasks was not solely due to participants being unable to solve the tasks using quantitative relations, but due to a lack of the spontaneous attention to the quantitative relations in the tasks. Furthermore, SFOR tendency was found to be related to arithmetic fluency among these participants. This is the first evidence to suggest that SFOR may be a partially distinct aspect of children’s existing mathematical competences. Study IV presented a follow-up study of the first graders who participated in Studies I and II, examining SFOR tendency as a predictor of their conceptual knowledge of fraction magnitudes in fourth grade. Results revealed that first graders’ SFOR tendency was a unique predictor of fraction conceptual knowledge in fourth grade, even after controlling for general mathematical skills. These results are the first to suggest that SFOR tendency may play a role in the development of rational number conceptual knowledge. Study V presents a longitudinal study of the development of 263 Finnish students’ rational number conceptual knowledge over a one year period. During this time participants completed a measure of conceptual knowledge of the magnitude representations and the density of rational numbers at three time points. First, a Latent Profile Analysis indicated that a four-class model, differentiating between those participants with high magnitude comparison and density knowledge, was the most appropriate. A Latent Transition Analysis reveal that few students display sustained conceptual change with density concepts, though conceptual change with magnitude representations is present in this group. Overall, this study indicated that there were severe deficiencies in conceptual knowledge of rational numbers, especially concepts of density. The longitudinal Study VI presented a synthesis of the previous studies in order to specifically detail the role of SFOR tendency in the development of rational number conceptual knowledge. Thus, the same participants from Study V completed a measure of SFOR, along with the rational number test, including a fourth time point. Results reveal that SFOR tendency was a predictor of rational number conceptual knowledge after two school years, even after taking into consideration prior rational number knowledge (through the use of residualized SFOR scores), arithmetic fluency, and non-verbal intelligence. Furthermore, those participants with higher-than-expected SFOR scores improved significantly more on magnitude representation and density concepts over the four time points. These results indicate that SFOR tendency is a strong predictor of rational number conceptual development in late primary school children. The results of the six studies reveal that within children’s existing mathematical competences there can be identified a spontaneous quantitative focusing tendency named spontaneous focusing on quantitative relations. Furthermore, this tendency is found to play a role in the development of rational number conceptual knowledge in primary school children. Results suggest that conceptual change with the magnitude representations and density of rational numbers is rare among this group of students. However, those children who are more likely to notice and use quantitative relations in situations that are not explicitly mathematical seem to have an advantage in the development of rational number conceptual knowledge. It may be that these students gain quantitative more and qualitatively better self-initiated deliberate practice with quantitative relations in everyday situations due to an increased SFOR tendency. This suggests that it may be important to promote this type of mathematical activity in teaching rational numbers. Furthermore, these results suggest that there may be a series of spontaneous quantitative focusing tendencies that have an impact on mathematical development throughout the learning trajectory.

Investigation of molecular polarizabilities and derivatives in halomethanes

The research undertaken was to obtain absolute Raman intensities for the symmetric stretching vibrations of the methyl halides, CH3X with (X=F, CI, Br), by experiment and theory. The intensities were experimentally measured using the Ar+ ion gas laser as excitation source, a Spex 14018 double monochromator and a RCA C-31034 photomultiplier tube as detector. These intensities arise from changes in the derivative of the polarizability (8 a'), with respect to vibration along a normal coordinate (8qi). It was intended that these derivatives obtained with respect to normal coordinates would be converted to derivatives with respect to internal coordinates, for a quantitative comparison with theory. Theoretical numerical polarizability derivatives for the stretching vibrations are obtained using the following procedure. A vibration was simulated in the molecule by increasi.ng and decreasing the respective bond by the amount ±o.oosA for the C-H bonds and ±o.oIA for the C-X (X=F, CI, Br) bond. The derivative was obtained by taking the difference in the polarizability for the equilibrium geometry and the geometry when a particular bond is changed. This difference, when divided by the amount of change in each bond and the number of bonds present results in the derivative of the polarizability with respect to internal coordinate i.e., !1u/!1r. These derivatives were obtained by two methods: I} ab initio molecular orbital calculation and 2} theory of atoms in molecules (AIM) analysis. Due to errors in the experimental setup only a qualitative analysis of the results was undertaken relative to the theory. Theoretically it is predicted that the symmetric carbonhalogen stretch vibrations are more intense than the respective carbon-hydrogen stretch, but only for the methyl chloride and bromide. The carbon fluorine stretch is less intense than the carbon-hydrogen stretch, a fact which is attributed to the small size and high electronegativity of the fluorine atom. The experimental observations are seen to agree qualitatively with the theory results. It is hoped that when the experiment is repeated, a quantitative comparison can be made. The analysis by the theory of atoms in molecules, along with providing polarizabilities and polarizability derivatives, gives additional information outlined below. The theory provides a pictorial description of the main factors contributing to the molecular polarizability and polarizability derivative. These contributions are from the charge transfer and atomic dipole terms i.e., transfer of charge from one atom to another and the reorganization of atomic electronic charge distribution due to presence of an electric field. The linear relationship between polarizability and molecular volume was also observed.

Investigations on the Dynamics of Combination Maps and the Analysis of Bifurcation in a Discontinuous Logistic Map

This thesis is a study of discrete nonlinear systems represented by one dimensional mappings.As one dimensional interative maps represent Poincarre sections of higher dimensional flows,they offer a convenient means to understand the dynamical evolution of many physical systems.It highlighting the basic ideas of deterministic chaos.Qualitative and quantitative measures for the detection and characterization of chaos in nonlinear systems are discussed.Some simple mathematical models exhibiting chaos are presented.The bifurcation scenario and the possible routes to chaos are explained.It present the results of the numerical computational of the Lyapunov exponents (λ) of one dimensional maps.This thesis focuses on the results obtained by our investigations on combinations maps,scaling behaviour of the Lyapunov characteristic exponents of one dimensional maps and the nature of bifurcations in a discontinous logistic map.It gives a review of the major routes to chaos in dissipative systems,namely, Period-doubling ,Intermittency and Crises.This study gives a theoretical understanding of the route to chaos in discontinous systems.A detailed analysis of the dynamics of a discontinous logistic map is carried out, both analytically and numerically ,to understand the route it follows to chaos.The present analysis deals only with the case of the discontinuity parameter applied to the right half of the interval of mapping.A detailed analysis for the n –furcations of various periodicities can be made and a more general theory for the map with discontinuities applied at different positions can be on a similar footing

Electronic and magnetic structure of LaMnO3 from hybrid periodic density-functional theory

The electronic and magnetic structures of the LaMnO3 compound have been studied by means of periodic calculations within the framework of spin polarized hybrid density-functional theory. In order to quantify the role of approximations to electronic exchange and correlation three different hybrid functionals have been used which mix nonlocal Fock and local Dirac-Slater exchange. Periodic Hartree-Fock results are also reported for comparative purposes. The A-antiferromagnetic ground state is properly predicted by all methods including Hartree-Fock exchange. In general, the different hybrid methods provide a rather accurate description of the band gap and of the two magnetic coupling constants, strongly suggesting that the corresponding description of the electronic structure is also accurate. An important conclusion emerging from this study is that the nature of the occupied states near the Fermi level is intermediate between the Hartree-Fock and local density approximation descriptions with a comparable participation of both Mn and O states.

Study on period search methods of variable stars: Application to ASAS and CRTS databases

Study on variable stars is an important topic of modern astrophysics. After the invention of powerful telescopes and high resolving powered CCD’s, the variable star data is accumulating in the order of peta-bytes. The huge amount of data need lot of automated methods as well as human experts. This thesis is devoted to the data analysis on variable star’s astronomical time series data and hence belong to the inter-disciplinary topic, Astrostatistics. For an observer on earth, stars that have a change in apparent brightness over time are called variable stars. The variation in brightness may be regular (periodic), quasi periodic (semi-periodic) or irregular manner (aperiodic) and are caused by various reasons. In some cases, the variation is due to some internal thermo-nuclear processes, which are generally known as intrinsic vari- ables and in some other cases, it is due to some external processes, like eclipse or rotation, which are known as extrinsic variables. Intrinsic variables can be further grouped into pulsating variables, eruptive variables and flare stars. Extrinsic variables are grouped into eclipsing binary stars and chromospheri- cal stars. Pulsating variables can again classified into Cepheid, RR Lyrae, RV Tauri, Delta Scuti, Mira etc. The eruptive or cataclysmic variables are novae, supernovae, etc., which rarely occurs and are not periodic phenomena. Most of the other variations are periodic in nature. Variable stars can be observed through many ways such as photometry, spectrophotometry and spectroscopy. The sequence of photometric observa- xiv tions on variable stars produces time series data, which contains time, magni- tude and error. The plot between variable star’s apparent magnitude and time are known as light curve. If the time series data is folded on a period, the plot between apparent magnitude and phase is known as phased light curve. The unique shape of phased light curve is a characteristic of each type of variable star. One way to identify the type of variable star and to classify them is by visually looking at the phased light curve by an expert. For last several years, automated algorithms are used to classify a group of variable stars, with the help of computers. Research on variable stars can be divided into different stages like observa- tion, data reduction, data analysis, modeling and classification. The modeling on variable stars helps to determine the short-term and long-term behaviour and to construct theoretical models (for eg:- Wilson-Devinney model for eclips- ing binaries) and to derive stellar properties like mass, radius, luminosity, tem- perature, internal and external structure, chemical composition and evolution. The classification requires the determination of the basic parameters like pe- riod, amplitude and phase and also some other derived parameters. Out of these, period is the most important parameter since the wrong periods can lead to sparse light curves and misleading information. Time series analysis is a method of applying mathematical and statistical tests to data, to quantify the variation, understand the nature of time-varying phenomena, to gain physical understanding of the system and to predict future behavior of the system. Astronomical time series usually suffer from unevenly spaced time instants, varying error conditions and possibility of big gaps. This is due to daily varying daylight and the weather conditions for ground based observations and observations from space may suffer from the impact of cosmic ray particles. Many large scale astronomical surveys such as MACHO, OGLE, EROS, xv ROTSE, PLANET, Hipparcos, MISAO, NSVS, ASAS, Pan-STARRS, Ke- pler,ESA, Gaia, LSST, CRTS provide variable star’s time series data, even though their primary intention is not variable star observation. Center for Astrostatistics, Pennsylvania State University is established to help the astro- nomical community with the aid of statistical tools for harvesting and analysing archival data. Most of these surveys releases the data to the public for further analysis. There exist many period search algorithms through astronomical time se- ries analysis, which can be classified into parametric (assume some underlying distribution for data) and non-parametric (do not assume any statistical model like Gaussian etc.,) methods. Many of the parametric methods are based on variations of discrete Fourier transforms like Generalised Lomb-Scargle peri- odogram (GLSP) by Zechmeister(2009), Significant Spectrum (SigSpec) by Reegen(2007) etc. Non-parametric methods include Phase Dispersion Minimi- sation (PDM) by Stellingwerf(1978) and Cubic spline method by Akerlof(1994) etc. Even though most of the methods can be brought under automation, any of the method stated above could not fully recover the true periods. The wrong detection of period can be due to several reasons such as power leakage to other frequencies which is due to finite total interval, finite sampling interval and finite amount of data. Another problem is aliasing, which is due to the influence of regular sampling. Also spurious periods appear due to long gaps and power flow to harmonic frequencies is an inherent problem of Fourier methods. Hence obtaining the exact period of variable star from it’s time series data is still a difficult problem, in case of huge databases, when subjected to automation. As Matthew Templeton, AAVSO, states “Variable star data analysis is not always straightforward; large-scale, automated analysis design is non-trivial”. Derekas et al. 2007, Deb et.al. 2010 states “The processing of xvi huge amount of data in these databases is quite challenging, even when looking at seemingly small issues such as period determination and classification”. It will be beneficial for the variable star astronomical community, if basic parameters, such as period, amplitude and phase are obtained more accurately, when huge time series databases are subjected to automation. In the present thesis work, the theories of four popular period search methods are studied, the strength and weakness of these methods are evaluated by applying it on two survey databases and finally a modified form of cubic spline method is intro- duced to confirm the exact period of variable star. For the classification of new variable stars discovered and entering them in the “General Catalogue of Vari- able Stars” or other databases like “Variable Star Index“, the characteristics of the variability has to be quantified in term of variable star parameters.

The Kineticist's Workbench: Combining Symbolic and Numerical Methods in the Simulation of Chemical Reaction Mechanisms

The Kineticist's Workbench is a program that simulates chemical reaction mechanisms by predicting, generating, and interpreting numerical data. Prior to simulation, it analyzes a given mechanism to predict that mechanism's behavior; it then simulates the mechanism numerically; and afterward, it interprets and summarizes the data it has generated. In performing these tasks, the Workbench uses a variety of techniques: graph- theoretic algorithms (for analyzing mechanisms), traditional numerical simulation methods, and algorithms that examine simulation results and reinterpret them in qualitative terms. The Workbench thus serves as a prototype for a new class of scientific computational tools---tools that provide symbiotic collaborations between qualitative and quantitative methods.

Networked Life: Module CIS 112, University of Pennsylvania, Spring 2008

What kind of science is appropriate for understanding the Facebook? How does Google find what you're looking for... ...and exactly how do they make money doing so? What structural properties might we expect any social network to have? How does your position in an economic network (dis)advantage you? How are individual and collective behavior related in complex networks? What might we mean by the economics of spam? What do game theory and the Paris subway have to do with Internet routing? What's going on in the pictures to the left and right? Networked Life looks at how our world is connected -- socially, economically, strategically and technologically -- and why it matters. The answers to the questions above are related. They have been the subject of a fascinating intersection of disciplines including computer science, physics, psychology, mathematics, economics and finance. Researchers from these areas all strive to quantify and explain the growing complexity and connectivity of the world around us, and they have begun to develop a rich new science along the way. Networked Life will explore recent scientific efforts to explain social, economic and technological structures -- and the way these structures interact -- on many different scales, from the behavior of individuals or small groups to that of complex networks such as the Internet and the global economy. This course covers computer science topics and other material that is mathematical, but all material will be presented in a way that is accessible to an educated audience with or without a strong technical background. The course is open to all majors and all levels, and is taught accordingly. There will be ample opportunities for those of a quantitative bent to dig deeper into the topics we examine. The majority of the course is grounded in scientific and mathematical findings of the past two decades or less.

On the exhaustiveness of truncation and dropping strategies in many-to-many matching markets

We consider two–sided many–to–many matching markets in which each worker may work for multiple firms and each firm may hire multiple workers. We study individual and group manipulations in centralized markets that employ (pairwise) stable mechanisms and that require participants to submit rank order lists of agents on the other side of the market. We are interested in simple preference manipulations that have been reported and studied in empirical and theoretical work: truncation strategies, which are the lists obtained by removing a tail of least preferred partners from a preference list, and the more general dropping strategies, which are the lists obtained by only removing partners from a preference list (i.e., no reshuffling). We study when truncation / dropping strategies are exhaustive for a group of agents on the same side of the market, i.e., when each match resulting from preference manipulations can be replicated or improved upon by some truncation / dropping strategies. We prove that for each stable mechanism, truncation strategies are exhaustive for each agent with quota 1 (Theorem 1). We show that this result cannot be extended neither to group manipulations (even when all quotas equal 1 – Example 1), nor to individual manipulations when the agent’s quota is larger than 1 (even when all other agents’ quotas equal 1 – Example 2). Finally, we prove that for each stable mechanism, dropping strategies are exhaustive for each group of agents on the same side of the market (Theorem 2), i.e., independently of the quotas.

Real options and game theoretical approaches to real estate development projects: multiple equilibria and the implications of different tie-breaking rules

This paper contributes to a fast growing literature which introduces game theory in the analysis of real option investments in a competitive setting. Specifically, in this paper we focus on the issue of multiple equilibria and on the implications that different equilibrium selections may have for the pricing of real options and for subsequent strategic decisions. We present some theoretical results of the necessary conditions to have multiple equilibria and we show under which conditions different tie-breaking rules result in different economic decisions. We then present a numerical exercise using the in formation set obtained on a real estate development in South London. We find that risk aversion reduces option value and this reduction decreases marginally as negative externalities decrease.

Markov models of aging: theory and practice

We review and structure some of the mathematical and statistical models that have been developed over the past half century to grapple with theoretical and experimental questions about the stochastic development of aging over the life course. We suggest that the mathematical models are in large part addressing the problem of partitioning the randomness in aging: How does aging vary between individuals, and within an individual over the lifecourse? How much of the variation is inherently related to some qualities of the individual, and how much is entirely random? How much of the randomness is cumulative, and how much is merely short-term flutter? We propose that recent lines of statistical inquiry in survival analysis could usefully grapple with these questions, all the more so if they were more explicitly linked to the relevant mathematical and biological models of aging. To this end, we describe points of contact among the various lines of mathematical and statistical research. We suggest some directions for future work, including the exploration of information-theoretic measures for evaluating components of stochastic models as the basis for analyzing experiments and anchoring theoretical discussions of aging.

Lie algebra methods for the applications to the statistical theory of turbulence

Approximate Lie symmetries of the Navier-Stokes equations are used for the applications to scaling phenomenon arising in turbulence. In particular, we show that the Lie symmetries of the Euler equations are inherited by the Navier-Stokes equations in the form of approximate symmetries that allows to involve the Reynolds number dependence into scaling laws. Moreover, the optimal systems of all finite-dimensional Lie subalgebras of the approximate symmetry transformations of the Navier-Stokes are constructed. We show how the scaling groups obtained can be used to introduce the Reynolds number dependence into scaling laws explicitly for stationary parallel turbulent shear flows. This is demonstrated in the framework of a new approach to derive scaling laws based on symmetry analysis [11]-[13].