Social influence, negotiation and cognition

To understand how personal agreements can be generated within complexly differentiated social systems, we develop an agent-based computational model of negotiation in which social influence plays a key role in the attainment of social and cognitive integration. The model reflects a view of social influence that is predicated on the interactions among such factors as the agents' cognition, their abilities to initiate and maintain social behaviour, as well as the structural patterns of social relations in which influence unfolds. Findings from a set of computer simulations of the model show that the degree to which agents are influenced depends on the network of relations in which they are located, on the order in which interactions occur, and on the type of information that these interactions convey. We also find that a fundamental role in explaining influence is played by how inclined the agents are to be concilatory with each other, how accurate their beliefs are, and how self-confident they are in dealing with their social interactions. Moreover, the model provides insights into the trade-offs typically involved in the exercise of social influence

The spectroscopic Hertzsprung-Russell diagram

The Hertzsprung-Russell diagram is an essential diagnostic diagram for stellar structure and evolution, which has now been in use for more than 100 years. Our spectroscopic Hertzsprung-Russell (sHR) diagram shows the inverse of the flux-mean gravity versus the effective temperature. Observed stars whose spectra have been quantitatively analyzed can be entered in this diagram without the knowledge of the stellar distance or absolute brightness. Observed stars can be as conveniently compared to stellar evolution calculations in the sHR diagram as in the Hertzsprung-Russell diagram. However, at the same time, our ordinate is proportional to the stellar mass-to-luminosity ratio, which can thus be directly determined. For intermediate- and low-mass star evolution at constant mass, we show that the shape of an evolutionary track in the sHR diagram is identical to that in the Hertzsprung-Russell diagram. We also demonstrate that for hot stars, their stellar Eddington factor can be directly read off the sHR diagram. For stars near their Eddington limit, we argue that a version of the sHR diagram may be useful where the gravity is exchanged by the effective gravity. We discuss the advantages and limitations of the sHR diagram, and show that it can be fruitfully applied to Galactic stars, but also to stars with known distance, e.g., in the LMC or in galaxies beyond the Local Group.Comment: 9 pages, 8 figures, Astronomy and Astrophysics, in pres

Hodge theory and derived categories of cubic fourfolds

Cubic fourfolds behave in many ways like K3 surfaces. Certain cubics - conjecturally, the ones that are rational - have specific K3s associated to them geometrically. Hassett has studied cubics with K3s associated to them at the level of Hodge theory, and Kuznetsov has studied cubics with K3s associated to them at the level of derived categories. These two notions of having an associated K3 should coincide. We prove that they coincide generically: Hassett's cubics form a countable union of irreducible Noether-Lefschetz divisors in moduli space, and we show that Kuznetsov's cubics are a dense subset of these, forming a non-empty, Zariski open subset in each divisor.Comment: 37 pages. Applications to algebraic cycles added, and other improvements following referees' suggestions. This is a slightly expanded version of the paper to appear in Duke Math

Competition and innovation: an inverted U relationship

This paper investigates the relationship between product market competition (PMC) and innovation. A Schumpeterian growth model is developed in which firms innovate ‘step-by-step’, and where both technological leaders and their followers engage in R&D activities. In this model, competition may increase the incremental profit from innovating; on the other hand, competition may also reduce innovation incentives for laggards. This model generates four main predictions which we test empirically. First, the relationship between product market competition (PMC) and innovation is an inverted U-shape: the escape competition effect dominates for low initial levels of competition, whereas the Schumpeterian effect dominates at higher levels of competition. Second, the equilibrium degree of technological ‘neck-and-neckness’ among firms should decrease with PMC. Third, the higher the average degree of ‘neck-and-neckness’ in an industry, the steeper the inverted-U relationship between PMC and innovation in that industry. Fourth, firms may innovate more if subject to higher debt-pressure, especially at lower levels of PMC. We confront these four predictions with a new panel data set on UK firms’ patenting activity at the US patenting office. The inverted U relationship, the neck and neck, and the debt pressure predictions are found to accord well with observed behavior in the data

Competition and innovation: an inverted U relationship?

This paper investigates the relationship between product market competition and innovation. It uses the radical policy reforms in the UK as instruments for changes in product market competition, and finds a robust inverted-U relationship between competition and patenting. It then develops an endogenous growth model with step-by-step innovation that can deliver this inverted-U pattern. In this model, competition has an ambiguous effect on innovation. On the one hand, it discourages laggard firms from innovating, as it reduces their rents from catching up with the leaders in the same industry. On the other hand, it encourages neck-and-neck firms to innovate in order to escape competition with their rival. The inverted-U pattern results from the interplay between these two effects, together with the effect of competition on the equilibrium industry structure. The model generates two additional predictions: on the relationship between competition and the average technological distance between leaders and followers across industries; and on the relationship between the distance of an industry to its technological frontier and the steepness of the inverted-U. Both predictions are supported by the data

The organisation of sociality: a manifesto for a new science of multi-agent systems

In this paper, we pose and motivate a challenge, namely the need for a new science of multi-agent systems. We propose that this new science should be grounded, theoretically on a richer conception of sociality, and methodologically on the extensive use of computational modelling for real-world applications and social simulations. Here, the steps we set forth towards meeting that challenge are mainly theoretical. In this respect, we provide a new model of multi-agent systems that reflects a fully explicated conception of cognition, both at the individual and the collective level. Finally, the mechanisms and principles underpinning the model will be examined with particular emphasis on the contributions provided by contemporary organisation theory

The contact angle in inviscid fluid mechanics

We show that in general, the specification of a contact angle condition at the contact line in inviscid fluid motions is incompatible with the classical field equations and boundary conditions generally applicable to them. The limited conditions under which such a specification is permissible are derived; however, these include cases where the static meniscus is not flat. In view of this situation, the status of the many `solutions' in the literature which prescribe a contact angle in potential flows comes into question. We suggest that these solutions which attempt to incorporate a phenomenological, but incompatible, condition are in some, imprecise sense `weak-type solutions'; they satisfy or are likely to satisfy, at least in the limit, the governing equations and boundary conditions everywhere except in the neighbourhood of the contact line. We discuss the implications of the result for the analysis of inviscid flows with free surfaces.Comment: 13 pages, no figures, no table

Machine-z: Rapid Machine Learned Redshift Indicator for Swift Gamma-ray Bursts

Studies of high-redshift gamma-ray bursts (GRBs) provide important information about the early Universe such as the rates of stellar collapsars and mergers, the metallicity content, constraints on the re-ionization period, and probes of the Hubble expansion. Rapid selection of high-z candidates from GRB samples reported in real time by dedicated space missions such as Swift is the key to identifying the most distant bursts before the optical afterglow becomes too dim to warrant a good spectrum. Here we introduce "machine-z", a redshift prediction algorithm and a "high-z" classifier for Swift GRBs based on machine learning. Our method relies exclusively on canonical data commonly available within the first few hours after the GRB trigger. Using a sample of 284 bursts with measured redshifts, we trained a randomized ensemble of decision trees (random forest) to perform both regression and classification. Cross-validated performance studies show that the correlation coefficient between machine-z predictions and the true redshift is nearly 0.6. At the same time our high-z classifier can achieve 80% recall of true high-redshift bursts, while incurring a false positive rate of 20%. With 40% false positive rate the classifier can achieve ~100% recall. The most reliable selection of high-redshift GRBs is obtained by combining predictions from both the high-z classifier and the machine-z regressor.Comment: Accepted to the Monthly Notices of the Royal Astronomical Society Journal (10 pages, 10 figures, and 3 Tables