Pendulum Integration and Elliptic Functions

Revisiting canonical integration of the classical pendulum around its unstable equilibrium, normal hyperbolic canonical coordinates are constructe

Persistence of Diophantine flows for quadratic nearly-integrable Hamiltonians under slowly decaying aperiodic time dependence

The aim of this paper is to prove a Kolmogorov-type result for a nearly-integrable Hamiltonian, quadratic in the actions, with an aperiodic time dependence. The existence of a torus with a prefixed Diophantine frequency is shown in the forced system, provided that the perturbation is real-analytic and (exponentially) decaying with time. The advantage consists of the possibility to choose an arbitrarily small decaying coefficient, consistently with the perturbation size.Comment: Several corrections in the proof with respect to the previous version. Main statement unchange

A rigorous implementation of the Jeans--Landau--Teller approximation

Rigorous bounds on the rate of energy exchanges between vibrational and translational degrees of freedom are established in simple classical models of diatomic molecules. The results are in agreement with an elementary approximation introduced by Landau and Teller. The method is perturbative theory ``beyond all orders'', with diagrammatic techniques (tree expansions) to organize and manipulate terms, and look for compensations, like in recent studies on KAM theorem homoclinic splitting.Comment: 23 pages, postscrip

Fractional Lindstedt series

The parametric equations of the surfaces on which highly resonant quasi-periodic motions develop (lower-dimensional tori) cannot be analytically continued, in general, in the perturbation parameter, i.e. they are not analytic functions of the perturbation parameter. However rather generally quasi-periodic motions whose frequencies satisfy only one rational relation ("resonances of order 1") admit formal perturbation expansions in terms of a fractional power of the perturbation parameter, depending on the degeneration of the resonance. We find conditions for this to happen, and in such a case we prove that the formal expansion is convergent after suitable resummation.Comment: 40 pages, 6 figure

Age-related changes in the impact of valence on self-referential processing in female adolescents and young adults

Adolescence is a period of self-concept development. In the current study, females aged 11–30 years (N = 210) completed two self-referential tasks. In a memory task, participants judged the descriptiveness of words for themselves or a familiar other and their recognition of these words was subsequently measured. In an associative-matching task, participants associated neutral shapes to either themselves or a familiar other and the accuracy of their matching judgements was measured. In the evaluative memory task, participants were more likely to remember self-judged than other-judged words and there was an age-related decrease in the size of this self-reference effect. Negative self-judgements showed a quadratic association with age, peaking around age 19. Participants were more likely to remember positive than negative words and there was an age-related increase in the magnitude of this positivity bias. In the neutral shapes task, there were no age-related changes in the self-reference effect. Overall, adolescent girls showed enhanced processing of self-relevant stimuli when it could be used to inform their self-concept and especially when it was negative

Motives and comprehension in a public goods game with induced emotions

This study analyses the sensitivity of public goods contributions through the lens of psychological motives. We report the results of a public goods experiment in which subjects were induced with the motives of care and anger through autobiographical recall. Subjects’ preferences, beliefs, and perceptions under each motive are compared with those of subjects experiencing a neutral autobiographical recall control condition. We find, but only for those subjects with the highest comprehension of the game, that care elicits significantly higher contributions than anger, with the control treatment in between. This positive influence of the care motive on unconditional giving is accounted for partly by preferences for giving and partly by beliefs concerning greater contributions by others. Anger also affects attention to own and other’s payoffs (measured by mouse tracking) and perceptions of the game’s incentive structure (cooperative or competitive)

Aspects of the planetary Birkhoff normal form

The discovery in [G. Pinzari. PhD thesis. Univ. Roma Tre. 2009], [L. Chierchia and G. Pinzari, Invent. Math. 2011] of the Birkhoff normal form for the planetary many--body problem opened new insights and hopes for the comprehension of the dynamics of this problem. Remarkably, it allowed to give a {\sl direct} proof of the celebrated Arnold's Theorem [V. I. Arnold. Uspehi Math. Nauk. 1963] on the stability of planetary motions. In this paper, using a "ad hoc" set of symplectic variables, we develop an asymptotic formula for this normal form that may turn to be useful in applications. As an example, we provide two very simple applications to the three-body problem: we prove a conjecture by [V. I. Arnold. cit] on the "Kolmogorov set"of this problem and, using Nehoro{\v{s}}ev Theory [Nehoro{\v{s}}ev. Uspehi Math. Nauk. 1977], we prove, in the planar case, stability of all planetary actions over exponentially-long times, provided mean--motion resonances are excluded. We also briefly discuss perspectives and problems for full generalization of the results in the paper.Comment: 44 pages. Keywords: Averaging Theory, Birkhoff normal form, Nehoro{\v{s}}ev Theory, Planetary many--body problem, Arnold's Theorem on the stability of planetary motions, Properly--degenerate kam Theory, steepness. Revised version, including Reviewer's comments. Typos correcte

Cooperation across multiple game theoretical paradigms is increased by fear more than anger in selfish individuals.

Cooperative decisions are well predicted by stable individual differences in social values but it remains unclear how they may be modulated by emotions such as fear and anger. Moving beyond specific decision paradigms, we used a suite of economic games and investigated how experimental inductions of fear or anger affect latent factors of decision making in individuals with selfish or prosocial value orientations. We found that, relative to experimentally induced anger, induced fear elicited higher scores on a cooperation factor, and that this effect was entirely driven by selfish participants. In fact, induced fear brought selfish individuals to cooperate similarly to prosocial individuals, possibly as a (selfish) mean to seek protection in others. These results suggest that two basic threat-related emotions, fear and anger, differentially affect a generalized form of cooperation and that this effect is buffered by prosocial value orientation

Overlapping mechanisms in implying and inferring

Prior psychological work on Gricean implicature has revealed much about how listeners infer (comprehension) but little about how speakers imply (production). This is surprising given the inherent link between the two. This study aimed to obtain a more integral understanding of implicatures by investigating the processes that are shared between inference and implication. In two experiments, a participant and a confederate engaged in a dialogue game that invited the use of implicatures. In each there was a global priming manipulation, in which a confederate predominantly used implicit or explicit utterances, and a local priming manipulation, in which the utterance structure varied from trial to trial. Participants could choose whether to imply or use an explicit expression. Our results revealed that speaker and listener align on their use of implicatures. We interpret the local priming results as providing evidence of shared implicature representations between speaker and listener, and the global priming results as a form of audience design. We also present a model of implicature production that explains our findings

Resummation of perturbation series and reducibility for Bryuno skew-product flows

We consider skew-product systems on T^d x SL(2,R) for Bryuno base flows close to constant coefficients, depending on a parameter, in any dimension d, and we prove reducibility for a large measure set of values of the parameter. The proof is based on a resummation procedure of the formal power series for the conjugation, and uses techniques of renormalisation group in quantum field theory.Comment: 30 pages, 12 figure