Existence of periodic orbits near heteroclinic connections

We consider a potential $W:R^m\rightarrow R$ with two different global minima $a_-, a_+$ and, under a symmetry assumption, we use a variational approach to show that the Hamiltonian system \begin{equation} \ddot{u}=W_u(u), \hskip 2cm (1) \end{equation} has a family of $T$-periodic solutions $u^T$ which, along a sequence $T_j\rightarrow+\infty$, converges locally to a heteroclinic solution that connects $a_-$ to $a_+$. We then focus on the elliptic system \begin{equation} \Delta u=W_u(u),\;\; u:R^2\rightarrow R^m, \hskip 2cm (2) \end{equation} that we interpret as an infinite dimensional analogous of (1), where $x$ plays the role of time and $W$ is replaced by the action functional $$J_R(u)=\int_R\Bigl(\frac{1}{2}\vert u_y\vert^2+W(u)\Bigr)dy.$$ We assume that $J_R$ has two different global minimizers $\bar{u}_-, \bar{u}_+:R\rightarrow R^m$ in the set of maps that connect $a_-$ to $a_+$. We work in a symmetric context and prove, via a minimization procedure, that (2) has a family of solutions $u^L:R^2\rightarrow R^m$, which is $L$-periodic in $x$, converges to $a_\pm$ as $y\rightarrow\pm\infty$ and, along a sequence $L_j\rightarrow+\infty$, converges locally to a heteroclinic solution that connects $\bar{u}_-$ to $\bar{u}_+$.Comment: 36 pages, 4 figure

Plenty of Fish in the Sea: Divorce Choice and the Quality of Singles

In the literature of marriage, divorce choices are usually assumed to not affect the distribution of types in the pool of singles. The scope of the present paper is to overcome this assumption. We analyse divorce choices when separation decision influences the distribution of singles and, thus, their expected quality. We consider a three-period model where heterogeneous individuals may unilaterally experience divorce and return to the marriage market. The choices of individuals are based on the change in the distribution of singles and the cost of waiting and divorcing, taking into consideration the individual’s eligibility in the marriage market. There are two main findings: Firstly, positive assortative matching dissolves with divorce for some intermediate types. Therefore, the endogenous positive assortative matching that usually emerges in models with nontransferable utility is weakened when matches can dissolve. Secondly, the existence of ranges where divorce emerges among individuals with positive assortative matching implies the existence of two disconnected classes of types. If matchings in the first period were to occur between individuals of different classes, such matches would be dissolved later

On the existence of connecting orbits for critical values of the energy

We consider an open connected set Ω and a smooth potential U which is positive in Ω and vanishes on â\u88\u82Ω. We study the existence of orbits of the mechanical system u¨=Ux(u), that connect different components of â\u88\u82Ω and lie on the zero level of the energy. We allow that â\u88\u82Ω contains a finite number of critical points of U. The case of symmetric potential is also considered

Simulating the Cost of Cooperation: A Recipe for Collaborative Problem-Solving

Collective problem-solving and decision-making, along with other forms of collaboration online, are central phenomena within ICT. There had been several attempts to create a system able to go beyond the passive accumulation of data. However, those systems often neglect important variables such as group size, the difficulty of the tasks, the tendency to cooperate, and the presence of selfish individuals (free riders). Given the complex relations among those variables, numerical simulations could be the ideal tool to explore such relationships. We take into account the cost of cooperation in collaborative problem solving by employing several simulated scenarios. The role of two parameters was explored: the capacity, the group’s capability to solve increasingly challenging tasks coupled with the collective knowledge of a group, and the payoff, an individual’s own benefit in terms of new knowledge acquired. The final cooperation rate is only affected by the cost of cooperation in the case of simple tasks and small communities. In contrast, the fitness of the community, the difficulty of the task, and the groups sizes interact in a non-trivial way, hence shedding some light on how to improve crowdsourcing when the cost of cooperation is high

About Linda Again: How Narratives and Group Reasoning Can Influence Conjunction Fallacy

Conjunction fallacy (together with other systematic reasoning errors) is usually explained in terms of the dual process theory of reasoning: Biases should be ascribed to fast and automatic processes, whereas slow and deliberative processes are responsible of producing answers that are correct with respect of normative criterion. The dual process theory is related to Bruner’s distinction between narrative and paradigmatic thought: Both modes of thought can be characterized by the two different processes of reasoning. In this paper, we explore the role of Bruner’s mode of thought manipulating also the difference between group vs individual reasoning. We observed that the narrative strategy of response induces more wrong answers. However, narrative-based strategies have higher effectiveness in the case of group reasoning. Our results suggest that narrative reasoning and group reasoning may induce violations of the conjunction rule when acceptable by the verisimilitude of the story. Five models are also presented in order to predict answer correctness and strategy of reasoning using a text analysis software

Modeling the overalternating bias with an asymmetric entropy measure

Psychological research has found that human perception of randomness is biased. In particular, people consistently show the overalternating bias: they rate binary sequences of symbols (such as Heads and Tails in coin flipping) with an excess of alternation as more random than prescribed by the normative criteria of Shannon's entropy. Within data mining for medical applications, Marcellin proposed an asymmetric measure of entropy that can be ideal to account for such bias and to quantify subjective randomness. We fitted Marcellin's entropy and Renyi's entropy (a generalized form of uncertainty measure comprising many different kinds of entropies) to experimental data found in the literature with the Differential Evolution algorithm. We observed a better fit for Marcellin's entropy compared to Renyi's entropy. The fitted asymmetric entropy measure also showed good predictive properties when applied to different datasets of randomness-related tasks. We concluded that Marcellin's entropy can be a parsimonious and effective measure of subjective randomness that can be useful in psychological research about randomness perception

Prevalence and Determinants of Bad Sleep Perception among Italian Children and Adolescents

Although sleep problems at young ages are well investigated, the prevalence of bad sleepers and the determinants of sleep quality perception remain unexplored in these populations. For this purpose, we addressed these issues in a sample of children (n = 307), preadolescents (n = 717), and adolescents (n = 406) who completed the School Sleep Habits Survey, addressing sleep quality perception, sleep habits, sleep features, daytime behavior and sleep disturbances, circadian preference, and dreaming. The sample was split in "good sleepers" and "bad sleepers", based on the answer to the question item assessing overall subjective sleep quality. Being a bad sleeper was reported by 11.7% of the sample, with significant between-groups differences (children: 8.3%; preadolescents: 11.3%; adolescents: 15.3%; p = 0.01). At all ages, relative to good sleepers, bad sleepers showed higher eveningness, sleepiness, and depression, longer sleep latency, more frequent insufficient sleep, nocturnal awakenings, sleep-wake behavioral problems, and unpleasant dreams (all p's ≤ 0.01). Sleep quality perception was predicted: in children, by depressed mood, eveningness, and unpleasant dreams (all p's ≤ 0.01); in preadolescents, by sleep latency, awakening frequency, depressed mood, sufficiency of sleep, and unpleasant dreams (all p's < 0.01); in adolescents, by awakening frequency, depressed mood, and sufficiency of sleep (all p's < 0.001). In children, bad subjective sleep quality appears to be mainly determined by daytime psychological features, for example, depressed mood, whereas at later ages, sleep characteristics, such as frequent awakenings, add to the former determinants. This could depend on (a) the appearance, with increasing age, of objective sleep modifications and (b) a greater attention paid by adolescents to their sleep characteristics