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We study the average long-time behavior of the binary opinions of a social group with peer-to-peer interactions under the influence of an external bias and a persuadable leader, a strongly-biased agent with a dynamic opinion with the intention of spreading it across the system. We use a generalized, fully-connected Ising model, with each spin representing the binary opinion of an agent at a given time and a single, super spin representing the opinion of the leader. External fields and interaction constants model the opinion bias and peer-to-peer interactions, respectively, while the temperature $T$ models an idealized social climate, representing an authoritarian regime if $T$ is low or a liberal one if $T$ is high. We derive a mean-field solution for the average magnetization $m$, the "social mood", and investigate how $m$ and the super spin magnetization vary as a function of $T$. We find that, depending on the initial conditions, due to the presence of metastable states, the sign of the average magnetization depends on the temperature. Finally, we verify that this effect is also present even if we consider only nearest-neighbor interactions within the social group.

Despite being responsible for state-of-the-art results in several computer vision and natural language processing tasks, neural networks have faced harsh criticism due to some of their current shortcomings. One of them is that neural networks are correlation machines prone to model biases within the data instead of focusing on actual useful causal relationships. This problem is particularly serious in application domains affected by aspects such as race, gender, and age. To prevent models from incurring on unfair decision-making, the AI community has concentrated efforts in correcting algorithmic biases, giving rise to the research area now widely known as fairness in AI. In this survey paper, we provide an in-depth overview of the main debiasing methods for fairness-aware neural networks in the context of vision and language research. We propose a novel taxonomy to better organize the literature on debiasing methods for fairness, and we discuss the current challenges, trends, and important future work directions for the interested researcher and practitioner., Comment: Submitted to ACM Computing Surveys - Special Issue on Trustworthy AI

Three-dimensional shell-like structures can be obtained spontaneously at the microscale from the self-folding of 2D templates of rigid panels. At least for simple structures, the motion of each panel is consistent with a Brownian process and folding occurs through a sequence of binding events, where pairs of panels meet at a specific closing angle. Here, we propose a lattice model to describe the dynamics of self-folding. As an example, we study the folding of a pyramid of N lateral faces. We combine analytical and numerical Monte Carlo simulations to find how the folding time depends on the number of faces, closing angle, and initial configuration. Implications for the study of more complex structures are discussed.

We study the effect of crystal field anisotropy in the underscreened $S=1$ Kondo lattice model. Starting from the two orbital Anderson lattice model and including a local anisotropy term, we show, through Schrieffer-Wolff transformation, that local anisotropy is equivalent to an anisotropic Kondo interaction ($J_{\parallel} \neq{J_{\perp}}$). The competition and coexistence between ferromagnetism and Kondo effect in this effective model is studied within a generalized mean-field approximation. Several regimes are obtained, depending on the parameters, exhibiting or not coexistence of magnetic order and Kondo effect. Particularly, we show that a re-entrant Kondo phase at low temperature can be obtained. We are also able to describe phases where the Kondo temperature is smaller than the Curie temperature ($T_K

The information available to robots in real tasks is widely distributed both in time and space, requiring the agent to search for relevant data. In humans, that face the same problem when sounds, images and smells are presented to their sensors in a daily scene, a natural system is applied: Attention. As vision plays an important role in our routine, most research regarding attention has involved this sensorial system and the same has been replicated to the robotics field. However,most of the robotics tasks nowadays do not rely only in visual data, that are still costly. To allow the use of attentive concepts with other robotics sensors that are usually used in tasks such as navigation, self-localization, searching and mapping, a generic attentional model has been previously proposed. In this work, feature mapping functions were designed to build feature maps to this attentive model from data from range scanner and sonar sensors. Experiments were performed in a high fidelity simulated robotics environment and results have demonstrated the capability of the model on dealing with both salient stimuli and goal-driven attention over multiple features extracted from multiple sensors.

Magnetic properties of uranium and neptunium compounds showing the coexistence of Kondo screening effect and ferromagnetic order are investigated within the Anderson lattice Hamiltonian with a two-fold degenerate $f$-level in each site, corresponding to $5f^2$ electronic configuration with $S=1$ spins. A derivation of the Schrieffer-Wolff transformation is presented and the resulting Hamiltonian has an effective $f$-band term, in addition to the regular exchange Kondo interaction between the $S=1$ $f$-spins and the $s=1/2$ spins of the conduction electrons. The obtained effective Kondo lattice model can describe both the Kondo regime and a weak delocalization of $5f$-electron. Within this model we compute the Kondo and Curie temperatures as a function of model parameters, namely the Kondo exchange interaction constant $J_K$, the magnetic intersite exchange interaction $J_H$ and the effective $f$-bandwidth. We deduce, therefore, a phase diagram of the model which yields the coexistence of Kondo effect and ferromagnetic ordering and also accounts for the pressure dependence of the Curie temperature of uranium compounds such as UTe., Comment: 9 pages, 4 figures

We revisit the short-time dynamics of 2D Ising model with three spin interactions in one direction and estimate the critical exponents $z,$ $\theta,$ $\beta$ and $\nu$. Taking properly into account the symmetry of the Hamiltonian we obtain results completely different from those obtained by Wang et al.. For the dynamic exponent $z$ our result coincides with that of the 4-state Potts model in two dimensions. In addition, results for the static exponents $\nu$ and $\beta$ agree with previous estimates obtained from finite size scaling combined with conformal invariance. Finally, for the new dynamic exponent $\theta$ we find a negative and close to zero value, a result also expected for the 4-state Potts model according to Okano et al., Comment: 12 pages, 9 figures, corrected Abstract mistypes, corrected equation on page 4 (Parameter Q)

We study behaviour of dynamical critical exponents of the two-dimensional Ising model with a line of defects. Simulations done at an early time (first 100 Monte Carlo steps) reveal that the critical exponent of Janssen et al (Z. Phys. B 73 539) depends on the strength of the exchange coupling constant (J') of the altered line. On the other hand, our simulations permit us to conclude that the dynamical critical exponent z is not sensitive to changes in J'. In adition, we investigate the possible invariance of the anomalous dimension of the magnetization at the beginning of the process., Comment: 8 figures