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We discuss a cost-effective approach to understand magnetic relaxation in the new generation of rare-earth single-molecule magnets. It combines ab initio calculations of the crystal field parameters, of the magneto-elastic coupling with local modes, and of the phonon density of states with fitting of only three microscopic parameters. Although much less demanding than a fully ab initio approach, the method gives important physical insights into the origin of the observed relaxation. By applying it to high-anisotropy compounds with very different relaxation, we demonstrate the power of the approach and pinpoint ingredients for improving the performance of single-molecule magnets.

We numerically investigate the properties of the quasihole excitations above the bosonic fractional Chern insulator state at filling nu = 1/2, in the specific case of the Harper-Hofstadter Hamiltonian with hard-core interactions. For this purpose, we employ a tree tensor network technique, which allows us to study systems with up to N = 18 particles on a 16 x 16 lattice and experiencing an additional harmonic confinement. First, we observe the quantization of the quasihole charge at fractional values and its robustness against the shape and strength of the impurity potentials used to create and localize such excitations. Then, we numerically characterize quasihole anyonic statistics by applying a discretized version of the relation connecting the statistics of quasiholes in the lowest Landau level to the depletions they create in the density profile [E. Macaluso et al., Phys. Rev. Lett. 123, 266801 (2019)]. Our results give a direct proof of the anyonic statistics for quasiholes of fractional Chern insulators, starting from a realistic Hamiltonian. Moreover, they provide strong indications that this property can be experimentally probed through local density measurements, making our scheme readily applicable in state-of-the-art experiments with ultracold atoms and superconducting qubits.

Deduction is the ability to draw necessary conclusions from previous knowledge. Here we propose a novel approach to understanding the neural basis of deduction, which exploits fine-grained inter-participant variability in such tasks. Participants solved deductive problems and were grouped by the behavioral strategies employed, i.e., whether they were sensitive to the logical form of syllogistic premises, whether the problems were solved correctly, and whether heuristic strategies were employed. Differential profiles of neural activity can predict membership of the first two of these groups. The predictive power of activity profiles is distributed non-uniformly across the brain areas activated by deduction. Activation in left ventro-lateral frontal (BA47) and lateral occipital (BA19) cortices predicts whether logically valid solutions are sought. Activation of left inferior lateral frontal (BA44/45) and superior medial frontal (BA6/8) cortices predicts sensitivity to the logical structure of problems. No specific pattern of activation was associated with the use of a non-logical heuristic strategy. Not only do these findings corroborate the hypothesis that left BA47, BA44/45 and BA6/8 are critical for making syllogistic deductions, but they also imply that they have different functional roles as components of a dedicated network. We propose that BA44/45 and BA6/8 are involved in the extraction and representation of the formal structure of a problem, while BA47 is involved in the selection and application of relevant inferential rules. Finally, our findings suggest that deductive reasoning can be best described as a cascade of cognitive processes requiring the concerted operation of several, functionally distinct, brain areas.

Amnestic mild cognitive impairment (a-MCI) is associated with the highest annual incidence of conversion to Alzheimer's disease (AD) (10-15%). a-MCI patients may have only a memory deficit (single domain: sd-a-MCI) or additional dysfunctions affecting other cognitive domains (multiple domain: md-a-MCI). Using functional magnetic resonance imaging (fMRI), we investigated brain activation in 16 sd-a-MCI patients and 14 controls during four different tasks assessing language, memory, attention and empathy functions. We found greater activation in sd-a-MCI compared with controls in the left inferior temporal gyrus (language), the right superior temporal gyrus (memory) and the right dorsal precentral gyrus (attention). Moreover, patients' activation correlated significantly with neuropsychological scores obtained at tests exploring the corresponding function. These findings indicate that fMRI is sensitive to detect early changes occurring in AD pathology and that individuals with sd-a-MCI show increased activation in multiple task-related brain regions. We suggest that these functional changes relate to the development of early compensatory mechanisms that reduce cognitive deficits associated with the progressive accumulation of brain damage.

Deduction allows us to draw consequences from previous knowledge. Deductive reasoning can be applied to several types of problem, for example, conditional, syllogistic, and relational. It has been assumed that the same cognitive operations underlie solutions to them all; however, this hypothesis remains to be tested empirically. We used event-related fMRI, in the same group of subjects, to compare reasoning-related activity associated with conditional and syllogistic deductive problems. Furthermore, we assessed reasoning-related activity for the two main stages of deduction, namely encoding of premises and their integration. Encoding syllogistic premises for reasoning was associated with activation of BA 44/45 more than encoding them for literal recall. During integration, left fronto-lateral cortex (BA 44/45, 6) and basal ganglia activated with both conditional and syllogistic reasoning. Besides that, integration of syllogistic problems additionally was associated with activation of left parietal (BA 7) and left ventro-lateral frontal cortex (BA 47). This difference suggests a dissociation between conditional and syllogistic reasoning at the integration stage. Our finding indicates that the integration of conditional and syllogistic reasoning is carried out by means of different, but partly overlapping, sets of anatomical regions and by inference, cognitive processes. The involvement of BA 44/45 during both encoding (syllogisms) and premise integration (syllogisms and conditionals) suggests a central role in deductive reasoning for syntactic manipulations and formal/linguistic representations. © 2010 Wiley-Liss, Inc.

Amnestic mild cognitive impairment (a-MCI) is associated with the highest annual incidence of conversion to Alzheimer's disease (AD) (10-15%). a-MCI patients may have only a memory deficit (single domain: sd-a-MCI) or additional dysfunctions affecting other cognitive domains (multiple domain: md-a-MCI). Using functional magnetic resonance imaging (fMRI), we investigated brain activation in 16 sd-a-MCI patients and 14 controls during four different tasks assessing language, memory, attention and empathy functions. We found greater activation in sd-a-MCI compared with controls in the left inferior temporal gyrus (language), the right superior temporal gyrus (memory) and the right dorsal precentral gyrus (attention). Moreover, patients' activation correlated significantly with neuropsychological scores obtained at tests exploring the corresponding function. These findings indicate that fMRI is sensitive to detect early changes occurring in AD pathology and that individuals with sd-a-MCI show increased activation in multiple task-related brain regions. We suggest that these functional changes relate to the development of early compensatory mechanisms that reduce cognitive deficits associated with the progressive accumulation of brain damage.