Dualities and dual pairs in Heyting algebras

We extract the abstract core of finite homomorphism dualities using the techniques of Heyting algebras and (combinatorial) categories.Comment: 17 pages; v2: minor correction

Gaps and dualities in Heyting categories

summary:We present an algebraic treatment of the correspondence of gaps and dualities in partial ordered classes induced by the morphism structures of certain categories which we call Heyting (such are for instance all cartesian closed categories, but there are other important examples). This allows to extend the results of [14] to a wide range of more general structures. Also, we introduce a notion of combined dualities and discuss the relation of their structure to that of the plain ones

Investigating microstructural variation in the human hippocampus using non-negative matrix factorization

In this work we use non-negative matrix factorization to identify patterns of microstructural variance in the human hippocampus. We utilize high-resolution structural and diffusion magnetic resonance imaging data from the Human Connectome Project to query hippocampus microstructure on a multivariate, voxelwise basis. Application of non-negative matrix factorization identifies spatial components (clusters of voxels sharing similar covariance patterns), as well as subject weightings (individual variance across hippocampus microstructure). By assessing the stability of spatial components as well as the accuracy of factorization, we identified 4 distinct microstructural components. Furthermore, we quantified the benefit of using multiple microstructural metrics by demonstrating that using three microstructural metrics (T1-weighted/T2-weighted signal, mean diffusivity and fractional anisotropy) produced more stable spatial components than when assessing metrics individually. Finally, we related individual subject weightings to demographic and behavioural measures using a partial least squares analysis. Through this approach we identified interpretable relationships between hippocampus microstructure and demographic and behavioural measures. Taken together, our work suggests non-negative matrix factorization as a spatially specific analytical approach for neuroimaging studies and advocates for the use of multiple metrics for data-driven component analyses

Adjoint functors in graph theory

We survey some uses of adjoint functors in graph theory pertaining to colourings, complexity reductions, multiplicativity, circular colourings and tree duality. The exposition of these applications through adjoint functors unifies the presentation to some extent, and also raises interesting questions

Exchange bias in GeMn nanocolumns: the role of surface oxidation

We report on the exchange biasing of self-assembled ferromagnetic GeMn nanocolumns by GeMn-oxide caps. The x-ray absorption spectroscopy analysis of this surface oxide shows a multiplet fine structure that is typical of the Mn2+ valence state in MnO. A magnetization hysteresis shift |HE|~100 Oe and a coercivity enhancement of about 70 Oe have been obtained upon cooling (300-5 K) in a magnetic field as low as 0.25 T. This exchange bias is attributed to the interface coupling between the ferromagnetic nanocolumns and the antiferromagnetic MnO-like caps. The effect enhancement is achieved by depositing a MnO layer on the GeMn nanocolumns.Comment: 7 pages, 5 figure

Interactional Structure Applied to the Identification and Generation of Visual Interactive Behavior: Robots that (Usually) Follow the Rules

Peer reviewe

Behavioral Phenotypes Associated with MPTP Induction of Partial Lesions in Common Marmosets (\u3cem\u3eCallithrix jacchus\u3c/em\u3e)

Parkinson’s disease is a chronic neurodegenerative disorder with the core motor features of resting tremor, bradykinesia, rigidity, and postural instability. Non-motor symptoms also occur, and include cognitive dysfunction, mood disorders, anosmia (loss of smell), and REM sleep disturbances. As the development of medications and other therapies for treatment of non-motor symptoms is ongoing, it is essential to have animal models that aid in understanding the neural changes underlying non-motor PD symptoms and serve as a testing ground for potential therapeutics. We investigated several non-motor symptoms in 10 adult male marmosets using the MPTP model, with both the full (n = 5) and partial (n = 5) MPTP dosing regimens. Baseline data in numerous domains were collected prior to dosing; assessments in these same domains occurred post-dosing for 12 weeks. Marmosets given the partial MPTP dose (designed to mimic the early stages of the disease) differed significantly from marmosets given the full MPTP dose in several ways, including behavior, olfactory discrimination, cognitive performance, and social responses. Importantly, while spontaneous recovery of PD motor symptoms has been previously reported in studies of MPTP monkeys and cats, we did not observe recovery of any non-motor symptoms. This suggests that the neurochemical mechanisms behind the non-motor symptoms of PD, which appear years before the onset of symptoms, are independent of the striatal dopaminergic transmission. We demonstrate the value of assessing a broad range of behavioral change to detect non-motor impairment, anosmia, and differences in socially appropriate responses, in the marmoset MPTP model of early PD

Motor sequences; separating the sequence from the motor: A longitudinal rsfMRI study

In motor learning, sequence specificity, i.e. the learning of specific sequential associations, has predominantly been studied using task-based fMRI paradigms. However, offline changes in resting state functional connectivity after sequence-specific motor learning are less well understood. Previous research has established that plastic changes following motor learning can be divided into stages including fast learning, slow learning and retention. A description of how resting state functional connectivity after sequence-specific motor sequence learning (MSL) develops across these stages is missing. This study aimed to identify plastic alterations in whole-brain functional connectivity after learning a complex motor sequence by contrasting an active group who learned a complex sequence with a control group who performed a control task matched for motor execution. Resting state fMRI and behavioural performance were collected in both groups over the course of 5 consecutive training days and at follow-up after 12 days to encompass fast learning, slow learning, overall learning and retention. Between-group interaction analyses showed sequence-specific decreases in functional connectivity during overall learning in the right supplementary motor area (SMA). We found that connectivity changes in a key region of the motor network, the superior parietal cortex (SPC) were not a result of sequence-specific learning but were instead linked to motor execution. Our study confirms the sequence-specific role of SMA that has previously been identified in online task-based learning studies, and extends it to resting state network changes after sequence-specific MSL