Parmenides Foundation

Topological states of matter can be classified only in terms of global topological invariants. These global topological invariants are encoded in terms of global observable topological phase factors in the state vectors of electrons. In condensed matter, the energy spectrum of the Hamiltonian operator has a band structure, meaning that it is piecewise continuous. The energy in each continuous piece depends on the quasi-momentum which varies in the Brillouin zone. Thus, the Brillouin zone of quasi-momentum variables constitutes the base localization space of the energy eigenstates of electrons. This is a continuous topological parameter space bearing the homotopy of a torus. Since the base localization space has the homotopy of a torus, if we vary the quasi-momentum in a direction, when the edge of the zone is reached, we obtain a closed path. Then, if we lift this loop from the base space to the sections of the sheaf-theoretic fibration induced by the localization of the energy eigenfunctions, we obtain a global topological phase factor which encodes the topological structure of the Brillouin zone. Because it is homotopically equivalent to a torus, the global phase factor turns out to be quantized, taking integer values. The experimental significance of this model stems from the recent discovery that there are observable global topological phase factors in fairly ordinary materials. In this communication, we show that it is the unitary representation theory of the discrete Heisenberg group in terms of commutative modular symplectic variables, giving rise to a joint commutative representation space endowed with an integral and Z2-invariant symplectic form that articulates the specific form of the topological conditions characterizing both the quantum Hall effect and the spin quantum Hall effect under a unified sheaf-theoretic cohomological framework.

Precise timing is essential for many kinds of human behavior. When a fastest response is not required, movements are initiated at the appropriate time requiring an anticipatory temporal component. Temporal mechanisms for movements with such an anticipatory component are not yet sufficiently understood; in particular, it is not known whether on the operational level for delayed movements distinct time windows are used or whether anticipatory control is characterized by continuous temporal processing. With a modified reaction-time paradigm, we asked participants to act with predefined time delays between 400 and 5000 ms; after each individual trial, a numerical feedback was provided which allowed correction of the response time for each next trial. Visual stimuli (Experiment 1) and auditory stimuli (Experiment 2) were used. In the statistical analyses, piecewise linear models and exponential decay models for the response variability of different delay times were compared. These analyses favored piecewise linear models; a decreasing variability with increasing delay of voluntary controlled actions was observed up to ~1 s, followed by close to constant variability beyond this delay. We suggest that precise temporal control of voluntary delayed movements is reached only after a "temporal twilight zone" of ~1 s, which apparently marks a temporal border between two different timing mechanisms.

Compared with traditional Western landscape paintings, Chinese traditional landscape paintings usually apply a reversed-geometric perspective and concentrate more on contextual information. Using functional magnetic resonance imaging (fMRI), we discovered an intracultural bias in the aesthetic appreciation of Western and Eastern traditional landscape paintings in European and Chinese participants. When viewing Western and Eastern landscape paintings in an fMRI scanner, participants showed stronger brain activation to artistic expressions from their own culture. Europeans showed greater activation in visual and sensory-motor brain areas, regions in the posterior cingulate cortex (PCC), and hippocampus when viewing Western compared to Eastern landscape paintings. Chinese participants exhibited greater neural activity in the medial and inferior occipital cortex and regions of the superior parietal lobule in response to Eastern compared to Western landscape paintings. On the behavioral level, the aesthetic judgments also differed between Western and Chinese participants when viewing landscape paintings from different cultures; Western participants showed for instance higher valence values when viewing Western landscapes, while Chinese participants did not show this effect when viewing Chinese landscapes. In general, our findings offer differentiated support for a cultural modulation at the behavioral level and in the neural architecture for high-level aesthetic appreciation.

Abstract Complexity of life forms on Earth has increased tremendously, primarily driven by subsequent evolutionary transitions in individuality, a mechanism in which units formerly being capable of independent replication combine to form higher-level evolutionary units. Although this process has been likened to the recursive combination of pre-adapted subsolutions in the framework of learning theory, no general mathematical formalization of this analogy has been provided yet. Here we show, building on former results connecting replicator dynamics and Bayesian update, that (i) evolution of a hierarchical population under multilevel selection is equivalent to Bayesian inference in hierarchical Bayesian models, and (ii) evolutionary transitions in individuality, driven by synergistic fitness interactions, is equivalent to learning the structure of hierarchical models via Bayesian model comparison. These correspondences support a learning theory oriented narrative of evolutionary complexification: the complexity and depth of the hierarchical structure of individuality mirrors the amount and complexity of data that has been integrated about the environment through the course of evolutionary history.

Education Diplomacy engages the business sector with educators, policymakers, and government agencies by building consensus on policy, practice, and lifelong outcomes and taps into business people's natural skills and influence. The Education Diplomat is an important role for all stakeholders to make a lasting difference in the lives of children, and thereby society at large.

The philosophical theory of an “autogenetic universe” (von Muller 2011, 2012, 2015) proposes new “categorial foundations” for science aiming to overcome the inherent limitations, incompatibilities, and structural pitfalls of the current scientific paradigm. The basic premise of the proposed new theory is that we live in an autogenetic universe, meaning that we live in a self-unfolding and strongly self-referential universe. In relation to this hypothesis, the theory of an “autogenetic universe” proposes a novel account of time and reality, which aims at a deeper re-conceptualization of these fundamental notions going beyond or underneath the structural reduction of the former to its linear-sequential aspect and the concurrent related reduction of the latter to its factual or event-like aspect. This is of particular significance in relation to the frontier area of theoretical physics aiming at a unification of quantum mechanics and general relativity, where it is argued that a key conceptual element for this purpose requires the relativization of facticity, namely of the event structures pertaining to a local space-time description capturing exclusively the factual portrait of reality. It is instructive to note that the notion of an unfolding universe has also been explored by means of a different approach in the work of (Kafatos and Nadeau 2013).