Academic integrity in the HyFlex learning environment.

This study analyzed how students' personality traits and course attendance preferences impact academic integrity in the HyFlex learning environment. 535 undergraduate students were given a choice among courses face-to-face (F2F), online, or a hybrid combination of both. The Big Five Inventory and the Academic Integrity Inventory were administered through online questionnaires to STEM students. The findings show that emotional stability and agreeableness positively relate to academic integrity irrespective of attendance mode. So do conscientiousness and agreeableness in the hybrid environment. Conversely, the primarily F2F attendance mode and the personality trait of extraversion are tied to markedly low levels of academic integrity. We conclude that unveiling students' personality traits associated with ethical behaviour would be beneficial when designing HyFlex courses in different learning environments, whether human (F2F), machine-made (online) or a combination of both (hybrid). This, in turn, contributes to better higher quality education and enhances academic integrity.

Consistent scaling of persistence time in metapopulations.

Recent theory and experimental work in metapopulations and metacommunities demonstrates that long-term persistence is maximized when the rate at which individuals disperse among patches within the system is intermediate; if too low, local extinctions are more frequent than recolonizations, increasing the chance of regional-scale extinctions, and if too high, dynamics exhibit region-wide synchrony, and local extinctions occur in near unison across the region. Although common, little is known about how the size and topology of the metapopulation (metacommunity) affect this bell-shaped relationship between dispersal rate and regional persistence time. Using a suite of mathematical models, we examined the effects of dispersal, patch number, and topology on the regional persistence time when local populations are subject to demographic stochasticity. We found that the form of the relationship between regional persistence time and the number of patches is consistent across all models studied; however, the form of the relationship is distinctly different among low, intermediate, and high dispersal rates. Under low and intermediate dispersal rates, regional persistence times increase logarithmically and exponentially (respectively) with increasing numbers of patches, whereas under high dispersal, the form of the relationship depends on local dynamics. Furthermore, we demonstrate that the forms of these relationships, which give rise to the bell-shaped relationship between dispersal rate and persistence time, are a product of recolonization and the region-wide synchronization (or lack thereof) of population dynamics. Identifying such metapopulation attributes that impact extinction risk is of utmost importance for managing and conserving the earth's evermore fragmented populations.

Modeling epidemics dynamics on heterogenous networks.

The dynamics of the SIS process on heterogenous networks, where different local communities are connected by airlines, is studied. We suggest a new modeling technique for travelers movement, in which the movement does not affect the demographic parameters characterizing the metapopulation. A solution to the deterministic reaction-diffusion equations that emerges from this model on a general network is presented. A typical example of a heterogenous network, the star structure, is studied in detail both analytically and using agent-based simulations. The interplay between demographic stochasticity, spatial heterogeneity and the infection dynamics is shown to produce some counterintuitive effects. In particular it was found that, while movement always increases the chance of an outbreak, it may decrease the steady-state fraction of sick individuals. The importance of the modeling technique in estimating the outcomes of a vaccination campaign is demonstrated.

Applications of geometrical criteria for transition to Hamiltonian chaos.

Using a recently developed geometrical method, we study the transition from order to chaos in an important class of Hamiltonian systems. We show agreement between this geometrical method and the surface of section technique applied to detect chaotic behavior. We give, as a particular illustration, detailed results for an important class of potentials obtained from the perturbation of an oscillator Hamiltonian by means of higher-order polynomials.

Detecting order and chaos in three-dimensional Hamiltonian systems by geometrical methods.

We use a geometrical method to distinguish between ordered and chaotic motion in three-dimensional Hamiltonian systems. We show that this method gives results in agreement with the computation of Lyapunov characteristic exponents. We discuss some examples of unstable Hamiltonian systems in three dimensions, giving, as a particular illustration, detailed results for a potential obtained from a Hamiltonian obtained from a Yang-Mills system.

Controlling effect of geometrically defined local structural changes on chaotic Hamiltonian systems.

An effective characterization of chaotic conservative Hamiltonian systems in terms of the curvature associated with a Riemannian metric tensor derived from the structure of the Hamiltonian has been extended to a wide class of potential models of standard form through definition of a conformal metric. The geodesic equations reproduce the Hamilton equations of the original potential model through an inverse map in the tangent space. The second covariant derivative of the geodesic deviation in this space generates a dynamical curvature, resulting in (energy-dependent) criteria for unstable behavior different from the usual Lyapunov criteria. We show here that this criterion can be constructively used to modify locally the potential of a chaotic Hamiltonian model in such a way that stable motion is achieved. Since our criterion for instability is local in coordinate space, these results provide a minimal method for achieving control of a chaotic system.