On Finding Two Posets that Cover Given Linear Orders

The Poset Cover Problem is an optimization problem where the goal is to determine a minimum set of posets that covers a given set of linear orders. This problem is relevant in the field of data mining, specifically in determining directed networks or models that explain the ordering of objects in a large sequential dataset. It is already known that the decision version of the problem is NP-Hard while its variation where the goal is to determine only a single poset that covers the input is in P. In this study, we investigate the variation, which we call the 2-Poset Cover Problem, where the goal is to determine two posets, if they exist, that cover the given linear orders. We derive properties on posets, which leads to an exact solution for the 2-Poset Cover Problem. Although the algorithm runs in exponential-time, it is still significantly faster than a brute-force solution. Moreover, we show that when the posets being considered are tree-posets, the running-time of the algorithm becomes polynomial, which proves that the more restricted variation, which we called the 2-Tree-Poset Cover Problem, is also in P.

Phenotypic plasticity under desert environment constraints: mandible variation in the dwarf fat-tailed jerboa, Pygeretmus pumilio (Rodentia: Dipodidae)

Arid areas have a comparatively narrow range of habitat types, with restricted variation in environmental parameters, leaving narrow boundaries for phenotypic variation to correlate with ecological variables. To test this presumption, we explored variation in size and shape of the mandible in the dwarf fat-tailed jerboa (Pygeretmus pumilio (Kerr, 1792)) under the constraints of a rigorous desert environment. Size varied significantly and predictably with geographic position and demonstrated a strong, nonlinear longitudinal pattern. Moreover, size was associated with several other climatic variables but not with soil properties or with proxies for primary productivity. Our results suggest that for rodents exposed to rapid and extreme changes, larger size may have multiple advantages, notably in maintaining euthermia during cold nights and efficient water metabolism under aridity stress, in accumulating fat reserves for hibernation, and in digging deeper burrows, better protected from surface extremes. Shape varied clinally along the longitudinal transect, and the pattern was affected more by temperature than by precipitation. We conclude that the success of dwarf fat-tailed jerboa in occupying an extensive geographic range relies on their ability to meet environmental heterogeneity through cohesive and diverse responses, including physiology, behaviour, life-history traits, and morphological plasticity.

You Do Not Mess with the Glia

Vertebrate neurons are enormously variable in morphology and distribution. While different glial cell types do exist, they are much less diverse than neurons. Over the last decade, we have conducted quantitative studies of the absolute numbers, densities, and proportions at which non-neuronal cells occur in relation to neurons. These studies have advanced the notion that glial cells are much more constrained than neurons in how much they can vary in both development and evolution. Recent evidence from studies on gene expression profiles that characterize glial cells—in the context of progressive epigenetic changes in chromatin during morphogenesis—supports the notion of constrained variation of glial cells in development and evolution, and points to the possibility that this constraint is related to the late differentiation of the various glial cell types. Whether restricted variation is a biological given (a simple consequence of late glial cell differentiation) or a physiological constraint (because, well, you do not mess with the glia without consequences that compromise brain function to the point of rendering those changes unviable), we predict that the restricted variation in size and distribution of glial cells has important consequences for neural tissue function that is aligned with their many fundamental roles being uncovered.

A Dynamic Model for Motion of an ROV due to On-Board Robotics

A new method in dynamics — the Moving Frame Method (MFM) — is used to conduct the analysis of how a robotic appendage (manipulator) on a Remotely Operated Vehicle (ROV) affects the motion of the ROV. An ROV performs multiple tasks on the seabed in the oil service industry. In most cases, an ROV pilot monitors and adjusts the movement of the vehicle due to induced motion by currents, buoyancy and the manipulators. Simulation data would assist the pilot and improve the stability of the ROV. This paper exploits a new method to analyze the induced movements of the ROV. The method uses the Special Euclidean Group (SE(3)) and the MFM. The method is supplemented with a restricted variation on the angular velocity to extract the equations of motion for the ROV. Then the equations of motion are solved numerically using Runge-Kutta Method and a reconstruction formula (founded upon the Cayley-Hamilton theorem) to secure the 3D rotations of the vehicle. The resulting motion is visualized with selected 2D plots. The 3D animation is displayed on a 3D web page. This paper closes with a summary of the simplifications used in the model and suggestions for advanced work.

Convergence of Variational Iteration Method for Fractional Delay Integrodifferential-Algebraic Equations

Fractional order delay integrodifferential-algebraic equations are often used for many practical modeling problems in science and engineering, which have time lag, memory, constraint limit, and so forth. These yield some difficulties in numerical computation. The iterative methods are good choice. In the present paper, we construct variational iteration method for solving them by using the appropriate restricted variation. This overcomes the difficulties caused by limitations of large storage amount and algebraic constraint and extends the previous conclusions.

Restricted variation in data envelopment analysis with undesirable factors in nature

In standard data envelopment analysis (DEA) models, inefficient decision-making units (DMUs) should change their inputs and outputs arbitrarily to meet the efficient frontier. However, in many real applications of DEA, because of some limitations in resources and DMU's ability, these variations cannot be made arbitrarily. Moreover, in some situations, undesirable factors with different disposability, strong or weak disposability, are found. In this paper, a DEA-based model is proposed to determine the relative efficiency of DMUs in such a restricted environment and in presence of undesirable factors. Indeed, variation levels of inputs and outputs are pre-defined and are considered to evaluate the performance of DMUs. Numerical examples are utilized to demonstrate the approach.

FINE STRUCTURES OF SOME LOW-LYING EXCITED STATES FOR Be-LIKE SYSTEM

The fine structure energies and fine structure splittings of some low-lying excited states of the beryllium isoelectronic sequence (Z = 4–20) are calculated with multi-configuration-interaction method and restricted variation method. The relativistic corrections and mass polarization are included. The results are in good agreement with other theoretical and experimental data.