Newtonian repulsion and radial confinement: Convergence toward steady state

We investigate the large time behavior of multi-dimensional aggregation equations driven by Newtonian repulsion, and balanced by radial attraction and confinement. In case of Newton repulsion with radial confinement we quantify the algebraic convergence decay rate toward the unique steady state. To this end, we identify a one-parameter family of radial steady states, and prove dimension-dependent decay rate in energy and 2-Wassertein distance, using a comparison with properly selected radial steady states. We also study Newtonian repulsion and radial attraction. When the attraction potential is quadratic it is known to coincide with quadratic confinement. Here, we study the case of perturbed radial quadratic attraction, proving that it still leads to one-parameter family of unique steady states. It is expected that this family to serve for a corresponding comparison argument which yields algebraic convergence toward steady repulsive-attractive solutions.

Culinary Versus Gastronomy

Food becomes one of main income of tourism sector which supports Gross Domestic Product. Food and beverage is also suspected to be the tourists’ motivation for travelling. People, publicly, and government recognize it more as culinary. However, there is a view that argumentation which is constructed by public seems to be not accordance with the real situation. Gastronomy, which accommodates foodshed, cooking, until foodscape and human behaviour, is perceived to be more appropriate as a comparison argument. Related to that matter, in this paper, researcher is trying to study and to compare two-sided definition of terminology over culinary and gastronomy as a way to eliminate argumentum ad populum. Keywords: culinary, gastronomy, foodshed, foodscape, argumentum ad populum

The performance of the quantum adiabatic algorithm on spike Hamiltonians

Spike Hamiltonians arise from optimization instances for which the adiabatic algorithm provably out performs classical simulated annealing. In this work, we study the efficiency of the adiabatic algorithm for solving the “the Hamming weight with a spike” problem by analyzing the scaling of the spectral gap at the critical point for various sizes of the barrier. Our main result is a rigorous lower bound on the minimum spectral gap for the adiabatic evolution when the bit-symmetric cost function has a thin but polynomially high barrier, which is based on a comparison argument and an improved variational ansatz for the ground state. We also adapt the discrete WKB method for the case of abruptly changing potentials and compare it with the predictions of the spin coherent instanton method which was previously used by Farhi, Goldstone and Gutmann. Finally, our improved ansatz for the ground state leads to a method for predicting the location of avoided crossings in the excited energy states of the thin spike Hamiltonian, and we use a recursion relation to understand the ordering of some of these avoided crossings as a step towards analyzing the previously observed diabatic cascade phenomenon.

PERSISTENCE, EXTINCTION AND STABILITY FOR NONLINEAR PLANKTON ALLELOPATHY MODEL WITH DELAYED NEGATIVE FEEDBACKS

By the techniques of comparison argument and Lyapunov-like functionals, some criteria about persistence and extinction of the species are obtained. And then, with the help of constructing Lyapunov functionals and some new analysis method, sufficient conditions, provided with the form of average value of a function, to guarantee the stability of the system are derived. Finally, some examples together with their numerical simulations show the feasibility of these main results. Our conclusions are different from many existing forms for nonlinear competitive systems.

ANALYSIS OF A DELAYED PREDATOR-PREY SYSTEM WITH IMPULSIVE STATE FEEDBACK

A delayed dynamical system model incorporating modified Leslie–Gower and Holling-type II schemes with state-dependent impulses is investigated for the case of small delay. The boundedness of solutions is analyzed by applying the comparison argument. Existence and stability of the semi-trivial periodic solution and the positive period-1 solution are discussed by using the variational principle, constructing Poincaré map and applying Floquet multiplier theory. Flip bifurcation is also investigated and some numerical simulation is presented in detail.

Global Stability for a Delayed Predator-Prey System with Stage Structure for the Predator

A delayed predator-prey system with stage structure for the predator is investigated. By analyzing the corresponding characteristic equations, the local stability of equilibria of the system is discussed. The existence of Hopf bifurcation at the positive equilibrium is established. By using an iteration technique and comparison argument, respectively, sufficient conditions are derived for the global stability of the positive equilibrium and two boundary equilibria of the system. Numerical simulations are carried out to illustrate the theoretical results.

Backward Recognition Masking in Relative Pitch Judgments

Backward recognition masking refers to interference of a second masking tone with recognition of a target tone presented earlier in time. The degree of interference has been found to decrease as the length of the silent interval separating the two tones increases. These results have been interpreted as representing interference of the masking tone upon the preperceptual storage and perceptual resolution of the target. It is logically possible, however, that the masking tone does not interfere with perceptual resolution but interferes with comparison of the target to a long-term memory representation. The current research was designed to provide a critical test of this alternative hypothesis by modifying the backward recognition masking task. Subjects determined whether the masking tone was higher or lower in pitch than the target tone. The frequencies of the target and masking tones varied randomly across trials. This ensured that the task could not be performed by comparing the target to a representation in long-term memory. Nevertheless, masking was obtained in this task, arguing against the comparison argument and in favor of the perceptual resolution interpretation. Given that masking was obtained under both ipsilateral and contralateral presentation of the tones, the results argue for a central preperceptual auditory storage that holds information after the inputs from the two ears are combined in the auditory system.