Solutions to optimization problems of convex type are typically characterized by saddle point conditions in which the primal vector is paired with a dual ‘multiplier’ vector. This paper investigates the behavior of such a primal-dual pair with respect to perturbations in parameters on which the problem depends. A necessary and sufficient condition in terms of certain matrices is developed for t...

In a natural environment, cast shadows abound. Objects cast shadows both upon themselves and upon background surfaces. Previous research on the perception of 3-D shape from cast shadows has only examined the informativeness of shadows cast upon flat background surfaces. In outdoor environments, however, background surfaces often possess significant curvature (large rocks, trees, hills, etc.), a...

Abstract The dynamics of a hysteretic relay oscillator with harmonic forcing is investigated. Periodic excitation the system results in periodic, quasi-periodic, chaotic and unbounded behavior. An explicit Poincaré map constructed an implicit constraint on switching time. stability fixed points corresponding to period-one solutions By varying parameters, we observed saddle-center pitchfork bifu...

A bstract In semi-classical systems, the exponential growth of out-of-time-order correlator (OTOC) is believed to be hallmark quantum chaos. However, on several occasions, it has been argued that, even in integrable OTOC can grow exponentially due presence unstable saddle points phase space. this work, we probe such an system exhibiting saddle-dominated scrambling through Krylov complexity and ...

The shading cue is supposed to be a major factor in monocular stereopsis. However, the hypothesis is hardly corroborated by available data. For instance, the conventional stimulus used in perception research, which involves a circular disk with monotonic luminance gradient on a uniform surround, is theoretically 'explained' by any quadric surface, including spherical caps or cups (the conventio...

Yellow Saddle Goatfish Algorithm (YSGA) is an optimization model inspired by the hunting behavior of yellow saddle goatfish which emulates their collaborative behaviors with chaser fish and blocker fish. To improve global convergence, chaotic maps have been combined YSGA in this paper. Chaotic a nonlinear deterministic system that displays complex, noisy-like, unpredictable behavior. Due to its...

In a model drift wave system that is interesting both in fluids and plasmas, we find that an embedded moving saddle point plays an important role at the onset of turbulence. Here the saddle point is actually a saddle steady wave, in its moving frame the wave system can be transformed into a set of coupled oscillators whose motion is affected by the saddle steady wave as if it is a potential. It...

Structural stability ensures that the qualitative behavior of a system is preserved under small perturbations. We study it for planar bimodal linear dynamical systems, that is, systems consisting of two linear dynamics acting on each side of a given hyperplane and assuming continuity along the separating hyperplane. We describe which one of these systems is structurally stable when (real) spira...

Recent work has considered the possibility of utilizing symbolic representations of controlled chaotic orbits for digital communication. We argue that dynamically a coding scheme usually leads to trajectories that live on a nonattracting but noise-resisting chaotic saddle embedded in the chaotic attractor. We present analyses and numerical computation which indicate that the channel capacity of...

We formally extend the energy landscape approach for the thermodynamics of liquids to account for saddle points. By considering the extensive nature of macroscopic potential energies, we derive the scaling behavior of saddles with system size, as well as several approximations for the properties of low-order saddles (i.e., those with only a few unstable directions). We then cast the canonical p...