Population-based Incremental Learning is shown require very sensitive scaling of its learning rate. The learning rate must scale with the system size in a problem-dependent way. This is shown in two problems: the needle-in-a haystack, in which the learning rate must vanish exponentially in the system size, and in a smooth function in which the learning rate must vanish like the square root of t...

height is amongst the most delicate subjects of geodesy. thanks to the global navigation satellite systems (gnss) like gps or glonass, 3d point positioning of points, by geometrical positioning, since years ago has become a common practice. the height derived from these ways has a geometrical concept. in civil projects the physical concept of the height is more demanded. orthometric height, , i...

In this paper, Harmonic Balance based methods, namely Incremental Method and the method of with Alternating Frequency Time traditionally used to compute periodic orbits smooth nonlinear dynamical systems, are employed investigate dynamics a non-smooth system, specifically piecewise linear oscillator play. The was period one orbits, including those exhibiting grazing large impacts. implemented c...

In this letter, an application of energy balance method is applied to solve the nonlinear oscillators with un force. Comparison is made between the modification of harmonic balance method and energy balance method. The results reveal that the energy balance method is very effective and simple. Energy balance method is very effective and convenient and quite accurate to both linear and nonlinear...

The atomic force microscope ~AFM! is a powerful tool for investigating surfaces at atomic scales. Harmonic balance and power balance techniques are introduced to analyze the tapping-mode dynamics of the atomic force microscope. The harmonic balance perspective explains observations hitherto unexplained in the AFM literature. A nonconservative model for the cantilever–sample interaction is devel...

The method of Unrestricted Harmonic Balance (UHB) as exposed and applied to purely t imedependent systems, stiff systems, and chemical waves in the preceding 3 papers is extended to the case of transcendental functions. So, e.g., exponential functions even in mass action kinetics systems occur, if a wider range of temperature is considered as is the case in continuous stirred tank reactors (CST...

In this paper we consider several families of potential non-isochronous systems and study their associated period functions. Firstly, we prove some properties of these functions, like their local behavior near the critical point or infinity, or their global monotonicity. Secondly, we show that these properties are also present when we approach to the same questions using the Harmonic Balance Me...

We propose two methods to find analytic periodic approximations intended for differential equations of Hill type. Here, we apply these methods on the simplest case of the Mathieu equation. The former has been inspired in the harmonic balance method and designed to find, making use on a given algebraic function, analytic approximations for the critical values and their corresponding periodic sol...

A new self-consistent dynamic electro-thermal model for power HBTs is presented coupling a circuit-oriented electrical model, fitted on experimental data, with a full frequency domain thermal model. The thermal model provides the exact frequency behaviour of the device thermal impedance through a quasi-3D approach. The electro-thermal self-consistent solution is achieved, in large-signal period...