Abstract: Nowadays, data center industry faces strong challenges for increasing the speed and data processing capacities while at the same time is trying to keep their devices a suitable working temperature without penalizing that capacity. Consequently, the cooling systems of this kind of facilities use a large amount of energy to dissipate the heat generated inside the servers, and developing new cooling techniques or perfecting those already existing would be a great advance in this type of industry. The installation of a temperature sensor matrix distributed in the structure of each server would provide the necessary information for collecting the required data for obtaining a temperature profile instantly inside them. However, the number of temperature probes required to obtain the temperature profiles with sufficient accuracy is very high and expensive. Therefore, other less intrusive techniques are employed where each point that characterizes the server temperature profile is obtained by solving differential equations through simulation methods, simplifying data collection techniques but increasing the time to obtain results. In order to reduce these calculation times, complicated and slow computational fluid dynamics simulations are replaced by simpler and faster finite element method simulations which solve the Burgers‘ equations by backward, forward and central discretization techniques after simplifying the energy and enthalpy conservation differential equations. The discretization methods employed for solving the first and second order derivatives of the obtained Burgers‘ equation after these simplifications are the key for obtaining results with greater or lesser accuracy regardless of the characteristic truncation error.
Abstract: Several numerical schemes utilizing central difference
approximations have been developed to solve the Goursat problem.
However, in a recent years compact discretization methods which
leads to high-order finite difference schemes have been used since it
is capable of achieving better accuracy as well as preserving certain
features of the equation e.g. linearity. The basic idea of the new
scheme is to find the compact approximations to the derivative terms
by differentiating centrally the governing equations. Our primary
interest is to study the performance of the new scheme when applied
to two Goursat partial differential equations against the traditional
finite difference scheme.
Abstract: In this paper, a PSO-based approach is proposed to
derive a digital controller for redesigned digital systems having an interval plant based on resemblance of the extremal gain/phase
margins. By combining the interval plant and a controller as an interval system, extremal GM/PM associated with the loop transfer function
can be obtained. The design problem is then formulated as an optimization problem of an aggregated error function revealing the deviation on the extremal GM/PM between the redesigned digital
system and its continuous counterpart, and subsequently optimized by
a proposed PSO to obtain an optimal set of parameters for the digital controller. Computer simulations have shown that frequency
responses of the redesigned digital system having an interval plant bare a better resemblance to its continuous-time counter part by the incorporation of a PSO-derived digital controller in comparison to those obtained using existing open-loop discretization methods.
Abstract: Many supervised induction algorithms require discrete
data, even while real data often comes in a discrete
and continuous formats. Quality discretization of continuous
attributes is an important problem that has effects on speed,
accuracy and understandability of the induction models. Usually,
discretization and other types of statistical processes are applied
to subsets of the population as the entire population is practically
inaccessible. For this reason we argue that the discretization
performed on a sample of the population is only an estimate of
the entire population. Most of the existing discretization methods,
partition the attribute range into two or several intervals using
a single or a set of cut points. In this paper, we introduce a
technique by using resampling (such as bootstrap) to generate
a set of candidate discretization points and thus, improving the
discretization quality by providing a better estimation towards
the entire population. Thus, the goal of this paper is to observe
whether the resampling technique can lead to better discretization
points, which opens up a new paradigm to construction of
soft decision trees.