The periodicity of Vostok ice core climate temperature and gas concentration data  indicate inherent long term past regularity of Earth’s climate, with a period of around 100,000 years, warming around 15,000 and cooling of around 85,000 years. At this point we are at the top of one of the warming periods. Vostok data cover around 430,000 years, ie 4 climate cycles (warming-cooling), of similar but not quite the same duration. In this paper we perform a detailed time and frequency analysis of these data for each of the cycles as well as their various combinations, including a full tested period of 430,000 years. Time correlation analysis allows for more accurate time lag estimate in each cycle already noted between temperature change and carbon dioxide content. We estimate these lags to lie between 1000-2500 years, longer than previously concluded. On the frequency side we perform Fast Fourier Analysis and identify full spectrum of harmonics for various cycles, and then perform energy analysis to identify which of the harmonics contributes the most. The idea is to reduce the computational load for further modeling and analysis using Kalman Filter based prediction method.  Once the prediction model is defined (a follow up paper) data will be split into two segments, Learning and Testing, in preparation of a Machine Learning fine tunning methodology. We can use last three or last two or even just last cycle to learn on, and then the current on going cycle to test on. This will result in real time prediction of relevant climate data. Assuming causal time regularity, more of these cycles are employed in training, more the prediction error for the next cycle should be reduced. Hence it is critical to perform very detailed time and frequency analysis of Vostok data as a solid data base for the prediction model to follow. 

A  hypothesis that the increasing application of both surface and ground water for irrigation of crops is a significant source of anthropogenic global warming is tested. In climate models, water is already assigned a major secondary amplifying role in warming, solely as a positive feedback from an atmosphere previously warmed by other GHGs. However, this conclusion ignores the direct anthropogenic forcing from increasing use of water in dry regions to grow crops for the human population. The area irrigated worldwide increased by around 1.5% annually between 1960 and 2000, almost trebling in magnitude.  Importantly, though only a small proportion of the Earth’s surface, this additional water vapour is dynamically focussed on dry land, intensifying its potential to elevate the troposphere and reduce the regional OLR. Our modelling analysis suggests that the increase in atmospheric water vapour from irrigation could be significantly more than 1% by 2050 compared to 1950, imposing a global forcing exceeding 1.0 W/m2.  Fortunately, this hypothesis can be tested, for example, using the satellite data on OLR acquired since the 1970s, relating this to local trends of increasing irrigation or major floods in arid regions. If found consistent with the data, current proposals to mitigate climate change by limiting combustion of fossil fuels may prove less effective. This prediction regarding the warming effect of increasing irrigation is tested using NCAR reanalysis data made possible by the natural experiments of the periodic flooding of Lake Eyre in Australia's semi-arid interior. It is recommended that this hypothesis be tested using data from local studies in irrigated regions such as changes in outgoing longwave radiation and in increased absorption of incoming shortwave radiation in air. 

The main motivation for this paper is to apply LQ and LQG methodologies for quadcopter control system. The developed control system is for both the rectangular position (xy) and altitude (z) as well as the orientation (attitude - angles around the axes) based on 6-Degree of Freedom (6DOF) mathematical model. 6DOF refers to the model with 3 linear and 3 angular motions. The altitude and attitude controllers are designed and the results presented in both the continuous and the discrete time cases. For the controller design, a nonlinear mathematical model was obtained first for 6DOF. The next step was to linearize the nonlinear model in hovering mode, and the final step was the reduction of the resulted linear model to be used as starting model for the controller design. The reduced linear model was tested for controllablity and observability. The control goal was to track a spatial trajectory with the quadcopter center of gravity under environment disturbances and sensor measurement errors. For this purpose, designed LQ controller was augmented by Kalman Filter state observer. The resultant controllers provide precise and robust performance for an input reference signal and for a regulation problem. After the transient response (of order of few seconds) the tracking error is acceptable which provides safe handling even under disturbances and measurement noises. The transient response can be furrther recuded by controllers fine tunning.

The objective of this paper is to present new and simple mathematical approach to deal with uncertainty transformation for fuzzy to random or random to fuzzy data. In particular we present a method to describe fuzzy (possibilistic) distribution in terms of a pair (or more) of related random (probabilistic) events, both fixed and variable. Our approach uses basic properties of both fuzzy and random distributions, and it assumes data is both possibilistic and probabilistic.  We show that the data fuzziness can be viewed as a non uniqueness of related random events, and prove our Uncertainty Balance Principle. We also show how Zadeh’s fuzzy-random Consistency Principle can be given precise mathematical meaning. Various types of fuzzy distributions are examined and several numerical examples presented.

In this paper we extend our previous results in dual approach to analysis and simulation of a complex ecological system of preys and predators. We first define nonlinear dynamic equations Lotka-Volterra Model (LVM) with three preys and three predators and then simulate the equivalent situation with an Agent Based Model (ABM) which models a variety of species attributes and behaviors using NetLogo simulation environment for ABM model. The idea is that the LVM and ABM methods reinforce each other as the predator-prey models become more complex and their dimensionality rises. In particular LVM’s parameters, components of community matrix,  can be fine tuned using ABM simulations. Dual approach may be able to answer and qualify some of the long standing ecological paradoxes.