Intrinsic Frequency Analysis and Fast Algorithms

Intrinsic Frequency (IF) has recently been introduced as an ample signal processing method for analyzing carotid and aortic pulse pressure tracings. The IF method has also been introduced as an effective approach for the analysis of cardiovascular system dynamics. The physiological significance, convergence and accuracy of the IF algorithm has been established in prior works. In this paper, we show that the IF method could be derived by appropriate mathematical approximations from the Navier-Stokes and elasticity equations. We further introduce a fast algorithm for the IF method based on the mathematical analysis of this method. In particular, we demonstrate that the IF algorithm can be made faster, by a factor or more than 100 times, using a proper set of initial guesses based on the topology of the problem, fast analytical solution at each point iteration, and substituting the brute force algorithm with a pattern search method. Statistically, we observe that the algorithm presented in this article complies well with its brute-force counterpart. Furthermore, we will show that on a real dataset, the fast IF method can draw correlations between the extracted intrinsic frequency features and the infusion of certain drugs. In general, this paper aims at a mathematical analysis of the IF method to show its possible origins and also to present faster algorithms

Sparse Time-Frequency Data Analysis: A Multi-Scale Approach

In this work, we further extend the recently developed adaptive data analysis method, the Sparse Time-Frequency Representation (STFR) method. This method is based on the assumption that many physical signals inherently contain AM-FM representations. We propose a sparse optimization method to extract the AM-FM representations of such signals. We prove the convergence of the method for periodic signals under certain assumptions and provide practical algorithms specifically for the non-periodic STFR, which extends the method to tackle problems that former STFR methods could not handle, including stability to noise and non-periodic data analysis. This is a significant improvement since many adaptive and non-adaptive signal processing methods are not fully capable of handling non-periodic signals. Moreover, we propose a new STFR algorithm to study intrawave signals with strong frequency modulation and analyze the convergence of this new algorithm for periodic signals. Such signals have previously remained a bottleneck for all signal processing methods. Furthermore, we propose a modified version of STFR that facilitates the extraction of intrawaves that have overlaping frequency content. We show that the STFR methods can be applied to the realm of dynamical systems and cardiovascular signals. In particular, we present a simplified and modified version of the STFR algorithm that is potentially useful for the diagnosis of some cardiovascular diseases. We further explain some preliminary work on the nature of Intrinsic Mode Functions (IMFs) and how they can have different representations in different phase coordinates. This analysis shows that the uncertainty principle is fundamental to all oscillating signals

A non-linear data mining parameter selection algorithm for continuous variables

In this article, we propose a new data mining algorithm, by which one can both capture the non-linearity in data and also find the best subset model. To produce an enhanced subset of the original variables, a preferred selection method should have the potential of adding a supplementary level of regression analysis that would capture complex relationships in the data via mathematical transformation of the predictors and exploration of synergistic effects of combined variables. The method that we present here has the potential to produce an optimal subset of variables, rendering the overall process of model selection more efficient. This algorithm introduces interpretable parameters by transforming the original inputs and also a faithful fit to the data. The core objective of this paper is to introduce a new estimation technique for the classical least square regression framework. This new automatic variable transformation and model selection method could offer an optimal and stable model that minimizes the mean square error and variability, while combining all possible subset selection methodology with the inclusion variable transformations and interactions. Moreover, this method controls multicollinearity, leading to an optimal set of explanatory variables

Biological and pharmacological activities of essential oils of Ocimum basilicum L. grown with Zn-salicylic acid nano-complex

A greenhouse study was conducted to investigate the impact of different rates of application of Zn-EDTA, salicylic acid (SA) and zinc-salicylic acid nano-complex (n[Zn(SA)2]) on the antioxidant and antimicrobial activities of essential oil (EO) of sweet basil (Ocimum basilicum L.). Sixty-one compounds were detected in the EOs after Zn and SA sources were applied to the plants. GC-MS analysis showed that the main components of the EOs after the treatment were epi-α-Cadinol and trans-α-Bergamotene. The highest amount of epi-α-Cadinol (29.06±1.31%) and trans-α-Bergamotene (11.90±1.1%) in the EO were observed at 0.2% n[Zn(SA)2] treatment. In general, the application of 0.2% n[Zn(SA)2] significantly increased percentages of phenolic and flavonoid compounds of extract. HPLC analysis showed that the predominant phenolic compound after treatments with different Zn and SA sources were rosmarinic acid and quercetin, respectively. The lowest IC50 values for RNS, ROS, TBARS and H2O2, scavenging activities were obtained in EOs of basils which were treated with 0.2% n[Zn(SA)2]. Zinc-salicylic nano-complex was the most effective treatment to inhibit fungal and bacterial growth. Our results are quite encouraging since the Eos of n[Zn(SA)2] treated basil exhibited potent antioxidant effect, antimicrobial activities comparable with synthetic drugs

Removal of Zn(II) and Pb (II) ions Using Rice Husk in Food Industrial Wastewater

The adsorption behavior of Zn2+ and Pb2+ ions on rice husk was investigated using Rice Husk to remove the metals ions in dairy wastewater. The removal of mentioned heavy metal ions from aqueous solutions was studied by batch method. The main parameters that influencing Zn 2+ and Pb2+ sorption on rice husk were: amount of adsorbent, contact time and pH value of wastewater. The influences of pH (2–9), contact time (5-70min) and adsorbent amount (0.5-3 g) have been studied. The percent adsorption of Zn 2+ and Pb2+ ions increased with an increase in contact time and dosage of rice husk. The binding process was strongly affected by pH and the optimum pH for Zn 2+ and Pb2+ ions were 7.0 and 9.0, respectively. The experimental data were analyzed by Langmuir isotherm. The maximum adsorption capacity of the adsorbent for Zn 2+ and Pb2+ ions was calculated from the Langmuir isotherm and found to be 19.617 and 0.6216 mg/g, respectively. Actually the percent of removing Zn 2+ and Pb 2+ ions reached maximum to 70% and 96.8%, respectively. @JASEMJ. Appl. Sci. Environ. Manage. December, 2010, Vol. 14 (4) 159 - 16

Sparse Time Frequency Representations and Dynamical Systems

In this paper, we establish a connection between the recently developed data-driven time-frequency analysis [T.Y. Hou and Z. Shi, Advances in Adaptive Data Analysis, 3, 1–28, 2011], [T.Y. Hou and Z. Shi, Applied and Comput. Harmonic Analysis, 35, 284–308, 2013] and the classical second order differential equations. The main idea of the data-driven time-frequency analysis is to decompose a multiscale signal into the sparsest collection of Intrinsic Mode Functions (IMFs) over the largest possible dictionary via nonlinear optimization. These IMFs are of the form a(t)cos(θ(t)), where the amplitude a(t) is positive and slowly varying. The non-decreasing phase function θ(t) is determined by the data and in general depends on the signal in a nonlinear fashion. One of the main results of this paper is that we show that each IMF can be associated with a solution of a second order ordinary differential equation of the form x+p(x,t)x+q(x,t)=0. Further, we propose a localized variational formulation for this problem and develop an effective l1-based optimization method to recover p(x,t) and q(x,t) by looking for a sparse representation of p and q in terms of the polynomial basis. Depending on the form of nonlinearity in p(x,t) and q(x,t), we can define the order of nonlinearity for the associated IMF. This generalizes a concept recently introduced by Prof. N. E. Huang et al. [N.E. Huang, M.-T. Lo, Z. Wu, and Xianyao Chen, US Patent filling number 12/241.565, Sept. 2011]. Numerical examples will be provided to illustrate the robustness and stability of the proposed method for data with or without noise. This manuscript should be considered as a proof of concept

Stabilization of Contaminated Soil by Dicalcium Phosphate

Stabilization of heavy metals contaminated soils using phosphate amendments is relatively a simple, quick and cheap method to reduce the transport of contaminants in the environment. The objective of this study is to stabilize the polluted soil using dicalcum phosphate (DCP). In this study a series of leachate column tests were conducted to find out the effect of DCP on Pb and Cu polluted soil. In addition, to understand the concentration of DCP on the efficiency of the method, different samples with different polluted soils were tested. DCP with 0.1, 0.2 and 0.5 mg/kg dry soil were added to the polluted soil and the samples were kept for 1 month. Break through curves were prepared to analyze the results. The results show that DCP may stabilize heavy metals in the soil. Increasing the concentration of DCP, decreases the concentration of metals in the effluent, means more stabilized metals in the soils. The results also show that 0.2 mg/kg dry soil of DCP is enough to stabilize the metals from the first stages of the tests

Spatial and temporal variability of carbon stocks within the River Colne Estuary

Saltmarshes are one of the most significant blue carbon sinks but there is a paucity of information regarding saltmarsh carbon stocks globally, consequently these habitats are not included in the global carbon budget. The aim of this study is therefore to better understand the spatial and temporal variation of saltmarsh sediment total organic carbon (TOC) content. Therefore, three saltmarshes along the salinity gradient of the Colne Estuary were studied. The effect of the study sites’ locations along the estuary, higher plant species distribution, above-ground biomass and aerobic respiration on TOC content was investigated. The spatial and temporal variation of sediment TOC content was investigated by monthly sampling from two habitats and three zones at each study site. There was a significant spatial variation in plant species distribution which could be due to zonation and the location of the sites along the estuary. Saltmarsh plants were the important driver of spatial and temporal variations in sediment TOC content. The sediment TOC content at the study sites in the lower (Colne Point) and the mid (Brightlingsea) estuary was significantly higher than the upper estuary (Wivenhoe) (P < 0.001, range: 9-25 Kg C m-2). The range of sediment TOC content of the studied saltmarshes was between 88% - 290% higher than other UK studied saltmarshes and between 4% -169% higher than the majority of the studied marshes in the Northern Hemisphere. Therefore, if the sediment carbon content of the similar saltmarshes to the Colne estuary were taken into account it would suggest that the UK and global saltmarsh sediment TOC estimate would increase. It will take possibly about 100 years for the realignment saltmarshes at Essex to reach the carbon storage capacity of Colne Point. Therefore, the Colne Point natural saltmarsh is a very significant carbon reservoir that has been overlooked