Prediction of naturally-occurring, industrially-induced and total trans fatty acids in butter, dairy spreads and Cheddar cheese using vibrational spectroscopy and multivariate data analysis

peer-reviewedThis study investigated the use of vibrational spectroscopy [near infrared (NIR), Fourier-transform mid-infrared (FT-MIR), Raman] and multivariate data analysis for (1) quantifying total trans fatty acids (TT), and (2) separately predicting naturally-occurring (NT; i.e., C16:1 t9; C18:1 trans-n, n = 6 … 9, 10, 11; C18:2 trans) and industrially-induced trans fatty acids (IT = TT – NT) in Irish dairy products, i.e., butter (n = 60), Cheddar cheese (n = 44), and dairy spreads (n = 54). Partial least squares regression models for predicting NT, IT and TT in each type of dairy product were developed using FT-MIR, NIR and Raman spectral data. Models based on NIR, FT-MIR and Raman spectra were used for the prediction of NT and TT content in butter; best prediction performance achieved a coefficient of determination in validation (R2V) ∼ 0.91–0.95, root mean square error of prediction (RMSEP) ∼ 0.07–0.30 for NT; R2V ∼ 0.92–0.95, RMSEP ∼ 0.23–0.29 for TT.This project was funded by the Irish Department of Agriculture, Food and the Marine as part of CheeseBoard 2015. Ming Zhao is a Teagasc Walsh Fellow

On the Decoding Complexity of Cyclic Codes Up to the BCH Bound

The standard algebraic decoding algorithm of cyclic codes $[n,k,d]$ up to the BCH bound $t$ is very efficient and practical for relatively small $n$ while it becomes unpractical for large $n$ as its computational complexity is $O(nt)$. Aim of this paper is to show how to make this algebraic decoding computationally more efficient: in the case of binary codes, for example, the complexity of the syndrome computation drops from $O(nt)$ to $O(t\sqrt n)$, and that of the error location from $O(nt)$ to at most $\max \{O(t\sqrt n), O(t^2\log(t)\log(n))\}$.Comment: accepted for publication in Proceedings ISIT 2011. IEEE copyrigh

An Efficient Parallel Algorithm for Spectral Sparsification of Laplacian and SDDM Matrix Polynomials

For "large" class $\mathcal{C}$ of continuous probability density functions (p.d.f.), we demonstrate that for every $w\in\mathcal{C}$ there is mixture of discrete Binomial distributions (MDBD) with $T\geq N\sqrt{\phi_{w}/\delta}$ distinct Binomial distributions $B(\cdot,N)$ that $\delta$-approximates a discretized p.d.f. $\widehat{w}(i/N)\triangleq w(i/N)/[\sum_{\ell=0}^{N}w(\ell/N)]$ for all $i\in[3:N-3]$, where $\phi_{w}\geq\max_{x\in[0,1]}|w(x)|$. Also, we give two efficient parallel algorithms to find such MDBD. Moreover, we propose a sequential algorithm that on input MDBD with $N=2^k$ for $k\in\mathbb{N}_{+}$ that induces a discretized p.d.f. $\beta$, $B=D-M$ that is either Laplacian or SDDM matrix and parameter $\epsilon\in(0,1)$, outputs in $\widehat{O}(\epsilon^{-2}m + \epsilon^{-4}nT)$ time a spectral sparsifier $D-\widehat{M}_{N} \approx_{\epsilon} D-D\sum_{i=0}^{N}\beta_{i}(D^{-1} M)^i$ of a matrix-polynomial, where $\widehat{O}(\cdot)$ notation hides $\mathrm{poly}(\log n,\log N)$ factors. This improves the Cheng et al.'s [CCLPT15] algorithm whose run time is $\widehat{O}(\epsilon^{-2} m N^2 + NT)$. Furthermore, our algorithm is parallelizable and runs in work $\widehat{O}(\epsilon^{-2}m + \epsilon^{-4}nT)$ and depth $O(\log N\cdot\mathrm{poly}(\log n)+\log T)$. Our main algorithmic contribution is to propose the first efficient parallel algorithm that on input continuous p.d.f. $w\in\mathcal{C}$, matrix $B=D-M$ as above, outputs a spectral sparsifier of matrix-polynomial whose coefficients approximate component-wise the discretized p.d.f. $\widehat{w}$. Our results yield the first efficient and parallel algorithm that runs in nearly linear work and poly-logarithmic depth and analyzes the long term behaviour of Markov chains in non-trivial settings. In addition, we strengthen the Spielman and Peng's [PS14] parallel SDD solver

The Multi-Biomarker Approach for Heart Failure in Patients with Hypertension

We assessed the predictive ability of selected biomarkers using N-terminal pro-brain natriuretic peptide (NT-proBNP) as the benchmark and tried to establish a multi-biomarker approach to heart failure (HF) in hypertensive patients. In 120 hypertensive patients with or without overt heart failure, the incremental predictive value of the following biomarkers was investigated: Collagen III N-terminal propeptide (PIIINP), cystatin C (CysC), lipocalin-2/NGAL, syndecan-4, tumor necrosis factor-α (TNF-α), interleukin 1 receptor type I (IL1R1), galectin-3, cardiotrophin-1 (CT-1), transforming growth factor β (TGF-β) and N-terminal pro-brain natriuretic peptide (NT-proBNP). The highest discriminative value for HF was observed for NT-proBNP (area under the receiver operating characteristic curve (AUC) = 0.873) and TGF-β (AUC = 0.878). On the basis of ROC curve analysis we found that CT-1 > 152 pg/mL, TGF-β 2.3 ng/mL, NT-proBNP > 332.5 pg/mL, CysC > 1 mg/L and NGAL > 39.9 ng/mL were significant predictors of overt HF. There was only a small improvement in predictive ability of the multi-biomarker panel including the four biomarkers with the best performance in the detection of HF—NT-proBNP, TGF-β, CT-1, CysC—compared to the panel with NT-proBNP, TGF-β and CT-1 only. Biomarkers with different pathophysiological backgrounds (NT-proBNP, TGF-β, CT-1, CysC) give additive prognostic value for incident HF in hypertensive patients compared to NT-proBNP alone.The study was financed by JUVENTUS PLUS grant 2012 (No. IP2011003271) of the Polish Ministry of Science and Higher Education (MNiSW) and research grant of Medical University in Lodz and MNiSW No. 502-03/5-139-02/502-54-008

On higher analogues of Courant algebroids

In this paper, we study the algebraic properties of the higher analogues of Courant algebroid structures on the direct sum bundle $TM\oplus\wedge^nT^*M$ for an $m$-dimensional manifold. As an application, we revisit Nambu-Poisson structures and multisymplectic structures. We prove that the graph of an $(n+1)$-vector field $\pi$ is closed under the higher-order Dorfman bracket iff $\pi$ is a Nambu-Poisson structure. Consequently, there is an induced Leibniz algebroid structure on $\wedge^nT^*M$. The graph of an $(n+1)$-form $\omega$ is closed under the higher-order Dorfman bracket iff $\omega$ is a premultisymplectic structure of order $n$, i.e. \dM\omega=0. Furthermore, there is a Lie algebroid structure on the admissible bundle $A\subset\wedge^{n}T^*M$. In particular, for a 2-plectic structure, it induces the Lie 2-algebra structure given in \cite{baez:classicalstring}.Comment: 13 page