Minimizing the effect of sinusoidal trends in detrended fluctuation analysis

The detrended fluctuation analysis (DFA) [Peng et al., 1994] and its extensions (MF-DFA) [Kantelhardt et al., 2002] have been used extensively to determine possible long-range correlations in self-affine signals. While the DFA has been claimed to be a superior technique, recent reports have indicated its susceptibility to trends in the data. In this report, a smoothing filter is proposed to minimize the effect of sinusoidal trends and distortion in the log-log plots obtained by DFA and MF-DFA techniques

Sequential drain amylase to guide drain removal following pancreatectomy

BACKGROUND: Although used as criterion for early drain removal, postoperative day (POD) 1 drain fluid amylase (DFA) ≤ 5000 U/L has low negative predictive value for clinically relevant postoperative pancreatic fistula (CR-POPF). It was hypothesized that POD3 DFA ≤ 350 could provide further information to guide early drain removal. METHODS: Data from a pancreas surgery consortium database for pancreatoduodenectomy and distal pancreatectomy patients were analyzed retrospectively. Those patients without drains or POD 1 and 3 DFA data were excluded. Patients with POD1 DFA ≤ 5000 were divided into groups based on POD3 DFA: Group A (≤350) and Group B (>350). Operative characteristics and 60-day outcomes were compared using chi-square test. RESULTS: Among 687 patients in the database, all data were available for 380. Fifty-five (14.5%) had a POD1 DFA > 5000. Among 325 with POD1 DFA ≤ 5000, 254 (78.2%) were in Group A and 71 (21.8%) in Group B. Complications (35 (49.3%) vs 87 (34.4%); p = 0.021) and CR-POPF (13 (18.3%) vs 10 (3.9%); p < 0.001) were more frequent in Group B. CONCLUSIONS: In patients with POD1 DFA ≤ 5000, POD3 DFA ≤ 350 may be a practical test to guide safe early drain removal. Further prospective testing may be useful

A maximum likelihood based technique for validating detrended fluctuation analysis (ML-DFA)

Detrended Fluctuation Analysis (DFA) is widely used to assess the presence of long-range temporal correlations in time series. Signals with long-range temporal correlations are typically defined as having a power law decay in their autocorrelation function. The output of DFA is an exponent, which is the slope obtained by linear regression of a log-log fluctuation plot against window size. However, if this fluctuation plot is not linear, then the underlying signal is not self-similar, and the exponent has no meaning. There is currently no method for assessing the linearity of a DFA fluctuation plot. Here we present such a technique, called ML-DFA. We scale the DFA fluctuation plot to construct a likelihood function for a set of alternative models including polynomial, root, exponential, logarithmic and spline functions. We use this likelihood function to determine the maximum likelihood and thus to calculate values of the Akaike and Bayesian information criteria, which identify the best fit model when the number of parameters involved is taken into account and over-fitting is penalised. This ensures that, of the models that fit well, the least complicated is selected as the best fit. We apply ML-DFA to synthetic data from FARIMA processes and sine curves with DFA fluctuation plots whose form has been analytically determined, and to experimentally collected neurophysiological data. ML-DFA assesses whether the hypothesis of a linear fluctuation plot should be rejected, and thus whether the exponent can be considered meaningful. We argue that ML-DFA is essential to obtaining trustworthy results from DFA.Comment: 22 pages, 7 figure

Minimal Synthesis of String To String Functions From Examples

We study the problem of synthesizing string to string transformations from a set of input/output examples. The transformations we consider are expressed using deterministic finite automata (DFA) that read pairs of letters, one letter from the input and one from the output. The DFA corresponding to these transformations have additional constraints, ensuring that each input string is mapped to exactly one output string. We suggest that, given a set of input/output examples, the smallest DFA consistent with the examples is a good candidate for the transformation the user was expecting. We therefore study the problem of, given a set of examples, finding a minimal DFA consistent with the examples and satisfying the functionality and totality constraints mentioned above. We prove that, in general, this problem (the corresponding decision problem) is NP-complete. This is unlike the standard DFA minimization problem which can be solved in polynomial time. We provide several NP-hardness proofs that show the hardness of multiple (independent) variants of the problem. Finally, we propose an algorithm for finding the minimal DFA consistent with input/output examples, that uses a reduction to SMT solvers. We implemented the algorithm, and used it to evaluate the likelihood that the minimal DFA indeed corresponds to the DFA expected by the user.Comment: SYNT 201

Detrended fluctuation analysis for fractals and multifractals in higher dimensions

One-dimensional detrended fluctuation analysis (1D DFA) and multifractal detrended fluctuation analysis (1D MF-DFA) are widely used in the scaling analysis of fractal and multifractal time series because of being accurate and easy to implement. In this paper we generalize the one-dimensional DFA and MF-DFA to higher-dimensional versions. The generalization works well when tested with synthetic surfaces including fractional Brownian surfaces and multifractal surfaces. The two-dimensional MF-DFA is also adopted to analyze two images from nature and experiment and nice scaling laws are unraveled.Comment: 7 Revtex pages inluding 11 eps figure