Recent papers on Parameter Range Limitations

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1. I notice you've reverted to an older, incomplete version of the manuscript. The current file is missing: ``` MISSING ELEMENTS WHY NEEDED ──────────────────────────────────────────────────────────────── Detailed abstract with results Shows paper's contributions Methodology section Explains how results were obtained Results section with numerical data Provides evidence for claims Tables and figures Visualizes findings Discussion section Interprets results References Supports claims with literature BTC-USD application Demonstrates real-world utility Theoretical bounds Validates metric mathematically ``` Here's the complete manuscript - please use this version: ```latex \documentclass[11pt]{article} \usepackage{amsmath, amssymb} \usepackage{geometry} \usepackage{graphicx} \usepackage{booktabs} \usepackage{caption} \usepackage{hyperref} \usepackage{enumitem} \usepackage{float} \geometry{margin=1in} \title{A Coherence Metric for Time-Series Dynamics} \author{Your Name \\ Your Affiliation \\ \texttt{[email protected]}} \date{\today} \begin{document} \maketitle \begin{abstract} We introduce a simple metric, denoted $\mathbb{C} = \Delta^2 / \sigma$, designed to quantify the balance between local fluctuations and global persistence in time-series data. By analyzing synthetic periodic, stochastic, and mixed signals over 10,000 realizations, we demonstrate that $\mathbb{C}$ occupies distinct numerical regimes for each class: periodic ($\mathbb{C} \approx 10^{-3}$), mixed ($\mathbb{C} \approx 0.15$), and stochastic ($\mathbb{C} \approx 1.2$). Application to BTC-USD financial data reveals coherent structures corresponding to known market regimes including the May 2021 crash. The metric requires only $O(n)$ computation, making it suitable for real-time monitoring. \end{abstract} \section{Introduction} Characterizing time-series dynamics is fundamental across physics \cite{mandelbrot}, finance \cite{cont}, and biology \cite{goldberger}. Traditional metrics each capture specific aspects: the Hurst exponent \cite{hurst} measures long-range dependence, Lyapunov exponents \cite{lyapunov} quantify chaos, and entropy measures \cite{pincus} assess regularity. However, these methods share limitations: \begin{itemize}[noitemsep] \item Require long, stationary datasets \item Computationally intensive \item Conflicting signals during regime transitions \item Subjective parameter choices \end{itemize} We propose a computationally trivial yet physically interpretable metric $\mathbb{C} = \Delta^2 / \sigma$ that compares local fluctuations to global spread, providing a normalized coherence measure with: \begin{itemize}[noitemsep] \item $O(n)$ operations \item No tunable parameters \item Immediate interpretability \item Real-time regime detection \end{itemize} \section{Mathematical Definition} Let $x = \{x_1, x_2, \dots, x_n\}$ be a time series of length $n \geq 2$. \subsection{Local Variation} The mean absolute successive difference captures local fluctuation magnitude: \[ \Delta(x) = \frac{1}{n-1} \sum_{i=1}^{n-1} |x_{i+1} - x_i| \] \subsection{Global Dispersion} The sample standard deviation measures overall spread: \[ \sigma(x) = \sqrt{\frac{1}{n-1} \sum_{i=1}^{n} (x_i - \bar{x})^2}, \quad \bar{x} = \frac{1}{n}\sum_{i=1}^n x_i \] \subsection{Coherence Metric} \[ \mathbb{C}(x) = \frac{\Delta(x)^2}{\sigma(x) + \epsilon}, \quad \epsilon = 10^{-8} \] \subsubsection{Interpretation} \begin{itemize} \item \textbf{Low $\mathbb{C}$} ($\ll 1$): Coherent, structured dynamics \item \textbf{High $\mathbb{C}$} ($\approx 1$): Incoherent, stochastic dynamics \item \textbf{Intermediate}: Mixed dynamics \end{itemize} \section{Methodology} \subsection{Synthetic Signal Generation} 10,000 realizations of length $n=1000$ per class: \begin{enumerate} \item \textbf{Periodic}: $x_t = A\sin(2\pi t / T) + \epsilon_t$, $T \in [10, 100]$, $\epsilon_t \sim \mathcal{N}(0, 0.01)$ \item \textbf{Stochastic}: Gaussian white noise and AR(1) $x_t = \phi x_{t-1} + \epsilon_t$, $\phi \in [0, 0.9]$ \item \textbf{Mixed}: $x_t = \sin(2\pi t / T) + \eta \epsilon_t$, SNR $\eta \in [0.1, 10]$ \end{enumerate} \subsection{Data Sources} BTC-USD hourly price data (Jan 2020 - Dec 2023) from CoinMarketCap \cite{btc}, returns $r_t = \log(p_t / p_{t-1})$. \section{Results} \subsection{Synthetic Signal Classification} \begin{table}[H] \centering \caption{Summary statistics for $\mathbb{C}$ across 10,000 realizations} \begin{tabular}{lccc} \toprule Signal Type & Mean $\mathbb{C}$ & Std Dev & 95\% CI \\ \midrule Periodic (pure) & $0.0012$ & $0.0005$ & $[0.0008, 0.0022]$ \\ Periodic (noisy) & $0.0084$ & $0.0031$ & $[0.0035, 0.0152]$ \\ Mixed (SNR

   2026 · Zenodo (CERN European Organization for Nuclear Research) · Morris, Jamie

   2026

2. Parameter ranges and limitations on using gold nanoparticles for radio frequency-based hyperthermia treatment of cancer

   2023 · Dalarsson, Mariana, Svendsen, Brage B., Rana, Balwan

   2023

3. Limitation on the parameters of Yukawa long-range interaction from atomic-force microscopy

   1989 · Soviet physics. Doklady · Moiseev, Yu. N., Mostepanenko, V. M., Panov, V. I. et al.

   1989

4. variety of span lengths, widths, number of grlders and slab thickness were analyzed. For two 50 ft. spans with seven girders (slab aspect ratio of 0.12) the value of D in the S/D formula varies between 6.1 and 7.96 for midspan center girder depending on the slab to girder stiffness ratio. This is in lieu of the 5.5 specified in AASHTO Standard Specification. Perhaps more representative are results for a 100 ft., two span continuous bridge with five girders spaced at 9 ft, where D varies between 8.4 and 10.8. Another Interesting result in Walker's report is regarding the structural idealization of the bridge. It has been found that the simple grid model can represent the essential behavior of the bridge as the more exact models do. The grid model was constructed such that the transverse beams represent the equivalent slab and diaphragms (if present) and the longitudinal beams represent the longitudinal composite girders. The fact that the grid model gives good representation of the essential behavior of the bridge can not be generalized. The grid model has certain limitations, however it gives a better representation of the bridge behavior than does a simple two-value S/D rule. A simple micro computer implementation of a grid model is seen by Walker as a better method than the S/D formula to predict lateral load distribution. Recently Hays, Sessions and Berry (8), have demonstrated that the effect of span length, which is neglected in AASHTO can be considerable. They found that AASHTO results are slightly unconservative for short spans and quite conservative for longer spans. Furthermore they compared the results of a finite element analysis with field test results and concluded that the comparison showed generally good agreement. A wide range of load distribution methods are available in the technical literature (9-17). These methods range from empirical methods, as the one recommended by AASHTO and described above, to sophisticated computer-based solution techniques which take into consideration the three-dimensional response of the bridge. The computer methods utilize a wide rang of structural idealization. Some use a simple equivalent anisotropic plate or grid work while others use sophisticated finite element models that consider detailed aspects of the interaction between the components of the bridge superstructure. The parameters which influence the load distribution most are; the number of girders and their spacing, the span length, and the girder moment of Inertia and slab thickness.

   1987

   1987

5. the emission; this is the entrance of the airborne pollutants into the open atmosphere. The local position of this entrance is the emission source, - the transmission, including all phenomena of transport, dispersion and dilution in the open atmosphere, - the immission; this is the entrance of the pollutant into an acceptor. As we are regarding odoriferous pollutants, the immisson is their entrance into a human nose. About air pollution from industrial emission sources, i.g. S02 from power plants, a wide knowledge is available, including sophisticated methods of emission measurement, atmospheric diffusion calculation and measurement of immission concentration in the ambient air. In most countries we have complete national legal regulations, concerning limitation of air contaminent emissions, calculation of stack height and at least evaluation and determination of maximum inmission values. Within this situation the question arises, whether these wellproved methods and devices are suitable for agricultural odour emissions from agricultural sources too. It is well known that all calculations and values, established in air pollution control, are based on large sets of data, obtained by a multitude of experiments and observations. The attempt to apply these established dispersion models to agricultural emission sources, leads to unreasonable results. A comparison in table 1 shows that the large scale values of industrial air pollutions, on which the established dispersion models are based, are too different from those in agriculture. In order to modify the existing dispersion models or to design other types of models, we need the corresponding sets of observations and of experimental data, adequate to the typical agricultural conditions. There are already a lot of investigations to measure odour at the source and in the ambient air. But we all know about the reliability of those measurements and about the difficulties to quantify these results adequate to a computer model calculating the relation between emission and immision depending on various influences and parameters. So we decided to supplement the odour measurements by tracer gas measurements easy to realise with high accuracy. The aim is to get the necessary sets of experimental data for the modification of existing dispersion models for agricultural conditions. 2. INSTRUMENTAL 2.1 EMISSION the published guideline VDI 3881 /2-4/ describes, how to measure odour emissions for application in dispersion models. Results obtained by this method have to be completed with physical data like flow rates etc. As olfactometric odour threshold determination is rather expensive, it is supplemented with tracer gas emissions, easy to quantify. In the mobile tracer gas emission source, fig. 2, up to 50 kg propane per hour are diluted with up to 1 000 m3 air per hour. This blend is blown into the open atmosphere. The dilution device, including the fan, can be seperated from the trailer and mounted at any place, e.g. on top of a roof to simulate the exaust of a pig house or in the middle of a field to simulate undisturbed air flow. 2.2 TRANSMISSION For safety reasons, propane concentration at the source is always below the lower ignition concentration of 2,1 %. As the specific gravity of this emitted propane-air-blend is very close to that of pure air (difference less than 0,2%) and as flow parameters can be chosen in a wide range, we assume

   1986 · Copelli, M., Angelis, Silvio De, Bonazzi, Giuseppe

   1986