Intrinsic Entropy Research Articles

FUZZY INTRINSIC MODE ENTROPY FOR DATA FEATURE EXTRACTION

The notion of fuzzy entropy (FuzzyEn) is extended to the multiscale case by combining FuzzyEn and empirical mode decomposition (EMD). The proposed technique, fuzzy intrinsic entropy (FIMEn) performs better than its predecessor intrinsic monde entropy (IMEn) and it is less dependent on the algorithmic parameters. In a pattern recognition context, FIMEn provides more separable clusters than IMEn when used for feature extraction, thus allowing for less classification error. The above results suggest that the proposed multiscale entropy metric is a very promising technique for evaluating data regularity and can be used effectively for feature extraction in pattern recognition problems.

Some aspects of virtual black holes

We first consider consistently third-quantize modified gravity. We then analyze certain aspects of virtual black holes in this third-quantized modified gravity. We see how a statistical mechanical origin for the Bekenstein-Hawking entropy naturally arises in this model. Furthermore, the area and hence the entropy of a real macroscopic black hole is quantized in this model. Virtual black holes cause a loss of quantum coherence, which gives an intrinsic entropy to all physical systems that can be used to define a direction of time and hence provide a solution to the problem of time.

Estimation of entropy rate in a fast physical random-bit generator using a chaotic semiconductor laser with intrinsic noise

We analyze the time for growth of bit entropy when generating nondeterministic bits using a chaotic semiconductor laser model. The mechanism for generating nondeterministic bits is modeled as a 1-bit sampling of the intensity of light output. Microscopic noise results in an ensemble of trajectories whose bit entropy increases with time. The time for the growth of bit entropy, called the memory time, depends on both noise strength and laser dynamics. It is shown that the average memory time decreases logarithmically with increase in noise strength. It is argued that the ratio of change in average memory time with change in logarithm of noise strength can be used to estimate the intrinsic dynamical entropy rate for this method of random bit generation. It is also shown that in this model the entropy rate corresponds to the maximum Lyapunov exponent.

Facetted patchy particles through entropy-driven patterning of mixed ligand SAMS

We present a microscopic theory that describes the ordering of two distinct ligands on the surface of a facetted nanoparticle. The theory predicts that when one type of ligand is significantly bulkier than all others, the larger ligands preferentially align themselves along the edges and vertices of the nanoparticle. Monte Carlo simulations confirm these predictions. We show that the intrinsic conformational entropy of the ligands stabilizes this novel edge-aligned phase.

Weak Target Detection Based on Intrinsic Mode Energy Entropy

Weak Target Detection Based on Intrinsic Mode Energy Entropy

Network Topology and Communication Data Rate for Consensusability of Discrete-Time Multi-Agent Systems

This paper investigates the joint effect of agent dynamic, network topology and communication data rate on consensusability of linear discrete-time multi-agent systems. Neglecting the finite communication data rate constraint and under undirected graphs, a necessary and sufficient condition for consensusability under a common control protocol is given, which explicitly reveals how the intrinsic entropy rate of the agent dynamic and the communication graph jointly affect consensusability. The result is established by solving a discrete-time simultaneous stabilization problem. A lower bound of the optimal convergence rate to consensus, which is shown to be tight for some special cases, is provided as well. Moreover, a necessary and sufficient condition for formationability of multi-agent systems is obtained. As a special case, the discrete-time second-order consensus is discussed where an optimal control gain is designed to achieve the fastest convergence. The effects of undirected graphs on consensability/formationability and optimal convergence rate are exactly quantified by the ratio of the second smallest to the largest eigenvalues of the graph Laplacian matrix. An extension to directed graphs is also made. The consensus problem under a finite communication data rate is finally investigated.

A Lossless Data Compression System for a Real-Time Application in HEP Data Acquisition

This paper presents a compression system optimized for the reduction of data from pulse digitizing electronics. Such systems are widely used in High Energy Physics experiments for the collection of signals from calorimeters, Time Projection Chambers and in general all detectors that produce a signal amplified and/or shaped to a linear pulse. The Time Projection Chamber of the ALICE experiment will be used as an illustration of our method, which we believe is widely adaptable to other data acquisition chains in High Energy Physics. To go beyond what can be achieved by conventional lossless compression schemes, which are ultimately limited by the intrinsic entropy of the incoming data, the proposed compression method makes use of a new scheme where instead of handling the data from the ADC as individual uncorrelated samples, an entire vector of samples is compressed. Our method works by first approximating the incoming vectors formed by the digitization of the shaped pulses with a set of digitized reference vectors stored in a memory and retaining only the differences between these vectors using Huffman compression. In standard data compression language, this corresponds to a vector quantization combined with Huffman coding. The performance of the described compression method was first evaluated by modeling the algorithm in Matlab using input data measured from the TPC in the ALICE experiment. A compression of 49% has been achieved. It has to be noted that the entropy computed on these same 10 bit original data was only 6.2 bit/symbol thus allowing a maximum compression factor of 38% only. The compression method was subsequently modeled in Verilog and synthesized to be combined with the other logic in the actual Read-out Control Unit of the ALICE TPC. First tests with actual hardware were performed using a Virtex-4 development board running at 80 MHz. The results showing the efficiency of the implementation using cosmic ray data are presented. The algorithm is executed in this hardware with a latency of around 24 clock cycles at 40 MHz and takes about 2000 logic slices to be implemented.

Intrinsic Mode Entropy Analysis of Tube-Wall Pressure Fluctuation Signals in the Kenics Static Mixer

The multi-scale nonlinear hydrodynamics in Kenics Static Mixer (KSM) with 100 mm in diameter and 2 in aspect ratio was investigated in this work. The time series of tube-wall pressure fluctuation signals were measured at different flow rates ranged of 100~600 L•h-1 and at different axial positions in the range of 420~580 mm away from the cross-section of mixer inlet. It is difficult for composite signals to make an effective analysis by Sample Entropy (SampEn) based on a single scale. The complexity of tube-wall pressure fluctuation signals in a Kenics static mixer was investigated using Intrinsic Mode Entropy (IMEn) based on Sample Entropy algorithm and Empirical Mode Decomposition (EMD) method. Data sampling length and tolerance are optimized based on intrinsic mode entropy. Results of multi-scale analysis of pressure fluctuations indicated that the Sample entropy reaches maximum in the first scale and progressively decreases according to increase of the decomposed order. It is clear that the movement of high frequency component of the pressure signal is the most complicated and is rich in randomness. With the decomposition scales increasing, the complexity of signal decreases and approaches periodic motion eventually. The intrinsic mode entropy of the tube wall pressure signals in KSM has similar development tendencies in different flow rates. Besides, as the flow rates increased, the macro-scale vortexes play a more and more important role and guide the system to develop toward the stable state.

Reheating in tachyonic inflationary models: Effects on the large scale curvature perturbations

We investigate the problem of perturbative reheating and its effects on the evolution of the curvature perturbations in tachyonic inflationary models. We derive the equations governing the evolution of the scalar perturbations for a system consisting of a tachyon and a perfect fluid. Assuming the perfect fluid to be radiation, we solve the coupled equations for the system numerically and study the evolution of the perturbations from the sub-Hubble to the super-Hubble scales. In particular, we analyze the effects of the transition from tachyon driven inflation to the radiation dominated epoch on the evolution of the large scale curvature and non-adiabatic pressure perturbations. We consider two different potentials to describe the tachyon and study the effects of two possible types of decay of the tachyon into radiation. We plot the spectrum of curvature perturbations at the end of inflation as well as at the early stages of the radiation dominated epoch. We find that reheating does not affect the amplitude of the curvature perturbations in any of these cases. These results corroborate similar conclusions that have been arrived at earlier based on the study of the evolution of the perturbations in the super-Hubble limit. We illustrate that, before the transition to the radiation dominated epoch, the relative non-adiabatic pressure perturbation between the tachyon and radiation decays in a fashion very similar to that of the intrinsic entropy perturbation associated with the tachyon. Moreover, we show that, after the transition, the relative non-adiabatic pressure perturbation dies down extremely rapidly during the early stages of the radiation dominated epoch. It is these behavior which ensure that the amplitude of the curvature perturbations remain unaffected during reheating. We also discuss the corresponding results for the popular chaotic inflation model in the case of the canonical scalar field.

Fault Diagnosis to a Rolling Bearing in a Blowing Machine Based on the Theories of EMD and Intrinsic Modal Energy Entropy

Based on the research of the theory and the experiment of EMD and Intrinsic Modal Energy Entropy，the vibration signal of a rolling bearing in a Blowing Machine of a certain factory was measured when working. Then the signal was decomposed by EMD, its Intrinsic Modal Energy Entropy was calculated and used as fault feature. Finally, using a Support Vector Classification System, a satisfied effect of fault diagnosis of a rolling bearing in a Blowing Machine was got. The experiment had confirmed that the method was advanced, reliable and practical. A new method was provided for fault diagnosis of rolling bearings in some Blowing Machines.

Eurekometrics: Analyzing the Nature of Discovery

Eurekometrics: Analyzing the Nature of Discovery

Intrinsic mode entropy based on multivariate empirical mode decomposition and its application to neural data analysis

Entropy, a measure of the regularity of a time series, has long been used to quantify the complexity of brain dynamics. Given the multiple spatiotemporal scales inherent in the brain, traditional entropy analysis based on a single scale is not adequate to accurately describe the underlying nonlinear dynamics. Intrinsic mode entropy (IMEn) is a recent development with appealing properties to estimate entropy over multiple time scales. It is a multiscale entropy measure that computes sample entropy (SampEn) over different scales of intrinsic mode functions extracted by empirical mode decomposition (EMD) method. However, it suffers from both mode-misalignment and mode-mixing problems when applied to multivariate time series data. In this paper, we address these two problems by employing the recently introduced multivariate empirical mode decomposition (MEMD). First, we extend the MEMD to multi-channel multi-trial neural data to ensure the IMEn matched at different scales. Second, for the discriminant analysis of IMEn, we propose to improve the discriminative ability by including variance that has not been used before in entropy analysis. Finally, we apply the proposed approach to the multi-electrode local field potentials (LFPs) simultaneously collected from visual cortical areas of macaque monkeys while performing a generalized flash suppression task. The results have shown that the entropy of LFP is indeed scale-dependent and is closely related to the perceptual conditions. The discriminative results of the perceptual conditions, revealed by support vector machine, show that the accuracy based on IMEn and variance reaches 83.05%, higher than that only by IMEn (76.27%). These results suggest that our approach is sensitive to capture the complex dynamics of neural data.

Stochastic thermodynamics of single enzymes and molecular motors

For a single enzyme or molecular motor operating in an aqueous solution of non-equilibrated solute concentrations, a thermodynamic description is developed on the level of an individual trajectory of transitions between states. The concept of internal energy, intrinsic entropy and free energy for states follows from a microscopic description using one assumption on time scale separation. A first-law energy balance then allows the unique identification of the heat dissipated in one transition. Consistency with the second law on the ensemble level enforces both stochastic entropy as third contribution to the entropy change involved in one transition and the local detailed balance condition for the ratio between forward and backward rates for any transition. These results follow without assuming weak coupling between the enzyme and the solutes, ideal solution behavior or mass action law kinetics. The present approach highlights both the crucial role of the intrinsic entropy of each state and the physically questionable role of chemiostats for deriving the first law for molecular motors subject to an external force under realistic conditions.

Coordination of discrete‐time multi‐agent systems via relative output feedback

AbstractThis paper investigates the joint effects of agent dynamic and network topology on the consensusability of linear discrete‐time multi‐agent systems via relative output feedback. An observer‐based distributed control protocol is proposed. A necessary and sufficient condition for consensusability under this control protocol is given, which explicitly reveals how the intrinsic entropy rate of the agent dynamic and the eigenratio of the undirected communication graph affect consensusability. As a special case, multi‐agent systems with discrete‐time double integrator dynamics are discussed where a simple control protocol directly using two‐step relative position feedback is provided to reach a consensus. Finally, the result is extended to solve the formation and formation‐based tracking problems. The theoretical results are illustrated by simulations. Copyright © 2010 John Wiley & Sons, Ltd.

Single-Parameter Quantification of the Sensitivity of a Molecular Collision to Molecular Polarization

This article introduces the concept of intrinsic entropy, S, of a molecular collision. Defined in rigorously quantum mechanical terms as the von Neumann entropy of the intrinsic density matrices of reagents and products, the intrinsic entropy is a dimensionless number in the 0 < or = S < or = 1 range. Its limits are associated with situations where the collision cross section is due to a single combination of reagent and product polarizations (S = 0) or where there is absolutely no selectivity with respect to the molecular polarizations (S = 1). The usefulness of the intrinsic entropy as a quantifier of the sensitivity of a molecular collision to molecular polarizations is demonstrated with examples for the benchmark H + D(2) reaction.

Extensive chaotic dynamics in neural networks in the balanced state

The irregular activity of neurons in the cortex [1] is thought to arise from strong input fluctuations [2], which result from a balance between excitatory and inhibitory synaptic inputs [3]. This is called the balanced state of cortical networks. However, recent studies of the underlying dynamics of the balanced state have led to contrary results, strongly depending on the used single neuron models [3, 4]. Here, we study the network dynamics of sparsely coupled theta neurons in the balanced state. The theta neuron model has an active spike generating mechanism and is the standard form of type I neurons [5]. In a random matrix approximation of the Jacobian, we derive an expression for the mean Lyapunov exponent. By analyzing the full set of Lyapunov exponents and the maximal Lyapunov vector in a numerically exact way, we reveal extensive spatio-temporal deterministic chaos. The studied networks exhibit high-dimensional chaotic attractors, giving rise to many dynamical degrees of freedom to encode information. At the same time, the intrinsic entropy production is surprisingly high, limiting information processing to the immediate stimulus response. Purely inhibitorily coupled networks

New perspective on the relation between dark energy perturbations and the late-time integrated Sachs-Wolfe effect

The effect of quintessence perturbations on the integrated Sachs-Wolfe (ISW) effect is studied for a mixed dynamical scalar field dark energy (DDE) and pressureless perfect fluid dark matter. A new and general methodology is developed to track the growth of the perturbations, which uses only the equation of state (EoS) parameter ${w}_{\mathrm{DDE}}(z)\ensuremath{\equiv}{p}_{\mathrm{DDE}}/{\ensuremath{\rho}}_{\mathrm{DDE}}$ of the scalar field DDE, and the initial values of the relative entropy perturbation (between the matter and DDE) and the intrinsic entropy perturbation of the scalar field DDE as inputs. We also derive a relation between the rest-frame sound speed ${\stackrel{^}{c}}_{s,\mathrm{DDE}}^{2}$ of an arbitrary scalar field DDE component and its EoS ${w}_{\mathrm{DDE}}(z)$. We show that the ISW signal differs from that expected in a $\ensuremath{\Lambda}\mathrm{CDM}$ cosmology by as much as $+20%$ to $\ensuremath{-}80%$ for parametrizations of ${w}_{\mathrm{DDE}}$ consistent with SNIa data, and about $\ifmmode\pm\else\textpm\fi{}20%$ for parametrizations of ${w}_{\mathrm{DDE}}$ consistent with $\mathrm{SNIa}+\mathrm{CMB}+\mathrm{BAO}$ data, at 95% confidence. Our results indicate that, at least in principle, the ISW effect can be used to phenomenologically distinguish a cosmological constant from DDE.

Combinatorial lemmas and applications to dynamics

The well-known combinatorial lemma of Karpovsky, Milman and Alon and a very recent one of Kerr and Li are extended. The obtained lemmas are applied to study the maximal pattern entropy introduced in the paper. It turns out that the maximal pattern entropy is equal to the supremum of sequence entropies over all sequences both in topological and measure-theoretical settings. Moreover, it is shown the maximal pattern entropy of any topological system is log k for some k ∈ N ∪ { ∞ } with k the maximal length of intrinsic sequence entropy tuples; and a zero-dimensional system has zero sequence entropy for any sequence if and only if the maximal pattern with respect to any open cover is of polynomial order.

THERMODYNAMICS OF MODIFIED BLACK HOLES FROM GRAVITY'S RAINBOW

We study the thermodynamics of modified black holes proposed in the context of gravity's rainbow. A notion of intrinsic temperature and entropy for these black holes is introduced. In particular for a specific class of modified Schwarzschild solutions, their temperature and entropy are obtained and compared with those previously obtained from modified dispersion relations in deformed special relativity. It turns out that the results of these two different strategies coincide, and this may be viewed as a support for the proposal of deformed equivalence principle.

Topological permutation entropy

Permutation entropy quantifies the diversity of possible ordering of the successively observed values a random or deterministic system can take, just as Shannon entropy quantifies the diversity of the values themselves. When the observable or state variable has a natural order relation, making permutation entropy possible to compute, then the asymptotic rate of growth in permutation entropy with word length forms an alternative means of describing the intrinsic entropy rate of a source. Herein, extending a previous result on metric entropy rate, we show that the topological permutation entropy rate for expansive maps equals the conventional topological entropy rate familiar from symbolic dynamics. This result is not limited to one-dimensional maps.