Entropy

274 KiB

Open AccessArticle

Entropy and Computation: The Landauer-Bennett Thesis Reexamined

by Meir Hemmo and Orly Shenker

Entropy 2013, 15(8), 3297-3311; https://doi.org/10.3390/e15083297 - 21 Aug 2013

Cited by 13 | Viewed by 6486

The so-called Landauer-Bennett thesis says that logically irreversible operations (physically implemented) such as erasure necessarily involve dissipation by at least kln2 per bit of lost information. We identify the physical conditions that are necessary and sufficient for erasure and show that the [...] Read more.

The so-called Landauer-Bennett thesis says that logically irreversible operations (physically implemented) such as erasure necessarily involve dissipation by at least kln2 per bit of lost information. We identify the physical conditions that are necessary and sufficient for erasure and show that the thesis does not follow from the principles of classical mechanics. In particular, we show that even if one assumes that information processing is constrained by the laws of classical mechanics, it need not be constrained by the Second Law of thermodynamics. Full article

(This article belongs to the Special Issue Maxwell’s Demon 2013)

► Show Figures

Figure 1

11348 KiB

Open AccessArticle

Fluctuations in the Energetic Properties of a Spark-Ignition Engine Model with Variability

by Pedro L. Curto-Risso, Alejandro Medina, Antonio Calvo-Hernández, Lev Guzmán-Vargas and Fernando Angulo-Brown

Entropy 2013, 15(8), 3277-3296; https://doi.org/10.3390/e15083367 - 19 Aug 2013

Cited by 8 | Viewed by 4034

Abstract

We study the energetic functions obtained in a simulated spark-ignited engine that incorporates cyclic variability through a quasi-dimensional combustion model. Our analyses are focused on the effects of the fuel-air equivalence ratio of the mixture simultaneously over the cycle-to-cycle fluctuations of heat release [...] Read more.

We study the energetic functions obtained in a simulated spark-ignited engine that incorporates cyclic variability through a quasi-dimensional combustion model. Our analyses are focused on the effects of the fuel-air equivalence ratio of the mixture simultaneously over the cycle-to-cycle fluctuations of heat release (Q_R) and the performance outputs, such as the power (P) and the efficiency (Q_R). We explore the fluctuant behavior for Q_R, P and n related to random variations of the basic physical parameters in an entrainment or eddy-burning combustion model. P and n show triangle shaped first return maps, while Q_R exhibits a structured map, especially at intermediated fuel-air ratios. Structure disappears to a considerable extent in the case of heat release and close-to-stoichiometry fuel-air ratios. By analyzing the fractal dimension to explore the presence of correlations at different scales, we find that whereas Q_R displays short-range correlations for intermediate values of the fuel ratio, both P and n are characterized by a single scaling exponent, denoting irregular fluctuations. A novel noisy loop-shaped P vs. n plot for a large number of engine cycles is obtained. This plot, which evidences different levels of irreversibilities as the fuel ratio changes, becomes the observed loop P vs. n curve when fluctuations are disregarded, and thus, only the mean values for efficiency and power are considered. Full article

► Show Figures

Figure 1

421 KiB

Open AccessArticle

Synchronization of a Class of Fractional-Order Chaotic Neural Networks

by Liping Chen, Jianfeng Qu, Yi Chai, Ranchao Wu and Guoyuan Qi

Entropy 2013, 15(8), 3265-3276; https://doi.org/10.3390/e15083355 - 14 Aug 2013

Cited by 71 | Viewed by 5689

Abstract

The synchronization problem is studied in this paper for a class of fractional-order chaotic neural networks. By using the Mittag-Leffler function, M-matrix and linear feedback control, a sufficient condition is developed ensuring the synchronization of such neural models with the Caputo fractional derivatives. [...] Read more.

The synchronization problem is studied in this paper for a class of fractional-order chaotic neural networks. By using the Mittag-Leffler function, M-matrix and linear feedback control, a sufficient condition is developed ensuring the synchronization of such neural models with the Caputo fractional derivatives. The synchronization condition is easy to verify, implement and only relies on system structure. Furthermore, the theoretical results are applied to a typical fractional-order chaotic Hopfield neural network, and numerical simulation demonstrates the effectiveness and feasibility of the proposed method. Full article

(This article belongs to the Special Issue Dynamical Systems)

► Show Figures

Figure 1

240 KiB

Open AccessArticle

Truncation Effects of Shift Function Methods in Bulk Water Systems

by Kazuaki Z. Takahashi

Entropy 2013, 15(8), 3249-3264; https://doi.org/10.3390/e15083339 - 13 Aug 2013

Cited by 14 | Viewed by 4479

Abstract

A reduction of the cost for long-range interaction calculation is essential for large-scale molecular systems that contain a lot of point charges. Cutoff methods are often used to reduce the cost of long-range interaction calculations. Molecular dynamics (MD) simulations can be accelerated by [...] Read more.

A reduction of the cost for long-range interaction calculation is essential for large-scale molecular systems that contain a lot of point charges. Cutoff methods are often used to reduce the cost of long-range interaction calculations. Molecular dynamics (MD) simulations can be accelerated by using cutoff methods; however, simple truncation or approximation of long-range interactions often offers serious defects for various systems. For example, thermodynamical properties of polar molecular systems are strongly affected by the treatment of the Coulombic interactions and may lead to unphysical results. To assess the truncation effect of some cutoff methods that are categorized as the shift function method, MD simulations for bulk water systems were performed. The results reflect two main factors, i.e., the treatment of cutoff boundary conditions and the presence/absence of the theoretical background for the long-range approximation. Full article

(This article belongs to the Special Issue Molecular Dynamics Simulation)

► Show Figures

Figure 1

280 KiB

Open AccessArticle

Limits and Optimization of Power Input or Output of Actual Thermal Cycles

by Emin Açıkkalp and Hasan Yamık

Entropy 2013, 15(8), 3219-3248; https://doi.org/10.3390/e15083309 - 12 Aug 2013

Cited by 30 | Viewed by 4290

Abstract

In classical thermodynamic, maximum power obtained from system (or minimum power supplied to system) defined as availability (exergy), but availability term is only used for reversible systems. In reality, there is no reversible system, all systems are irreversible, because reversible cycles doesn’t include [...] Read more.

In classical thermodynamic, maximum power obtained from system (or minimum power supplied to system) defined as availability (exergy), but availability term is only used for reversible systems. In reality, there is no reversible system, all systems are irreversible, because reversible cycles doesn’t include constrains like time or size and they operates in quasi-equilibrium state. Purpose of this study is to define limits of the all basic thermodynamic cycles and to provide finite-time exergy models for irreversible cycles and to obtain the maximum (or minimum) available power for irreversible (finite-time exergy) cycles. In this study, available power optimization and performance limits were defined all basic irreversible thermodynamic cycles, by using first and second law of thermodynamic. Finally, these results were evaluated in terms of cycles’ first and second law efficiency, COP, power output (or input) and exergy destruction. Full article

► Show Figures

Figure 1

1462 KiB

Open AccessArticle

Local Feature Extraction and Information Bottleneck-Based Segmentation of Brain Magnetic Resonance (MR) Images

by Pengcheng Shen and Chunguang Li

Entropy 2013, 15(8), 3205-3218; https://doi.org/10.3390/e15083295 - 9 Aug 2013

Cited by 8 | Viewed by 3895

Abstract

Automated tissue segmentation of brain magnetic resonance (MR) images has attracted extensive research attention. Many segmentation algorithms have been proposed for this issue. However, due to the existence of noise and intensity inhomogeneity in brain MR images, the accuracy of the segmentation results [...] Read more.

Automated tissue segmentation of brain magnetic resonance (MR) images has attracted extensive research attention. Many segmentation algorithms have been proposed for this issue. However, due to the existence of noise and intensity inhomogeneity in brain MR images, the accuracy of the segmentation results is usually unsatisfactory. In this paper, a high-accuracy brain MR image segmentation algorithm based on the information bottleneck (IB) method is presented. In this approach, the MR image is first mapped into a “local-feature space”, then the IB method segments the brain MR image through an information theoretic formulation in this local-feature space. It automatically segments the image into several clusters of voxels, by taking the intensity information and spatial information of voxels into account. Then, after the IB-based clustering, each cluster of voxels is classified into one type of brain tissue by threshold methods. The performance of the algorithm is studied based on both simulated and real T1-weighted 3D brain MR images. Our results show that, compared with other well-known brain image segmentation algorithms, the proposed algorithm can improve the accuracy of the segmentation results substantially. Full article

► Show Figures

Figure 1

Figure 1
The flow diagram of the information bottleneck (IB)-based segmentation method. Full article ">Figure 2
Tanimoto’s performance metric of the proposed segmentation algorithm on the simulated 3D brain magnetic resonance (MR) images from BrainWeb. (a) For gray matter (GM) segmentation; (b) for white matter (WM) segmentation. Full article ">Figure 3
Tanimoto’s performance metric of different segmentation algorithms on 20 normal 3D brain MR images from the Internet brain segmentation repository (IBSR). (a) For GM segmentation; (b) for WM segmentation. Full article ">Figure 4
Four real T1-weighted brain MR images (first row), the corresponding segmentation results obtained by our algorithms (second row) and the corresponding ground truths (third row). Full article ">Figure 5
Detailed IB-based clustering results for the same four examples of MR scans as those shown in <a href="#entropy-15-03205-f004" class="html-fig">Figure 4</a> (a1–a4). Results displayed in one column correspond to one example. Full article ">Figure 6
Tanimoto’s performance metric of our algorithm under different values of β and <math display="inline"> <msub> <mi>M</mi> <mtext>initial</mtext> </msub> </math> for the image, <math display="inline"> <mrow> <mo>“</mo> <mn>1</mn> <mo>_</mo> <mn>24</mn> <mo>”</mo> </mrow> </math>. (a) For GM segmentation; (b) for WM segmentation. Full article ">Figure 7
Tanimoto’s performance metric of our algorithm under different value of β and <math display="inline"> <msub> <mi>M</mi> <mtext>initial</mtext> </msub> </math> for the image, <math display="inline"> <mrow> <mo>“</mo> <mn>15</mn> <mo>_</mo> <mn>3</mn> <mo>”</mo> </mrow> </math>. (a) For GM segmentation; (b) for WM segmentation. Full article ">

397 KiB

Open AccessArticle

Linearized Transfer Entropy for Continuous Second Order Systems

by Jonathan M. Nichols, Frank Bucholtz and Joe V. Michalowicz

Entropy 2013, 15(8), 3186-3204; https://doi.org/10.3390/e15083276 - 7 Aug 2013

Cited by 12 | Viewed by 4124

Abstract

The transfer entropy has proven a useful measure of coupling among components of a dynamical system. This measure effectively captures the influence of one system component on the transition probabilities (dynamics) of another. The original motivation for the measure was to quantify such [...] Read more.

The transfer entropy has proven a useful measure of coupling among components of a dynamical system. This measure effectively captures the influence of one system component on the transition probabilities (dynamics) of another. The original motivation for the measure was to quantify such relationships among signals collected from a nonlinear system. However, we have found the transfer entropy to also be a useful concept in describing linear coupling among system components. In this work we derive the analytical transfer entropy for the response of coupled, second order linear systems driven with a Gaussian random process. The resulting expression is a function of the auto- and cross-correlation functions associated with the system response for different degrees-of-freedom. We show clearly that the interpretation of the transfer entropy as a measure of "information flow" is not always valid. In fact, in certain instances the "flow" can appear to switch directions simply by altering the degree of linear coupling. A safer way to view the transfer entropy is as a measure of the ability of a given system component to predict the dynamics of another. Full article

(This article belongs to the Special Issue Transfer Entropy)

► Show Figures

Figure 1

Figure 1
Physical system modeled by Equation (<a href="#FD10-entropy-15-03186" class="html-disp-formula">10</a>). Here, an <math display="inline"> <mrow> <mi>M</mi> <mo>=</mo> <mn>5</mn> </mrow> </math> DOF structure is represented by masses coupled together via both restoring and dissipative elements. Forcing is applied at the end mass. Full article ">Figure 2
Time delay transfer entropy between masses two and three (top row) and one and five (bottom row) of a 5 DOF system driven at mass, <math display="inline"> <mrow> <mi>P</mi> <mo>=</mo> <mn>5</mn> </mrow> </math>. Full article ">Figure 3
Time delay transfer entropy between the forcing (denoted as DOF “0”) and mass three for the 5 DOF system driven at mass, <math display="inline"> <mrow> <mi>P</mi> <mo>=</mo> <mn>5</mn> </mrow> </math>. The plot is consistent with the interpretation of information moving from the forcing to mass three. Full article ">Figure 4
Difference in time delay transfer entropy between the driven mass five and each other DOF as a function of <math display="inline"> <msub> <mi>k</mi> <mn>3</mn> </msub> </math>. A positive difference indicates <math display="inline"> <mrow> <mi>T</mi> <msub> <mi>E</mi> <mrow> <mi>i</mi> <mo>→</mo> <mi>j</mi> </mrow> </msub> <mo>></mo> <mi>T</mi> <msub> <mi>E</mi> <mrow> <mi>j</mi> <mo>→</mo> <mi>i</mi> </mrow> </msub> </mrow> </math> and is commonly used to indicate that information is moving from mass i to mass j. Based on this interpretation, negative values indicate information moving from the driven end to the base; positive values indicate the opposite. Even for this linear system, choosing different masses in the analysis can produce very different results. In fact, <math display="inline"> <mrow> <mi>T</mi> <msub> <mi>E</mi> <mrow> <mn>2</mn> <mo>→</mo> <mn>5</mn> </mrow> </msub> <mo>-</mo> <mi>T</mi> <msub> <mi>E</mi> <mrow> <mn>5</mn> <mo>→</mo> <mn>2</mn> </mrow> </msub> </mrow> </math> implies a different direction of information transfer, depending on the strength of the coupling, <math display="inline"> <msub> <mi>k</mi> <mn>3</mn> </msub> </math> Full article ">Figure 5
Difference in time-delayed transfer entropy (TDTE) among different combinations of masses. By the traditional interpretation of TE, negative values indicate information moving from the driven end to the base; positive values indicate the opposite. Full article ">

1932 KiB

Open AccessArticle

A Maximum Entropy-Based Chaotic Time-Variant Fragile Watermarking Scheme for Image Tampering Detection

by Young-Long Chen, Her-Terng Yau and Guo-Jheng Yang

Entropy 2013, 15(8), 3170-3185; https://doi.org/10.3390/e15083260 - 5 Aug 2013

Cited by 21 | Viewed by 4504

Abstract

The fragile watermarking technique is used to protect intellectual property rights while also providing security and rigorous protection. In order to protect the copyright of the creators, it can be implanted in some representative text or totem. Because all of the media on [...] Read more.

The fragile watermarking technique is used to protect intellectual property rights while also providing security and rigorous protection. In order to protect the copyright of the creators, it can be implanted in some representative text or totem. Because all of the media on the Internet are digital, protection has become a critical issue, and determining how to use digital watermarks to protect digital media is thus the topic of our research. This paper uses the Logistic map with parameter u = 4 to generate chaotic dynamic behavior with the maximum entropy 1. This approach increases the security and rigor of the protection. The main research target of information hiding is determining how to hide confidential data so that the naked eye cannot see the difference. Next, we introduce one method of information hiding. Generally speaking, if the image only goes through Arnold’s cat map and the Logistic map, it seems to lack sufficient security. Therefore, our emphasis is on controlling Arnold’s cat map and the initial value of the chaos system to undergo small changes and generate different chaos sequences. Thus, the current time is used to not only make encryption more stringent but also to enhance the security of the digital media. Full article

(This article belongs to the Special Issue Dynamical Systems)

► Show Figures

Figure 1

472 KiB

Open AccessArticle

Low-Temperature Behaviour of Social and Economic Networks

by Diego Garlaschelli, Sebastian E. Ahnert, Thomas M. A. Fink and Guido Caldarelli

Entropy 2013, 15(8), 3148-3169; https://doi.org/10.3390/e15083238 - 5 Aug 2013

Cited by 11 | Viewed by 6084

Abstract

Real-world social and economic networks typically display a number of particular topological properties, such as a giant connected component, a broad degree distribution, the small-world property and the presence of communities of densely interconnected nodes. Several models, including ensembles of networks, also known [...] Read more.

Real-world social and economic networks typically display a number of particular topological properties, such as a giant connected component, a broad degree distribution, the small-world property and the presence of communities of densely interconnected nodes. Several models, including ensembles of networks, also known in social science as Exponential Random Graphs, have been proposed with the aim of reproducing each of these properties in isolation. Here, we define a generalized ensemble of graphs by introducing the concept of graph temperature, controlling the degree of topological optimization of a network. We consider the temperature-dependent version of both existing and novel models and show that all the aforementioned topological properties can be simultaneously understood as the natural outcomes of an optimized, low-temperature topology. We also show that seemingly different graph models, as well as techniques used to extract information from real networks are all found to be particular low-temperature cases of the same generalized formalism. One such technique allows us to extend our approach to real weighted networks. Our results suggest that a low graph temperature might be a ubiquitous property of real socio-economic networks, placing conditions on the diffusion of information across these systems. Full article

(This article belongs to the Special Issue Social Networks and Information Diffusion)

► Show Figures

Figure 1

440 KiB

Open AccessArticle

Communicating through Probabilities: Does Quantum Theory Optimize the Transfer of Information?

by William K. Wootters

Entropy 2013, 15(8), 3130-3147; https://doi.org/10.3390/e15083220 - 2 Aug 2013

Cited by 10 | Viewed by 5260

Abstract

A quantum measurement can be regarded as a communication channel, in which the parameters of the state are expressed only in the probabilities of the outcomes of the measurement. We begin this paper by considering, in a non-quantum-mechanical setting, the problem of communicating [...] Read more.

A quantum measurement can be regarded as a communication channel, in which the parameters of the state are expressed only in the probabilities of the outcomes of the measurement. We begin this paper by considering, in a non-quantum-mechanical setting, the problem of communicating through probabilities. For example, a sender, Alice, wants to convey to a receiver, Bob, the value of a continuous variable, θ, but her only means of conveying this value is by sending Bob a coin in which the value of θ is encoded in the probability of heads. We ask what the optimal encoding is when Bob will be allowed to flip the coin only a finite number of times. As the number of tosses goes to infinity, we find that the optimal encoding is the same as what nature would do if we lived in a world governed by real-vector-space quantum theory. We then ask whether the problem might be modified, so that the optimal communication strategy would be consistent with standard, complex-vector-space quantum theory. Full article

(This article belongs to the Special Issue Quantum Information 2012)

► Show Figures

Figure 1

3902 KiB

Open AccessArticle

Estimation Bias in Maximum Entropy Models

by Jakob H. Macke, Iain Murray and Peter E. Latham

Entropy 2013, 15(8), 3109-3129; https://doi.org/10.3390/e15083109 - 2 Aug 2013

Cited by 5 | Viewed by 8277

Abstract

Maximum entropy models have become popular statistical models in neuroscience and other areas in biology and can be useful tools for obtaining estimates of mutual information in biological systems. However, maximum entropy models fit to small data sets can be subject to sampling [...] Read more.

Maximum entropy models have become popular statistical models in neuroscience and other areas in biology and can be useful tools for obtaining estimates of mutual information in biological systems. However, maximum entropy models fit to small data sets can be subject to sampling bias; i.e., the true entropy of the data can be severely underestimated. Here, we study the sampling properties of estimates of the entropy obtained from maximum entropy models. We focus on pairwise binary models, which are used extensively to model neural population activity. We show that if the data is well described by a pairwise model, the bias is equal to the number of parameters divided by twice the number of observations. If, however, the higher order correlations in the data deviate from those predicted by the model, the bias can be larger. Using a phenomenological model of neural population recordings, we find that this additional bias is highest for small firing probabilities, strong correlations and large population sizes—for the parameters we tested, a factor of about four higher. We derive guidelines for how long a neurophysiological experiment needs to be in order to ensure that the bias is less than a specified criterion. Finally, we show how a modified plug-in estimate of the entropy can be used for bias correction. Full article

(This article belongs to the Special Issue Estimating Information-Theoretic Quantities from Data)

► Show Figures

Figure 1

294 KiB

Open AccessArticle

On the Topological Entropy of Some Skew-Product Maps

by Jose S. Cánovas

Entropy 2013, 15(8), 3100-3108; https://doi.org/10.3390/e15083100 - 31 Jul 2013

Cited by 4 | Viewed by 5488

Abstract

The aim of this short note is to compute the topological entropy for a family of skew-product maps, whose base is a subshift of finite type, and the fiber maps are homeomorphisms defined in one dimensional spaces. We show that the skew-product map [...] Read more.

The aim of this short note is to compute the topological entropy for a family of skew-product maps, whose base is a subshift of finite type, and the fiber maps are homeomorphisms defined in one dimensional spaces. We show that the skew-product map does not increase the topological entropy of the subshift. Full article

(This article belongs to the Special Issue Dynamical Systems)

► Show Figures

Figure 1

180 KiB

Open AccessArticle

Folding Kinetics of Riboswitch Transcriptional Terminators and Sequesterers

by Ben Sauerwine and Michael Widom

Entropy 2013, 15(8), 3088-3099; https://doi.org/10.3390/e15083088 - 31 Jul 2013

Cited by 5 | Viewed by 5848

Abstract

To function as gene regulatory elements in response to environmental signals, riboswitches must adopt specific secondary structures on appropriate time scales. We employ kinetic Monte Carlo simulation to model the time-dependent folding during transcription of thiamine pyrophosphate (TPP) riboswitch expression platforms. According to [...] Read more.

To function as gene regulatory elements in response to environmental signals, riboswitches must adopt specific secondary structures on appropriate time scales. We employ kinetic Monte Carlo simulation to model the time-dependent folding during transcription of thiamine pyrophosphate (TPP) riboswitch expression platforms. According to our simulations, riboswitch transcriptional terminators, which must adopt a specific hairpin configuration by the time they have been transcribed, fold with higher efficiency than Shine-Dalgarno sequesterers, whose proper structure is required only at the time of ribosomal binding. Our findings suggest both that riboswitch transcriptional terminator sequences have been naturally selected for high folding efficiency, and that sequesterers can maintain their function even in the presence of significant misfolding. Full article

(This article belongs to the Special Issue Entropy and RNA Structure, Folding and Mechanics)

► Show Figures

Figure 1

Figure 1
Secondary structure of the aptamer and terminator of the Bacillus subtilis ykoF riboswitch. (a) Bound state, aptamer formed, transcription off. The P1 stem of the aptamer (pink) conflicts with the antiterminator (green), allowing formation of the terminator (blue), and, thus, halting transcription via the poly-U pause site (orange). (b) Unbound state, aptamer unformed, transcription on. Destabilizing the aptamer allows formation of the antiterminator, which conflicts with the terminator, and, hence, allows transcription to proceed. Full article ">Figure 2
Normalized distributions of folding performances for terminator- and sequesterer-type riboswitches from a wide range of prokaryotes. (a) Histograms of folding fractions, f, combined for all sequences, s, of each specific type. (b) Histograms of folding efficiencies, <math display="inline"> <msub> <mi>e</mi> <mi>s</mi> </msub> </math>, for individual sequences, s. (c) Cumulative distribution of folding efficiencies, including extended terminators. Full article ">Figure 3
Proportion of thiamine pyrophosphate (TPP) terminators (black line) and sequesterers (red line) that fold efficiently (i.e., with <math display="inline"> <mrow> <mi>e</mi> <mo>≥</mo> <mn>0.8</mn> </mrow> </math>) at various timescales, ρ. Data points indicate the individual folding efficiencies, <math display="inline"> <msub> <mi>e</mi> <mi>s</mi> </msub> </math>, of each hairpin sequence, s. The green line at <math display="inline"> <mrow> <mi>ρ</mi> <mo>=</mo> <mn>4000</mn> </mrow> </math> Monte Carlo (MC) steps/nt transcribed indicates the timescale for <math display="inline"> <mrow> <msub> <mi>τ</mi> <mi>K</mi> </msub> <mo>=</mo> <mn>5</mn> <mi>μ</mi> </mrow> </math>s and <math display="inline"> <mrow> <msub> <mi>R</mi> <mi>t</mi> </msub> <mo>=</mo> <mn>50</mn> </mrow> </math> nt/s. Full article ">Figure 4
Frequency weighted sequence logos [<a href="#B15-entropy-15-03088" class="html-bibr">15</a>] for TPP rho-independent transcriptional terminators (a) and Shine-Dalgarno sequesterers (b). Regions 1–5 correspond, respectively, to the first half of the <math display="inline"> <msup> <mn>5</mn> <mo>′</mo> </msup> </math> side of the stem, the second half of the same, the loop, the first half of the <math display="inline"> <msup> <mn>3</mn> <mo>′</mo> </msup> </math> side of the stem and the second half of the same. Full article ">Figure 5
Alternate folds of low efficiency terminators and sequesterers. (a,b) Most common specific fold and MFE structure of the Tte-ThiD terminator sequence. Nucleotides forming the stem of the terminator are highlighted in blue, while the poly-U pause site is in orange. (c,d) Most common specific fold and MFE structure of Sm-ThiC. The Shine-Dalgarno sequence is highlighted in blue, while the translation start site is highlighted in orange. Full article ">Figure 6
Free energy landscapes in units of kcal/mol. Completely unbound structures have energy of zero. Basins of depth less than 2.5 have been suppressed Tte-ThiD. (a) Structure number 6 corresponds to the most common fold (<a href="#entropy-15-03088-f005" class="html-fig">Figure 5</a>a). Sm-ThiC; (b) Structure number 5 corresponds to the most common fold (<a href="#entropy-15-03088-f005" class="html-fig">Figure 5</a>c). In both cases, structure number 1 is the MFE fold (<a href="#entropy-15-03088-f005" class="html-fig">Figure 5</a>b,d). Full article ">

713 KiB

Open AccessArticle

Flow of Information during an Evolutionary Process: The Case of Influenza A Viruses

by Víctor Serrano-Solís and Marco V. José

Entropy 2013, 15(8), 3065-3087; https://doi.org/10.3390/e15083065 - 29 Jul 2013

Cited by 2 | Viewed by 5202

Abstract

The hypothesis that Mutual Information (MI) dendrograms of influenza A viruses reflect informational groups generated during viral evolutionary processes is put forward. Phylogenetic reconstructions are used for guidance and validation of MI dendrograms. It is found that MI profiles display an oscillatory behavior [...] Read more.

The hypothesis that Mutual Information (MI) dendrograms of influenza A viruses reflect informational groups generated during viral evolutionary processes is put forward. Phylogenetic reconstructions are used for guidance and validation of MI dendrograms. It is found that MI profiles display an oscillatory behavior for each of the eight RNA segments of influenza A. It is shown that dendrograms of MI values of geographically and historically different segments coming from strains of RNA virus influenza A turned out to be unexpectedly similar to the clusters, but not with the topology of the phylogenetic trees. No matter how diverse the RNA sequences are, MI dendrograms crisply discern actual viral subtypes together with gain and/or losses of information that occur during viral evolution. The amount of information during a century of evolution of RNA segments of influenza A is measured in terms of bits of information for both human and avian strains. Overall the amount of information of segments of pandemic strains oscillates during viral evolution. To our knowledge this is the first description of clades of information of the viral subtypes and the estimation of the flow content of information, measured in bits, during an evolutionary process of a virus. Full article

► Show Figures

Figure 1

Figure 1
Mutual Information of A(H1N1) from 1918 (red curves) and from 2009 (black curves): (A) S1; (B) S4; (C) S6. Full article ">Figure 2
Dendrograms of the Mutual Information for: S1 (A1); S4 (B1); S6 (C1); and S8 (D1) segments of the RNA genome of influenza A. Maximum Likelihood Phylogenetic Reconstructions visualized as cladograms for: S1 (A2) LogLk (Log-likelihood) = −9150.268; S4 (B2) LogLk = −12865.908; S6 (C2) LogLk = −8565.225; and S8 (D2) LogLk = −3181.513. The numbers at each split in ML trees correspond to the Shimodaira-Hasegawa reliability estimate test which is part of the default parameter values of FastTree. Full article ">Figure 2 Cont.
Dendrograms of the Mutual Information for: S1 (A1); S4 (B1); S6 (C1); and S8 (D1) segments of the RNA genome of influenza A. Maximum Likelihood Phylogenetic Reconstructions visualized as cladograms for: S1 (A2) LogLk (Log-likelihood) = −9150.268; S4 (B2) LogLk = −12865.908; S6 (C2) LogLk = −8565.225; and S8 (D2) LogLk = −3181.513. The numbers at each split in ML trees correspond to the Shimodaira-Hasegawa reliability estimate test which is part of the default parameter values of FastTree. Full article ">Figure 2 Cont.
Dendrograms of the Mutual Information for: S1 (A1); S4 (B1); S6 (C1); and S8 (D1) segments of the RNA genome of influenza A. Maximum Likelihood Phylogenetic Reconstructions visualized as cladograms for: S1 (A2) LogLk (Log-likelihood) = −9150.268; S4 (B2) LogLk = −12865.908; S6 (C2) LogLk = −8565.225; and S8 (D2) LogLk = −3181.513. The numbers at each split in ML trees correspond to the Shimodaira-Hasegawa reliability estimate test which is part of the default parameter values of FastTree. Full article ">Figure 3
Control experiments: (A) MI dendrogram from randomization of the actual viral sequences; (B) MI dendrogram from randomization of the MI values from the original viral sequences. Full article ">Figure 4
Average amount of information for: S1 (A1); S4 (B1 and inset at other scale); S6 (C1); and S8 (D1) as a function of time from 1918 to 2009 in human (red curves) and from 1902 to 2011 in avian (blue curves) subtypes of the RNA genome of influenza A. Full article ">Figure 4 Cont.
Average amount of information for: S1 (A1); S4 (B1 and inset at other scale); S6 (C1); and S8 (D1) as a function of time from 1918 to 2009 in human (red curves) and from 1902 to 2011 in avian (blue curves) subtypes of the RNA genome of influenza A. Full article ">

263 KiB

Open AccessArticle

Casimir Friction between Dense Polarizable Media

by Johan S. Høye and Iver Brevik

Entropy 2013, 15(8), 3045-3064; https://doi.org/10.3390/e15083045 - 29 Jul 2013

Cited by 23 | Viewed by 4243

Abstract

The present paper—a continuation of our recent series of papers on Casimir friction for a pair of particles at low relative particle velocity—extends the analysis, so as to include dense media. The situation becomes, in this case, more complex, due to induced dipolar [...] Read more.

The present paper—a continuation of our recent series of papers on Casimir friction for a pair of particles at low relative particle velocity—extends the analysis, so as to include dense media. The situation becomes, in this case, more complex, due to induced dipolar correlations, both within planes and between planes. We show that the structure of the problem can be simplified by regarding the two half-planes as a generalized version of a pair of particles. It turns out that macroscopic parameters, such as permittivity, suffice to describe the friction, also in the finite density case. The expression for the friction force per unit surface area becomes mathematically well-defined and finite at finite temperature. We give numerical estimates and compare them with those obtained earlier by Pendry (1997) and by Volokitin and Persson (2007). We also show in an appendix how the statistical methods that we are using correspond to the field theoretical methods more commonly in use. Full article

340 KiB

Open AccessArticle

What Do Leaders Know?

by Giacomo Livan and Matteo Marsili

Entropy 2013, 15(8), 3031-3044; https://doi.org/10.3390/e15083031 - 26 Jul 2013

Cited by 7 | Viewed by 5287

Abstract

The ability of a society to make the right decisions on relevant matters relies on its capability to properly aggregate the noisy information spread across the individuals of which it is made. In this paper, we study the information aggregation performance of a [...] Read more.

The ability of a society to make the right decisions on relevant matters relies on its capability to properly aggregate the noisy information spread across the individuals of which it is made. In this paper, we study the information aggregation performance of a stylized model of a society, whose most influential individuals—the leaders—are highly connected among themselves and uninformed. Agents update their state of knowledge in a Bayesian manner by listening to their neighbors. We find analytical and numerical evidence of a transition, as a function of the noise level in the information initially available to agents, from a regime where information is correctly aggregated, to one where the population reaches consensus on the wrong outcome with finite probability. Furthermore, information aggregation depends in a non-trivial manner on the relative size of the clique of leaders, with the limit of a vanishingly small clique being singular. Full article

(This article belongs to the Special Issue Social Networks and Information Diffusion)

► Show Figures

Figure 1

11053 KiB

Open AccessArticle

Optimization of Curvilinear Tracing Applied to Solar Physics and Biophysics

by Markus J. Aschwanden, Bart De Pontieu and Eugene A. Katrukha

Entropy 2013, 15(8), 3007-3030; https://doi.org/10.3390/e15083007 - 26 Jul 2013

Cited by 28 | Viewed by 6583

Abstract

We developed an automated pattern recognition code that is particularly well suited to extract one-dimensional curvilinear features from two-dimensional digital images. A former version of this Oriented Coronal Curved Loop Tracing (OCCULT) code was applied to spacecraft images of magnetic loops in the [...] Read more.

We developed an automated pattern recognition code that is particularly well suited to extract one-dimensional curvilinear features from two-dimensional digital images. A former version of this Oriented Coronal Curved Loop Tracing (OCCULT) code was applied to spacecraft images of magnetic loops in the solar corona, recorded with the NASA spacecraft, Transition Region And Coronal Explorer (TRACE), in extreme ultra-violet wavelengths. Here, we apply an advanced version of this code (OCCULT-2), also, to similar images from the Solar Dynamics Observatory (SDO), to chromospheric H-α images obtained with the Swedish Solar Telescope (SST) and to microscopy images of microtubule filaments in live cells in biophysics. We provide a full analytical description of the code, optimize the control parameters and compare the automated tracing with visual/manual methods. The traced structures differ by up to 16 orders of magnitude in size, which demonstrates the universality of the tracing algorithm. Full article

(This article belongs to the Special Issue Advanced Signal Processing in Heliospheric Physics)

► Show Figures

Figure 1

298 KiB

Open AccessArticle

Time Evolution of Relative Entropies for Anomalous Diffusion

by Janett Prehl, Frank Boldt, Christopher Essex and Karl Heinz Hoffmann

Entropy 2013, 15(8), 2989-3006; https://doi.org/10.3390/e15082989 - 26 Jul 2013

Cited by 14 | Viewed by 6522

Abstract

The entropy production paradox for anomalous diffusion processes describes a phenomenon where one-parameter families of dynamical equations, falling between the diffusion and wave equations, have entropy production rates (Shannon, Tsallis or Renyi) that increase toward the wave equation limit unexpectedly. Moreover, also surprisingly, [...] Read more.

The entropy production paradox for anomalous diffusion processes describes a phenomenon where one-parameter families of dynamical equations, falling between the diffusion and wave equations, have entropy production rates (Shannon, Tsallis or Renyi) that increase toward the wave equation limit unexpectedly. Moreover, also surprisingly, the entropy does not order the bridging regime between diffusion and waves at all. However, it has been found that relative entropies, with an appropriately chosen reference distribution, do. Relative entropies, thus, provide a physically sensible way of setting which process is “nearer” to pure diffusion than another, placing pure wave propagation, desirably, “furthest” from pure diffusion. We examine here the time behavior of the relative entropies under the evolution dynamics of the underlying one-parameter family of dynamical equations based on space-fractional derivatives. Full article

(This article belongs to the Special Issue Distance in Information and Statistical Physics Volume 2)

► Show Figures

Figure 1

242 KiB

Open AccessReview

On the Entropy of a Class of Irreversible Processes

by Jurgen Honig

Entropy 2013, 15(8), 2975-2988; https://doi.org/10.3390/e15082975 - 26 Jul 2013

Cited by 6 | Viewed by 5437

Abstract

We review a recent technique for determining the entropy change accompanying certain classes of irreversible processes involving changes in the state of a system anchored to a reservoir. Time is introduced as a parameter to specify the corresponding entropy evolution of the system. [...] Read more.

We review a recent technique for determining the entropy change accompanying certain classes of irreversible processes involving changes in the state of a system anchored to a reservoir. Time is introduced as a parameter to specify the corresponding entropy evolution of the system. The procedural details are outlined and their relation to the standard treatment of irreversible processes is examined. Full article

(This article belongs to the Special Issue Entropy and the Second Law of Thermodynamics)

► Show Figures

Figure 1

3725 KiB

Open AccessReview

Towards Realising Secure and Efficient Image and Video Processing Applications on Quantum Computers

by Abdullah M. Iliyasu

Entropy 2013, 15(8), 2874-2974; https://doi.org/10.3390/e15082874 - 26 Jul 2013

Cited by 59 | Viewed by 9638

Abstract

Exploiting the promise of security and efficiency that quantum computing offers, the basic foundations leading to commercial applications for quantum image processing are proposed. Two mathematical frameworks and algorithms to accomplish the watermarking of quantum images, authentication of ownership of already watermarked images [...] Read more.

Exploiting the promise of security and efficiency that quantum computing offers, the basic foundations leading to commercial applications for quantum image processing are proposed. Two mathematical frameworks and algorithms to accomplish the watermarking of quantum images, authentication of ownership of already watermarked images and recovery of their unmarked versions on quantum computers are proposed. Encoding the images as 2ⁿ-sized normalised Flexible Representation of Quantum Images (FRQI) states, with n-qubits and 1-qubit dedicated to capturing the respective information about the colour and position of every pixel in the image respectively, the proposed algorithms utilise the flexibility inherent to the FRQI representation, in order to confine the transformations on an image to any predetermined chromatic or spatial (or a combination of both) content of the image as dictated by the watermark embedding, authentication or recovery circuits. Furthermore, by adopting an apt generalisation of the criteria required to realise physical quantum computing hardware, three standalone components that make up the framework to prepare, manipulate and recover the various contents required to represent and produce movies on quantum computers are also proposed. Each of the algorithms and the mathematical foundations for their execution were simulated using classical (i.e., conventional or non-quantum) computing resources, and their results were analysed alongside other longstanding classical computing equivalents. The work presented here, combined together with the extensions suggested, provide the basic foundations towards effectuating secure and efficient classical-like image and video processing applications on the quantum-computing framework. Full article

(This article belongs to the Special Issue Quantum Information 2012)

► Show Figures

Graphical abstract

Journal Menu

Journal Browser

Entropy, Volume 15, Issue 8 (August 2013) – 20 articles , Pages 2874-3311

Further Information

Guidelines

MDPI Initiatives

Follow MDPI