“A Mathematical Theory of Communication”, was published in 1948 by Claude Shannon to address the problems in the field of data compression and communication over (noisy) communication channels. Since then the concepts and ideas developed in Shannon's work have formed the basis of information theory, a corenerstone of statistical learning and inference and has been playing key role in disciplines such as physics and thermodynamics, probability and statistics, computational sciences and biological sciences. In my talk, I will review the key information theory based concepts and describe examples of their applications in three major areas of research in bioinformatics and computational biology - gene regulatory network inference, disease-gene association analysis and biological sequence analysis.
On the Relationship between City Mobility and Blocks Uniformity
The spatial and topological organization of cities have a great influence on the lives of their inhabitants, including mobility efficiency. Entropy has been largely adopted for the characterization of the most varied natural and human-made systems and structures. In this work, we apply entropy to characterize the uniformity of spatial coverage allowed by the geometry, reflected by the area, of city blocks. It is suggested that this measurement can predict several properties of real cities, such as mobility. We consider several real-world cities, from which the average minimal shortest path length is also calculated and compared with the entropy of the block areas. Several interesting results have been found and are discussed in the article.
Entropy Based Approach for Analysis of Spatio-Temporal Urban Growth Dynamics
Relative Entropy (RE) is defined as the measure of degree of randomness of any geographical variable (i.e., urban growth). It is an effective indicator to evaluate the patterns of urban growth either compact or dispersed. In the present study RE has been used for evaluating the urban growth of Dehradun city. Dehradun, the capital of Uttarakhand is situated in the foothills of Himalayas, has undergone rapid urbanization. Landsat, Thematic Mapper (TM) satellite data of years 2000, 2010 and 2019 has been used in the study. Built-up cover outside municipal limits and within municipal limits was classified for the given time period. Road network and city centre of the study area were also delineated using satellite data. RE was calculated for period 2000–2010 and 2010–2019 with respect to the road network and city centre. High values of RE indicate higher levels of urban sprawl whereas lower values indicate compactness. Urban growth pattern over a period of 19 years was examined with the help of RE.
Ecosystems’ microbiome organization is the epitomic feature of ecosystem function and an incredibly fascinating system considering its complexity, ecology and evolution, and practical applications for individual and population health. Due to its ‘’unknowns’’ the microbiome also provides the opportunity to test and develop information theoretic models that mimic and predict its dynamics. A novel information and network theoretic model that predicts microbiome network organization, diversity, dynamics and stability for the human gut microbiome is presented. The model is able to classify health states based on microbiome entropic patterns, that, in the optimal biological function are related to neutral scale-free information organization of species interactions. The healthy state is characterized by an optimal metabolic function that is predicted by macroecological quintessential indicators whose variability is meaningful of state transitions. Information propagation analyses detect total species importance, proportional to outgoing information flow, which can be use for microbial engineering or disease diagnosis and etiognosis. Finally a link with ocean microbial ecosystems is highlighted as well as the collectivity-diversity-dynamics triality.
Entropy Production and the Maximum Entropy of the Universe
The entropy of the observable universe has been calculated as Suni ~ 10104 k and is dominated by the entropy of super massive black holes. Irreversible processes in the universe can only happen if there is an entropy gap between the entropy of the observable universe Suni and its maximum entropy Smax: = Smax - Suni. Thus, the entropy gap is a measure of the remaining potentially available free energy in the observable universe. To compute one needs to know the value of Smax. There is no consensus on whether Smax is a constant or is time-dependent. A time-dependent Smax(t) has been used to represent instantaneous upper limits on entropy growth. However, if we define Smax as a constant equal to the final entropy of the observable universe at its heat death: Smax Smax,HD, we can interpret T as a measure of the remaining potentially available (but not instantaneously available) free energy of the observable universe. The time-dependent slope dSuni/dt (t) then becomes the best estimate of current entropy-production and T dSuni/dt(t) is the upper limit to free energy extraction.
The Potential of L-band UAVSAR Data for the Extraction of Mangrove Land Cover using Entropy and Anisotropy based Classification
Mangroves forests serve as an ecosystem stabilizer since they play an important role in providing habitats for many terrestrial and aquatic species along with a huge capability of carbon sequestration and absorbing greenhouse gases. The process of conversion of carbon dioxide into biomass is very rapid in mangrove forests. Mangroves play a crucial role in protecting the human settlement and arresting shoreline erosion by reducing wave height up to a great extent as they form a natural barricade against high sea tides and windstorms. In most cases, human settlement in the vicinity of mangrove forests has affected the eco-system of the forest and placed them in environmental pressure. Since, a continuous mapping, monitoring, and preservation of coastal mangroves may help in climate resilience, therefore a mangrove land cover extraction method using remotely sensed L-band full-pol UAVSAR data (acquired on 25-Feb-2016) based on Entropy (H) and Anisotropy (A) concept has been proposed in this study. The k-Mean clustering has been applied to the subsetted (1-Entropy)*(Anisotropy) image generated by PolSARpro_v5.0 software’s H/A/Alpha Decomposition. The mangrove land cover of the study area was extracted to be 116.07 Km2 using k-Mean clustering and validated with the mangrove land cover area provided by Global Mangrove Watch (GMW) data.
In practice, the critical step in build machine learning models of big data (BD) often involves costly in terms of time and computing resources procedure of parameter tuning with grid search. Due to the size BD are comparable to mesoscopic physical systems. Hence, methods of statistical physics could be applied to BD. The paper shows that topic modeling (a clustering method for large document collections) demonstrates self-similar behavior under the condition of a varying number of clusters. Such behavior allows using a renormalization technique. A combination of renormalization procedure with Rényi entropy approach allows for fast searching of the optimal number of clusters. In this paper, the renormalization procedure is developed for the Latent Dirichlet Allocation (LDA) model with variational Expectation-Maximization algorithm. The experiments were conducted on two document collections with a known number of clusters in Russian and English languages, respectively. The paper presents results for three versions of the renormalization procedure: (1) a renormalization with the random merging of clusters, (2) a renormalization based on minimal values of Kullback-Leibler divergence and (3) a renormalization with merging clusters with minimal values of Rényi entropy where entropy is computed for each topic separately. The paper shows that the renormalization procedure allows finding the optimal number of topics ten times faster than grid search without significant loss of quality.
Graph Entropy Associated with Multilevel Atomic Excitation
A graph-model is presented to describe multilevel atomic structure. As an example, we take the double L configuration in alkali-metal atoms with hyperfine structure and nuclear spin I = 3/2, as a graph with four vertices. Links are treated as coherence. We introduce the transition matrix which describes the connectivity matrix in static graph-model. In general, the transition matrix describes spatiotemporal behavior of the dynamic graph-model. Furthermore, it describes multiple connections and self-looping of vertices. The atomic excitation is made by short pulses, in order that the hyperfine structure is well resolved. Entropy associated with the proposed dynamic graph-model is used to identify transitions as well as local stabilization in the system without invoking the energy concept of the propagated pulses.
Specifics of Shannon Entropy Transferring Between Solar Magnetic Modes
Based on Shannon entropy transfer estimation technique and Stanford’s solar global magnetic field harmonic coefficients, several new facts about solar magnetic modes have been found. The entropy transferring between most of modes has been subjected to steady modulation with period near 72 solar rotations (5.38 years). As rule, amplitudes of entropy transferring modulation were less or equal 0.1 bit/solar rotation. These modulations had no relations with intensity or configuration of the solar magnetic fields. All solar magnetic modes can be divided into three different groups, which are entropy sources, entropy transmitters, and entropy targets. Thus: even zonal modes (l; m): (8; 0), (6; 0), (4; 0) are sources of Shannon’s entropy. The group of Shannon’s entropy transmitters, mainly, consists of modes having sectors (m > 0). Two zonal odd modes (1; 0) and (3; 0) are Shannon’s entropy targets. It has been shown that the most of medium and small-scale solar magnetic modes (order l > 3; degree m > 0) are interdependent. The features and physical sense of these dependencies have been analyzed. In result, the conclusion has been made that an unknown process should take place in the Sun, which controls the cluster of dependent magnetic modes in accordance with some scenario. Such scenario have been revealed by means of studying the special distributions of the global surface magnetic fields. In according to the scenario the tesseral-quadrupole (l = 2; m = 1) polarity distributions have been appeared periodically. The periodicity (T~72 solar rotations) was synchronized with the phases of modulation of the Shannon entropy transfer from the tesseral-quadrupole mode. The rotation rate of the tesseral-quadrupole polarity patterns is close to Bartels rotation rate.
A New Perspective on the Kauzmann Entropy Paradox: A Four-Dimensional Crystal/Glass Quantum Critical Point
In this article, a new perspective on the Kauzmann point is presented. We model the solidifying liquid by a quaternion orientational order parameter and find that the Kauzmann point is analogous to a quantum critical point. The “ideal glass transition" that occurs at the Kauzmann temperature is the point at which the configurational entropy of an undercooled metastable liquid equals that of its crystalline counterpart. We identify this point as a first order quantum critical point. We suggest that this quantum critical point belongs to quaternion ordered systems that exist in four- and three-dimensions. This “Kauzmann quantum critical point” can be considered to be a higher-dimensional analogue to the superfluid-to-Mott insulator quantum phase transition which occurs in two- and one-dimensional complex ordered systems. Such quantum critical points are driven by tuning a non-thermal frustration parameter, and result due to characteristic softening of a ‘Higgs’ type mode that corresponds to amplitude fluctuations of the order parameter. The first-order nature of the finite temperature Kauzmann quantum critical point is seen as a consequence of the discrete change of the topology of the ground state manifold that applies to crystalline and non-crystalline solid states.