Information Complexity Measure Research Articles

Complexity Measures in the Tight-Binding Model

Abstract The deformation of a wave packet is a significant topic in classical and quantum mechanics. Understanding this phenomenon is relevant in the study of various physical systems. In this work, we characterize the evolution of a highly localized wave packet in a tight-binding lattice. We investigate the behavior of the probability distribution associated with the wave packet and the accompanying complexity measures. We take information entropy, disequilibrium, disorder, and complexity measures to describe the localization-delocalization process from a highly localized initial pulse, showing the particles moving in a lattice. The main result is obtained from the entropy definition (Logarithmic and Linear) and the inverse of the participant ratio to describe the expected localization-delocalization process, evoking two definitions of Complexity: CLMC and CSDL .

A hybridized consistent Akaike type information criterion for regression models in the presence of multicollinearity

Consistent Akaike information criterion (CAIC) is an adjusted form of classical AIC. This criterion was developed by modifying the penalty. As a result, we propose a novel AIC type criterion, called CAIC The proposed criterion includes a dynamic parameter for controlling the penalty further. The distinctive feature of CAIC is to penalize multicollinearity level considering the information complexity measures. CAIC requires the parameter, and in addition, a procedure is proposed to estimate based on the information complexity of the regression model. Monte Carlo simulations and real data set examples demonstrate that CAIC performs better than classical information criteria for the potential multicollinearity problems.

Complexity and aesthetics in generative and evolutionary art

In this paper we examine the concept of complexity as it applies to generative and evolutionary art and design. Complexity has many different, discipline specific definitions, such as complexity in physical systems (entropy), algorithmic measures of information complexity and the field of “complex systems”. We apply a series of different complexity measures to three different evolutionary art datasets and look at the correlations between complexity and individual aesthetic judgement by the artist (in the case of two datasets) or the physically measured complexity of generative 3D forms. Our results show that the degree of correlation is different for each set and measure, indicating that there is no overall “better” measure. However, specific measures do perform well on individual datasets, indicating that careful choice can increase the value of using such measures. We then assess the value of complexity measures for the audience by undertaking a large-scale survey on the perception of complexity and aesthetics. We conclude by discussing the value of direct measures in generative and evolutionary art, reinforcing recent findings from neuroimaging and psychology which suggest human aesthetic judgement is informed by many extrinsic factors beyond the measurable properties of the object being judged.

Consumer Online Search with Partially Revealed Information

Modern-day search platforms generally have two layers of information presentation. The outer layer displays the collection of search results with attributes selected by platforms, and consumers click on a product to reveal all its attributes in the inner layer. The information revealed in the outer layer affects the search costs and the probability of finding a match. To address the managerial question of optimal information layout, we create an information complexity measure of the outer layer, namely orderedness entropy, and study the consumer search process for information at the expense of time and cognitive costs. We first conduct online random experiments to show that consumers respond to and actively reduce cognitive cost for which our information complexity measure provides a representation. Then, using a unique and rich panel tracking consumer search behaviors at a large online travel agency (OTA), we specify a novel sequential search model that jointly describes the refinement search and product clicking decisions. We find that cognitive cost is a major component of search cost, while loading time cost has a much smaller share. By varying the information revealed in the outer layer, we propose information layouts that Pareto-improve both revenue and consumer welfare for our OTA. This paper was accepted by Juanjuan Zhang, marketing.

Minimal Design Principles for Icosahedral Virus Capsids

The geometrical structures of single- and multiple-shell icosahedral virus capsids are reproduced as the targets that minimize the cost corresponding to relatively simple design functions. Capsid subunits are first identified as building blocks at a given coarse-grained scale and then represented in these functions as point particles located on an appropriate number of concentric spherical surfaces. Minimal design cost is assigned to optimal spherical packings of the particles. The cost functions are inspired by the packings favored for the Thomson problem, which minimize the electrostatic potential energy between identical charged particles. In some cases, icosahedral symmetry constraints are incorporated as external fields acting on the particles. The simplest cost functions can be obtained by separating particles in disjoint nonequivalent sets with distinct interactions, or by introducing interacting holes (the absence of particles). These functions can be adapted to reproduce any capsid structure found in real viruses. Structures absent in Nature require significantly more complex designs. Measures of information content and complexity are assigned to both the cost functions and the capsid geometries. In terms of these measures, icosahedral structures and the corresponding cost functions are the simplest solutions.

Pengukuran Metrik Kompleksitas Model Proses Bisnis Sekolah

School as an institution that has a primary mission to educate and develop the character of the nation through a series of learning activities. School is an organization whose success goals are largely determined by the leadership style and organizational paradigm that is shared by all school components. Schools as organizations have business processes as a collection of procedures or activities that can define business objectives or objectives, generally in the context of organizational structures that can define functional roles and relationships within the organization. The main purpose of BPMN is to provide a notation that is easy to use and can be understood by everyone involved in business, which includes business analysts who model business processes, technical developers who build systems that carry out business, and various levels of management that must be able to read and understand processes diagram quickly so that it can help in decision making. To measure the complexity of a business process, complexity metrics are measured. This study uses the Cognitve Information Complexity Measure (CICM) method. Researchers took 3 SOPs of national education standards namely SOP curriculum development resulting in a standard value of complexity 425.1496, SOP for the Learning Process produced a standard value of complexity 2091.333 and SOP for Teacher Recruitment resulted in a standard value of complexity of 1145.49.

Maximal Covariance Complexity-Based Penalized Likelihood Method in High Dimensional Data

Classification of cancer and selection of genes is one of the most important application of DNA microarray data. As a result of the higher dimensionality of microarray data, classification and selection of gene techniques are frequently employed to support the professional systems in the diagnosing ability of cancer with higher precision in classification. Least absolute shrinkage and selection operator (LASSO) is one of the most popular method for cancer classification and gene selection in high dimensional data. However, Lasso has limitations of being biased and cannot select variables more than the sample size (n) in gene selection and classification of high dimensional microarray data. To address this problems, LASSO-C1F was proposed using scale invariant measure of maximal information complexity of covariance matrix denoted with weight modifications as data-adaptive alternative to the fairly arbitrary choice of the regularization term in the least absolute shrinkage and selection operator (LASSO). The results indicated the effectiveness of the proposed method LASSO-C1F over the classical LASSO. The evaluation criteria result shows that the proposed method, LASSO-C1F has a better performance in terms of AUC and number of genes selected.

Application of Information and Complexity Measures to Neutron Stars Structure

We apply several information and statistical complexity measures to neutron stars structure. Neutron stars is a classical example where the gravitational field and quantum behaviour are combined and produce a macroscopic dense object. We concentrate our study on the connection between complexity and neutron star properties, like maximum mass and the corresponding radius, applying a specific set of realistic equation of states. Moreover, the effect of the strength of the gravitational field on the neutron star structure and consequently on the complexity measure is also investigated. It is seen that neutron stars, consistent with astronomical observations so far, are ordered systems (low complexity), which cannot grow in complexity as their mass increases. This is a result of the interplay of gravity, the short-range nuclear force and the very short-range weak interaction.

Information entropy and complexity measure in generalized Kratzer potential

Shannon entropy (S), Fisher information (I) and a measure equivalent to Fisher-Shannon complexity (CIS) of a ro-vibrational state of diatomic molecules (O2, O2+, NO, NO+) with generalized Kratzer potential is analyzed. Exact analytical expression of Ir is derived for the arbitrary state, whereas the same could be done for Ip with {n,ℓ,m=0} state. It is found that shifting from neutral to the cationic system, Ir increases while Sr decreases, consistent with the interpretation of a localization in the probability distribution. Additionally, this study reveals that CIS increases with the number of nodes in a system.

From Molecules to Life: Quantifying the Complexity of Chemical and Biological Systems in the Universe

Life is a complex phenomenon and much research has been devoted to both understanding its origins from prebiotic chemistry and discovering life beyond Earth. Yet, it has remained elusive how to quantify this complexity and how to compare chemical and biological units on one common scale. Here, a mathematical description of molecular complexity was applied allowing to quantitatively assess complexity of chemical structures. This in combination with the orthogonal measure of information complexity resulted in a two-dimensional complexity space ranging over the entire spectrum from molecules to organisms. Entities with a certain level of information complexity directly require a functionally complex mechanism for their production or replication and are hence indicative for life-like systems. In order to describe entities combining molecular and information complexity, the term biogenic unit was introduced. Exemplified biogenic unit complexities were calculated for ribozymes, protein enzymes, multimeric protein complexes, and even an entire virus particle. Complexities of prokaryotic and eukaryotic cells, as well as multicellular organisms, were estimated. Thereby distinct evolutionary stages in complexity space were identified. The here developed approach to compare the complexity of biogenic units allows for the first time to address the gradual characteristics of prebiotic and life-like systems without the need for a definition of life. This operational concept may guide our search for life in the Universe, and it may direct the investigations of prebiotic trajectories that lead towards the evolution of complexity at the origins of life.

Citizen Science and Topology of Mind: Complexity, Computation and Criticality in Data-Driven Exploration of Open Complex Systems

Recently emerging data-driven citizen sciences need to harness an increasing amount of massive data with varying quality. This paper develops essential theoretical frameworks, example models, and a general definition of complexity measure, and examines its computational complexity for an interactive data-driven citizen science within the context of guided self-organization. We first define a conceptual model that incorporates the quality of observation in terms of accuracy and reproducibility, ranging between subjectivity, inter-subjectivity, and objectivity. Next, we examine the database’s algebraic and topological structure in relation to informational complexity measures, and evaluate its computational complexities with respect to an exhaustive optimization. Conjectures of criticality are obtained on the self-organizing processes of observation and dynamical model development. Example analysis is demonstrated with the use of biodiversity assessment database—the process that inevitably involves human subjectivity for management within open complex systems.

Information Theoretical Methods as Discerning Quantifiers of the Equations of State of Neutron Stars

In this work we use the statistical measures of information entropy, disequilibrium and complexity to discriminate different approaches and parametrizations for different equations of state for quark stars. We confirm the usefulness of such quantities to quantify the role of interactions in such stars. We find that within this approach, a quark matter equation of state such as SU(2) NJL with vectorial coupling and phase transition is slightly favoured and deserves deeper studies.

Impact of familiarity on information complexity in human-computer interfaces

A quantitative measure of information complexity remains very much desirable in HCI field, since it may aid in optimization of user interfaces, especially in human-computer systems for controlling complex objects. Our paper is dedicated to exploration of subjective (subject-depended) aspect of the complexity, conceptualized as information familiarity. Although research of familiarity in human cognition and behaviour is done in several fields, the accepted models in HCI, such as Human Processor or Hick-Hyman’s law do not generally consider this issue. In our experimental study the subjects performed search and selection of digits and letters, whose familiarity was conceptualized as frequency of occurrence in numbers and texts. The analysis showed significant effect of information familiarity on selection time and throughput in regression models, although the R 2 values were somehow low. Still, we hope that our results might aid in quantification of information complexity and its further application for optimizing interaction in human-machine systems.

Measures of Morphological Complexity of Gray Matter on Magnetic Resonance Imaging for Control Age Grouping

Current brain-age prediction methods using magnetic resonance imaging (MRI) attempt to estimate the physiological brain age via some kind of machine learning of chronological brain age data to perform the classification task. Such a predictive approach imposes greater risk of either over-estimate or under-estimate, mainly due to limited training data. A new conceptual framework for more reliable MRI-based brain-age prediction is by systematic brain-age grouping via the implementation of the phylogenetic tree reconstruction and measures of information complexity. Experimental results carried out on a public MRI database suggest the feasibility of the proposed concept.

Application of chaos measures to a simplified boids flocking model

Swarm intelligence systems are characterised by the emergence of structure without explicit external control, the coexistence of many stable states and the existence of state transitions with significant change of the system dynamics. Despite these characteristics being shared with the dynamics of chaotic systems, little is known of the potential relationship between swarm and chaotic systems. If indeed there is a relationship between the two, it may be possible to complement the current subjective and quantitative measures used for identifying swarming dynamics with the objective measures used in chaotic systems. This study shows that a simplified version of the original Reynolds’ ‘boids’ (short for ‘birdoid’) model and two degraded versions of the simplified model display flocking dynamics based on current measures of group and order. The simplified version of the original boids model and one of the degraded forms also show chaotic dynamics using three proposed measures of information flow, complexity and sensitivity to initial conditions. A novel $$\hbox {Chaos}_\mathrm{composite}$$ measure is introduced which combines all three measures into a single measure and shows promise for characterising flocking dynamics and potentially swarming dynamics. The measures proposed in this study, therefore, may have potential for predicting and controlling the behaviour of swarm intelligence systems.

Information theoretical methods as discerning quantifiers of the equations of state of neutron stars

Abstract In this work we use the statistical measures of information entropy, disequilibrium and complexity to discriminate different approaches and parametrizations for different equations of state for quark stars. We confirm the usefulness of such quantities to quantify the role of interactions in such stars. We find that within this approach, a quark matter equation of state such as SU(2) NJL with vectorial coupling and phase transition is slightly favoured and deserves deeper studies.

Systematic Study of Information Measures, Statistical Complexity and Atomic Structure Properties

We present a comparative study of several information and statistical complexity measures in order to examine a possible correlation with certain experimental properties of atomic structure. Comparisons are also carried out quantitatively using Pearson correlation coefficient. In particular, it is shown that Fisher information in momentum space is very sensitive to shell effects. It is also seen that three measures expressed in momentum space that is Fisher information, Fisher-Shannon plane and LMC complexity are associated with atomic radius, ionization energy, electronegativity, and atomic dipole polarizability. Our results indicate that a momentum space treatment of atomic periodicity is superior to a position space one. Finally we present a relation that emerges between Fisher information and the second moment of the probability distribution in momentum space i.e. an energy functional of interest in (e,2e) experiments.

SU-E-J-135: Measurements of Non-Linearity Features of Breathing Patterns Using Recurrence Quantification Analysis (RQA) and Dynamic Complexity (DC)

Purpose: To investigate if there exists a difference in breathing patterns between patients treated with SBRT and IMRT using RQA and DC (using K2: correlation entropy and D2: correlation dimension) measures. Methods: 9 patients treated with SBRT and 8 treated with IMRT were scanned with 4D CT and the breathing patterns were acquired. One of the SBRT patients was scanned with and without meditation. Each breathing signal consisted of a scalar time series and recurrence quantification analysis (RQA) was utilized to determine the following measures: Periodicity of the system as percentage of recurrence points (%RR), determinism (DET), maximum diagonal line length (L_max) whose inverse the divergence (DIV) is measure for how fast trajectories diverge from each other, the average diagonal line length (L) that can be interpreted as the mean prediction time of the signal, and the entropy (ENTR) a measure of information complexity. In addition the invariant measures of K2 and D2 were also estimated. A locally nonlinear forecast was applied to predict future breathing signals of N time step ahead for the patient with and without meditation. Results: Our results showed %RR has significant correlation with L_max and has inverse correlation with DIV. DET has significant correlation with Lmax, L, ENTR and DIV. Independent t test suggests there is no difference between the SBRT and IMRT groups in terms of the RQA measures and K2. Patient that had undergone meditation showed improvement in %RR, L_max, DIV, K2 and had an estimated correlation dimension of 1.7. Prediction showed similar results for one and three time step ahead but meditation one had better prediction horizon when time step was higher. Conclusion: RQA is a powerful tool that allows one to analyze the dynamic nature of breathing pattern. No significant difference was found in the dynamical complexity of SBRT and IMRT patients.

HydroZIP: How Hydrological Knowledge can Be Used to Improve Compression of Hydrological Data

From algorithmic information theory, which connects the information content of a data set to the shortest computer program that can produce it, it is known that there are strong analogies between compression, knowledge, inference and prediction. The more we know about a data generating process, the better we can predict and compress the data. A model that is inferred from data should ideally be a compact description of those data. In theory, this means that hydrological knowledge could be incorporated into compression algorithms to more efficiently compress hydrological data and to outperform general purpose compression algorithms. In this study, we develop such a hydrological data compressor, named HydroZIP, and test in practice whether it can outperform general purpose compression algorithms on hydrological data from 431 river basins from the Model Parameter Estimation Experiment (MOPEX) data set. HydroZIP compresses using temporal dependencies and parametric distributions. Resulting file sizes are interpreted as measures of information content, complexity and model adequacy. These results are discussed to illustrate points related to learning from data, overfitting and model complexity.

Information Complexity Based Modeling in the Presence of Length-Biased Sampling

We utilize an Information Complexity Measure (ICOMP) based modeling approach to determine possible contamination due to length-biased sampling. The ICOMP approach considers both the lack of fit (goodness of fit) and the inherent information complexity of each of the distributions with respect to the real distribution of the data.