We explored the statistics of filtering of simple patterns on a number of deterministic and random graphs as a tractable simple example of information processing in complex systems. In this problem, multiple inputs map to the same output, and the statistics of filtering is represented by the distribution of this degeneracy. For a few simple filter patterns on a ring we obtained an exact solution of the problem and described numerically more difficult filter setups. For each of the filter patterns and networks we found a few numbers essentially describing the statistics of filtering and compared them for different networks. Our results for networks with diverse architectures appear to be essentially determined by two factors: whether the graphs structure is deterministic or random, and the vertex degree. We find that filtering in random graphs produces a much richer statistics than in deterministic graphs. This statistical richness is reduced by increasing the graph’s degree.

Distributed Systems architectures are becoming the standard computational model for processing and transportation of information, especially for Cloud Computing environments. The increase in demand for application processing and data management from enterprise and end-user workloads continues to move from a single-node client-server architecture to a distributed multitier design where data processing and transmission are segregated. Software development must considerer the orchestration required to provision its core components in order to deploy the services efficiently in many independent, loosely coupled - physically and virtually interconnected - data centers spread geographically, across the globe. This network routing challenge can be modeled as a variation of the Travelling Salesman Problem (TSP). This paper proposes a new optimization algorithm for optimum route selection using Algorithmic Information Theory. The Kelly criterion for a Shannon-Bernoulli process is used to generate a reliable quantitative algorithm to find a near optimal solution tour. The algorithm is then verified by comparing the results with heuristic solutions in 3 test cases. A statistical analysis is designed to measure the significance of the results between the algorithms and the entropy function can be derived from the distribution. The tested results shown an improvement in the solution quality by producing routes with smaller length and time requirements. The quality of the results proves the flexibility of the proposed algorithm for problems with different complexities without relying in nature-inspired models such as Genetic Algorithms and Simulated Annealing. This algorithm can be used by orchestration applications to deploy services across large cluster of nodes by making better decision in the route design.

The question does P = NP has confounded mathematicians and computer scientists alike for over 50 years and although there is an almost unanimous agreement that it in fact does not, there still is no absolute proof. In this paper, I attempt to prove to that P does not equal NP.

In mathematics, the Riemann hypothesis is a conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part 1/2. Many consider it to be the most important unsolved problem in pure mathematics. It is one of the seven Millennium Prize Problems selected by the Clay Mathematics Institute to carry a US 1,000,000 prize for the first correct solution. We prove the Riemann hypothesis using the Complexity Theory. Number theory is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. The Goldbach's conjecture is one of the most important and unsolved problems in number theory. Nowadays, it is one of the open problems of Hilbert and Landau. We show the Goldbach's conjecture is true using the Complexity Theory as well. An important complexity class is 1NSPACE(S(n)) for some S(n). These mathematical proofs are based on if some unary language belongs to 1NSPACE(S(log n)), then the binary version of that language belongs to 1NSPACE(S(n)) and vice versa.

This paper aims to analyze the effects of Covid-19 on financial markets from the perspective of Complexity. The Covid-19 pandemic has caused turmoil in financial markets and is already one of the most important financial crises in history, causing a fall in several stock markets as well as great volatility. Unlike past crises, which in most cases were caused either by problems of fiscal deficits or in the financial system, this crisis has its origin in an epidemic disease, which occurred in Wuhan, China, and quickly spread across the globe affecting transport networks, commerce and finance, and will affect the public debt of many countries. This is a systemic situation in which there is a need to consider several interconnected systems, financial instability and high financial risk, something that econophysics and some complexity theorists already do. Therefore, this paper intends to show, theoretically, the systemic and complex character of the recent financial crisis caused by Covid-19.

Questions: Elevation, biodiversity, and forest structure are commonly correlated, but their relationships near the positive extremes of biodiversity and elevation are unclear. We asked 1) How does forest structure vary with elevation in a high biodiversity, high topographic complexity region? 2) Does forest structure predict vascular plant biodiversity? 3) Is plant biodiversity more strongly related to elevation or to forest structure? Location: Great Smoky Mountains National Park, USAMethods: We used terrestrial LiDAR scanning (TLS) to characterize vegetation structure in 12 forest plots. We combined two new canopy structural complexity metrics with traditional TLS-derived forest structural metrics and vascular plant biodiversity data to investigate correlations among forest structure metrics, biodiversity, and elevation. Results: Forest structure varied widely across plots spanning the elevational range of GRSM. Our new measures of canopy density (Depth) and structural complexity (σDepth) were sensitive to structural variations and effectively summarized horizontal and vertical dimensions of structural complexity. Vascular plant biodiversity was negatively correlated with elevation, and more strongly positively correlated with vegetation structure variables. Conclusions: The strong correlations we observed between canopy structural complexity and biodiversity suggest that structural complexity metrics could be used to assay plant biodiversity over large areas in concert with airborne and spaceborne platforms.

We present a general process for the halting problem, valid regardless of the time and space computational complexity of the decision problem. It can be interpreted as the maximization of entropy for the utility function of a given Shannon-Kolmogorov-Bernoulli process. Applications to non-polynomials problems are given. The new interpretation of information rate proposed in this work is a method that models the solution space boundaries of any decision problem (and non polynomial problems in general) as a communication channel by means of Information Theory. We described a sort method that order objects using the intrinsic information content distribution for the elements of a constrained solution space - modeled as messages transmitted through any communication systems. The limits of the search space are defined by the Kolmogorov-Chaitin complexity of the sequences encoded as Shannon-Bernoulli strings. We conclude with a discussion about the implications for general decision problems in Turing machines.

What is the function of cognition? On one influential account, cognition evolved to co-ordinate behaviour with environmental change or complexity (Godfrey-Smith 1996). Liberal interpretations of this view ascribe cognition to an extraordinarily broad set of biological systems – even bacteria, which modulate their activity in response to salient external cues, would seem to qualify as cognitive agents. However, equating cognition with adaptive flexibility per se glosses over important distinctions in the way biological organisms deal with environmental complexity. Drawing on contemporary advances in theoretical biology and computational neuroscience, we cash these distinctions out in terms of different kinds of generative models, and the representational and uncertainty-resolving capacities they afford. This analysis leads us to propose a formal criterion for delineating cognition from other, more pervasive forms of adaptive plasticity. On this view, biological cognition is rooted in a particular kind of functional organisation; namely, that which enables the agent to detach from the present and engage in counterfactual (active) inference.

It is impossible to fully grasp reality and the universe without a sound understanding of quantum science, i.e. theory. The aim of this paper is twofold, namely first presenting what quantum information processing consists of, and then consequently discussing the implications of quantum science to the understanding of reality. I shall claim that the world is fully quantum, and the classical world is but a limit case of the quantum world. The crux of the argument is that quantum information can be taken as a living phenomenon. Quantum information processing (QIP) has been mainly the subject of computational approaches (Cooper and Hodges, 2016). Here we take it as the way in which information allows for a non-dualistic explanation of the world. In this sense, quantum information processing consists in understanding how entanglement stands as the ground for a coherent reality yet highly dynamical, vibrant and vivid. Information, I argue, is a living phenomenon that creates itself out of nothing. Quantum information is a relational view of entities, systems, phenomena, and events (Auletta, 2005).

In the last decades, it has been established that astrocytes play key roles in the regulation of neuronal morphology. However, the contribution of astrocyte-derived small extracellular vesicles (sEVs) to morphological differentiation of neurons has only recently been addressed. Here, we showed that cultured astrocytes expressing a GFP tagged version of the stress-regulated astrocytic enzyme Aldolase C (Aldo C-GFP) release small extracellular vesicles (sEVs) which are transferred into cultured hippocampal neurons. Surprisingly, Aldo C-GFP-containing sEVs (Aldo C-GFP sEVs) displayed an exacerbated capacity to reduce the dendritic complexity in developing hippocampal neurons compared to sEVs derived from control (i.e. GFP-expressing) astrocytes. Using bioinformatics and biochemical tools, we found that the total content of overexpressed Aldo C-GFP correlates with an increased content of endogenous miRNA-26a-5p in both total astrocyte homogenates and sEVs. Notably, neurons magnetofected with a nucleotide sequence that mimics endogenous miRNA-26a-5p (mimic 26a-5p) not only decreased the levels of neuronal proteins associated to morphogenesis regulation and also reproduced morphological changes induced by Aldo-C-GFP sEVs. Furthermore, neurons magnetofected with a sequence targeting miRNA-26a-5p (antago 26a-5p) were largely resistant to Aldo C-GFP sEVs. Our results support a novel and complex level of astrocyte-to-neuron communication mediated by astrocyte-derived sEVs and the activity of their miRNA content.

Software project complexity increases day by day because the software engineering products is being used in the solution of more technically difficult problem and the size of project continuous to grow. The increase complexity causes to high numbers of software project failures in term of time, cost and quality. The main question regarding to this problem is how to handle or cope with this complexity. There is no single way to handle this, software engineer uses different perspective to handle complexity without affecting the overall project performance. A management perspective recognizes that the success of complex project requires good project management. A technically perspective reveals new paradigms for software development i.e.; object oriented and formal methods etc. and software engineer also look for automation perspective in order to reduce the complexity issues. In this paper we will find out the main software project complexity factors by focusing on the management aspects of software project development and also the problems of managing complexity in software engineering products from these different perspectives. The paper is divided in three main sections; paradigms of software development, project management in term of time, cost and quality and third one is automated support that includes methods and tools used to manage the complexity.

This paper addresses the issues of how we can quantify structural information for nonparametric distributions and how we can detect its changes. Structural information refers to an index for a global understanding of a data distribution. When we consider the problem of clustering using a parametric model such as a Gaussian mixture model, the number of mixture components (clusters) can be thought of as structural information in the model. However, there does not exist any notion of structural information for nonparametric modeling of data. In this paper we introduce a novel notion of {\em kernel complexity} (KC) as structural information in the nonparametric setting. The key idea of KC is to combine the information bias inspired by the Gini index with the information quantity measured in terms of the normalized maximum likelihood (NML) code length. We empirically show that KC has a property similar to the number of clusters in a parametric model. We further propose a framework for structural change detection with KC in nonparametric distributions. With synthetic and real data sets we empirically demonstrate that our framework enables us to detect structural changes underlying the data and their early warning signals.

Static standing postural stability has been measured by multiscale entropy (MSE), which is used to measure complexity. In this study, we used the average entropy (AE) to measure the static standing postural stability, as AE is a good measure of disorder. The center of pressure (COP) trajectories were collected from 11 subjects under four kinds of balance situation, from stable to unstable: bipedal with open eyes, bipedal with closed eyes, unipedal with open eyes, and unipedal with closed eyes. The AE, entropy of entropy (EoE), and MSE methods were used to analyze these COP data, and EoE was found to be a good measure of complexity. The AE of the 11 subjects sequentially increased by 100%as the balance situations progressed from stable to unstable, but the results of EoE and MSE did not follow this trend. Therefore, AE, rather than EoE or MSE, is a good measure of static standing postural stability. Furthermore, the comparison of EoE and AE plots exhibited an inverted U curve, which is another example of a complexity versus disorder inverted U curve.

Cancers remain the lead cause of disease-related, pediatric death in North America. The emerging field of complex systems has redefined cancer networks as a computational system with intractable algorithmic complexity. Herein, a tumor and its heterogeneous phenotypes are discussed as dynamical systems having multiple, strange attractors. Machine learning, network science and algorithmic information dynamics are discussed as current tools for cancer network reconstruction. Deep Learning architectures and computational fluid models are proposed for better forecasting gene expression patterns in cancer ecosystems. Cancer cell decision-making is investigated within the framework of complex systems and complexity theory.

It is important to reduce the computation complexity while maintaining the accuracy of convolution neural networks. We deem it is possible to further reduce the network complexity while ensuring the accuracy. In this paper, we propose a novel feature extraction network called DSRNet which is lightweight but effective. DSRNet follows the basic ideas of stacking modules and short connection, introduces Depthwise Separable convolution and utilizes the Dilated convolution. The proposed network has fewer parameters and achieves outstanding speed. We conducted comprehensive experiments on CIFAR10, CIFAR100 and STL10 datasets, and the results showed the DSRNet has great performance improvement in terms of accuracy and speed.

The perspective suggests an unorthodox interpretation of cancer dynamics in terms of strange attractors and fluid turbulence. The relevance of strange attractors in tumor growth-invasion dynamics and chemical pattern formation are reviewed. Chemical turbulence, fractals and chaos are discussed as the principal characteristics of tumor ecosystems and their complex cybernetics. To conclude, cancers are presented as complex systems exhibiting chaotic gene expression dynamics.

Project complexity is usually considered as one of main causes of cost overruns, resulting in poor performance and thus project failure. However, empirical studies focused on evaluating its effects on project cost remain lacking. Given this circumstance, this study attempts to develop the relationships between project cost and the multidimensional project complexity elements. We establish complexity as a multidimensional factor including the task, organization, market, legal, and environment complexities. This study uses an empirical evidence-based structural model to account for the relationships between project cost and project complexity. By doing so, a quantitative assessment of multi-dimensional project complexity has been developed. The findings suggest that task and organization complexities have direct effects on project cost, while market, legal and external environment complexities have indirect effects on project cost. The practical contribution is that the findings can improve the understanding of which dimension of complexity significantly influence project cost, and the need to focus efforts on strategically addressing that complexities.

This work presents some characteristics of MoNet, a computerized platform for the modeling and visualization of complex systems. Emphasis is on the ideas that allowed the successful progressive development of this modeling platform, which goes along with the implementation of applications to the modeling of several studied systems. The platform has the capacity to represent different aspects of systems modeled at different observation scales. This tool offers advantages in the sense of favoring the perception of the phenomenon of the emergence of information, associated with changes of scale. Some criteria used for the construction of this modeling platform are included. The power of current computers has made practical representing graphic resources such as shapes, line thickness, overlaying-text tags, colors and transparencies, in the graphical modeling of systems made up of many elements. By visualizing diagrams conveniently designed to highlight contrasts, these modeling platforms allow the recognition of patterns that drive our understanding of systems and their structure. Graphs that reflect the benefits of the tool regarding the visualization of systems at different scales of observation are presented to illustrate the application of the platform.

As shown earlier, the algorithmic complexity, like Shannon information and Boltzmann entropy, tends to increase in accordance with the general law of complification. However, the algorithmic complexity of most material systems does not reach its maximum, i.e. chaotic state, due to the various laws of nature that create certain structures. The complexity of such structures is very different from the algorithmic complexity, and we intuitively feel that its maximal value should be somewhere between order and chaos. I propose a formula for calculation such structural complexity, which can be called - structuredness. The structuredness of any material system is determined by structures of three main types: stable, dissipative, and post-dissipative. The latter are defined as stable structures created by dissipative ones, directly or indirectly. Post-dissipative structures, as well as stable, can exist for an unlimited time, but at the micro level only, without energy influx. The appearance of such structures leads to the “ratchet” process, which determines the structuregenesis in non-living and, especially, in living systems. This process allows systems with post-dissipative structures to develop in the direction of maximum structuring due to the gradual accumulation of these structures, even when such structuring contradicts the general law of complification.

Integrated information theory (IIT) proposes a measure of integrated information (Φ) to capture the level of consciousness for a physical system in a given state. Unfortunately, calculating Φ itself is currently only possible for very small model systems, and far from computable for the kinds of systems typically associated with consciousness (brains). Here, we consider several proposed measures and computational approximations, some of which can be applied to larger systems, and test if they correlate well with Φ. While these measures and approximations capture intuitions underlying IIT and some have had success in practical applications, it has not been shown that they actually quantify the type of integrated information specified by the latest version of IIT. In this study, we evaluated these approximations and heuristic measures, based not on practical or clinical considerations, but rather based on how well they estimate the Φ values of model systems. To do this, we simulated networks consisting of 3–6 binary linear threshold nodes randomly connected with excitatory and inhibitory connections. For each system, we then constructed the system’s state transition probability matrix (TPM), as well as its state transition matrix (STM) over time for all possible initial states. From these matrices, we calculated, approximations to Φ, and measures based on state differentiation, state entropy, state uniqueness, and integrated information. All measures were correlated with Φ in a state dependent and state independent manner. Our findings suggest that Φ can be approximated closely in small binary systems by using one or more of the readily available approximations (r > 0.95), but without major reductions in computational demands. Furthermore, Φ correlated strongly with measures of signal complexity (LZ, r_s = 0.722), decoder based integrated information (Φ*, r_s = 0.816), and state differentiation (D1, r_s = 0.827), on the system level (state independent). These measures could allow for efficient estimation of Φ on a group level, or as accurate predictors of low, but not high, Φ systems. While it’s uncertain whether the results extend to larger systems or systems with other dynamics, we stress the importance that measures aimed at being practical alternatives to Φ are at a minimum rigorously tested in an environment where the ground truth can be established.

This year marks the 20th anniversary of the discovery that proteins with various cellular functions can be temporarily immobilized in the nucleolus, a process known as nucleolar sequestration. This review reflects on the progress made to understand the physiological roles of nucleolar sequestration and the mechanisms involved in protein immobilization. We discuss how nucleolar sequestration consists of a highly choreographed amyloidogenic liquid-to-solid phase transition that converts the nucleolus into Amyloid bodies (A-bodies). The study of solid condensates A-bodies will offer unique perspectives on cellular assembly of membrane-less compartments and provide alternative insights on pathological amyloidogenesis involved in neurological disorders.

We evaluate the complexity of Colombian climate from extreme behavior of gauge temperature and precipitation, using the the novel Tsallis' non-extensive entropy principle based on physical information through the q-index. We find the spatial structure of non additive universal categories (q-index) and compare with some complex systems with the potential to have some degree of dynamical affinity. Our results evidence the great dynamical variability of regional climate expressed in the large range of values of $q$-index, and the high degree of non-extensitivity for both temperature and precipitation.

Cancers are complex, adaptive ecosystems. They remain the leading cause of disease-related death among children in North America. As we approach computational oncology and Deep Learning Healthcare, our mathematical models of cancer dynamics must be revised. Recent findings support the perspective that cancer-microenvironment interactions consist of turbulent flows. As such, cancer pattern formation, protein-folding and metastatic invasion are discussed herein as processes driven by chemical turbulence within the framework of complex systems theory. Current state-of-the-art quantitative approaches used in reconstructing cancer stem cell networks are reviewed. To conclude, cancer stem cells are presented as strange attractors of the Waddington landscape.

I review previous attempts, including recent ones, to introduce technical aspects of digital information and computation into the discussion of ethics. I survey some limitations and advantages of these attempts to produce guiding principles at different scales. In particular, I briefly introduce and discuss questions, approaches, challenges, and limitations based on, or related to, simulation, information theory, integrated information, computer simulation, intractability, algorithmic complexity, and measures of computational organisation and sophistication. I discuss and propose a set of features that ethical frameworks must possess in order to be considered well-grounded, both in theoretical and methodological terms. I will show that while global ethical frameworks that are uncomputable are desirable because they provide non-teleological direction and open-ended meaning, constrained versions should be able to provide guidelines at more local and immediate time scales. In connection to the ethics of artificial intelligence, one point that must be underscored about computational approaches is that (General) AI should only embrace an ethical framework that we humans are willing to adopt. I think that such a framework is possible, taking the form of a general and universal (in the sense of computation) framework built from first computational principles.

In this paper we present a review of recent developments in AI towards the possibility of an artificial intelligence equals that of human intelligence. AI technology has always shown a stepwise increase in its capacity and complexity. The last step took place several years ago, with the increased progress in deep neural network technology. Each such step goes hand in hand with our understanding of ourselves and our understanding of human cognition. Indeed, AI was always about the question of understanding human nature. AI percolates into our lives, changing our environment. We believe that the next few steps in AI technology, and in our understanding of human behavior, will bring about much more powerful machines, flexible enough to resemble human behavior. In this context, there are two research fields: Artificial Social Intelligence (ASI) and General Artificial Intelligence (AGI). The authors also allude to one of the main challenges for AI, embodied cognition, and explain how it can viewed as an opportunity for further progress in AI research.

In mathematics, one always aims to obtain new frameworks from specific ones. This also stratified to the regality of graphs, where one can produce numerous new graphs from a specific set of graphs. In this work we define some classes of pyramid graphs created by a gear graph and we derive straightforward formulas of the complexity of these graphs, using linear algebra matrix analysis techniques and employing knowledges of Chebyshev polynomials.

We investigate the physics of a medium-size quantum particle' gases, of the order of hundreds or thousands of fermions/bosons (far below the thermodynamic limit $N \, \rightarrow \, 10^{24}$). Appeal to microcanonical ensemble becomes then unavoidable. The so-called statistical complexity is our protagonist. Interesting facts are uncovered, both for fermions and bosons, yielded by statistical quantifiers.

Spatial data conflation plays a fundamental role in in many aspects of modern Geographic Information Systems (GIS) research and development such as geospatial data visualization, incremental updating of databases and disaster evaluation. The primary objective of conflation is to derive valuable information based on the comparison of multiple spatial data sources of homogeneous or heterogeneous nature. This paper reviews the state of art of the concept of conflation, feature matching, the most important progresses of conflation between image and road network data, and the complexity of spatial conflation.

In this paper we study the normal bases for Galois ring extension ${{R}} / {Z}_{p^r}$ where ${R}$ = ${GR}$(p^r, n). We present a criterion on normal basis for ${{R}} / {Z}_{p^r}$ and reduce this problem to one of finite field extension $\overline{R} / \overline{Z}_{p^r}=F_{q} / F_{p} (q=p^n)$ by Theorem 1. We determine all optimal normal bases for Galois ring extension.

We present a new method of estimating fitness of countries and complexity of products by exploiting a non-linear non-homogeneous map applied to the publicly available information on the goods exported by a country. The non homogeneous terms guarantee both convergence and stability. After a suitable rescaling of the relevant quantities, the non homogeneous terms are eventually set to zero so that this new method is parameter free. This new map reproduces the findings of the method proposed by Tacchella et al. [1], and allows for an approximate analytic solution in case of actual binarized matrices based on the Revealed Comparative Advantage (RCA) indicator. This solution is connected with a new quantity describing the neighborhood of nodes in bipartite graphs, representing in this work the relations between countries and exported products. Moreover, we define the new indicator of country net-efficiency quantifying how a country efficiently invests in capabilities able to generate innovative complex high quality products. Eventually, we demonstrate analytically the local convergence of the algorithm.

In this work we identify combinations of technological activities that signal the presence local capabilities in a country to successfully export a product. We use country-level patent and trade data to generate a multi-layer network, and we apply maximization of entropy to generate synthetic data to effectively divide signal from noise. We show that in several sectors the signal far exceed the noise. Our exercise provides robust evidence of the presence of synergies between technologies to explain trade performances in specific markets. This can be highly useful for policy makers, to inform industrial and innovation policies.

This study presents an analysis of the spatial and temporal distribution of the two large destructive earthquakes that occurred in Lake Van area on October 23, and November 9, 2011, together with the azimuth-dependent distribution of the seismic activity and microseismicity clusters after the mainshocks, associated with the complex rupture processes of their aftershock sequence. The sequence began with the magnitude Mw 7.1 earthquake of 23 October and a second destructive earthquake of Mw 5.6. The aftershock sequences of the two mainshocks were linked to the local crustal faults beneath Lake Van area, followed successively and produced unusually intense activity and significant damage in the area. The main purposes of this study are to document the spatial and temporal distribution and evolution of the October 23, 2011 aftershock hypocenters and the azimuth-dependent distribution of seismic activity, and to understand the spatial and temporal character of the aftershock sequence using the distributional and evolutional patterns of the aftershock hypocenters. A total of 10,000 aftershocks were obtained from seismic data with a high signal-to-noise ratio over collected over three years from October 23, 2011 to March 2014. These aftershocks were plotted for the time periods from November 2011 through March 2012 to March 2014 and ≈ 5000 aftershocks were retained in the depth versus distance cross-sections to detect the clusters in the first step of study (November 2011–March 2012). The focal depth distribution of the aftershock clusters, the migration of hypocenter activity and microseismicity clusters were analyzed and the distributional patterns of the detected clusters were assessed using the geometric distribution of the aftershock hypocenters. The spatial and temporal distribution of aftershocks reveal interesting key features of the deep rupture complexity of the Van earthquake: (1) most prominent aftershocks have been located in the upper crust at depths shallower than 10 km beneath ruptured area, indicating that the upper crust is brittle and seismogenic; (2) two spatial clusters have been detected at 8-10 km depths and the upward extrapolation of these clusters intersects with faults; the main cluster (60 km wide) bounded by inferred reverse faults (f3 and f4) and the central cluster (25–30 km wide) bounded by faults (f1 and f2); (3) these spatial clusters form the largest volumetric pattern of the conical-shaped cluster at depths of about 25–30 km of the azimuth-dependent rotational projections, suggesting azimuthal distributions of deep rupture characteristics; and (4) the strongest temporal cluster of microseismicity derived from temporal distribution of aftershocks has been detected within an area of about 2.5–3.0 km² and it is spatially observed at 20 km depth within the central cluster, suggesting progressive failure of the adjacent patches of possible fault.

This work is a generalization of the Lopez-Ruiz, Mancini and Calbet (LMC); and Shiner, Davison and Landsberg (SDL) complexity measures, considering that the state of a system or process is represented by a dynamical variable during a certain time interval. As the two complexity measures are based on the calculation of informational entropy, an equivalent information source is defined and, as time passes, the individual information associated to the measured parameter is the seed to calculate instantaneous LMC and SDL measures. To show how the methodology works, an example with economic data is presented.

We compared performance of a novel encoding Lempel-Ziv complexity (ELZC) with approximate entropy (ApEn), sample entropy (SmpEn) and permutation entropy (PerEn) as nonlinear metric to assess ECG quality. Firstly to compare performance of discerning randomness and inherent nonlinear properties within time series, this study calculated the aforementioned four nonlinear complexity values on several typical artificial time series i.e., Gauss noise, two kinds of noisy time series, two kinds of Logistic series and periodic series, respectively. Then for analyzing sensitivity of the aforementioned four complexity methods to content level of different types noise within ECG recordings, we investigated variation trend of ELZC, ApEn, SmpEn and PerEn in several synthetic ECG recordings containing different types noise (i.e., baseline wander, muscle artefacts, electrode motion, power line and mixed noise) and different signal noise ratios (i.e., 15, 10, 5, 0, −5 and −10 dB). Finally, the four complexity methods were employed to classify the quality of real ECG recordings from the PhysioNet/Computing in Cardiology Challenge 2011 (CINC 2011) of the MIT databases, then receiver operating characteristic curves (ROC) and their corresponding area under curve (AUC) were yielded. The results showed ELZC could not only distinguish randomness and chaotic within time series but also reflect content level of noise within time series, and the highest AUC of PerEn, ELZC, SmpEn and ApEn were 0.850, 0.695, 0.474 and 0.461, respectively. The results demonstrated PerEn and ELZC were more effectively than ApEn and SmpEn for assessing ECG quality.

Reconfiguration is concerned with relationships among solutions to a problem instance, where the reconfiguration of one solution to another is a sequence of steps such that each step produces an intermediate feasible solution. The solution space can be represented as a reconfiguration graph, where two vertices representing solutions are adjacent if one can be formed from the other in a single step. Work in the area encompasses both structural questions (Is the reconfiguration graph connected?) and algorithmic ones (How can one find the shortest sequence of steps between two solutions?) This survey discusses techniques, results, and future directions in the area.

In the clinical electrophysiologic practice, the reading and comparing electroencephalographic (EEG) recordings some times is insufficient and take to much time. That is why in the last years it has begun to introduce new methods of EEG analysis, that give a better and faster understanding of the EEG dynamics and allow a rapid intervention in the patient's treatment. Tools coming from the information theory or nonlinear system as an entropy and complexity have been shown to be a very good alternative to address this problem. In this work we introduce a novel method -the permutation Lempel-ziv complexity vs permutation entropy map. This method was applied to EEG of two patients with specific diagnosed pathologies during respective follow up processes of pharmacological changes in order to detect changes that are not evident with the usual inspection method. Our results show that the proposed method are useful for observing an evolutionary retrospective clinical effects of pharmacological interventions in both patients, and from these, to follow the clinical response to the proposed treatment.

Quantum computers are machines that are designed to use quantum mechanics in order to improve upon classical computers by running quantum algorithms. One of the main applications of quantum computing is solving optimization problems. For addressing optimization problems, we can use linear programming. Linear programming is a method to obtain the best possible outcome in a special case of mathematical programming. Application areas of this problem consist of resource allocation, production scheduling, parameter estimation, etc. In our study, we look at quantum speedup ratios of HHL Algorithm for different scenarios of linear programming. In a first scenario we look quantum speedup ratio (S(N)) as a function of phase transition and the ratio (κ) between the greatest and smallest eigenvalues of the matrix in linear equation system. As a second scenario, we investigate the changes in S(N) as a function of κ and s, which is the coefficient for defining the matrix as s-sparse.

Quantum computers are machines that are designed to use quantum mechanics in order to improve upon classical computers by running quantum algorithms. One of the main applications of quantum computing is solving optimization problems. For addressing optimization problems we can use linear programming. Linear programming is a method to obtain the best possible outcome in a special case of mathematical programming. Application areas of this problem consist of resource allocation, production scheduling, parameter estimation, etc. In our study, we looked at the duality of resource allocation problems. First, we chose a real world optimization problem and looked at its solution with linear programming. Then, we restudied this problem with a quantum algorithm in order to understand whether if there is a speedup of the solution. The improvement in computation is analysed and some interesting results are reported.

Natural time is a new time domain introduced in 2001. The analysis of time series associated with a complex system in natural time may provide useful information and may reveal properties that are usually hidden when studying the system in conventional time. In this new time domain, an entropy has been defined and complexity measures based on this entropy as well as its value under time-reversal have been introduced and found applications in various complex systems. Here, we review these applications in the electric signals that precede rupture, e.g., earthquakes, in the analysis of electrocardiograms, as well as in global atmospheric phenomena like the El Nino/La Nina Southern Oscillation.

Recently emerging data-driven citizen sciences need to harness increasing amount of massive data with varying quality. This paper develops essential theoretical frameworks and example models and examine its computational complexity for interactive data-driven citizen science within the context of guided self-organization. We first define a conceptual model that incorporates 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 exhaustive optimization. Conjectures of criticality are obtained on 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 the management in open complex systems.

Synergistic effects between reactions, reagents and catalysts can lead to minor heats of reaction and occur as an inherent result of multi-component reactions (MCRs) and their extensions. They enable syntheses to be performed at a low energy level and the number of synthesis steps to be drastically reduced in comparison with ‘classical’ two-component reactions. The very high potential for variability, diversity and complexity of MCRs additionally generates an extremely diverse range of products, thus bringing us closer to the aim of being able to produce tailor-made and extremely low-priced materials, drugs and libraries.

This paper examines the correlation between numbers of computer cores in parallel genetic algorithms. The objective to determine the linear polynomial complementary equation in order represent the relation between number of parallel processing and optimum solutions. Model this relation as optimization function (f(x)) which able to produce many simulation results. F(x) performance is outperform genetic algorithms. Compression results between genetic algorithm and optimization function is done. Also the optimization function give model to speed up genetic algorithm. Optimization function is a complementary transformation which maps a TSP given to linear without changing the roots of the polynomials.

Warren Weaver, writing about the function that science should have in mankind’s developing future, ideas and ideals, proposed to classify scientific problems into ‘problems of simplicity’, ‘problems of disorganised complexity’, and ‘problems of organised complexity’ — the huge complementary class to which all biological, human, and social problems belong. Problems of simplicity have few components and variables and have been extensively addressed in the last 400 years. Problems of disorganised complexity have a huge number of individually erratic components and variables, but possess collective regularities that can be analysed by resourcing to stochastic methods. Yet, problems of organised complexity do not yield easily to classical or statistical treatment since interrelations among phenomenon elements change during its evolution alongside commonly used state variables, affecting behaviour and outcome. Moreover, organisation, the focal point in this complementary class, is still an elusive concept despite the gigantic efforts undertaken since a century ago to tame it. This paper addresses the description, representation and study of phenomena in the ‘problems of organised complexity’ class. Grounded on relational mathematical constructs, a theoretical framework providing operational definitions and schemes for formally modelling organisations and interaction of organisations is introduced. This framework extends the general systems’ concept and provides a novel perspective for addressing organised complexity phenomena as a collection of interacting organisations.

Embryonic development proceeds through a series of differentiation events. The mosaic version of this process (binary cell divisions) can be analyzed by comparing early development of Ciona intestinalis and Caenorhabditis elegans. To do this, we reorganize lineage trees into differentiation trees using the graph theory ordering of relative cell volume. Lineage and differentiation trees provide us with means to classify each cell using binary codes. Extracting data characterizing lineage tree position, cell volume, and nucleus position for each cell during early embryogenesis, we conduct several statistical analyses, both within and between taxa. We compare both cell volume distributions and cell volume across developmental time within and between single species and assess differences between lineage tree and differentiation tree orderings. This enhances our understanding of the differentiation events in a model of pure mosaic embryogenesis and its relationship to evolutionary conservation. We also contribute several new techniques for assessing both differences between lineage trees and differentiation trees, and differences between differentiation trees of different species. The results suggest that at the level of differentiation trees, there are broad similarities between distantly related mosaic embryos that might be essential to understanding evolutionary change and phylogeny reconstruction. Differentiation trees may therefore provide a basis for an Evo-Devo Postmodern Synthesis.