Rényi entropy-complexity causality space: a novel neurocomputational tool for detecting scale-free features in EEG/iEEG data.

Scale-free brain activity, linked with learning, the integration of different time scales, and the formation of mental models, is correlated with a metastable cognitive basis. The spectral slope, a key aspect of scale-free dynamics, was proposed as a potential indicator to distinguish between different sleep stages. Studies suggest that brain networks maintain a consistent scale-free structure across wakefulness, anesthesia, and recovery. Although differences in anesthetic sensitivity between the sexes are recognized, these variations are not evident in clinical electroencephalographic recordings of the cortex. Recently, changes in the slope of the power law exponent of neural activity were found to correlate with changes in Rényi entropy, an extended concept of Shannon's information entropy. These findings establish quantifiers as a promising tool for the study of scale-free dynamics in the brain. Our study presents a novel visual representation called the Rényi entropy-complexity causality space, which encapsulates complexity, permutation entropy, and the Rényi parameter q. The main goal of this study is to define this space for classical dynamical systems within theoretical bounds. In addition, the study aims to investigate how well different time series mimicking scale-free activity can be discriminated. Finally, this tool is used to detect dynamic features in intracranial electroencephalography (iEEG) signals. To achieve these goals, the study implementse the Bandt and Pompe method for ordinal patterns. In this process, each signal is associated with a probability distribution, and the causal measures of Rényi entropy and complexity are computed based on the parameter q. This method is a valuable tool for analyzing simulated time series. It effectively distinguishes elements of correlated noise and provides a straightforward means of examining differences in behaviors, characteristics, and classifications. For the iEEG experimental data, the REM state showed a greater number of significant sex-based differences, while the supramarginal gyrus region showed the most variation across different modes and analyzes. Exploring scale-free brain activity with this framework could provide valuable insights into cognition and neurological disorders. The results may have implications for understanding differences in brain function between the sexes and their possible relevance to neurological disorders.

A network model of social contacts with small-world and scale-free features, tunable connectivity, and geographic restrictions.

Small-world networks and scale-free networks are well-known theoretical models within the realm of complex graphs. These models exhibit "low" average shortest-path length; however, key distinctions are observed in their degree distributions and average clustering coefficients: in small-world networks, the degree distribution is bell-shaped and the clustering is "high"; in scale-free networks, the degree distribution follows a power law and the clustering is "low". Here, a model for generating scale-free graphs with "high" clustering is numerically explored, since these features are concurrently identified in networks representing social interactions. In this model, the values of average degree and exponent of the power-law degree distribution are both adjustable, and spatial limitations in the creation of links are taken into account. Several topological metrics are calculated and compared for computer-generated graphs. Unexpectedly, the numerical experiments show that, by varying the model parameters, a transition from a power-law to a bell-shaped degree distribution can occur. Also, in these graphs, the degree distribution is most accurately characterized by a pure power-law for values of the exponent typically found in real-world networks.

Calculation of Effective Thermal Conductivity for Human Skin Using the Fractal Monte Carlo Method.

In this work, an effective thermal conductivity (ETC) for living tissues, which directly affects the energy transport process, is determined. The fractal scaling and Monte Carlo methods are used to describe the tissue as a porous medium, and blood is considered a Newtonian and non-Newtonian fluid for comparative and analytical purposes. The effect of the principal variables-such as fractal dimensions DT and Df, porosity, and the power-law index, n-on the temperature profiles as a function of time and tissue depth, for one- and three-layer tissues, besides temperature distribution, are presented. ETC was improved by considering high tissue porosity, low tortuosity, and shear-thinning fluids. In three-layer tissues with different porosities, perfusion with a non-Newtonian fluid contributes to the understanding of the heat transfer process in some parts of the human body.

Adiabatic Amplification of the Harmonic Oscillator Energy When the Frequency Passes through Zero.

We study the evolution of the energy of a harmonic oscillator when its frequency slowly varies with time and passes through a zero value. We consider both the classical and quantum descriptions of the system. We show that after a single frequency passage through a zero value, the famous adiabatic invariant ratio of energy to frequency (which does not hold for a zero frequency) is reestablished again, but with the proportionality coefficient dependent on the initial state. The dependence on the initial state disappears after averaging over the phases of initial states with the same energy (in particular, for the initial vacuum, the Fock and thermal quantum states). In this case, the mean proportionality coefficient is always greater than unity. The concrete value of the mean proportionality coefficient depends on the power index of the frequency dependence on a time near the zero point. In particular, the mean energy triplicates if the frequency tends to zero linearly. If the frequency attains zero more than once, the adiabatic proportionality coefficient strongly depends on the lengths of time intervals between zero points, so that the mean energy behavior becomes quasi-stochastic after many passages through a zero value. The original Born-Fock theorem does not work after the frequency passes through zero. However, its generalization is found: the initial Fock state becomes a wide superposition of many Fock states, whose weights do not depend on time in the new adiabatic regime. When the mean energy triplicates, the initial Nth Fock state becomes a superposition of, roughly speaking, 6N states, distributed nonuniformly. The initial vacuum and low-order Fock states become squeezed, as well as the initial thermal states with low values of the mean energy.

Antigen receptor therapy in bone metastasis via optimal control for different human life stages.

In this work we propose a bone metastasis model using power law growth functions in order to describe the biochemical interactions between bone cells and cancer cells. Experimental studies indicate that bone remodeling cycles are different for human life stages: childhood, young adulthood, and adulthood. In order to include such differences in our study, we estimate the model parameter values for each human life stage via bifurcation analysis. Results reveal an intrinsic relationship between the active period of remodeling cycles and the proliferation of cancer cells. Subsequently, using optimal control theory we analyze a possible antigen receptor therapy as a new treatment for bone metastasis. Theoretical results such as existence of optimal solutions are proved. Numerical simulations for late stages of bone metastasis are presented and a discussion of our results is carried out.

Power laws in the Roman Empire: a survival analysis.

The Roman Empire shaped western civilization, and many Roman principles are embodied in modern institutions. Although its political institutions proved both resilient and adaptable, allowing it to incorporate diverse populations, the Empire suffered from many conflicts. Indeed, most emperors died violently, from assassination, suicide or in battle. These conflicts produced patterns in the length of time that can be identified by statistical analysis. In this paper, we study the underlying patterns associated with the reign of the Roman emperors by using statistical tools of survival data analysis. We consider all the 175 Roman emperors and propose a new power-law model with change points to predict the time-to-violent-death of the Roman emperors. This model encompasses data in the presence of censoring and long-term survivors, providing more accurate predictions than previous models. Our results show that power-law distributions can also occur in survival data, as verified in other data types from natural and artificial systems, reinforcing the ubiquity of power-law distributions. The generality of our approach paves the way to further related investigations not only in other ancient civilizations but also in applications in engineering and medicine.

Steric and Slippage Effects on Mass Transport by Using an Oscillatory Electroosmotic Flow of Power-Law Fluids.

In this paper, the combined effect of the fluid rheology, finite-sized ions, and slippage toward augmenting a non-reacting solute's mass transport due to an oscillatory electroosmotic flow (OEOF) is determined. Bikerman's model is used to include the finite-sized ions (steric effects) in the original Poisson-Boltzmann (PB) equation. The volume fraction of ions quantifies the steric effects in the modified Poisson-Boltzmann (MPB) equation to predict the electrical potential and the ion concentration close to the charged microchannel walls. The hydrodynamics is affected by slippage, in which the slip length was used as an index for wall hydrophobicity. A conventional finite difference scheme was used to solve the momentum and species transport equations in the lubrication limit together with the MPB equation. The results suggest that the combined slippage and steric effects promote the best conditions to enhance the mass transport of species in about 90% compared with no steric effect with proper choices of the Debye length, Navier length, steric factor, Womersley number, and the tidal displacement.

A Framework to Assess the Citation Performance of Complex Innovation Systems.

Scientometric indicators are useful to evaluate the relevance of scientific research, to prepare rankings, and to evaluate and inform research policies. That is why the choice of appropriate indicators is a matter of primary concern. This article aims to introduce a framework to decide the appropriate type of indicator for assessing the citation-based performance of complex innovation systems. The framework is two-fold: First, it brings the methodology to decide when the use of standard average based indicators is granted, and when scale-invariant indicators are mandatory. Second, it provides the procedures to build scale-invariant indicators to assess the relative impact of complex innovation systems. The framework is validated empirically through the evaluation of the relative impact of the Chilean science system in 2017. The result suggests that the Chilean science system has characteristics of a complex innovation system such as the distribution of citations fits to a power law with an exponential cutoff - 2.77 ± 0.09 and a power-law correlation between the size of the system and its impact 1.29 ± 0.11 . Furthermore, the framework shows to be efficient to compare fields of vastly different sizes.

Sequential and Binomial Sampling Plans to Estimate Thrips tabaci Population Density on Onion.

Thrips tabaci Lindeman is a worldwide onion pest that causes economic losses of 10-60%, depending on many factors. Population sampling is essential for applying control tactics and preventing damage by the insect. Conventional sampling methods are criticized as time consuming, while fixed-precision binomial and sequential sampling plans may allow reliable estimations with a more efficient use of time. The aim of this work was to develop binomial and sequential sampling for fast reliable estimation of T. tabaci density on an onion. Forty-one commercial 1.0-ha onion plots were sampled (sample size n = 200) to characterize the spatial distribution of T. tabaci using Taylor's power law (a = 2.586 and b = 1.511). Binomial and sequential enumerative sampling plans were then developed with precision levels of 0.10, 0.15 and 0.25. Sampling plans were validated with bootstrap simulations (1000 samples) using 10 independent data sets. Bootstrap simulation indicated that precision was satisfactory for all repetitions of the sequential sampling plan, while binomial sampling met the fixed precision in 80% of cases. Both methods reduced sampling time by around 80% relative to conventional sampling. These precise and less time-consuming sampling methods can contribute to implementation of control tactics within the integrated pest management approach.

How relevant is the decision of containment measures against COVID-19 applied ahead of time?

The cumulative number of confirmed infected individuals by the new coronavirus outbreak until April 30th, 2020, is presented for the countries: Belgium, Brazil, United Kingdom (UK), and the United States of America (USA). After an initial period with a low incidence of newly infected people, a power-law growth of the number of confirmed cases is observed. For each country, a distinct growth exponent is obtained. For Belgium, UK, and USA, countries with a large number of infected people, after the power-law growth, a distinct behavior is obtained when approaching saturation. Brazil is still in the power-law regime. Such updates of the data and projections corroborate recent results regarding the power-law growth of the virus and their strong Distance Correlation between some countries around the world. Furthermore, we show that act in time is one of the most relevant non-pharmacological weapons that the health organizations have in the battle against the COVID-19, infectious disease caused by the most recently discovered coronavirus. We study how changing the social distance and the number of daily tests to identify infected asymptomatic individuals can interfere in the number of confirmed cases of COVID-19 when applied in three distinct days, namely April 16th (early), April 30th (current), and May 14th (late). Results show that containment actions are necessary to flatten the curves and should be applied as soon as possible.

Relación especie-área y distribución de la abundancia de especies en una comunidad vegetal de un inselberg tropical: efecto del tamaño de los parches / Species-area relation and species abundance distribution in a plant community on a tropical inselberg: effect of patch size

Resumen Aunque los inselbergs son afloramientos rocosos icónicos con un alto valor biogeográfico, poco se conoce sobre los mecanismos responsables de la estructuración de comunidades vegetales. El objetivo de esta investigación fue evaluar cómo el tamaño de los parches de vegetación influye en la relación especie-área y distribución de la abundancia de especies de una comunidad en un inselberg del Monumento Natural "Piedra La Tortuga", región Guayana, Venezuela. Por este motivo, se establecieron tres preguntas de investigación: ¿Cuál es el efecto del tamaño de los parches sobre la riqueza de especies? ¿Qué tipo de modelo especie-área (SAR) presenta mejor ajuste en esos parches de vegetación? ¿Cómo es la distribución de las abundancias de las especies (SADs) es inducida por el tamaño de los parches? Se realizó un muestreo aleatorio estratificado en parches que oscilaron entre 0.34 y 14.8 m2, totalizando 40 unidades muestrales (226 m2). Todos los individuos encontrados en los 40 parches fueron identificados a nivel de especie. La composición florística en las diferentes muestras estuvo representada por 19 familias, 22 géneros y 24 especies, de las cuales 50 % son endémicas de inselbergs y dos están amenazadas de extinción. Se identificaron dos grupos de tamaños de parches (grandes 8-15 m2 y pequeños ≤ 7.9 m2) en relación a la abundancia y composición de especies, con diferencias significativas entre los grupos. Las curvas de acumulación de especies para cada grupo de tamaño de parche muestran una tendencia contrastante con marcadas diferencias en la riqueza observada entre los grupos de tamaños de parches. Las curvas de los modelos SADs tuvieron un ajuste significativo de la serie geométrica en las dos categorías de parches. El modelo SAR de la función potencia presentó los mejores ajustes especie-área, donde el aumento del área de los parches explicó un 82 % de la variación en el aumento del número de especies. Los resultados de este estudio demuestran por primera vez como el tamaño de los parches de vegetación de un inselberg tropical tiene una fuerte influencia sobre la riqueza, distribución de la abundancia y composición de especies. Así mismo, se determinó que el modelo geométrico SAD presentó el mejor ajuste en la comunidad en función del tamaño de los parches como un indicador de recursos, donde la abundancia de una especie puede ser equivalente a una proporción del espacio ocupado. También se presume que los cambios de tamaño de los parches, podría estar asociado con la disponibilidad de nutrientes y agua, como ha sido demostrado en otros ambientes de tierras secas. En algunos estudios se ha argumentado que la variación en la composición de especies entre los perfiles de vegetación de inselbergs tropicales está condicionada principalmente por la estructura del hábitat y el déficit hídrico. Sin embargo, no se había discutido cómo el tamaño de los parches de vegetación tiene un efecto en la riqueza. Los análisis SADs y SAR pueden proporcionar explicaciones complementarias sobre la estructuración de comunidades vegetales en inselbergs.

Abstract Although inselbergs are iconic rock outcrops with a high biogeographic value, little is known about drivers responsible for the plant community assembly. The aim of this research was to evaluate how the patch size distribution of vegetation influences the species-area relationship and species abundance distribution of a community in an inselberg of the "Piedra La Tortuga" Natural Monument of the Guayana region, Venezuela. In this context, three research questions were established: What is the effect of patch size on species richness? What species-area model (SAR) has the best fit in those vegetation patches? How is the distribution of species abundances (SADs) induced by the patch size distribution? A stratified random sampling was performed in patches ranging from 0.34 to 14.8 m2, totaling 40 sampling units (226 m2). All individuals found in the 40 patches were identified at species level. The floristic composition in the different samples was represented by 19 families, 22 genera and 24 species, of which 50 % are endemic to inselbergs and two, are threatened of extinction. Two groups of patch sizes were identified (large 8-15 m2 and small ≤ 7.9 m2) in relation to the abundance and composition of species. The species accumulation curves for each patch size group show a contrasting tendency with marked differences in the observed richness among patch size groups. The curves of the SADs models had a significant adjustment of the geometric series in the two categories of patches. The SAR model of the power function presented the best species-area adjustments, where the increase in patch area accounted for 82 % of the variation in the increase in the number of species. The results of this study demonstrate for the first time how vegetation patches of a tropical inselberg have a strong influence on richness, abundance distribution and species composition. Likewise, it was determined that the SAD geometric model presented the best fit in the community as a function of patch size as a resource indicator, where the abundance of a species can be equivalent to a proportion of the space occupied. It is also presumed that changes in patch sizes could be associated with nutrient and water availability, as has been demonstrated in other dryland environments. In some studies it has been argued that variation in species composition among vegetation profiles of tropical inselbergs is mainly conditioned by habitat structure and water deficit. However, it had not been discussed how the size of patches of vegetation has an effect on richness. SADs and SAR analyzes can provide complementary explanations on community assembly in inselbergs. Rev. Biol. Trop. 66(2): 937-951. Epub 2018 June 01.

Rheological properties of tamarind (Tamarindus indica L.) seed mucilage obtained by spray-drying as a novel source of hydrocolloid.

Tamarind seed mucilage (TSM) was extracted and obtained by spray drying. The power law model well described the rheological behavior of the TSM dispersions with determination coefficients R2 higher than 0.93. According to power law model, non-Newtonian shear thinning behavior was observed at all concentrations (0.5%, 1%, 1.5% and 2%) and temperatures (25, 30, 40, and 60°C) studied. Increasing temperature decreased the viscosity and increased the flow behavior index, opposite effect was observed when increasing the concentration. The temperature effect was more pronounced at 2.0% TSM concentration with an activation energy of 20.25kJ/mol. A clear dependence of viscosity on pH was observed, as pH increased from acidic to alkaline conditions, the viscosity increased. It was found that the rheological properties of TSM were affected by the sucrose and salts and their concentrations as well due to the addition of ions (or sucrose) decreases repulsion and allows molecule expansion promoting a significant reduction in viscosity. These results suggest that TMS could be applied in the production of foods that require additives with thickening capacity.

Interfacial Electric Effects on a Non-Isothermal Electroosmotic Flow in a Microcapillary Tube Filled by Two Immiscible Fluids.

In this work, a non-isothermal electroosmotic flow of two immiscible fluids within a uniform microcapillary is theoretically studied. It is considered that there is an annular layer of a non-Newtonian liquid, whose behavior follows the power-law model, adjacent to the inside wall of the capillary, which in turn surrounds an inner flow of a second conducting liquid that is driven by electroosmosis. The inner fluid flow exerts an interfacial force, dragging the annular fluid due to shear and Maxwell stresses at the interface between the two fluids. Because the Joule heating effect may be present in electroosmotic flow (EOF), temperature gradients can appear along the microcapillary, making the viscosity coefficients of both fluids and the electrical conductivity of the inner fluid temperature dependent. The above makes the variables of the flow field in both fluids, velocity, pressure, temperature and electric fields, coupled. An additional complexity of the mathematical model that describes the electroosmotic flow is the nonlinear character due to the rheological behavior of the surrounding fluid. Therefore, based on the lubrication theory approximation, the governing equations are nondimensionalized and simplified, and an asymptotic solution is determined using a regular perturbation technique by considering that the perturbation parameter is associated with changes in the viscosity by temperature effects. The principal results showed that the parameters that notably influence the flow field are the power-law index, an electrokinetic parameter (the ratio between the radius of the microchannel and the Debye length) and the competition between the consistency index of the non-Newtonian fluid and the viscosity of the conducting fluid. Additionally, the heat that is dissipated trough the external surface of the microchannel and the sensitivity of the viscosity to temperature changes play important roles, which modify the flow field.

Finite size scaling in the local abundances of geographic populations

We analyzed the statistical distribution of intra-specific local abundances for a set North American breeding bird species. We constructed frequency plots for every species and found that they showed long-tail power-law behavior, truncated at an upper abundance cut-off value. Based on finite size scaling arguments, we investigated whether frequency curves may be considered scaled copies of each other. Data collapse was possible after taking powers of the total abundance of each species, in order to correct deviations from the underlying universal finite size scaling function (UFSS). The UFSS power law exponent oscillated in time within the regime of unbounded variance, which is consistent with the wild fluctuations that characterize ecological phenomena. We speculate that our results may eventually be linked to other law-like macroecological phenomena, such as energetic constraints reported in allometric scaling.

Degradación quíiica del poli(etilen tereftalato) / Chemical degradttion of poly(ethylene terephthalate) / Degradação uímicca do poli(tereftalato de etileo))

En este trabajo se analizó la degradación del poli(etilen tereftalato) variando la temperatura y la concentración de hidróxido de potasio en 1-butanol, manteniendo constante el tamaño y peso de la muestra. El intervalo de temperatura utilizada fue de 110 ºCa 150 ºC y las concentraciones de hidróxido de potasio en 1-butanol en el intervalo 0,4 a 4,4 molar. Para estas condiciones de concentración y temperatura se observó la degradación de un 99% de poli(etilen tereftalato) en un tiempo de una hora. Se obtuvieron dos fases: una orgánica y una sólida. La fase sólida es un polvo soluble en soluciones ácidas. Este producto degradado corresponde probablemente al tereftalato de potasio. A una temperatura de 150 ºC y una concentración de 3,34 M se estudió la cinética de degradación del poli(etilen tereftalato) en función del tiempo. A partir de los resultados y comparando con modelos matemáticos de degradación encontrados en la literatura, se propone que la degradación del poli(etilen tereftalato) sigue un modelo de degradación de power law.

In this work the degradation of poly(ethylene terephthalate) was analyzed by varying the temperature and the concentration of potassium hydroxide in 1-butanol holding constant the size and weight of the sample. The temperature range used was from 110ºC to 150ºC and concentrations of potassium hydroxide in 1-butanol in the range of 0,4 to 4,4 molar, obtaining 99% degradation of poly(ethylene terephthalate) in one hour. The temperature of 150°C and the concentration of 3,34 M were used to study the degradation of poly(ethylene terephthalate) as a function of time. We obtained two phases, an organic phase and solid phase. The solid phase is a soluble in acidic solutions. The solid phase probably corresponds to the of potassium terephthalate. From the results and comparing with models of degradation found in the literature this work suggests that poly(ethylene terephthalate) degradation reaction occurs type power law.

Neste trabalho, se analisou a degradação de poli(tereftalato de etileno) através da variação da temperatura e da concentração de hidróxido de potássio em 1-butanol, segurando o tamanho e o peso constante da amostra. A faixa de temperatura utilizada foi 110° C a 150° C e concentrações de hidróxido de potássio em 1-butanol, intervalo de 0,4-4,4 molar. Para que essas variações são 99% de degradação do poli(teref-talato de etileno) em um tempo de uma hora. Foram obtidas duas fases: uma fase orgânica e uma fase sólida. A fase sólida é um pó solúvel em soluções ácidas. Isso provavelmente corresponde ao produto degradado de tereftalato de potássio. Foram utilizadas uma temperatura de 150 °C e uma concentração de 3,34 M para estudar a cinética de degradação do poli(teref-talato de etileno) como uma função do tempo. A partir dos resultados e comparando com modelos matemáticos de degradação encontrados na literatura, se sugere que a degradação do poli(tereftalato de etileno) é um modelo de degradação do tipo lei de potência.