Improving compliance around protected areas through fair administration of rules.

Protected area management often depends heavily on law enforcement to secure compliance with rules. However, this can contribute to conflict between protected area authorities and local people, negatively affecting both human well-being and conservation outcomes. Compliance is affected by many factors, including whether those who enforce rules are perceived to do so fairly, as well as the perceived rule-related behavior of others. We used factorial survey experiments to explore how fair respondents living around protected areas in Indonesia and Tanzania perceive sanctions distributed by law enforcers to be. We presented scenarios to respondents to assess how crime type, offender characteristics, and corruption influenced their judgments regarding the fairness of administered sanctions. We also assessed how descriptive norms and corruption influenced individuals' willingness to obey protected area rules. Data were collected from 229 people in Indonesia and 217 in Tanzania. Results showed that in both locations, lawful sanctions, such as arrests or warnings, were perceived as fairer, and sanctions that involved corruption were perceived as least fair. Attitudes toward protected area rules, corruption, and descriptive norms all influenced people's willingness to comply, whereas multidimensional poverty did not. Our results highlight the need for conservation policy and practice to move beyond narratives that focus on the need for more law enforcement. To improve protected area compliance and secure better outcomes for people and nature, conservation must focus on ensuring the fair administration of rules and enhancing the legitimacy of rules themselves.

Mejoras en el cumplimiento alrededor de las áreas protegidas mediante la administración imparcial de reglas Resumen El manejo de áreas protegidas casi siempre depende de la aplicación de la ley para asegurar el cumplimiento de las reglas. Sin embargo, esto puede contribuir al conflicto entro las autoridades de las áreas protegidas y los locales, lo que afecta negativamente al bienestar humano y a los resultados de conservación. El cumplimiento se ve afectado por muchos factores, incluido si se percibe que quienes aplican las reglas lo hacen de manera imparcial, así como el comportamiento relacionado a las reglas de las demás. Aplicamos experimentos de censo factorial para explorar cómo los respondientes imparciales que viven en torno a las áreas protegidas en Indonesia y Tanzania perciben las sanciones distribuidas por los agentes de la ley. Les presentamos escenarios para analizar cómo el tipo de crimen, características del ofensor y la corrupción influyen sobre sus juicios con respecto a la imparcialidad de las sanciones administradas. También analizamos cómo las normas descriptivas y la corrupción influyen sobre la voluntad individual de obedecer las reglas del área protegida. Recolectamos los datos de 299 personas en Indonesia y 217 en Tanzania. Los resultados mostraron que, en ambas localidades, las sanciones legales, como arrestos o advertencias, eran percibidas como más justas, y las sanciones que involucraban corrupción eran percibidas como las menos justas. Todas las actitudes hacia las reglas de las áreas protegidas, la corrupción y las normas descriptivas influyeron sobre la voluntad de las personas para obedecer, mientras que la pobreza multidimensional no influyó. Nuestros resultados enfatizan la necesidad de que las políticas y prácticas de conservación vayan más allá de las narrativas que se enfocan en la necesidad de una mayor aplicación de la ley. Para incrementar el cumplimiento en las áreas protegidas y asegurar mejores resultados para las personas y la naturaleza, la conservación debe enfocarse en garantizar la administración imparcial de las reglas e incrementar su legitimidad.

Symplectic Geometry Aspects of the Parametrically-Dependent Kardar-Parisi-Zhang Equation of Spin Glasses Theory, Its Integrability and Related Thermodynamic Stability.

A thermodynamically unstable spin glass growth model described by means of the parametrically-dependent Kardar-Parisi-Zhang equation is analyzed within the symplectic geometry-based gradient-holonomic and optimal control motivated algorithms. The finitely-parametric functional extensions of the model are studied, and the existence of conservation laws and the related Hamiltonian structure is stated. A relationship of the Kardar-Parisi-Zhang equation to a so called dark type class of integrable dynamical systems, on functional manifolds with hidden symmetries, is stated.

A Time Two-Mesh Compact Difference Method for the One-Dimensional Nonlinear Schrödinger Equation.

The nonlinear Schrödinger equation is an important model equation in the study of quantum states of physical systems. To improve the computing efficiency, a fast algorithm based on the time two-mesh high-order compact difference scheme for solving the nonlinear Schrödinger equation is studied. The fourth-order compact difference scheme is used to approximate the spatial derivatives and the time two-mesh method is designed for efficiently solving the resulting nonlinear system. Comparing to the existing time two-mesh algorithm, the novelty of the new algorithm is that the fine mesh solution, which becomes available, is also used as the initial guess of the linear system, which can improve the calculation accuracy of fine mesh solutions. Compared to the two-grid finite element methods (or finite difference methods) for nonlinear Schrödinger equations, the numerical calculation of this method is relatively simple, and its two-mesh algorithm is implemented in the temporal direction. Taking advantage of the discrete energy, the result with O(τC4+τF2+h4) in the discrete L2-norm is obtained. Here, τC and τF are the temporal parameters on the coarse and fine mesh, respectively, and h is the space step size. Finally, some numerical experiments are conducted to demonstrate its efficiency and accuracy. The numerical results show that the new algorithm gives highly accurate results and preserves conservation laws of charge and energy. Furthermore, by comparing with the standard nonlinear implicit compact difference scheme, it can reduce the CPU time without loss of accuracy.

A dynamic neural field model of continuous input integration.

The ability of neural systems to turn transient inputs into persistent changes in activity is thought to be a fundamental requirement for higher cognitive functions. In continuous attractor networks frequently used to model working memory or decision making tasks, the persistent activity settles to a stable pattern with the stereotyped shape of a "bump" independent of integration time or input strength. Here, we investigate a new bump attractor model in which the bump width and amplitude not only reflect qualitative and quantitative characteristics of a preceding input but also the continuous integration of evidence over longer timescales. The model is formalized by two coupled dynamic field equations of Amari-type which combine recurrent interactions mediated by a Mexican-hat connectivity with local feedback mechanisms that balance excitation and inhibition. We analyze the existence, stability and bifurcation structure of single and multi-bump solutions and discuss the relevance of their input dependence to modeling cognitive functions. We then systematically compare the pattern formation process of the two-field model with the classical Amari model. The results reveal that the balanced local feedback mechanisms facilitate the encoding and maintenance of multi-item memories. The existence of stable subthreshold bumps suggests that different to the Amari model, the suppression effect of neighboring bumps in the range of lateral competition may not lead to a complete loss of information. Moreover, bumps with larger amplitude are less vulnerable to noise-induced drifts and distance-dependent interaction effects resulting in more faithful memory representations over time.

Conservation law for self-paced movements.

Optimal control models of biological movements introduce external task factors to specify the pace of movements. Here, we present the dual to the principle of optimality based on a conserved quantity, called "drive," that represents the influence of internal motivation level on movement pace. Optimal control and drive conservation provide equivalent descriptions for the regularities observed within individual movements. For regularities across movements, drive conservation predicts a previously unidentified scaling law between the overall size and speed of various self-paced hand movements in the absence of any external tasks, which we confirmed with psychophysical experiments. Drive can be interpreted as a high-level control variable that sets the overall pace of movements and may be represented in the brain as the tonic levels of neuromodulators that control the level of internal motivation, thus providing insights into how internal states affect biological motor control.

Statistics of Mendelian segregation-A mixture model.

Mendel's law of segregation explains why genetic variation can be maintained over time. In diploid organisms, an offspring receives one allele from each parent, not just half of the blended genetic material of the parents. Which of the two alleles is received is purely random. This stochastic process generates genetic variation among members of the same family, called Mendelian segregation variance or within-family variance. In statistics, the genetic value of a quantitative trait for an offspring follows a mixture distribution consisting of the four alleles of the two parents, guided by a Mendelian variable from each parent. The mixture model allows us to partition the total genetic variance into between-family and within-family variances. In the absence of inbreeding, the genetic variance splits half to the between-family variance and half to the within-family variance. With inbreeding, however, the between-family variance is increased at the cost of the within-family variance, leading to a net increase of the total genetic variance. This study defines multiple Mendelian variables and develops a mixture model of quantitative genetics. The phenomenon that allelic variance is maintained over time is guided by "the law of conservation of allelic variance" in biology, which is comparable to "the law of conservation of mass" in physics.

Wiring cost and topological participation of the mouse brain connectome.

Brain connectomes are topologically complex systems, anatomically embedded in 3D space. Anatomical conservation of "wiring cost" explains many but not all aspects of these networks. Here, we examined the relationship between topology and wiring cost in the mouse connectome by using data from 461 systematically acquired anterograde-tracer injections into the right cortical and subcortical regions of the mouse brain. We estimated brain-wide weights, distances, and wiring costs of axonal projections and performed a multiscale topological and spatial analysis of the resulting weighted and directed mouse brain connectome. Our analysis showed that the mouse connectome has small-world properties, a hierarchical modular structure, and greater-than-minimal wiring costs. High-participation hubs of this connectome mediated communication between functionally specialized and anatomically localized modules, had especially high wiring costs, and closely corresponded to regions of the default mode network. Analyses of independently acquired histological and gene-expression data showed that nodal participation colocalized with low neuronal density and high expression of genes enriched for cognition, learning and memory, and behavior. The mouse connectome contains high-participation hubs, which are not explained by wiring-cost minimization but instead reflect competitive selection pressures for integrated network topology as a basis for higher cognitive and behavioral functions.

A conservation law for virus infection kinetics in vitro.

Conservation laws are among the most important properties of a physical system, but are not commonplace in biology. We derived a conservation law from the basic model for viral infections which consists in a small set of ordinary differential equations. We challenged the conservation law experimentally for the case of a virus infection in a cell culture. We found that the derived, conserved quantity remained almost constant throughout the infection period, implying that the derived conservation law holds in this biological system. We also suggest a potential use for the conservation law in evaluating the accuracy of experimental measurements.

2-Site versus 3-site models of ATP hydrolysis by F1-ATPase: definitive mathematical proof using combinatorics and conservation equations.

The F1-ATPase enzyme is the smallest-known molecular motor that rotates in 120° steps, driven by the hydrolysis of ATP. It is a multi-subunit enzyme that contains three catalytic sites. A central question is how the elementary chemical reactions that occur in the three sites are coupled to mechanical rotation. Various models and coupling schemes have been formulated in an attempt to answer this question. They can be classified as 2-site (bi-site) models, exemplified by Boyer's binding change mechanism first proposed 50 years ago, and 3-site (tri-site) models such as Nath's torsional mechanism, first postulated 25 years ago and embellished 1 year back. Experimental data collated using diverse approaches have conclusively shown that steady-state ATP hydrolysis by F1-ATPase occurs in tri-site mode. Hence older models have been continually modified to make them conform to the new facts. Here, we have developed a pure mathematical approach based on combinatorics and conservation laws to test if proposed models are 2-site or 3-site. Based on this novel combinatorial approach, we have proved that older and modified models are effectively bi‒site models in that catalysis and rotation in F1-ATPase occurs in these models with only two catalytic sites occupied by bound nucleotide. Hence these models contradict consensus experimental data. The recent 2023 model of ATP hydrolysis by F1-ATPase has been proved to be a true tri-site model based on our novel mathematical approach. Such pure mathematical proofs constitute an important step forward for ATP mechanism. However, in what must be considered an aspect with great scientific potential, the power of such mathematical proofs has not been fully exploited to solve molecular biological problems, in our opinion. We believe that the creative application of pure mathematical proofs (for another example see Nath in Theory Biosci 141:249-260, 2022) can help resolve with finality various longstanding molecular-level issues that arise as a matter of course in the analysis of fundamental biological problems. Such issues have proved extraordinarily difficult to resolve by standard experimental, theoretical, or computational approaches.

Saddle-node bifurcation of viscous profiles.

Traveling wave solutions of viscous conservation laws, that are associated to Lax shocks of the inviscid equation, have generically a transversal viscous profile. In the case of a non-transversal viscous profile we show by using Melnikov theory that a parametrized perturbation of the profile equation leads generically to a saddle-node bifurcation of these solutions. An example of this bifurcation in the context of magnetohydrodynamics is given. The spectral stability of the traveling waves generated in the saddle-node bifurcation is studied via an Evans function approach. It is shown that generically one real eigenvalue of the linearization of the viscous conservation law around the parametrized family of traveling waves changes its sign at the bifurcation point. Hence this bifurcation describes the basic mechanism of a stable traveling wave which becomes unstable in a saddle-node bifurcation.

Injection of Gelling Systems to a Layered Reservoir for Conformance Improvement.

The paper describes the introduction and estimation of performance criteria for the gelling agent injection technology based on a general approach to modeling physical and chemical enhanced oil recovery (EOR) methods. The current mathematical models do not include performance criteria for the process of gelling agent injection and do not allow for assessing the level of success of a treatment job in production wells. The paper introduces such criteria for the first time. To simulate the effect on injection wells, the mass conservation laws and the generalized flow law are used, and closing relations for the gelling rate are taken into account. A conformance control coefficient is introduced which characterizes the positive effect of well treatments and injectivity drop which characterizes the negative effect. The performance criteria allow for identifying the wells where the treatment jobs were the most successful. The model verification, based on the comparison of post-treatment injectivity estimated in the developed model, with Rosneft's field data showed a satisfactory match. The developed correlations can be used as the basis for a surrogate model that allows for avoiding building sector geological and flow simulation models of the treated zone.

Statistical mechanics of Floquet quantum matter: exact and emergent conservation laws.

Equilibrium statistical mechanics rests on the assumption of chaotic dynamics of a system modulo the conservation laws of local observables: extremization of entropy immediately gives Gibbs' ensemble (GE) for energy conserving systems and a generalized version of it (GGE) when the number of local conserved quantities is more than one. Through the last decade, statistical mechanics has been extended to describe the late-time behaviour of periodically driven (Floquet) quantum matter starting from a generic state. The structure built on the fundamental assumptions of ergodicity and identification of the relevant conservation laws in this inherently non-equilibrium setting. More recently, it has been shown that the statistical mechanics of Floquet systems has a much richer structure due to the existence ofemergentconservation laws: these are approximate but stable conservation laws arisingdue to the drive, and are not present in the undriven system. Extensive numerical and analytical results support perpetual stability of these emergent (though approximate) conservation laws, probably even in the thermodynamic limit. This banks on the recent finding of a sharp threshold for Floquet thermalization in clean, interacting non-integrable Floquet systems. This indicates to the possibility of stable Floquet phases of matter in disorder-free systems. This review intends to give a self-contained theoretical overview of these developments for a broad physics audience. We conclude by briefly surveying the current experimental scenario.

Legislation advancement of one health in China in the context of the COVID-19 pandemic: From the perspective of the wild animal conservation law.

The outbreak of COVID-19 epidemic is endangering the health of all humans and requires the urgent attention and active response of all countries and all areas of society. Existing studies have shown that wild animals are one of the sources of high-risk virus infection affecting human health, and human activities have largely shaped the routes of virus transmission. To protect wildlife is to protect human health. We should follow the concept of One Health to make corresponding legislation, so as to better coordinate the relationship among human health, animal health and environmental health. Since the outbreak of COVID-19 epidemic, China has taken many effective measures to prevent its spreading, including revision of the Wild Animal Conservation Law. All sectors of the Chinese society have issued a strong appeal to pursue One Health and even specific legislative proposals. Because the current Wild Animal Conservation Law fails to properly reflect the concept of One Health, which is the root cause of the imperfect design of the system and the key to the unsatisfactory effectiveness of the legal application. China's new Wild Animal Conservation Law is expected to make a large-scale and systematic revision, which should fully implement the concept of One Health.

New Constitutive Model for the Size Effect on Flow Stress Based on the Energy Conservation Law.

In this study, a new model involving energy is established to characterize the size effect on flow stress. The new model treats the experimental machine and the specimen as an isolated system, and this isolated system satisfies the Energy Conservation Law. The total work performed on the specimen by the experimental machine is nearly equal to the energy consumed by the specimen plastic deformation and the energy consumed by friction (which can be ignored when working without friction). The new model predicts the energy consumption of the specimen deformation by quantifying the total energy input to the specimen by the experimental machine and then obtaining the relevant parameters of the constitutive model. Through uniaxial tensile tests of pure nickel thin sheets with various thickness/average grain sizes (t/d), the new model was used to optimize the parameters of the existing constitutive model that predicts the flow stress of specimens with different t/d. The prediction accuracy of the optimized constitutive model is improved, especially for specimens with a t/d < 1. The new model is established from the perspective of energy input to avoid the analysis of the material deformation mechanism and improve the prediction accuracy.

Bond graph modelling of the cardiac action potential: implications for drift and non-unique steady states.

Mathematical models of cardiac action potentials have become increasingly important in the study of heart disease and pharmacology, but concerns linger over their robustness during long periods of simulation, in particular due to issues such as model drift and non-unique steady states. Previous studies have linked these to violation of conservation laws, but only explored those issues with respect to charge conservation in specific models. Here, we propose a general and systematic method of identifying conservation laws hidden in models of cardiac electrophysiology by using bond graphs, and develop a bond graph model of the cardiac action potential to study long-term behaviour. Bond graphs provide an explicit energy-based framework for modelling physical systems, which makes them well suited for examining conservation within electrophysiological models. We find that the charge conservation laws derived in previous studies are examples of the more general concept of a 'conserved moiety'. Conserved moieties explain model drift and non-unique steady states, generalizing the results from previous studies. The bond graph approach provides a rigorous method to check for drift and non-unique steady states in a wide range of cardiac action potential models, and can be extended to examine behaviours of other excitable systems.

Cumulative distribution function solutions of advection-reaction equations with uncertain parameters.

We derive deterministic cumulative distribution function (CDF) equations that govern the evolution of CDFs of state variables whose dynamics are described by the first-order hyperbolic conservation laws with uncertain coefficients that parametrize the advective flux and reactive terms. The CDF equations are subjected to uniquely specified boundary conditions in the phase space, thus obviating one of the major challenges encountered by more commonly used probability density function equations. The computational burden of solving CDF equations is insensitive to the magnitude of the correlation lengths of random input parameters. This is in contrast to both Monte Carlo simulations (MCSs) and direct numerical algorithms, whose computational cost increases as correlation lengths of the input parameters decrease. The CDF equations are, however, not exact because they require a closure approximation. To verify the accuracy and robustness of the large-eddy-diffusivity closure, we conduct a set of numerical experiments which compare the CDFs computed with the CDF equations with those obtained via MCSs. This comparison demonstrates that the CDF equations remain accurate over a wide range of statistical properties of the two input parameters, such as their correlation lengths and variance of the coefficient that parametrizes the advective flux.