Maximum entropy determination of mammalian proteome dynamics

Full understanding of proteostasis and energy utilization in cells will require knowledge of the fraction of cell proteins being degraded with different half-lives and their rates of synthesis. We therefore developed a method to determine such information that combines mathematical analysis of protein degradation kinetics obtained in pulse-chase experiments with Bayesian data fitting using the maximum entropy principle. This approach will enable rapid analyses of whole-cell protein dynamics in different cell types, physiological states, and neurodegenerative disease. Using it, we obtained surprising insights about protein stabilities in cultured cells normally and upon activation of proteolysis by mTOR inhibition and increasing cAMP or cGMP. It revealed that >90% of protein content in dividing mammalian cell lines is long-lived, with half-lives of 24 to 200 h, and therefore comprises much of the proteins in daughter cells. The well-studied short-lived proteins (half-lives < 10 h) together comprise <2% of cell protein mass, but surprisingly account for 10 to 20% of measurable newly synthesized protein mass. Evolution thus appears to have minimized intracellular proteolysis except to rapidly eliminate misfolded and regulatory proteins.

Valence and interactions in judicial voting

The collective statistics of voting on judicial courts present hints about their inner workings. Many approaches for studying these statistics, however, assume that judges' decisions are conditionally independent: a judge reaches a decision based on the case at hand and his or her personal views. In reality, judges interact. We develop a minimal model that accounts for judge bias, depending on the context of the case, and peer interaction. We apply the model to voting data from the US Supreme Court. We find strong evidence that interaction is an important factor across natural courts from 1946 to 2021. We also find that, after accounting for interaction, the recovered biases differ from highly cited ideological scores. Our method exemplifies how physics and complexity-inspired modelling can drive the development of theoretical models and improved measures for political voting. This article is part of the theme issue 'A complexity science approach to law and governance'.

Why Does Cross-Sectional Analyst Coverage Incorporate Market-Wide Information?

This paper shows that the empirical distribution of cross-sectional analyst coverage in China's stock markets follows an exponential law in a given month from 2011 to 2020. The findings hold in both the emerging (Shanghai) and the developed market (Hong Kong). Moreover, the unique distribution parameter (i.e., mean) is directly related to the amount of market-wide information. Average analyst coverage exhibits a significant negative predictive power for stock-market uncertainty, highlighting the role of security analysts in diminishing the total uncertainty. The exponential law can be derived from the maximum entropy principle (MEP). When analysts, who are constrained by average ability in generating information (i.e., the first-order moment), strive to maximize the amount of market-wide information, this objective yields the exponential distribution. Contrary to the conventional wisdom that security analysts specialize in the generation of firm-specific information, empirical findings suggest that analysts primarily produce market-wide information for 25 countries. Nevertheless, it remains unclear why cross-sectional analyst coverage reflects market-wide information, this paper provides an entropy-based explanation.

Analysis of environmental factors influencing lumpy skin disease outbreak seasonality and assessment of its spread risk in the Saratovskaya oblast of Russia

Background and Aim

Lumpy skin disease (LSD) is a transboundary viral disease of cattle that causes serious economic losses due to a significant decrease in meat and milk productivity. This study analyzed the influence of natural and anthropogenic environmental factors on LSD spread seasonality and assessed the risk of LSD outbreaks in the Saratovskaya oblast of the Russian Federation.

Materials and Methods

Data on LSD outbreaks and environmental factors during different seasons were collected for the period 2011-2020 in the Balkan Peninsula, Middle East, and Russia. Risk assessment was performed using mathematical modeling with generalized linear regression and maximum entropy.

Results

Fourteen statistically significant environmental factors influencing LSD spread were identified. The analysis of MaxEnt models built using the selected factors showed that the presence of the pathogen is mostly exerted by: the density of susceptible cattle (an increased risk is observed at a density above 10 and 20 heads/10 km2 in winter and autumn, with a permanent risk in spring and summer), the density of water bodies (the risk is increased at any density in winter and autumn, in the range of 13-23.5 m2/km2 in spring, in the ranges of 0-8 and over 14.5 m2/km2 in summer), and average monthly precipitation rate (the most risky are 105-185 mm/month in winter, 35 mm in spring, 15-105 mm in summer, and above 50 mm in autumn).

Conclusion

LSD tends to spread during the warm season. Compared with other test zones, the Saratovskaya oblast has a negligible risk of disease spread (in winter), low risk (in spring), or medium risk (in summer and autumn). The annual risk is low to medium.

The ability to sense the environment is heterogeneously distributed in cell populations

Channel capacity of signaling networks quantifies their fidelity in sensing extracellular inputs. Low estimates of channel capacities for several mammalian signaling networks suggest that cells can barely detect the presence/absence of environmental signals. However, given the extensive heterogeneity and temporal stability of cell state variables, we hypothesize that the sensing ability itself may depend on the state of the cells. In this work, we present an information-theoretic framework to quantify the distribution of sensing abilities from single-cell data. Using data on two mammalian pathways, we show that sensing abilities are widely distributed in the population and most cells achieve better resolution of inputs compared to an 'average cell'. We verify these predictions using live-cell imaging data on the IGFR/FoxO pathway. Importantly, we identify cell state variables that correlate with cells' sensing abilities. This information-theoretic framework will significantly improve our understanding of how cells sense in their environment.

Maximum Entropy Criterion for Moment Indeterminacy of Probability Densities

We deal with absolutely continuous probability distributions with finite all-positive integer-order moments. It is well known that any such distribution is either uniquely determined by its moments (M-determinate), or it is non-unique (M-indeterminate). In this paper, we follow the maximum entropy approach and establish a new criterion for the M-indeterminacy of distributions on the positive half-line (Stieltjes case). Useful corollaries are derived for M-indeterminate distributions on the whole real line (Hamburger case). We show how the maximum entropy is related to the symmetry property and the M-indeterminacy.

Correcting prevalence estimation for biased sampling with testing errors

Sampling for prevalence estimation of infection is subject to bias by both oversampling of symptomatic individuals and error-prone tests. This results in naïve estimators of prevalence (ie, proportion of observed infected individuals in the sample) that can be very far from the true proportion of infected. In this work, we present a method of prevalence estimation that reduces both the effect of bias due to testing errors and oversampling of symptomatic individuals, eliminating it altogether in some scenarios. Moreover, this procedure considers stratified errors in which tests have different error rate profiles for symptomatic and asymptomatic individuals. This results in easily implementable algorithms, for which code is provided, that produce better prevalence estimates than other methods (in terms of reducing and/or removing bias), as demonstrated by formal results, simulations, and on COVID-19 data from the Israeli Ministry of Health.

Complex Networks and Interacting Particle Systems

Complex networks is a growing discipline aimed at understanding large interacting systems. One of its goals is to establish a relation between the interactions of a system and the networks structure that emerges. Taking a Lennard-Jones particle system as an example, we show that when interactions are governed by a potential, the notion of structure given by the physical arrangement of the interacting particles can be interpreted as a binary approximation to the interaction potential. This approximation simplifies the calculation of the partition function of the system and allows to study the stability of the interaction structure. We compare simulated results with those from the approximated partition function and show how the network and system perspective complement each other. With this, we draw a direct connection between the interactions of a molecular system and the network structure it forms and assess the degree to which it describes the system. We conclude by discussing the advantages and limitations of this method for weighted networks, as well as how this concept might be extended to more general systems.

Assessing the Potential Distribution of Oxalis latifolia, a Rapidly Spreading Weed, in East Asia under Global Climate Change

Oxalis latifolia, a perennial herbaceous weed, is a highly invasive species that poses a threat to agricultural lands worldwide. East Asia is under a high risk of invasion of O. latifolia under global climate change. To evaluate this risk, we employed maximum entropy modeling considering two shared socio-economic pathways (SSP2-4.5 and SSP5-8.5). Currently, a small portion (8.02%) of East Asia is within the O. latifolia distribution, with the highest coverages in Chinese Taipei, China, and Japan (95.09%, 9.8%, and 0.24%, respectively). However, our projections indicated that this invasive weed will likely be introduced to South Korea and North Korea between 2041 and 2060 and 2081 and 2100, respectively. The species is expected to cover approximately 9.79% and 23.68% (SSP2-4.5) and 11.60% and 27.41% (SSP5-8.5) of the total land surface in East Asia by these time points, respectively. South Korea and Japan will be particularly susceptible, with O. latifolia potentially invading up to 80.73% of their territory by 2081-2100. Mongolia is projected to remain unaffected. This study underscores the urgent need for effective management strategies and careful planning to prevent the introduction and limit the expansion of O. latifolia in East Asian countries.

On Bayesian mechanics: a physics of and by beliefs

The aim of this paper is to introduce a field of study that has emerged over the last decade, called Bayesian mechanics. Bayesian mechanics is a probabilistic mechanics, comprising tools that enable us to model systems endowed with a particular partition (i.e. into particles), where the internal states (or the trajectories of internal states) of a particular system encode the parameters of beliefs about external states (or their trajectories). These tools allow us to write down mechanical theories for systems that look as if they are estimating posterior probability distributions over the causes of their sensory states. This provides a formal language for modelling the constraints, forces, potentials and other quantities determining the dynamics of such systems, especially as they entail dynamics on a space of beliefs (i.e. on a statistical manifold). Here, we will review the state of the art in the literature on the free energy principle, distinguishing between three ways in which Bayesian mechanics has been applied to particular systems (i.e. path-tracking, mode-tracking and mode-matching). We go on to examine a duality between the free energy principle and the constrained maximum entropy principle, both of which lie at the heart of Bayesian mechanics, and discuss its implications.

Decision-Making Teaching Practice Based on the Maximum Entropy Method in a Water Engineering Economics Course

The purpose of this paper is to put forward a decision model with wide applicability and differentiated decision scheme scores so as to improve the ability of students to learn during a water engineering economics course. The main novelty and contributions of this paper are that the multi-attribute decision-making method proposed is more objective and does not require rich subjective experience from decision-makers in the application process, which is particularly suitable for beginners who are learning in a water engineering economics course. The method involves standardizing each index value of the decision scheme first, constructing the objective function of maximum entropy distribution, calculating the weight of each index by the genetic algorithm, and finally ranking the pros and cons of the scheme according to the score of each scheme. The example results of three water engineering scheme decisions show that the maximum entropy model proposed in this paper can achieve reasonable decision results, and there is a large degree of differentiation between the decision schemes. The proposed scheme, a decision maximum entropy model, has wide applicability, can improve the rationality of the decisions made regarding water engineering schemes, and can be popularized and applied when teaching decision-making in water engineering economics courses.

MaxEnt Modeling for Predicting the Potential Wintering Distribution of Eurasian Spoonbill (Platalea leucorodia leucorodia) under Climate Change in China

Global climate change has become a trend and is one of the main factors affecting biodiversity patterns and species distributions. Many wild animals adapt to the changing living environment caused by climate change by changing their habitats. Birds are highly sensitive to climate change. Understanding the suitable wintering habitat of the Eurasian Spoonbill (Platalea leucorodia leucorodia) and its response to future climatic change is essential for its protection. In China, it was listed as national grade II key protected wild animal in the adjusted State List of key protected wild animals in 2021, in Near Threatened status. Few studies on the distribution of the wintering Eurasian Spoonbill have been carried out in China. In this study, we simulated the suitable habitat under the current period and modeled the distribution dynamics of the wintering Eurasian Spoonbill in response to climate change under different periods by using the MaxEnt model. Our results showed that the current suitable wintering habitats for the Eurasian Spoonbill are mainly concentrated in the middle and lower reaches of the Yangtze River. Distance from the water, precipitation of the driest quarter, altitude, and mean temperature of the driest quarter contributed the most to the distribution model for the wintering Eurasian Spoonbill, with a cumulative contribution of 85%. Future modeling showed that the suitable distribution of the wintering Eurasian Spoonbill extends to the north as a whole, and the suitable area shows an increasing trend. Our simulation results are helpful in understanding the distribution of the wintering Eurasian Spoonbill under different periods in China and support species conservation.

Assessing risk from invasive alien plants in China: Reconstructing invasion history and estimating distribution patterns of Lolium temulentum and Aegilops tauschii

INTRODUCTION

The establishment of invasive alien plants (IAPs) is primarily driven by climate warming and human activities, and their populations have a negative impact on agricultural economics, ecological systems, and human health. Lolium temulentum and Aegilops tauschii are critical IAPs in China because they reduce the quality of cereal grains and decrease wheat yields. Lolium temulentum is a winter-temperate weed that spreads easily and is poisonous to humans and animals. Aegilops tauschii is resistant to herbicides, has a high reproductive rate, and frequently grows in wheat. Both species have been listed in the Ministry of Agriculture and Rural Affairs of the People's Republic of China's management catalog since 2006.

METHODS

In the present study, the historical occurrence and invasion of each species were collected and reconstructed, which showed that the population outbreak of L. temulentum began in 2010, whereas that of A. tauschii began in 2000. Using the optimal MaxEnt model, the geographical distributions of L. temulentum and A. tauschii were predicted based on screened species occurrences and environmental variables under the current and three future scenarios in the 2030s and 2050s (i.e., SSP1-2.6, SSP2-4.5, and SSP5-8.5).

RESULTS

The mean AUC values were 0.867 and 0.931 for L. temulentum and A. tauschii, respectively. Human influence index (HII), mean temperature of coldest quarter (bio11), and precipitation of coldest quarter (bio19) were the most significant variables for L. temulentum, whereas human influence index, temperature seasonality (standard deviation×100) (bio4), and annual mean temperature (bio1) were the critical environmental variables for A. tauschi. Suitable habitat areas in China for L. temulentum and A. tauschii currently covered total areas of 125 × 10⁴ and 235 × 10⁴ km², respectively. Future suitable areas of L. temulentum reached the maximum under SSP2-4.5, from 2021 to 2060, whereas for A. tauschii they reached the maximum under SSP5-8.5, from 2021 to 2060. Furthermore, the overlap area under the current climate conditions for L. temulentum and A. tauschii was approximately 90 × 10⁴ km², mainly located in Hubei, Anhui, Jiangsu, Shandong, Henan, Shaanxi, Shanxi, and Hebei. The overlap areas decreased in the 2030s, increased in the 2050s, and reached a maximum under SSP1-2.6 (or SSP2-4.5) with an approximate area of 104 × 10⁴ km². The centroid of L. temulentum in Henan was transferred to the southwest, whereas for A. tauschii it transferred to higher latitudes in the northeast.

DISCUSSION

Our findings provide a practical reference for the early warning, control, and management of these two destructive IAP populations in China.

Neural assemblies uncovered by generative modeling explain whole-brain activity statistics and reflect structural connectivity

Patterns of endogenous activity in the brain reflect a stochastic exploration of the neuronal state space that is constrained by the underlying assembly organization of neurons. Yet, it remains to be shown that this interplay between neurons and their assembly dynamics indeed suffices to generate whole-brain data statistics. Here, we recorded the activity from ∼40,000 neurons simultaneously in zebrafish larvae, and show that a data-driven generative model of neuron-assembly interactions can accurately reproduce the mean activity and pairwise correlation statistics of their spontaneous activity. This model, the compositional Restricted Boltzmann Machine (cRBM), unveils ∼200 neural assemblies, which compose neurophysiological circuits and whose various combinations form successive brain states. We then performed in silico perturbation experiments to determine the interregional functional connectivity, which is conserved across individual animals and correlates well with structural connectivity. Our results showcase how cRBMs can capture the coarse-grained organization of the zebrafish brain. Notably, this generative model can readily be deployed to parse neural data obtained by other large-scale recording techniques.

A New Evidence Weight Combination and Probability Allocation Method in Multi-Sensor Data Fusion

A single sensor is prone to decline recognition accuracy in the face of a complex environment, while the existing multi-sensor evidence theory fusion methods do not comprehensively consider the impact of evidence conflict and fuzziness. In this paper, a new evidence weight combination and probability allocation method is proposed, which calculated the degree of evidence fuzziness through the maximum entropy principle, and also considered the impact of evidence conflict on fusing results. The two impact factors were combined to calculate the trusted discount and reallocate the probability function. Finally, Dempster's combination rule was used to fuse every piece of evidence. On this basis, experiments were first conducted to prove that the existing weight combination methods produce results contrary to common sense when handling high-conflicting and high-clarity evidence, and then comparative experiments were conducted to prove the effectiveness of the proposed evidence weight combination and probability allocation method. Moreover, it was verified, on the PAMAP2 data set, that the proposed method can obtain higher fusing accuracy and more reliable fusing results in all kinds of behavior recognition. Compared with the traditional methods and the existing improved methods, the weight allocation method proposed in this paper dynamically adjusts the weight of fuzziness and conflict in the fusing process and improves the fusing accuracy by about 3.3% and 1.7% respectively which solved the limitations of the existing weight combination methods.

Predictive Modeling of Kudzu (Pueraria montana) Habitat in the Great Lakes Basin of the United States

Kudzu (Pueraria montana [Lour.] Merr. var. lobata [Willd.] Maesen & S.M. Almeida ex Sanjappa & Predeep) is an invasive woody vine widespread throughout much of the southeastern United States. New occurrences and recent studies using climatic parameters suggest that the Midwestern region of the United States is at the greatest risk of kudzu invasion. As there are already multiple reports of kudzu within the Great Lakes basin and no previous landscape models exist specifically for the basin, we developed probability models from existing spatial data (forest type, geology, land cover, precipitation, temperature, and known kudzu locations) by using maximum entropy methods at the national, regional, and basin scales. All three models had relatively high accuracy and strong positive correlation between predicted and observed values. Based on evaluation of the models using a testing data set, we determined a presence threshold and categorized areas within each model as suitable or unsuitable habitat. We pooled the models and calculated mean habitat suitability within the Great Lakes basin. Much of the southern half of the basin was suitable for kudzu. Continuing management and further monitoring of kudzu spread are likely necessary to limit further introduction and mitigate spread of kudzu within the Great Lakes region.

Predicting Plasmodium knowlesi transmission risk across Peninsular Malaysia using machine learning-based ecological niche modeling approaches

The emergence of potentially life-threatening zoonotic malaria caused by Plasmodium knowlesi nearly two decades ago has continued to challenge Malaysia healthcare. With a total of 376 P. knowlesi infections notified in 2008, the number increased to 2,609 cases in 2020 nationwide. Numerous studies have been conducted in Malaysian Borneo to determine the association between environmental factors and knowlesi malaria transmission. However, there is still a lack of understanding of the environmental influence on knowlesi malaria transmission in Peninsular Malaysia. Therefore, our study aimed to investigate the ecological distribution of human P. knowlesi malaria in relation to environmental factors in Peninsular Malaysia. A total of 2,873 records of human P. knowlesi infections in Peninsular Malaysia from 1st January 2011 to 31st December 2019 were collated from the Ministry of Health Malaysia and geolocated. Three machine learning-based models, maximum entropy (MaxEnt), extreme gradient boosting (XGBoost), and ensemble modeling approach, were applied to predict the spatial variation of P. knowlesi disease risk. Multiple environmental parameters including climate factors, landscape characteristics, and anthropogenic factors were included as predictors in both predictive models. Subsequently, an ensemble model was developed based on the output of both MaxEnt and XGBoost. Comparison between models indicated that the XGBoost has higher performance as compared to MaxEnt and ensemble model, with AUC_ROC values of 0.933 ± 0.002 and 0.854 ± 0.007 for train and test datasets, respectively. Key environmental covariates affecting human P. knowlesi occurrence were distance to the coastline, elevation, tree cover, annual precipitation, tree loss, and distance to the forest. Our models indicated that the disease risk areas were mainly distributed in low elevation (75-345 m above mean sea level) areas along the Titiwangsa mountain range and inland central-northern region of Peninsular Malaysia. The high-resolution risk map of human knowlesi malaria constructed in this study can be further utilized for multi-pronged interventions targeting community at-risk, macaque populations, and mosquito vectors.

Slope Entropy Normalisation by Means of Analytical and Heuristic Reference Values

Slope Entropy (SlpEn) is a very recently proposed entropy calculation method. It is based on the differences between consecutive values in a time series and two new input thresholds to assign a symbol to each resulting difference interval. As the histogram normalisation value, SlpEn uses the actual number of unique patterns found instead of the theoretically expected value. This maximises the information captured by the method but, as a consequence, SlpEn results do not usually fall within the classical [0,1] interval. Although this interval is not necessary at all for time series classification purposes, it is a convenient and common reference framework when entropy analyses take place. This paper describes a method to keep SlpEn results within this interval, and improves the interpretability and comparability of this measure in a similar way as for other methods. It is based on a max-min normalisation scheme, described in two steps. First, an analytic normalisation is proposed using known but very conservative bounds. Afterwards, these bounds are refined using heuristics about the behaviour of the number of patterns found in deterministic and random time series. The results confirm the suitability of the approach proposed, using a mixture of the two methods.

Estimating Ocean Heat Uptake Using Boundary Green's Functions: A Perfect-Model Test of the Method

Ocean heat uptake is caused by "excess heat" being added to the ocean surface by air-sea fluxes and then carried to depths by ocean transports. One way to estimate excess heat in the ocean is to propagate observed sea surface temperature (SST) anomalies downward using a Green's function (GF) representation of ocean transports. Taking a "perfect-model" approach, we test this GF method using a historical simulation, in which the true excess heat is diagnosed. We derive GFs from two approaches: (a) simulating GFs using idealized tracers, and (b) inferring GFs from simulated CFCs and climatological tracers. In the model world, we find that combining simulated GFs with SST anomalies reconstructs the Indo-Pacific excess heat with a root-mean-square error of 26% for depth-integrated changes; the corresponding number is 34% for inferred GFs. Simulated GFs are inaccurate because they are coarse grained in space and time to reduce computational cost. Inferred GFs are inaccurate because observations are insufficient constraints. Both kinds of GFs neglect the slowdown of the North Atlantic heat uptake as the ocean warms up. SST boundary conditions contain redistributive cooling in the Southern Ocean, which causes an underestimate of heat uptake there. All these errors are of comparable magnitude, and tend to compensate each other partially. Inferred excess heat is not sensitive to: (a) small changes in the shape of prior GFs, or (b) additional constraints from SF₆ and bomb ¹⁴C.

Reweighting methods for elucidation of conformation ensembles of proteins

Proteins are inherently dynamic macromolecules that exist in equilibrium among multiple conformational states, and motions of protein backbone and side chains are fundamental to biological function. The ability to characterize the conformational landscape is particularly important for intrinsically disordered proteins, multidomain proteins, and weakly bound complexes, where single-structure representations are inadequate. As the focus of structural biology shifts from relatively rigid macromolecules toward larger and more complex systems and molecular assemblies, there is a need for structural approaches that can paint a more realistic picture of such conformationally heterogeneous systems. Here, we review reweighting methods for elucidation of structural ensembles based on experimental data, with the focus on applications to multidomain proteins.

Symplectic Foliation Structures of Non-Equilibrium Thermodynamics as Dissipation Model: Application to Metriplectic Nonlinear Lindblad Quantum Master Equation

The idea of a canonical ensemble from Gibbs has been extended by Jean-Marie Souriau for a symplectic manifold where a Lie group has a Hamiltonian action. A novel symplectic thermodynamics and information geometry known as "Lie group thermodynamics" then explains foliation structures of thermodynamics. We then infer a geometric structure for heat equation from this archetypal model, and we have discovered a pure geometric structure of entropy, which characterizes entropy in coadjoint representation as an invariant Casimir function. The coadjoint orbits form the level sets on the entropy. By using the KKS 2-form in the affine case via Souriau's cocycle, the method also enables the Fisher metric from information geometry for Lie groups. The fact that transverse dynamics to these symplectic leaves is dissipative, whilst dynamics along these symplectic leaves characterize non-dissipative phenomenon, can be used to interpret this Lie group thermodynamics within the context of an open system out of thermodynamics equilibrium. In the following section, we will discuss the dissipative symplectic model of heat and information through the Poisson transverse structure to the symplectic leaf of coadjoint orbits, which is based on the metriplectic bracket, which guarantees conservation of energy and non-decrease of entropy. Baptiste Coquinot recently developed a new foundation theory for dissipative brackets by taking a broad perspective from non-equilibrium thermodynamics. He did this by first considering more natural variables for building the bracket used in metriplectic flow and then by presenting a methodical approach to the development of the theory. By deriving a generic dissipative bracket from fundamental thermodynamic first principles, Baptiste Coquinot demonstrates that brackets for the dissipative part are entirely natural, just as Poisson brackets for the non-dissipative part are canonical for Hamiltonian dynamics. We shall investigate how the theory of dissipative brackets introduced by Paul Dirac for limited Hamiltonian systems relates to transverse structure. We shall investigate an alternative method to the metriplectic method based on Michel Saint Germain's PhD research on the transverse Poisson structure. We will examine an alternative method to the metriplectic method based on the transverse Poisson structure, which Michel Saint-Germain studied for his PhD and was motivated by the key works of Fokko du Cloux. In continuation of Saint-Germain's works, Hervé Sabourin highlights the, for transverse Poisson structures, polynomial nature to nilpotent adjoint orbits and demonstrated that the Casimir functions of the transverse Poisson structure that result from restriction to the Lie-Poisson structure transverse slice are Casimir functions independent of the transverse Poisson structure. He also demonstrated that, on the transverse slice, two polynomial Poisson structures to the symplectic leaf appear that have Casimir functions. The dissipative equation introduced by Lindblad, from the Hamiltonian Liouville equation operating on the quantum density matrix, will be applied to illustrate these previous models. For the Lindblad operator, the dissipative component has been described as the relative entropy gradient and the maximum entropy principle by Öttinger. It has been observed then that the Lindblad equation is a linear approximation of the metriplectic equation.

Decoding 'Maximum Entropy' Deconvolution

For over five decades, the mathematical procedure termed "maximum entropy" (M-E) has been used to deconvolve structure in spectra, optical and otherwise, although quantitative measures of performance remain unknown. Here, we examine this procedure analytically for the lowest two orders for a Lorentzian feature, obtaining expressions for the amount of sharpening and identifying how spurious structures appear. Illustrative examples are provided. These results enhance the utility of this widely used deconvolution approach to spectral analysis.

Optimizing the human learnability of abstract network representations

Information can often be viewed as a network of associations between concepts. Humans build mental models of information networks in the world around them, yet those models consistently contain some errors. Here, we present a computational framework for simulating the optimization of human network learning by intentionally emphasizing or exaggerating some network features over others. We demonstrate in a computational model of human learning that targeted emphasis and de-emphasis can substantially enhance a learner’s grasp of network structure. Further, we identify how optimal emphasis patterns vary with the topology of the target network structure to be learned, as well as the baseline accuracy of the human learner. Our findings illuminate the principles of design and the optimization of network learnability.

Precisely how humans process relational patterns of information in knowledge, language, music, and society is not well understood. Prior work in the field of statistical learning has demonstrated that humans process such information by building internal models of the underlying network structure. However, these mental maps are often inaccurate due to limitations in human information processing. The existence of such limitations raises clear questions: Given a target network that one wishes for a human to learn, what network should one present to the human? Should one simply present the target network as-is, or should one emphasize certain parts of the network to proactively mitigate expected errors in learning? To investigate these questions, we study the optimization of network learnability in a computational model of human learning. Evaluating an array of synthetic and real-world networks, we find that learnability is enhanced by reinforcing connections within modules or clusters. In contrast, when networks contain significant core–periphery structure, we find that learnability is best optimized by reinforcing peripheral edges between low-degree nodes. Overall, our findings suggest that the accuracy of human network learning can be systematically enhanced by targeted emphasis and de-emphasis of prescribed sectors of information.

Digital computing through randomness and order in neural networks

We propose that coding and decoding in the brain are achieved through digital computation using three principles: relative ordinal coding of inputs, random connections between neurons, and belief voting. Due to randomization and despite the coarseness of the relative codes, we show that these principles are sufficient for coding and decoding sequences with error-free reconstruction. In particular, the number of neurons needed grows linearly with the size of the input repertoire growing exponentially. We illustrate our model by reconstructing sequences with repertoires on the order of a billion items. From this, we derive the Shannon equations for the capacity limit to learn and transfer information in the neural population, which is then generalized to any type of neural network. Following the maximum entropy principle of efficient coding, we show that random connections serve to decorrelate redundant information in incoming signals, creating more compact codes for neurons and therefore, conveying a larger amount of information. Henceforth, despite the unreliability of the relative codes, few neurons become necessary to discriminate the original signal without error. Finally, we discuss the significance of this digital computation model regarding neurobiological findings in the brain and more generally with artificial intelligence algorithms, with a view toward a neural information theory and the design of digital neural networks.

Quality-Achieving Reliability Assessment of Rolling Bearing Based on Bootstrap Maximum Entropy Method and Similarity Method

Rolling bearing reliability is often affected by the processing quality, however the life reliability or operating reliability do not involve the study of rolling bearing processing quality assessment. In order to avoid bearing failure caused by bearing processing quality, it is necessary to evaluate the reliability of the bearing quality assurance capability. The difficulty in reliable evaluation of bearing's quality assurance capability is how to quantify the uncertain relationships between the bearing quality and its influence factors, and then determine the weight of different influencing factors. Therefore, in this paper, a novel method for determining the weight of bearing quality-influencing factors based on bootstrap maximum entropy method and similarity method is proposed, and then the quality-achieving reliability model is established. The experimental results show that the proposed method can effectively quantify the relationship between the bearing quality and its influencing factors, and accurately assess the bearing quality assurance capability and bearing quality processing level under the condition of a small number of experimental bearings. Compared with other quality-achieving reliability method, the proposed method is more effective.

Enhancing computational enzyme design by a maximum entropy strategy

Although computational enzyme design is of great importance, the advances utilizing physics-based approaches have been slow, and further progress is urgently needed. One promising direction is using machine learning, but such strategies have not been established as effective tools for predicting the catalytic power of enzymes. Here, we show that the statistical energy inferred from homologous sequences with the maximum entropy (MaxEnt) principle significantly correlates with enzyme catalysis and stability at the active site region and the more distant region, respectively. This finding decodes enzyme architecture and offers a connection between enzyme evolution and the physical chemistry of enzyme catalysis, and it deepens our understanding of the stability-activity trade-off hypothesis for enzymes. Overall, the strong correlations found here provide a powerful way of guiding enzyme design.

Modelling habitat suitability of the invasive tick Rhipicephalus microplus in West Africa

Ticks have medical and economic importance due to their ability to transmit pathogens to humans and animals. In tropical and sub-tropical countries, tick-borne diseases (TBD) are among the most important diseases affecting livestock and humans. The fast spread of ticks and TBD requires a quick development and application of efficient prevention and/or control programs. Therefore, prior investigations on TBD and related vectors epidemiology, for instance, through accurate epidemiological models, are mandatory. This study aims to develop models to forecast suitable habitat for Rhipicephalus microplus distribution in West Africa. Tick occurrences were assembled from 10 different studies carried out in six West African countries in the past decade. Six statistical models (maximum entropy in a single model and generalised linear model, generalised additive model, random forest, boosted regression tree and support vector machine model in an ensemble model) were applied and compared to predict the habitat suitability of R. microplus distribution in West Africa. Each model was evaluated with the area under the receiver operating characteristic curve (AUC), the true skill statistic (TSS) and the Boyce index (BI). The selected models had good performance according to their AUC (above .8), TSS (above .7) and BI (above .8). Temperature played a key role in MaxEnt model, whereas normalised difference vegetation index (NDVI) was the most important variable in the ensemble model. The model predictions showed coastal countries of West Africa as more suitable for R. microplus. However, some Sahelian areas seems also favourable. We stress the importance of vector surveillance and control in countries that have not yet detected R. microplus but are in the areas predicted to host suitable habitat. Indeed, awareness-raising and training of different stakeholders must be reinforced for better prevention and control of this tick in these different countries according to their status.

Promoting the Development of Astragalus mongholicus Bunge Industry in Guyang County (China) Based on MaxEnt and Remote Sensing

To provide high-quality Astragalus mongholicus Bunge to domestic and foreign markets and maintain sustainable development of the A. mongholicus industry, Firstly, we evaluated the impact of environmental factors and planting areas on the A. mongholicus industry. The maximum entropy method (MaxEnt) was utilized to simulate the suitability distribution of A. mongholicus and establish the relationship between the active component contents of A. mongholicus and ecological factors through linear regression analysis. The random forest algorithm was subsequently used to perform feature selection and classification extraction on Sentinel-2 imagery covering the study area. Furthermore, the planting, processing, and sales of A. mongholicus in Guyang County were investigated, and the roles of stakeholders in the value chains were analyzed. The results demonstrated that precipitation of the warmest quarter, minimum temperature of the coldest month, standard deviation of seasonal temperature changes, range of mean annual temperature, and mean diurnal range [mean of monthly (max temp - min temp)] were the five environmental variables that contributed the most to the growth of A. mongholicus. The most influential factor on the distribution of high-quality A. mongholicus was the mean temperature of the coldest quarter. The classification results of image features showed that the planting areas of A. mongholicus was consistent with the suitable planting areas predicted by MaxEnt, which can provide data support to the relevant departments for the macro development of the A. mongholicus industry. In the production of A. mongholicus, 10 value chains were constructed, and the study demonstrated that the behavior of stakeholders, target markets, and the selected planting area had a significant impact on the quality of A. mongholicus.

Entropy and Turbulence Structure

Some new perspectives are offered on the spectral and spatial structure of turbulent flows, in the context of conservation principles and entropy. In recent works, we have shown that the turbulence energy spectra are derivable from the maximum entropy principle, with good agreement with experimental data across the entire wavenumber range. Dissipation can also be attributed to the Reynolds number effect in wall-bounded turbulent flows. Within the global energy and dissipation constraints, the gradients (d/dy+ or d²/dy+²) of the Reynolds stress components neatly fold onto respective curves, so that function prescriptions (dissipation structure functions) can serve as a template to expand to other Reynolds numbers. The Reynolds stresses are fairly well prescribed by the current scaling and dynamical formalism so that the origins of the turbulence structure can be understood and quantified from the entropy perspective.

Entropy-Based Temporal Downscaling of Precipitation as Tool for Sediment Delivery Ratio Assessment

Many regions around the globe are subjected to precipitation-data scarcity that often hinders the capacity of hydrological modeling. The entropy theory and the principle of maximum entropy can help hydrologists to extract useful information from the scarce data available. In this work, we propose a new method to assess sub-daily precipitation features such as duration and intensity based on daily precipitation using the principle of maximum entropy. Particularly in arid and semiarid regions, such sub-daily features are of central importance for modeling sediment transport and deposition. The obtained features were used as input to the SYPoME model (sediment yield using the principle of maximum entropy). The combined method was implemented in seven catchments in Northeast Brazil with drainage areas ranging from 10⁻³ to 10⁺² km² in assessing sediment yield and delivery ratio. The results show significant improvement when compared with conventional deterministic modeling, with Nash–Sutcliffe efficiency (NSE) of 0.96 and absolute error of 21% for our method against NSE of −4.49 and absolute error of 105% for the deterministic approach.

Numerical Algorithms for Estimating Probability Density Function Based on the Maximum Entropy Principle and Fup Basis Functions

Estimation of the probability density function from the statistical power moments presents a challenging nonlinear numerical problem posed by unbalanced nonlinearities, numerical instability and a lack of convergence, especially for larger numbers of moments. Despite many numerical improvements over the past two decades, the classical moment problem of maximum entropy (MaxEnt) is still a very demanding numerical and statistical task. Among others, it was presented how Fup basis functions with compact support can significantly improve the convergence properties of the mentioned nonlinear algorithm, but still, there is a lot of obstacles to an efficient pdf solution in different applied examples. Therefore, besides the mentioned classical nonlinear Algorithm 1, in this paper, we present a linear approximation of the MaxEnt moment problem as Algorithm 2 using exponential Fup basis functions. Algorithm 2 solves the linear problem, satisfying only the proposed moments, using an optimal exponential tension parameter that maximizes Shannon entropy. Algorithm 2 is very efficient for larger numbers of moments and especially for skewed pdfs. Since both Algorithms have pros and cons, a hybrid strategy is proposed to combine their best approximation properties.

How do African elephants utilize the landscape during wet season? A habitat connectivity analysis for Sioma Ngwezi landscape in Zambia

The influence of environmental factors on the distribution and persistence of African elephants (Loxodonta africana) is pertinent to policy makers and managers to formulate balanced plans for different land-use types.The study focuses on movement of elephants and how they utilize foraging areas in Sioma Ngwezi landscape in Zambia by answering the following questions: (1) Which environmental variables and land-cover class predict the movement of elephants during the wet season in Sioma Ngwezi landscape? (2) What is the wet season suitable habitat for elephants in Sioma Ngwezi landscape? (3) What are the major wet season movement corridors for elephants in Sioma Ngwezi landscape?We used GPS telemetry data from the collared elephants to assess habitat connectivity. Maximum entropy (MaxEnt) and linkage mapper were the tools used to predict habitat suitability, movement corridors, and barriers in the landscape during the wet season.The study identified elevation, land cover, and NDVI as the most important environmental predictors that modify the dispersal of elephants in the landscape during the wet season. Additionally, a total of 36 potential wet season corridors were identified connecting 15 core areas mainly used for foraging and protection from poachers in the landscape. Of these, 24 corridors were highly utilized and are suggested as priority corridors for elephant movement in the landscape.The identified wet season habitats and functional corridors may help to combat elephant poaching by patrolling areas with high relative probability of elephant presence. The findings may also help abate human-elephant conflict such as crop-raiding by managing identified corridors that run into agriculture zones in the game management area.

Field-theoretic density estimation for biological sequence space with applications to 5' splice site diversity and aneuploidy in cancer

Density estimation in sequence space is a fundamental problem in machine learning that is also of great importance in computational biology. Due to the discrete nature and large dimensionality of sequence space, how best to estimate such probability distributions from a sample of observed sequences remains unclear. One common strategy for addressing this problem is to estimate the probability distribution using maximum entropy (i.e., calculating point estimates for some set of correlations based on the observed sequences and predicting the probability distribution that is as uniform as possible while still matching these point estimates). Building on recent advances in Bayesian field-theoretic density estimation, we present a generalization of this maximum entropy approach that provides greater expressivity in regions of sequence space where data are plentiful while still maintaining a conservative maximum entropy character in regions of sequence space where data are sparse or absent. In particular, we define a family of priors for probability distributions over sequence space with a single hyperparameter that controls the expected magnitude of higher-order correlations. This family of priors then results in a corresponding one-dimensional family of maximum a posteriori estimates that interpolate smoothly between the maximum entropy estimate and the observed sample frequencies. To demonstrate the power of this method, we use it to explore the high-dimensional geometry of the distribution of 5' splice sites found in the human genome and to understand patterns of chromosomal abnormalities across human cancers.

Leak Detection in Water Pipes Based on Maximum Entropy Version of Least Square Twin K-Class Support Vector Machine

Numerous novel improved support vector machine (SVM) methods are used in leak detection of water pipelines at present. The least square twin K-class support vector machine (LST-KSVC) is a novel simple and fast multi-classification method. However, LST-KSVC has a non-negligible drawback that it assigns the same classification weights to leak samples, including outliers that affect classification, these outliers are often situated away from the main leak samples. To overcome this shortcoming, the maximum entropy (MaxEnt) version of the LST-KSVC is proposed in this paper, called the MLT-KSVC algorithm. In this classification approach, classification weights of leak samples are calculated based on the MaxEnt model. Different sample points are assigned different weights: large weights are assigned to primary leak samples and outliers are assigned small weights, hence the outliers can be ignored in the classification process. Leak recognition experiments prove that the proposed MLT-KSVC algorithm can reduce the impact of outliers on the classification process and avoid the misclassification color block drawback in linear LST-KSVC. MLT-KSVC is more accurate compared with LST-KSVC, TwinSVC, TwinKSVC, and classic Multi-SVM.

TOLOMEO, a Novel Machine Learning Algorithm to Measure Information and Order in Correlated Networks and Predict Their State

We present ToloMEo (TOpoLogical netwOrk Maximum Entropy Optimization), a program implemented in C and Python that exploits a maximum entropy algorithm to evaluate network topological information. ToloMEo can study any system defined on a connected network where nodes can assume N discrete values by approximating the system probability distribution with a Pottz Hamiltonian on a graph. The software computes entropy through a thermodynamic integration from the mean-field solution to the final distribution. The nature of the algorithm guarantees that the evaluated entropy is variational (i.e., it always provides an upper bound to the exact entropy). The program also performs machine learning, inferring the system’s behavior providing the probability of unknown states of the network. These features make our method very general and applicable to a broad class of problems. Here, we focus on three different cases of study: (i) an agent-based model of a minimal ecosystem defined on a square lattice, where we show how topological entropy captures a crossover between hunting behaviors; (ii) an example of image processing, where starting from discretized pictures of cell populations we extract information about the ordering and interactions between cell types and reconstruct the most likely positions of cells when data are missing; and (iii) an application to recurrent neural networks, in which we measure the information stored in different realizations of the Hopfield model, extending our method to describe dynamical out-of-equilibrium processes.

A New Total Uncertainty Measure from A Perspective of Maximum Entropy Requirement

The Dempster-Shafer theory (DST) is an information fusion framework and widely used in many fields. However, the uncertainty measure of a basic probability assignment (BPA) is still an open issue in DST. There are many methods to quantify the uncertainty of BPAs. However, the existing methods have some limitations. In this paper, a new total uncertainty measure from a perspective of maximum entropy requirement is proposed. The proposed method can measure both dissonance and non-specificity in BPA, which includes two components. The first component is consistent with Yager's dissonance measure. The second component is the non-specificity measurement with different functions. We also prove the desirable properties of the proposed method. Besides, numerical examples and applications are provided to illustrate the effectiveness of the proposed total uncertainty measure.

Using the Semantic Information G Measure to Explain and Extend Rate-Distortion Functions and Maximum Entropy Distributions

In the rate-distortion function and the Maximum Entropy (ME) method, Minimum Mutual Information (MMI) distributions and ME distributions are expressed by Bayes-like formulas, including Negative Exponential Functions (NEFs) and partition functions. Why do these non-probability functions exist in Bayes-like formulas? On the other hand, the rate-distortion function has three disadvantages: (1) the distortion function is subjectively defined; (2) the definition of the distortion function between instances and labels is often difficult; (3) it cannot be used for data compression according to the labels’ semantic meanings. The author has proposed using the semantic information G measure with both statistical probability and logical probability before. We can now explain NEFs as truth functions, partition functions as logical probabilities, Bayes-like formulas as semantic Bayes’ formulas, MMI as Semantic Mutual Information (SMI), and ME as extreme ME minus SMI. In overcoming the above disadvantages, this paper sets up the relationship between truth functions and distortion functions, obtains truth functions from samples by machine learning, and constructs constraint conditions with truth functions to extend rate-distortion functions. Two examples are used to help readers understand the MMI iteration and to support the theoretical results. Using truth functions and the semantic information G measure, we can combine machine learning and data compression, including semantic compression. We need further studies to explore general data compression and recovery, according to the semantic meaning.

Graphical Models in Reconstructability Analysis and Bayesian Networks

Reconstructability Analysis (RA) and Bayesian Networks (BN) are both probabilistic graphical modeling methodologies used in machine learning and artificial intelligence. There are RA models that are statistically equivalent to BN models and there are also models unique to RA and models unique to BN. The primary goal of this paper is to unify these two methodologies via a lattice of structures that offers an expanded set of models to represent complex systems more accurately or more simply. The conceptualization of this lattice also offers a framework for additional innovations beyond what is presented here. Specifically, this paper integrates RA and BN by developing and visualizing: (1) a BN neutral system lattice of general and specific graphs, (2) a joint RA-BN neutral system lattice of general and specific graphs, (3) an augmented RA directed system lattice of prediction graphs, and (4) a BN directed system lattice of prediction graphs. Additionally, it (5) extends RA notation to encompass BN graphs and (6) offers an algorithm to search the joint RA-BN neutral system lattice to find the best representation of system structure from underlying system variables. All lattices shown in this paper are for four variables, but the theory and methodology presented in this paper are general and apply to any number of variables. These methodological innovations are contributions to machine learning and artificial intelligence and more generally to complex systems analysis. The paper also reviews some relevant prior work of others so that the innovations offered here can be understood in a self-contained way within the context of this paper.

Entropy, Information, and the Updating of Probabilities

This paper is a review of a particular approach to the method of maximum entropy as a general framework for inference. The discussion emphasizes pragmatic elements in the derivation. An epistemic notion of information is defined in terms of its relation to the Bayesian beliefs of ideally rational agents. The method of updating from a prior to posterior probability distribution is designed through an eliminative induction process. The logarithmic relative entropy is singled out as a unique tool for updating (a) that is of universal applicability, (b) that recognizes the value of prior information, and (c) that recognizes the privileged role played by the notion of independence in science. The resulting framework-the ME method-can handle arbitrary priors and arbitrary constraints. It includes the MaxEnt and Bayes' rules as special cases and, therefore, unifies entropic and Bayesian methods into a single general inference scheme. The ME method goes beyond the mere selection of a single posterior, and also addresses the question of how much less probable other distributions might be, which provides a direct bridge to the theories of fluctuations and large deviations.

Maximum Entropy Principle Underlies Wiring Length Distribution in Brain Networks

A brain network comprises a substantial amount of short-range connections with an admixture of long-range connections. The portion of long-range connections in brain networks is observed to be quantitatively dissimilar across species. It is hypothesized that the length of connections is constrained by the spatial embedding of brain networks, yet fundamental principles that underlie the wiring length distribution remain unclear. By quantifying the structural diversity of a brain network using Shannon's entropy, here we show that the wiring length distribution across multiple species-including Drosophila, mouse, macaque, human, and C. elegans-follows the maximum entropy principle (MAP) under the constraints of limited wiring material and the spatial locations of brain areas or neurons. In addition, by considering stochastic axonal growth, we propose a network formation process capable of reproducing wiring length distributions of the 5 species, thereby implementing MAP in a biologically plausible manner. We further develop a generative model incorporating MAP, and show that, for the 5 species, the generated network exhibits high similarity to the real network. Our work indicates that the brain connectivity evolves to be structurally diversified by maximizing entropy to support efficient interareal communication, providing a potential organizational principle of brain networks.

Improved Approach for the Maximum Entropy Deconvolution Problem

The probability density function (pdf) valid for the Gaussian case is often applied for describing the convolutional noise pdf in the blind adaptive deconvolution problem, although it is known that it can be applied only at the latter stages of the deconvolution process, where the convolutional noise pdf tends to be approximately Gaussian. Recently, the deconvolutional noise pdf was approximated with the Edgeworth Expansion and with the Maximum Entropy density function for the 16 Quadrature Amplitude Modulation (QAM) input but no equalization performance improvement was seen for the hard channel case with the equalization algorithm based on the Maximum Entropy density function approach for the convolutional noise pdf compared with the original Maximum Entropy algorithm, while for the Edgeworth Expansion approximation technique, additional predefined parameters were needed in the algorithm. In this paper, the Generalized Gaussian density (GGD) function and the Edgeworth Expansion are applied for approximating the convolutional noise pdf for the 16 QAM input case, with no need for additional predefined parameters in the obtained equalization method. Simulation results indicate that improved equalization performance is obtained from the convergence time point of view of approximately 15,000 symbols for the hard channel case with our new proposed equalization method based on the new model for the convolutional noise pdf compared to the original Maximum Entropy algorithm. By convergence time, we mean the number of symbols required to reach a residual inter-symbol-interference (ISI) for which reliable decisions can be made on the equalized output sequence.

Entropic Dynamics on Gibbs Statistical Manifolds

Entropic dynamics is a framework in which the laws of dynamics are derived as an application of entropic methods of inference. Its successes include the derivation of quantum mechanics and quantum field theory from probabilistic principles. Here, we develop the entropic dynamics of a system, the state of which is described by a probability distribution. Thus, the dynamics unfolds on a statistical manifold that is automatically endowed by a metric structure provided by information geometry. The curvature of the manifold has a significant influence. We focus our dynamics on the statistical manifold of Gibbs distributions (also known as canonical distributions or the exponential family). The model includes an “entropic” notion of time that is tailored to the system under study; the system is its own clock. As one might expect that entropic time is intrinsically directional; there is a natural arrow of time that is led by entropic considerations. As illustrative examples, we discuss dynamics on a space of Gaussians and the discrete three-state system.

DynaMETE: a hybrid MaxEnt-plus-mechanism theory of dynamic macroecology

The Maximum Entropy Theory of Ecology (METE) predicts the shapes of macroecological metrics in relatively static ecosystems, across spatial scales, taxonomic categories and habitats, using constraints imposed by static state variables. In disturbed ecosystems, however, with time-varying state variables, its predictions often fail. We extend macroecological theory from static to dynamic by combining the MaxEnt inference procedure with explicit mechanisms governing disturbance. In the static limit, the resulting theory, DynaMETE, reduces to METE but also predicts a new scaling relationship among static state variables. Under disturbances, expressed as shifts in demographic, ontogenic growth or migration rates, DynaMETE predicts the time trajectories of the state variables as well as the time-varying shapes of macroecological metrics such as the species abundance distribution and the distribution of metabolic rates over individuals. An iterative procedure for solving the dynamic theory is presented. Characteristic signatures of the deviation from static predictions of macroecological patterns are shown to result from different kinds of disturbance. By combining MaxEnt inference with explicit dynamical mechanisms of disturbance, DynaMETE is a candidate theory of macroecology for ecosystems responding to anthropogenic or natural disturbances.

Changes in pairwise correlations during running reshape global network state in the main olfactory bulb

Neural codes for sensory inputs have been hypothesized to reside in a broader space defined by ongoing patterns of spontaneous activity. To understand the structure of this spontaneous activity in the olfactory system, we performed high-density recordings of neural populations in the main olfactory bulb of awake mice. We observed changes in pairwise correlations of spontaneous activity between mitral and tufted (M/T) cells when animals were running, which resulted in an increase in the entropy of the population. Surprisingly, pairwise maximum entropy models that described the population activity using only assumptions about the firing rates and correlations of neurons were better at predicting the global structure of activity when animals were stationary as compared to when they were running, implying that higher order (3rd, 4th order) interactions governed population activity during locomotion. Taken together, we found that locomotion alters the functional interactions that shape spontaneous population activity at the earliest stages of olfactory processing, one synapse away from the sensory receptors in the nasal epithelium. These data suggest that the coding space available for sensory representations responds adaptively to the animal's behavioral state.NEW & NOTEWORTHY The organization and structure of spontaneous population activity in the olfactory system places constraints of how odor information is represented. Using high-density electrophysiological recordings of mitral and tufted cells, we found that running increases the dimensionality of spontaneous activity, implicating higher order interactions among neurons during locomotion. Behavior, thus, flexibly alters neuronal activity at the earliest stages of sensory processing.

A Neural Network MCMC Sampler That Maximizes Proposal Entropy

Markov Chain Monte Carlo (MCMC) methods sample from unnormalized probability distributions and offer guarantees of exact sampling. However, in the continuous case, unfavorable geometry of the target distribution can greatly limit the efficiency of MCMC methods. Augmenting samplers with neural networks can potentially improve their efficiency. Previous neural network-based samplers were trained with objectives that either did not explicitly encourage exploration, or contained a term that encouraged exploration but only for well structured distributions. Here we propose to maximize proposal entropy for adapting the proposal to distributions of any shape. To optimize proposal entropy directly, we devised a neural network MCMC sampler that has a flexible and tractable proposal distribution. Specifically, our network architecture utilizes the gradient of the target distribution for generating proposals. Our model achieved significantly higher efficiency than previous neural network MCMC techniques in a variety of sampling tasks, sometimes by more than an order magnitude. Further, the sampler was demonstrated through the training of a convergent energy-based model of natural images. The adaptive sampler achieved unbiased sampling with significantly higher proposal entropy than a Langevin dynamics sample. The trained sampler also achieved better sample quality.

Potential Distributions of the Invasive Barnacle Scale Ceroplastes cirripediformis (Hemiptera: Coccidae) Under Climate Change and Implications for Its Management

Ceroplastes cirripediformis Comstock is one of the most destructive invasive pests that have caused various negative impacts to agricultural, ornamental, and greenhouse plants. Since it is time- and labor-consuming to control C. cirripediformis, habitat evaluation of this pest may be the most cost-effective method for predicting its dispersal and avoiding its outbreaks. Here, we evaluated the effects of climatic variables on distribution patterns of C. cirripediformis and produced a global risk map for its outbreak under current and future climate scenarios using the Maximum Entropy (MaxEnt) model. Our results showed that mean temperature of driest quarter (Bio 9), precipitation of coldest quarter (Bio 19), precipitation of warmest quarter (Bio 18), and mean temperature of wettest quarter (Bio 8) were the main factors influencing the current modeled distribution of C. cirripediformis, respectively, contributing 41.9, 29.4, 18.8, and 7.9%. The models predicted that, globally, potential distribution of C. cirripediformis would be across most zoogeographical regions under both current and future climate scenarios. Moreover, in the future, both the total potential distribution region and its area of highly suitable habitat are expected to expand slightly in all representative concentration pathway scenarios. The information generated from this study will contribute to better identify the impacts of climate change upon C. cirripediformis's potential distribution while also providing a scientific basis for forecasting insect pest spread and outbreaks. Furthermore, this study serves an early warning for the regions of potential distribution, predicted as highly suitable habitats for this pest, which could promote its prevention and control.

Assessing the Present and Future Habitat Suitability of Caligus rogercresseyi (Boxshall and Bravo, 2000) for Salmon Farming in Southern Chile

The sea louse (Caligus rogercresseyi) is the most relevant parasite for the farmed salmon industry in Chile, the second largest producer worldwide. Although spatial patterns of C. rogercresseyi have been addressed from data obtained from established monitoring and surveillance programs, studies on its spatial ecology are limited. A wide geographic distribution of C. rogercresseyi is presumed in Chile; however, how this species could potentially be distributed in space is unknown. Our study presents an analysis of the habitat suitability for C. rogercresseyi in the entire area occupied by marine sites of salmon farms in Chile. Habitat suitability modeling was used to explore the likelihood of species spatial occurrence based on environmental characteristics. Due to the expanding salmon industry in southern Chile, we studied C. rogercresseyi habitat suitability models for present (average of 2005-2010) and two future projections (2050 and 2100) under different climate change scenarios. Models were constructed with the maxent algorithm using a large database of spatial C. rogercresseyi occurrences from the Chilean fisheries health authority and included 23 environmental variables obtained from the Ocean Rasters for Analysis of Climate and Environment (Bio-ORACLE). Habitat suitability models indicated that water temperature, water salinity, and current velocity of waters were the most important characteristics limiting C. rogercresseyi distribution in southern Chile. Habitat suitability models for current climate indicated a heterogeneous pattern with C. rogercresseyi being present in waters with temperature range 12.12-7.08°C (sd = 0.65), salinity range 33.7-25.5 pss (sd = 1.73), and current water velocity range 0.23-0.01 m-1 (sd = 0.02). Predictions for future projections in year 2050 and year 2100 suggest new clumped dispersion of the environmental conditions for C. rogercresseyi establishment. Our results suggest complexity and a wide dispersion of the biogeographic distribution of the C. rogercresseyi habitat suitability with potential implications for control strategies and environmental issues for salmon farming in Chile. Further investigations are required into C. rogercresseyi distribution in southern Chile considering the possible effect of climate change.

Understanding between-cluster variation in prevalence and limits for how much variation is plausible

In clinical trials and observational studies of clustered binary data, understanding between-cluster variation is essential: in sample size and power calculations of cluster randomised trials, for example, the intra-cluster correlation coefficient is often specified. However, quantifications of between-cluster variation can be unintuitive, and an intra-cluster correlation coefficient as low as 0.04 may correspond to surprisingly large between-cluster differences. We suggest that understanding is improved through visualising the implied distribution of true cluster prevalences - possibly by assuming they follow a beta distribution - or by calculating their standard deviation, which is more readily interpretable than the intra-cluster correlation coefficient. Even so, the bounded nature of binary data complicates the interpretation of variances as primary measures of uncertainty, and entropy offers an attractive alternative. Appealing to maximum entropy theory, we propose the following rule of thumb: that plausible intra-cluster correlation coefficients and standard deviations of true cluster prevalences are both bounded above by the overall prevalence, its complement, and one third. We also provide corresponding bounds for the coefficient of variation, and for a different standard deviation and intra-cluster correlation defined on the log odds scale. Using previously published data, we observe the quantities defined on the log odds scale to be more transportable between studies with different outcomes with different prevalences than the intra-cluster correlation and coefficient of variation. The latter increase and decrease, respectively, as prevalence increases from 0% to 50%, and the same is true for our bounds. Our work will help clinical trialists better understand between-cluster variation and avoid specifying implausibly high values for the intra-cluster correlation in sample size and power calculations.

Hamiltonian modelling of macro-economic urban dynamics

The rapid urbanization makes the understanding of the evolution of urban environments of utmost importance to steer societies towards better futures. Many studies have focused on the emerging properties of cities, leading to the discovery of scaling laws mirroring the dependence of socio-economic indicators on city sizes. However, few efforts have been devoted to the modelling of the dynamical evolution of cities, as reflected through the mutual influence of socio-economic variables. Here, we fill this gap by presenting a maximum entropy generative model for cities written in terms of a few macro-economic variables, whose parameters (the effective Hamiltonian, in a statistical-physical analogy) are inferred from real data through a maximum-likelihood approach. This approach allows for establishing a few results. First, nonlinear dependencies among indicators are needed for an accurate statistical description of the complexity of empirical correlations. Second, the inferred coupling parameters turn out to be quite robust along different years. Third, the quasi time-invariance of the effective Hamiltonian allows guessing the future state of a city based on a previous state. Through the adoption of a longitudinal dataset of macro-economic variables for French towns, we assess a significant forecasting accuracy.

Inferring Authors' Relative Contributions to Publications from the Order of Their Names When Default Order Is Alphabetical

In attributing individual credit for co-authored academic publications, one issue is how to apportion (unequal) credit, based on the order of authorship. Apportioning credit for completed joint undertakings has always been a challenge. Academic promotion committees are faced with such tasks regularly, when trying to infer a candidate’s contribution to an article they coauthored with others. We propose a method for achieving this goal in disciplines (such as the author’s) where the default order is alphabetical. The credits are those maximizing Shannon entropy subject to order constraints.