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.

Physical models of bacterial chromosomes.

The interplay between bacterial chromosome organization and functions such as transcription and replication can be studied in increasing detail using novel experimental techniques. Interpreting the resulting quantitative data, however, can be theoretically challenging. In this minireview, we discuss how connecting experimental observations to biophysical theory and modeling can give rise to new insights on bacterial chromosome organization. We consider three flavors of models of increasing complexity: simple polymer models that explore how physical constraints, such as confinement or plectoneme branching, can affect bacterial chromosome organization; bottom-up mechanistic models that connect these constraints to their underlying causes, for instance, chromosome compaction to macromolecular crowding, or supercoiling to transcription; and finally, data-driven methods for inferring interpretable and quantitative models directly from complex experimental data. Using recent examples, we discuss how biophysical models can both deepen our understanding of how bacterial chromosomes are structured and give rise to novel predictions about bacterial chromosome organization.

Reliability of energy landscape analysis of resting-state functional MRI data.

Energy landscape analysis is a data-driven method to analyse multidimensional time series, including functional magnetic resonance imaging (fMRI) data. It has been shown to be a useful characterization of fMRI data in health and disease. It fits an Ising model to the data and captures the dynamics of the data as movement of a noisy ball constrained on the energy landscape derived from the estimated Ising model. In the present study, we examine test-retest reliability of the energy landscape analysis. To this end, we construct a permutation test that assesses whether or not indices characterizing the energy landscape are more consistent across different sets of scanning sessions from the same participant (i.e. within-participant reliability) than across different sets of sessions from different participants (i.e. between-participant reliability). We show that the energy landscape analysis has significantly higher within-participant than between-participant test-retest reliability with respect to four commonly used indices. We also show that a variational Bayesian method, which enables us to estimate energy landscapes tailored to each participant, displays comparable test-retest reliability to that using the conventional likelihood maximization method. The proposed methodology paves the way to perform individual-level energy landscape analysis for given data sets with a statistically controlled reliability.

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'.

Update of the geographic range of Humboldt's squirrel monkeys (Saimiri cassiquiarensis cassiquiarensis Lesson, 1840) using a model-based approach.

Saimiri cassiquiarensis cassiquiarensis (Cebidae) is a primate subspecies with a wide distribution in the Amazonian region of Brazil, Colombia, and Venezuela. However, the boundaries of its geographic range remain poorly defined. This study presents new occurrence localities for this subspecies and updates its distribution using a compiled data set of 140 occurrence records based on literature, specimens vouchered in scientific collections, and new field data to produce model-based range maps. After cleaning our data set, we updated the subspecies' extent of occurrence, which was used in model calibration. We then modeled the subspecies' range using a maximum entropy algorithm (MaxEnt). The final model was adjusted using a fixed threshold, and we revised this polygon based on known geographic barriers and parapatric congeneric ranges. Our findings indicate that this subspecies is strongly associated with lowland areas, with consistently high daily temperatures. We propose modifications to all range boundaries and estimate that 3% of the area of occupancy (AOO, as defined by IUCN) has already been lost due to deforestation, resulting in a current range of 224,469 km2. We also found that 54% of their AOO is currently covered by protected areas (PAs). Based on these results, we consider that this subspecies is currently properly classified as Least Concern, because it occupies an extensive range, which is relatively well covered by PAs, and is currently experiencing low rates of deforestation.

Saimiri cassiquiarensis cassiquiarensis (Cebidae) é uma subespécie de primata com ampla distribuição na região amazônica do Brasil, Colômbia e Venezuela. No entanto, os limites de sua distribuição geográfica permanecem mal definidos. Este estudo apresenta novas localidades de ocorrência para essa subespécie e atualiza sua distribuição usando 140 registros de ocorrência compilados com base na literatura, espécimes depositados em coleções científicas e novos registros de campo para produzir mapas de distribuição baseados em modelos. Após a limpeza do nosso banco de dados, atualizamos a extensão de ocorrência da subespécie, que foi usada na calibração do modelo. Em seguida, modelamos a área de distribuição da subespécie usando um algoritmo de entropia máxima (MaxEnt). O modelo final foi ajustado usando um limiar fixo e revisamos esse polígono com base em barreiras geográficas conhecidas e na distribuição de congêneres parapátricas. Nosso modelo sugere que a espécie é fortemente associada a áreas planas, com temperaturas diárias consistentemente altas. Propomos modificações em todos os limites da área de distribuição e estimamos que 3% da área de ocupação (AOO, conforme definida pela IUCN) da subespécie já foi perdida devido ao desmatamento, resultando em uma área de distribuição atual de 224,469 km2. Também estimamos que 54% de sua AOO encontra­se atualmente coberta por áreas protegidas. Com base nesses resultados, consideramos que a subespécie está apropriadamente classificada como Pouco Preocupante, pois ocupa uma área extensa, que é relativamente bem coberta por áreas protegidas e atualmente apresenta baixas taxas de desmatamento.

Detecting Spatial Patterns of Peatland Greenhouse Gas Sinks and Sources with Geospatial Environmental and Remote Sensing Data.

Peatlands play a key role in the circulation of the main greenhouse gases (GHG) - methane (CH4), carbon dioxide (CO2), and nitrous oxide (N2O). Therefore, detecting the spatial pattern of GHG sinks and sources in peatlands is pivotal for guiding effective climate change mitigation in the land use sector. While geospatial environmental data, which provide detailed spatial information on ecosystems and land use, offer valuable insights into GHG sinks and sources, the potential of directly using remote sensing data from satellites remains largely unexplored. We predicted the spatial distribution of three major GHGs (CH4, CO2, and N2O) sinks and sources across Finland. Utilizing 143 field measurements, we compared the predictive capacity of three different data sets with MaxEnt machine-learning modeling: (1) geospatial environmental data including climate, topography and habitat variables, (2) remote sensing data (Sentinel-1 and Sentinel-2), and (3) a combination of both. The combined dataset yielded the highest accuracy with an average test area under the receiver operating characteristic curve (AUC) of 0.845 and AUC stability of 0.928. A slightly lower accuracy was achieved using only geospatial environmental data (test AUC 0.810, stability AUC 0.924). In contrast, using only remote sensing data resulted in reduced predictive accuracy (test AUC 0.763, stability AUC 0.927). Our results suggest that (1) reliable estimates of GHG sinks and sources cannot be produced with remote sensing data only and (2) integrating multiple data sources is recommended to achieve accurate and realistic predictions of GHG spatial patterns.

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.

Maximum Geometric Quantum Entropy.

Any given density matrix can be represented as an infinite number of ensembles of pure states. This leads to the natural question of how to uniquely select one out of the many, apparently equally-suitable, possibilities. Following Jaynes' information-theoretic perspective, this can be framed as an inference problem. We propose the Maximum Geometric Quantum Entropy Principle to exploit the notions of Quantum Information Dimension and Geometric Quantum Entropy. These allow us to quantify the entropy of fully arbitrary ensembles and select the one that maximizes it. After formulating the principle mathematically, we give the analytical solution to the maximization problem in a number of cases and discuss the physical mechanism behind the emergence of such maximum entropy ensembles.

Towards Multi-Objective Object Push-Grasp Policy Based on Maximum Entropy Deep Reinforcement Learning under Sparse Rewards.

In unstructured environments, robots need to deal with a wide variety of objects with diverse shapes, and often, the instances of these objects are unknown. Traditional methods rely on training with large-scale labeled data, but in environments with continuous and high-dimensional state spaces, the data become sparse, leading to weak generalization ability of the trained models when transferred to real-world applications. To address this challenge, we present an innovative maximum entropy Deep Q-Network (ME-DQN), which leverages an attention mechanism. The framework solves complex and sparse reward tasks through probabilistic reasoning while eliminating the trouble of adjusting hyper-parameters. This approach aims to merge the robust feature extraction capabilities of Fully Convolutional Networks (FCNs) with the efficient feature selection of the attention mechanism across diverse task scenarios. By integrating an advantage function with the reasoning and decision-making of deep reinforcement learning, ME-DQN propels the frontier of robotic grasping and expands the boundaries of intelligent perception and grasping decision-making in unstructured environments. Our simulations demonstrate a remarkable grasping success rate of 91.6%, while maintaining excellent generalization performance in the real world.

Small and Simple Systems That Favor the Arrow of Time.

The 2nd law of thermodynamics yields an irreversible increase in entropy until thermal equilibrium is achieved. This irreversible increase is often assumed to require large and complex systems to emerge from the reversible microscopic laws of physics. We test this assumption using simulations and theory of a 1D ring of N Ising spins coupled to an explicit heat bath of N Einstein oscillators. The simplicity of this system allows the exact entropy to be calculated for the spins and the heat bath for any N, with dynamics that is readily altered from reversible to irreversible. We find thermal-equilibrium behavior in the thermodynamic limit, and in systems as small as N=2, but both results require microscopic dynamics that is intrinsically irreversible.

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.

Spatiotemporal distribution and environmental influences of severe fever with thrombocytopenia syndrome in Shandong Province, China.

BACKGROUND: Severe fever with thrombocytopenia syndrome (SFTS) is an emerging infectious disease discovered in China in 2009. The purpose of this study was to describe the spatiotemporal distribution of SFTS and to identify its environmental influencing factors and potential high-risk areas in Shandong Province, China. METHODS: Data on the SFTS incidence from 2010 to 2021 were collected. Spatiotemporal scan statistics were used to identify the time and area of SFTS clustering. The maximum entropy (MaxEnt) model was used to analyse environmental influences and predict high-risk areas. RESULTS: From 2010 to 2021, a total of 5705 cases of SFTS were reported in Shandong. The number of SFTS cases increased yearly, with a peak incidence from April to October each year. Spatiotemporal scan statistics showed the existence of one most likely cluster and two secondary likely clusters in Shandong. The most likely cluster was in the eastern region, from May to October 2021. The first secondary cluster was in the central region, from May to October 2021. The second secondary cluster was in the southeastern region, from May to September 2020. The MaxEnt model showed that the mean annual wind speed, NDVI, cattle density and annual cumulative precipitation were the key factors influencing the occurrence of SFTS. The predicted risk map showed that the area of high prevalence was 28,120 km2, accounting for 18.05% of the total area of the province. CONCLUSIONS: The spatiotemporal distribution of SFTS was heterogeneous and influenced by multidimensional environmental factors. This should be considered as a basis for delineating SFTS risk areas and developing SFTS prevention and control measures.

Entropic Density Functional Theory.

A formulation of density functional theory (DFT) is constructed as an application of the method of maximum entropy for an inhomogeneous fluid in thermal equilibrium. The use of entropy as a systematic method to generate optimal approximations is extended from the classical to the quantum domain. This process introduces a family of trial density operators that are parameterized by the particle density. The optimal density operator is that which maximizes the quantum entropy relative to the exact canonical density operator. This approach reproduces the variational principle of DFT and allows a simple proof of the Hohenberg-Kohn theorem at finite temperature. Finally, as an illustration, we discuss the Kohn-Sham approximation scheme at finite temperature.

Prediction of Potential Suitable Distribution Areas for an Endangered Salamander in China.

Climate change has been considered to pose critical threats for wildlife. During the past decade, species distribution models were widely used to assess the effects of climate change on the distribution of species' suitable habitats. Among all the vertebrates, amphibians are most vulnerable to climate change. This is especially true for salamanders, which possess some specific traits such as cutaneous respiration and low vagility. The Wushan salamander (Liua shihi) is a threatened and protected salamander in China, with its wild population decreasing continuously. The main objective of this study was to predict the distribution of suitable habitat for L. shihi using the ENMeval parameter-optimized MaxEnt model under current and future climate conditions. Our results showed that precipitation, cloud density, vegetation type, and ultraviolet radiation were the main environmental factors affecting the distribution of L. shihi. Currently, the suitable habitats for L. shihi are mainly concentrated in the Daba Mountains, including northeastern Chongqing and western Hubei Provinces. Under the future climate conditions, the area of suitable habitats increased, which mainly occurred in central Guizhou Province. This study provided important information for the conservation of L. shihi. Future studies can incorporate more species distribution models to better understand the effects of climate change on the distribution of L. shihi.

Fluorescence correlation spectroscopy in the study of the interaction between hyaluronan and positively charged surfactants.

The interaction between fluorescently labeled hyaluronan and cationic surfactants was studied using Fluorescence Correlation Spectroscopy. The hyaluronan was selected at two different molecular weights - specifically, 274 kDa and 710 kDa. Cetyltrimethylammonium bromide and Septonex® were chosen as cationic surfactants to interact with the negatively charged biopolymer. The study focused on changes in the diffusive behavior of a biopolymer that interacts with surfactant molecules in an aqueous environment. Various methods were applied to evaluate the obtained data, these including, among others, the Maximum Entropy Method, which provides the distributional dependences of diffusion coefficients. Without the surfactant, the studied biopolymers showed diffusion behavior comparable to that found in previously published studies. In the presence of surfactants, more intense interaction was observed between Cetyltrimethylammonium bromide and Septonex®. Comparing the molecular weights, the retention of intermolecular aggregates after the precipitation region for the lower weight and the disintegration of these aggregates for the higher weight were observed; moreover, they showed diffusion behavior comparable to the samples without the presence of the surfactant.

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.

Potential impact of climate change on the distribution of Capricornis milneedwardsii, a vulnerable mammal in China.

Climate change significantly impacted on the survival, development, distribution, and abundance of living organisms. The Chinese serow Capricornis milneedwardsii, known as the "four unlike," is a Class II nationally protected species in China. In this study, we predicted the geographical suitability of C. milneedwardsii under current and future climatic conditions using MaxEnt. The model simulations resulted in area under the receiver operating characteristic curve (AUC) values above 0.9 for both current and future climate scenarios, indicating the excellent performance, high accuracy, and credibility of the MaxEnt model. The results also showed that annual precipitation (Bio12), slope, elevation, and mean temperature of wettest quarter (Bio8) were the key environmental variables affecting the distribution of C. milneedwardsii, with contributions of 31.2%, 26.4%, 11%, and 10.3%, respectively. The moderately and highly suitable habitats were mainly located in the moist area of China, with a total area of 34.56 × 104 and 16.61 × 104 km2, respectively. Under future climate change scenarios, the areas of suitability of C. milneedwardsii showed an increasing trend. The geometric center of the total suitable habitats of C. milneedwardsii would show the trend of northwest expansion and southeast contraction. These findings could provide a theoretical reference for the protection of C. milneedwardsii in the future.

Prediction of the potential distribution of Chimonobambusautilis (Poaceae, Bambusoideae) in China, based on the MaxEnt model.

Chimonobambusautilis is a unique edible bamboo species valued for its economic and nutritional benefits. However, its existence in natural habitats is at risk due to environmental shifts and human interventions. This research utilised the maximum entropy model (MaxEnt) to predict potential habitats for Ch.utilis in China, identifying key environmental factors influencing its distribution and analysing changes in suitable habitats under future climate conditions. The results show that the results of the MaxEnt model have high prediction accuracy, with an AUC (Area Under the receiver operating characteristic Curve) value of 0.997. Precipitation in the driest month (Bio14), altitude (Alt) and isothermality (Bio03) emerged as the primary environmental factors influencing the Ch.utilis distribution. Currently, the suitable habitats area for Ch.utilis is 10.55 × 104 km2. Projections for the 2050s and 2090s indicate potential changes in suitable habitats ranging from -3.79% to 10.52%. In general, the most suitable habitat area will decrease and shrink towards higher latitude areas in the future. This study provides a scientific basis for the introduction, cultivation and conservation of Ch.utilis.

Predicting potential and quality distribution of Anisodus tanguticus (Maxim.) Pascher under different climatic conditions in the Qinghai-Tibet plateau.

Anisodus tanguticus (Maxim.) Pascher, a distinctive medicinal plant native to the Qinghai-Tibet Plateau, China, has garnered attention due to increasing market demand. This study explores the impact of environmental factors on the distribution and levels of active compounds namely anisodamine, anisodine, and atropine within A. tanguticus. Our goal was to identify suitable cultivation areas for this plant. This study employs the maximum entropy model to simulate the suitable area of A. tanguticus under current conditions and three climate change scenarios during the 2050s and 2070s. The finding revealed that altitude, precipitation in the warmest season (Bio 18), the average annual temperature (Bio 1) exerted significant influences on the distribution of A. tanguticus. Among the environmental factors considered, temperature difference between day and night (Bio 2) had the most substantial impact on the distribution of anisodamine, temperature seasonal variation variance (Bio 4) predominantly influenced anisodine distribution, and Bio 1 had the greatest effected on the distribution of atropine. The suitable areas primarily exist in the eastern Qinghai-Tibet Plateau in China, encompassing a total area of 30.78 × 104 km2. Under the climate scenarios for the future, the suitable areas exhibit increasing trends of approximately 30.2%, 30.3%, and 39.8% by the 2050s, and 25.1%, 48.8%, and 60.1% by the 2070s. This research would provide theoretical suggestions for the protection, and cultivation management of A. tanguticus resources to face the challenge of global climate change.

Habitat for Coilia nasus in southern Zhejiang Province, China, based on a maximum entropy model.

As an important fishery resource and endangered species, studying the habitat of Coilia nasus (C. nasus) is highly significant. This study used fishery survey data from southern Zhejiang coastal waters from 2016 to 2020, employing a maximum entropy model (MaxEnt) to map the habitat distribution of C. nasus. Model performance was evaluated using two metrics: the area under the curve (AUC) of the receiver operating characteristic curve for the training and test sets and true skill statistics (TSS). This study aimed to predict the habitat distribution of C. nasus and explore how environmental variables influence habitat suitability. The results indicated that the models for each season had strong predictive performance, with AUC values above 0.8 and TSS values exceeding 0.6, indicating that they could accurately predict the presence of C. nasus. In the study area, C. nasus was primarily found in brackish or marine waters near bays and coastal islands. Among all environmental factors, salinity (S) and bottom temperature (BOT) had the highest correlations with habitat distribution, although these correlations varied across seasons. The findings of this study provide empirical evidence and a reference for the conservation and management of C. nasus and for the designation of its protected areas.