Dynamic maximum entropy provides accurate approximation of structured population dynamics.
Ontology highlight
ABSTRACT:
SUBMITTER: Bod'ova K
PROVIDER: S-EPMC8668141 | biostudies-literature |
REPOSITORIES: biostudies-literature
Similar Datasets
Project description:Recently a new blind equalization method was proposed for the 16QAM constellation input inspired by the maximum entropy density approximation technique with improved equalization performance compared to the maximum entropy approach, Godard's algorithm, and others. In addition, an approximated expression for the minimum mean square error (MSE) was obtained. The idea was to find those Lagrange multipliers that bring the approximated MSE to minimum. Since the derivation of the obtained MSE with respect to the Lagrange multipliers leads to a nonlinear equation for the Lagrange multipliers, the part in the MSE expression that caused the nonlinearity in the equation for the Lagrange multipliers was ignored. Thus, the obtained Lagrange multipliers were not those Lagrange multipliers that bring the approximated MSE to minimum. In this paper, we derive a new set of Lagrange multipliers based on the nonlinear expression for the Lagrange multipliers obtained from minimizing the approximated MSE with respect to the Lagrange multipliers. Simulation results indicate that for the high signal to noise ratio (SNR) case, a faster convergence rate is obtained for a channel causing a high initial intersymbol interference (ISI) while the same equalization performance is obtained for an easy channel (initial ISI low).
| S-EPMC3958749 | biostudies-other
Project description:The increasing number of scientific literature on the Web and the absence of efficient tools used for classifying and searching the documents are the two most important factors that influence the speed of the search and the quality of the results. Previous studies have shown that the usage of ontologies makes it possible to process document and query information at the semantic level, which greatly improves the search for the relevant information and makes one step further towards the Semantic Web. A fundamental step in these approaches is the annotation of documents with ontology concepts, which can also be seen as a classification task. In this paper we address this issue for the biomedical domain and present a new automated and robust method, based on a Maximum Entropy approach, for annotating biomedical literature documents with terms from the Medical Subject Headings (MeSH).The experimental evaluation shows that the suggested Maximum Entropy approach for annotating biomedical documents with MeSH terms is highly accurate, robust to the ambiguity of terms, and can provide very good performance even when a very small number of training documents is used. More precisely, we show that the proposed algorithm obtained an average F-measure of 92.4% (precision 99.41%, recall 86.77%) for the full range of the explored terms (4,078 MeSH terms), and that the algorithm's performance is resilient to terms' ambiguity, achieving an average F-measure of 92.42% (precision 99.32%, recall 86.87%) in the explored MeSH terms which were found to be ambiguous according to the Unified Medical Language System (UMLS) thesaurus. Finally, we compared the results of the suggested methodology with a Naive Bayes and a Decision Trees classification approach, and we show that the Maximum Entropy based approach performed with higher F-Measure in both ambiguous and monosemous MeSH terms.
| S-EPMC3337257 | biostudies-literature
Project description:Continuous cultures of mammalian cells are complex systems displaying hallmark phenomena of nonlinear dynamics, such as multi-stability, hysteresis, as well as sharp transitions between different metabolic states. In this context mathematical models may suggest control strategies to steer the system towards desired states. Although even clonal populations are known to exhibit cell-to-cell variability, most of the currently studied models assume that the population is homogeneous. To overcome this limitation, we use the maximum entropy principle to model the phenotypic distribution of cells in a chemostat as a function of the dilution rate. We consider the coupling between cell metabolism and extracellular variables describing the state of the bioreactor and take into account the impact of toxic byproduct accumulation on cell viability. We present a formal solution for the stationary state of the chemostat and show how to apply it in two examples. First, a simplified model of cell metabolism where the exact solution is tractable, and then a genome-scale metabolic network of the Chinese hamster ovary (CHO) cell line. Along the way we discuss several consequences of heterogeneity, such as: qualitative changes in the dynamical landscape of the system, increasing concentrations of byproducts that vanish in the homogeneous case, and larger population sizes.
| S-EPMC6411232 | biostudies-literature
Project description:Advances in mass spectrometry among other technologies have allowed for quantitative, reproducible, proteome-wide measurements of levels of phosphorylation as signals propagate through complex networks in response to external stimuli under different conditions. However, computational approaches to infer elements of the signaling network strictly from the quantitative aspects of proteomics data are not well established. We considered a method using the principle of maximum entropy to infer a network of interacting phosphotyrosine sites from pairwise correlations in a mass spectrometry data set and derive a phosphorylation-dependent interaction network solely from quantitative proteomics data. We first investigated the applicability of this approach by using a simulation of a model biochemical signaling network whose dynamics are governed by a large set of coupled differential equations. We found that in a simulated signaling system, the method detects interactions with significant accuracy. We then analyzed a growth factor mediated signaling network in a human mammary epithelial cell line that we inferred from mass spectrometry data and observe a biologically interpretable, small-world structure of signaling nodes, as well as a catalog of predictions regarding the interactions among previously uncharacterized phosphotyrosine sites. For example, the calculation places a recently identified tumor suppressor pathway through ARHGEF7 and Scribble, in the context of growth factor signaling. Our findings suggest that maximum entropy derived network models are an important tool for interpreting quantitative proteomics data.
| S-EPMC2728537 | biostudies-literature
Project description:Modern electrophysiological recordings and optical imaging techniques have revealed a diverse spectrum of spatiotemporal neural activities underlying fundamental cognitive processing. Oscillations, traveling waves and other complex population dynamical patterns are often concomitant with sensory processing, information transfer, decision making and memory consolidation. While neural population models such as neural mass, population density and kinetic theoretical models have been used to capture a wide range of the experimentally observed dynamics, a full account of how the multi-scale dynamics emerges from the detailed biophysical properties of individual neurons and the network architecture remains elusive. Here we apply a recently developed coarse-graining framework for reduced-dimensional descriptions of neuronal networks to model visual cortical dynamics. We show that, without introducing any new parameters, how a sequence of models culminating in an augmented system of spatially-coupled ODEs can effectively model a wide range of the observed cortical dynamics, ranging from visual stimulus orientation dynamics to traveling waves induced by visual illusory stimuli. In addition to an efficient simulation method, this framework also offers an analytic approach to studying large-scale network dynamics. As such, the dimensional reduction naturally leads to mesoscopic variables that capture the interplay between neuronal population stochasticity and network architecture that we believe to underlie many emergent cortical phenomena.
| S-EPMC7304648 | biostudies-literature
Project description:Maximum entropy (MaxEnt) spectral reconstruction methods provide a powerful framework for spectral estimation of nonuniformly sampled datasets. Many methods exist within this framework, usually defined based on the magnitude of a Lagrange multiplier in the MaxEnt objective function. An algorithm is presented here that utilizes accelerated first-order convex optimization techniques to rapidly and reliably reconstruct nonuniformly sampled NMR datasets using the principle of maximum entropy. This algorithm - called CAMERA for Convex Accelerated Maximum Entropy Reconstruction Algorithm - is a new approach to spectral reconstruction that exhibits fast, tunable convergence in both constant-aim and constant-lambda modes. A high-performance, open source NMR data processing tool is described that implements CAMERA, and brief comparisons to existing reconstruction methods are made on several example spectra.
| S-EPMC4818692 | biostudies-literature
Project description:Neural activity coordinated across different scales from neuronal circuits to large-scale brain networks gives rise to complex cognitive functions. Bridging the gap between micro- and macroscale processes, we present a novel framework based on the maximum entropy model to infer a hybrid resting-state structural connectome, representing functional interactions constrained by structural connectivity. We demonstrate that the structurally informed network outperforms the unconstrained model in simulating brain dynamics, wherein by constraining the inference model with the network structure we may improve the estimation of pairwise BOLD signal interactions. Further, we simulate brain network dynamics using Monte Carlo simulations with the new hybrid connectome to probe connectome-level differences in excitation-inhibition balance between apolipoprotein E (APOE)-ε4 carriers and noncarriers. Our results reveal sex differences among APOE-ε4 carriers in functional dynamics at criticality; specifically, female carriers appear to exhibit a lower tolerance to network disruptions resulting from increased excitatory interactions. In sum, the new multimodal network explored here enables analysis of brain dynamics through the integration of structure and function, providing insight into the complex interactions underlying neural activity such as the balance of excitation and inhibition.
| S-EPMC9205431 | biostudies-literature
Project description:Quantiles are available in various problems for developing probability distributions. In some problems quantiles are elicited from experts and used for fitting parametric models, which induce non-elicited information. In some other problems comparisons are made with a quantile of an assumed model which is noncommittal to the quantile information. The maximum entropy (ME) principle provides models that avoid these issues. However, the information theory literature has been mainly concerned about models based on moment information. This paper explores the ME models that are the minimum elaborations of the uniform and moment-based ME models by quantiles. This property provides diagnostics for the utility of elaboration in terms of the information value of each type of information over the other. The ME model with quantiles and moments is represented as the mixture of truncated distributions on consecutive intervals whose shapes and existence are determined by the moments. Elaborations of several ME distributions by quantiles are presented. The ME model based only on quantiles elicited by the fixed interval method possesses a useful property for pooling information elicited from multiple experts. The elaboration of Laplace distribution is an extension of the information theory connection with minimum risk under symmetric loss functions to the asymmetric linear loss. This extension produces a new Asymmetric Laplace distribution. Application examples compare ME priors with a parametric model fitted to elicited quantiles, illustrate measuring uncertainty and disagreement of economic forecasters based on elicited probabilities, and adjust ME models for a fundamental quantile in an inventory management problem.
| S-EPMC7414396 | biostudies-literature
Project description:Recognition of pathogens relies on families of proteins showing great diversity. Here we construct maximum entropy models of the sequence repertoire, building on recent experiments that provide a nearly exhaustive sampling of the IgM sequences in zebrafish. These models are based solely on pairwise correlations between residue positions but correctly capture the higher order statistical properties of the repertoire. By exploiting the interpretation of these models as statistical physics problems, we make several predictions for the collective properties of the sequence ensemble: The distribution of sequences obeys Zipf's law, the repertoire decomposes into several clusters, and there is a massive restriction of diversity because of the correlations. These predictions are completely inconsistent with models in which amino acid substitutions are made independently at each site and are in good agreement with the data. Our results suggest that antibody diversity is not limited by the sequences encoded in the genome and may reflect rapid adaptation to antigenic challenges. This approach should be applicable to the study of the global properties of other protein families.
| S-EPMC2851784 | biostudies-literature
Project description:We introduce a Maximum Entropy model able to capture the statistics of melodies in music. The model can be used to generate new melodies that emulate the style of a given musical corpus. Instead of using the n-body interactions of (n-1)-order Markov models, traditionally used in automatic music generation, we use a k-nearest neighbour model with pairwise interactions only. In that way, we keep the number of parameters low and avoid over-fitting problems typical of Markov models. We show that long-range musical phrases don't need to be explicitly enforced using high-order Markov interactions, but can instead emerge from multiple, competing, pairwise interactions. We validate our Maximum Entropy model by contrasting how much the generated sequences capture the style of the original corpus without plagiarizing it. To this end we use a data-compression approach to discriminate the levels of borrowing and innovation featured by the artificial sequences. Our modelling scheme outperforms both fixed-order and variable-order Markov models. This shows that, despite being based only on pairwise interactions, our scheme opens the possibility to generate musically sensible alterations of the original phrases, providing a way to generate innovation.
| S-EPMC5569059 | biostudies-literature