混交林测树因子概率分布模型的构建及应用

基于最大熵原理,针对目前对混交林测树因子概率分布模型研究的不足,提出了联合最大熵概率密度函数,该函数具有如下特点：1）函数的每一组成部分都是相互联系的最大熵函数,故可以综合混交林各主要组成树种测树因子的概率分布信息;2）函数是具有双权重的概率表达式,能体现混交林结构复杂的特点,在最大限度地利用混交林每一主要树种测树因子概率分布信息的同时,还能精确地全面反映混交林测树因子概率分布规律;3）函数的结构简洁、性能优良.用天目山自然保护区的混交林样地对混交林测树因子概率分布模型进行了应用与检验,结果表明：模型的拟合精度(R²=0.9655)与检验精度(R²=
0.9772)都较高.说明联合最大熵概率密度函数可以作为混交林测树因子概率分布模型,为全面了解混交林林分结构提供了一种可行的方法.     

最大信息熵原理与群体遗传平衡

建立了用最大信息熵原理推导群体遗传平衡定律的统一数学模型,并给出了模型的统一解,此解正是Hardy-Weinberg定律所给出的平衡群体的基因型频率,说明当群体信息熵达到最大时,群体基因型频率不再变化,即达到“平衡”。这证明了最大熵分布就是Hardy-Weinberg平衡分布。Hardy-Weinberg平衡定律与最大信息熵原理的内在一致性说明,杂交和随机交配是一个不可逆过程,使群体基因型信息熵增大,无序性增,是选择和近亲交配使群体的信息熵降低,有序性增加,育种过程实际就是调节群体信息熵的过程。过程信息熵的含义是表示一个概率分布的不确定性,最大熵原理意味着在一定的约束条件,选择具有最大不确定性的分布,从而其分布是最为随机的。最大熵原理在信息,工程,天文,地理,图像处理,模式识别等自然科学和社会科学领域都有广泛的成功应用,本文从群体遗传学角度证明了这一原理具有普遍适用性。熵是描述系统状态的函数,而最大熵原理则表明了系统发展变化的趋势,系统的最终状态必然是熵增加至最大值的状态,对于任何系统都是如此。因此,群体遗传系统的平衡定律可以统一用最大熵原理进行判定和描述;任意群体的基因型信息熵在随机交配世代传递时有不断增加的趋势;在一定约束条件下基因型信息熵达到最大值时,就称之为达到遗传平衡。本文将信息论原理应用于群体遗传学研究,揭示了基因信息熵的生物学意义,并表明可以用信息学和控制论的原理和方法来研究群体遗传学问题。     

基于Agent模型的生态公平指数构建与模拟

伴随着社会经济的发展,社会公平逐渐成为热点话题。社会公平问题不但体现在社会现象上,还对生态系统起着重要的影响。通过构建资本交换自主体模型,模拟社会财富分配动态过程,可观测资本交换熵指数变化情况,从而解释熵增原理。除此以外,不同系统的最终状态能达到的最大熵指数不同,用熵增原理与本文构建的最大熵指数模型可以对系统的生态公平进行纵向或横向评价。构建的资本交换熵模型也可以证明最大熵原理,同时,财富集中的现象将会使生态环境的选择权完全交予富人群体,影响可持续发展。     

Limitations of entropy maximization in ecology: a reply to Haegeman and Loreau

Haegeman and Loreau published a paper that is primarily a criticism of a maximum entropy model of trait-based community assembly (by Shipley et al.) and purports to show the limitations of this method in ecology. However, they misunderstood the basic purpose, logic and justification of the maximum entropy formalism and, because of this, leveled criticisms of Shipley et al. that are unfounded. Part of the confusion can be traced to sloppy presentation of the underlying approach in Shipley et al. The confusion arises because maximum entropy models are justified based on information theory and Bayesian logic while the interpretation that Haegeman and Loreau present is based on substantive empirical assumptions about microstate allocations and a combinatorial argument that do not apply to maximum entropy models and which I do not apply to my model in particular.     

关于最大信息熵原理与群体遗传平衡一致性的探讨

汪小龙等建立了用最大信息熵原理推导一个基因座上群体遗传平衡的统一数学模型,并给出了模型的最大值解,此解正是Hardy-Weinberg平衡定律所给出的基因型频率。这说明当群体基因型信息熵最大时,群体基因型频率不再变化,达到平衡状态,从而证明了最大信息熵原理与Hardy-Weinberg平衡定律具有一致性,同时指出这一结论可以推广至有迁移、突变、选择、遗传漂变、近亲交配的群体以及多个基因座情形。概括地说就是：最大信息熵原理与群体遗传平衡具有一致性。但是,他们仅仅证明了最大信息熵原理与一个基因座上Hardy-Weinberg平衡定律具有一致性,本文在这个范围内将其推广至多个基因座,且每一个基因座均为复等位基因情形。至于最大信息熵原理是否与其它的群体遗传平衡具有一致性,他们的结论仅仅是猜想,并未严格推导。事实上,要想将这种一致性推广到迁移、突变、随机漂变和近亲交配等群体,则不见得正确。      

Maximum entropy,logistic regression,and species abundance

There is considerable debate about the utility of statistical mechanics in predicting diversity patterns in terms of life history traits. Here, I reflect on this debate and show that a community is controlled by the balance of two opposite forces: the entropic part (the natural tendency of the system to be in the configuration with the highest possible entropy) and environmental, ecological and evolutionary constraints maintaining order (reducing entropy). The Boltzmann distribution law that can be derived from the maximum entropy formalism provides a fundamental model for linking species abundance to life history traits and environmental constraining factors. This model predicts a global pattern of diversity evenness along a latitudinal gradient. Although the Boltzmann distribution and the logistic regression models represent two fundamentally different approaches, the two models have an identical mathematical form. Their identical formalisms facilitate the interpretation of logistic regression models with statistical mechanics, and reveal several limitations of the maximum entropy formalism. I argued that although maximum entropy formalism is a promising tool for modeling species abundances and for linking microscopic quantities of individual life history traits to macroscopic patterns of diversity, it is necessary to revise the Boltzmann distribution law for successful prediction of species abundance.     

A theoretical method for distinguishing between soluble and membrane proteins

A method for distinguishing between membrane and soluble proteins in an amino acid sequence was developed, using only two parameters associated with the hydrophobicity: the average hydrophobicity and the power spectral density of period longer than 30 residues. The power spectral density was calculated by a maximum entropy method of Fourier transformation. Membrane proteins could be distinguished from soluble proteins with a distinction rate as high as 97%. This fact strongly suggests that the morphology of proteins, i.e., membrane or soluble forms, is determined thermodynamically through the hydrophobicity of polypeptides.     

Enzyme kinetics and the maximum entropy production principle

A general proof is derived that entropy production can be maximized with respect to rate constants in any enzymatic transition. This result is used to test the assumption that biological evolution of enzyme is accompanied with an increase of entropy production in its internal transitions and that such increase can serve to quantify the progress of enzyme evolution. The state of maximum entropy production would correspond to fully evolved enzyme. As an example the internal transition ES?EP in a generalized reversible Michaelis-Menten three state scheme is analyzed. A good agreement is found among experimentally determined values of the forward rate constant in internal transitions ES→EP for three types of β-Lactamase enzymes and their optimal values predicted by the maximum entropy production principle, which agrees with earlier observations that β-Lactamase enzymes are nearly fully evolved. The optimization of rate constants as the consequence of basic physical principle, which is the subject of this paper, is a completely different concept from a) net metabolic flux maximization or b) entropy production minimization (in the static head state), both also proposed to be tightly connected to biological evolution.     

Entropy convergence in hydrophobic hydration: a scaled particle theory analysis

The occurrence of entropy convergence in hydrophobic hydration is verified from available experimental thermodynamic data for both noble gases and hydrocarbons. The entropy convergence phenomenon can be reproduced by means of the scaled particle theory, provided that a temperature-dependent hard sphere diameter is used for water molecules. The calculated work of cavity creation shows a non-monotonic temperature dependence with a flat maximum slightly above 100 degrees C, irrespective of the cavity size. The corresponding cavity entropy changes converge approximately 100 degrees C, in qualitative agreement with the experimental finding.     

ConFind: a robust tool for conserved sequence identification

SUMMARY: ConFind (conserved region finder) identifies regions of conservation in multiple sequence alignments that can serve as diagnostic targets. Designed to work with a large number of closely related, highly variable sequences, ConFind provides robust handling of alignments containing partial sequences and ambiguous characters. Conserved regions are defined in terms of minimum region length, maximum informational entropy (variability) per position, number of exceptions allowed to the maximum entropy criterion and the minimum number of sequences that must contain a non-ambiguous character at a position to be considered for inclusion in a conserved region. Comparison of the calculated entropy for an alignment of 95 influenza A hemagglutinin sequences with random deletions results in a 98% reduction in the average error in ConFind relative to the 'Find Conserved Regions' option in BioEdit. REQUIREMENTS: ConFind requires Python 2.3, but Python 2.4 or an upgrade of the optparse module to Optik 1.5 is suggested. The program is known to run under Linux and DOS.     

Metabolic networks evolve towards states of maximum entropy production

A metabolic network can be described by a set of elementary modes or pathways representing discrete metabolic states that support cell function. We have recently shown that in the most likely metabolic state the usage probability of individual elementary modes is distributed according to the Boltzmann distribution law while complying with the principle of maximum entropy production. To demonstrate that a metabolic network evolves towards such state we have carried out adaptive evolution experiments with Thermoanaerobacterium saccharolyticum operating with a reduced metabolic functionality based on a reduced set of elementary modes. In such reduced metabolic network metabolic fluxes can be conveniently computed from the measured metabolite secretion pattern. Over a time span of 300 generations the specific growth rate of the strain continuously increased together with a continuous increase in the rate of entropy production. We show that the rate of entropy production asymptotically approaches the maximum entropy production rate predicted from the state when the usage probability of individual elementary modes is distributed according to the Boltzmann distribution. Therefore, the outcome of evolution of a complex biological system can be predicted in highly quantitative terms using basic statistical mechanical principles.     

Maximum entropy modeling of short sequence motifs with applications to RNA splicing signals.

We propose a framework for modeling sequence motifs based on the maximum entropy principle (MEP). We recommend approximating short sequence motif distributions with the maximum entropy distribution (MED) consistent with low-order marginal constraints estimated from available data, which may include dependencies between nonadjacent as well as adjacent positions. Many maximum entropy models (MEMs) are specified by simply changing the set of constraints. Such models can be utilized to discriminate between signals and decoys. Classification performance using different MEMs gives insight into the relative importance of dependencies between different positions. We apply our framework to large datasets of RNA splicing signals. Our best models out-perform previous probabilistic models in the discrimination of human 5' (donor) and 3' (acceptor) splice sites from decoys. Finally, we discuss mechanistically motivated ways of comparing models.     

Application of the maximum entropy method to absorption kinetic rate processes

The maximum entropy method, originally developed for astronomical image restoration, has already been successfully applied to a variety of biophysical problems. Through numerical inverse Laplace transformation, the method determines the lifetime distribution function with the largest informational entropy. Starting from a flat distribution, it results in the consistent selection of a single distribution from the numerous possible ones that correctly fit the data. In this paper, we discuss the application of the method to kinetic processes that have both rise and decay components, and test the algorithm with different signal to noise ratio generated data. It is proved that the mass conservation constraint can be taken into account by reducing the search to a lower dimensional subspace. The effect of noise on the width of lifetime distribution is studied and it is shown that an inherent entropy connected to the underlying kinetics can be separated from the noise generated entropy. The possibility of the application of the method to the photocycle kinetics of bacteriorhodopsin is also shown.     

Pf1 Inovirus. Electron density distribution calculated by a maximum entropy algorithm from native fibre diffraction data to 3 A resolution and single isomorphous replacement data to 5 A resolution

We have calculated the electron density distribution of the Pf1 strain of filamentous bacteriophage by a maximum entropy method. In the calculation we included native X-ray fibre diffraction data extending to 3 A resolution in the meridional direction on 60 layerlines that are resolved to 4 A in the equatorial direction, and lower resolution data from a single isomorphous derivative iodinated on the Tyr25 residue. The electron density map indicates that the 46-residue protein subunit is a single, gently curved stretch of alpha-helix with its axis at an angle of about 20 degrees to the axis of the virion. The alpha-helix subunit curves around the virion axis by about 1/6 turn, and decreases from about 27 A radius to about 13 A radius in the virion as the amino acid sequence of the subunit runs from the N terminus to the C terminus. Nearest-neighbour alpha-helical subunits are about 10 A apart along their length, and the axis of each subunit makes an unexpected negative angle with its nearest neighbours in the virion. To confirm the validity of the maximum entropy calculation, we have varied the constraints on the calculation. All variations result in either a map that is close to the original map or a map that cannot be interpreted in terms of secondary structure: we find only one map that makes structural sense.     

Determination of the spatial characteristics of an RF electrodeless discharge by the method of emission tomography

The spatial distribution of the density of mercury atoms in the 7³ S state in a spherical RF electrode-less gas-discharge lamp is reconstructed by the method of emission tomography. The local values of the corresponding emission coefficients, which are proportional to the density of mercury atoms in the 7³ S state, are determined from integral (over the plasma volume) measurements of the lamp radiation at a wavelength of 546.1 nm with the help of an algorithm based on the maximum entropy method. The results obtained show that, for all of the operating modes under study, the profile of the density of mercury atoms in the 7³ S state has a minimum in the center of the lamp and a maximum near its wall. At a generator current of 100 mA and cold-spot temperature of 41°C, the density of mercury atoms in the 7³ S state is observed to drop substantially both in the center of the lamp and near its wall, the density in the center being reduced to almost zero. An explanation of this phenomenon is proposed.     

Ecological significance of root tip rotation for seedling establishment of Oryza sativa L

How plant seeds secure root penetration into soil to obtain good seedling establishment is one of the basic ecological problems. In this study, seminal root growth was investigated to clarify the cause of varietal difference of seedling establishment in direct seeding of rice in flooded paddy fields, with special reference to root tip rotation. In a field experiment, seedling establishment percentage had a weak correlation with seminal root elongation rate but was not correlated with apparent seedling weight in water, which has been reported to be the cause of floating seedlings resulting in poor seedling establishment. Root tip rotation was analyzed for indoor-grown seedlings using spectrum analysis: the maximum entropy method (MEM) was used. Maximum entropy method power spectrum analysis clarified that maximum MEM power density (practically corresponds to spiral angle) detected in the frequency range above 0.1 cycles mm^-1 was highly and positively correlated to seedling establishment percentage in the field experiment. Maximum MEM power density in high correlation with seedling establishment was mostly found around frequencies of 0.2 cycles mm^–1, which corresponded to 2.0–3.4 cycles of root tip rotation per day. From these results, root tip rotation (circumnutation) with a larger spiral angle was suggested to play an important role in the establishment of rice seedlings on flooded and very soft soil. A possible explanation for why a larger spiral angle was advantageous for seedling establishment is that if buoyancy and seedling weight are constant, a larger pushing force of the seminal root is available without causing floating of a seedling, due to the upward force being a reaction of the seminal root pushing force.     

Estimation by Maximum Entropy Subject to Second-Order Conditions

If the variance, V = V(μ, ?) is some known function of the mean, μ = μ(β), where ? and β may include unknown parameters, then given empirical data, this paper describes how to estimate the unknown parameters by choosing them to satisfy the variance/mean relationship, and simultaneously to require that the sampling probability distribution has maximum entropy. Bounds for the estimated values of the unknown parameters can be obtained by a further application of the maximum entropy principle. The power variance function, V(μ)=λμ^? is discussed, including some special cases of λ and ?. The procedure is briefly compared with quasi- likelihood, and illustrated by some numerical examples.     

A maximum entropy criterion of filtering and coding for stationary autoregressive signals: Its physical interpretations and suggestions for its application to neural information transmission

The operations of encoding and decoding in communication agree with filtering operations of convolution and deconvolution for Gaussian signal processing. In an analogy with power transmission in thermodynamics, an autoregressive model of information transmission is proposed for representing a continuous communication system which requires a pair of an internal noise source and a signal source to encode or decode a message. In this model transinformation (informational entropy) equals the increase in stationary nonequilibrium organization formed through the amplification of white noise by a positive feedback system. The channel capacity is finite due to the existence of inherent noise in the system. The maximum entropy criterion in information dynamics corresponds to the 2^nd law of thermodynamics. If the process is stationary, the communication system is invertible, and has the maximum efficiency of transformation. The total variation in informational entropy is zero in the cycle of the invertible system, while in the noninvertible system the entropy of decoding is less than that of encoding. A noisy autoregressive coding which maximizes transinformation is optimum, but is also ideal.     

A simple derivation and classification of common probability distributions based on information symmetry and measurement scale

Commonly observed patterns typically follow a few distinct families of probability distributions. Over one hundred years ago, Karl Pearson provided a systematic derivation and classification of the common continuous distributions. His approach was phenomenological: a differential equation that generated common distributions without any underlying conceptual basis for why common distributions have particular forms and what explains the familial relations. Pearson's system and its descendants remain the most popular systematic classification of probability distributions. Here, we unify the disparate forms of common distributions into a single system based on two meaningful and justifiable propositions. First, distributions follow maximum entropy subject to constraints, where maximum entropy is equivalent to minimum information. Second, different problems associate magnitude to information in different ways, an association we describe in terms of the relation between information invariance and measurement scale. Our framework relates the different continuous probability distributions through the variations in measurement scale that change each family of maximum entropy distributions into a distinct family. From our framework, future work in biology can consider the genesis of common patterns in a new and more general way. Particular biological processes set the relation between the information in observations and magnitude, the basis for information invariance, symmetry and measurement scale. The measurement scale, in turn, determines the most likely probability distributions and observed patterns associated with particular processes. This view presents a fundamentally derived alternative to the largely unproductive debates about neutrality in ecology and evolution.     

Analysis of brush-particle interactions using self-consistent-field theory

Non-specific protein adsorption can be reduced by attaching polymer chains by one end to a sorbent surface. End-grafted polymer modified surfaces have also found application in size-based chromatographic bioseparations. To better understand how to tailor surfaces for these applications, a numerical SCF model has been used to calculate theoretical results for the polymer density distribution of interacting polymer chains around a solute particle positioned at a fixed distance from a surface. In addition, the excess energy required to move the particle into the polymer chains (interaction energy) is calculated using a statistical mechanical treatment of the lattice model. The effect of system variables such as particle size, chain length, surface density and Flory interaction parameters on density distributions and interaction energies is also studied. Calculations for the interaction of a solute particle with a surface covered by many polymer chains (a brush) show that the polymer segments will fill in behind the particle quite rapidly as it moves toward the surface. When there is no strong energetic attraction between the polymer and solute we predict that the interaction energy will be purely repulsive upon compression due to losses in conformational entropy of the polymer chains. Above a critical chain length, which depends upon particle size, a maximum in the force required to move the particle toward the surface is observed due to an engulfment of the particle as chains attempt to access the free volume behind the particle. If an attraction exists between the polymer and solute, such that a minimum in the interaction energy is seen, the optimum conditions for solute repulsion occur at the highest surface density attainable. Long chain length can lead to increased solute concentration within the polymer layer due to the fact that an increased number of favourable polymer–solute contacts are able to occur than with short chains at a similar entropic penalty.