Generating probabilistic boolean networks from a prescribed transition probability matrix

Probabilistic Boolean networks (PBNs) have received much attention in modeling genetic regulatory networks. A PBN can be regarded as a Markov chain process and is characterised by a transition probability matrix. In this study, the authors propose efficient algorithms for constructing a PBN when its transition probability matrix is given. The complexities of the algorithms are also analysed. This is an interesting inverse problem in network inference using steady-state data. The problem is important as most microarray data sets are assumed to be obtained from sampling the steady-state.     

Detecting small attractors of large Boolean networks by function‐reduction‐based strategy

Boolean networks (BNs) are widely used to model gene regulatory networks and to design therapeutic intervention strategies to affect the long‐term behaviour of systems. A central aim of Boolean‐network analysis is to find attractors that correspond to various cellular states, such as cell types or the stage of cell differentiation. This problem is NP‐hard and various algorithms have been used to tackle it with considerable success. The idea is that a singleton attractor corresponds to n consistent subsequences in the truth table. To find these subsequences, the authors gradually reduce the entire truth table of Boolean functions by extending a partial gene activity profile (GAP). Not only does this process delete inconsistent subsequences in truth tables, it also directly determines values for some nodes not extended, which means it can abandon the partial GAPs that cannot lead to an attractor as early as possible. The results of simulation show that the proposed algorithm can detect small attractors with length p = 4 in BNs of up to 200 nodes with average indegree K = 2.Inspec keywords: Boolean functions, genetics, cellular biophysicsOther keywords: detecting small attractors, function‐reduction‐based strategy, model gene regulatory networks, therapeutic intervention strategies, Boolean‐network analysis, cellular states, NP‐hard, singleton attractor, Boolean functions, partial gene activity profile, cell differentiation     

Integer programming‐based method for observability of singleton attractors in Boolean networks

Boolean network (BN) is a popular mathematical model for revealing the behaviour of a genetic regulatory network. Furthermore, observability, an important network feature, plays a significant role in understanding the underlying network. Several studies have been done on analysis of observability of BNs and complex networks. However, the observability of attractor cycles, which can serve as biomarker detection, has not yet been addressed in the literature. This is an important, interesting and challenging problem that deserves a detailed study. In this study, a novel problem was first proposed on attractor observability in BNs. Identification of the minimum set of consecutive nodes can be used to discriminate different attractors. Furthermore, it can serve as a biomarker for different disease types (represented as different attractor cycles). Then a novel integer programming method was developed to identify the desired set of nodes. The proposed approach is demonstrated and verified by numerical examples. The computational results further illustrates that the proposed model is effective and efficient.Inspec keywords: integer programming, Boolean algebra, complex networks, diseasesOther keywords: disease, consecutive nodes, biomarker detection, attractor cycles, complex networks, genetic regulatory network, mathematical model, Boolean networks, singleton attractors, integer programming‐based method     

Optimal control policy for probabilistic Boolean networks with hard constraints

It is well known that the control/intervention of some genes in a genetic regulatory network is useful for avoiding undesirable states associated with some diseases like cancer. For this purpose, both optimal finitehorizon control and infinite-horizon control policies have been proposed. Boolean networks (BNs) and its extension probabilistic Boolean networks (PBNs) as useful and effective tools for modelling gene regulatory systems have received much attention in the biophysics community. The control problem for these models has been studied widely. The optimal control problem in a PBN can be formulated as a probabilistic dynamic programming problem. In the previous studies, the optimal control problems did not take into account the hard constraints, i.e. to include an upper bound for the number of controls that can be applied to the captured PBN. This is important as more treatments may bring more side effects and the patients may not bear too many treatments. A formulation for the optimal finite-horizon control problem with hard constraints introduced by the authors. This model is state independent and the objective function is only dependent on the distance between the desirable states and the terminal states. An approximation method is also given to reduce the computational cost in solving the problem. Experimental results are given to demonstrate the efficiency of our proposed formulations and methods.     

On Construction of Sparse Probabilistic Boolean Networks

In this paper we envisage building Probabilistic Boolean Networks (PBNs) from a prescribed stationary distribution. This is an inverse problem of huge size that can be subdivided into two parts — viz. (i) construction of a transition probability matrix from a given stationary distribution (Problem ST), and (ii) construction of a PBN from a given transition probability matrix (Problem TP). A generalized entropy approach has been proposed for Problem ST and a maximum entropy rate approach for Problem TP respectively. Here we propose to improve both methods, by considering a new objective function based on the entropy rate with an additional term of $L_α$-norm that can help in getting a sparse solution. A sparse solution is useful in identifying the major component Boolean networks (BNs) from the constructed PBN. These major BNs can simplify the identification of the network structure and the design of control policy, and neglecting non-major BNs does not change the dynamics of the constructed PBN to a large extent. Numerical experiments indicate that our new objective function is effective in finding a better sparse solution.     

Unipolar terminal-attractor-based neural associative memory with adaptive threshold and perfect convergence

A perfectly convergent unipolar neural associative-memory system based on nonlinear dynamical terminal attractors is presented. With adaptive setting of the threshold values for the dynamic iteration for the unipolar binary neuron states with terminal attractors, perfect convergence is achieved. This achievement and correct retrieval are demonstrated by computer simulation. The simulations are completed (1) by exhaustive tests with all of the possible combinations of stored and test vectors in small-scale networks and (2) by Monte Carlo simulations with randomly generated stored and test vectors in large-scale networks with an M/N ratio of 4 (M is the number of stored vectors; N is the number of neurons ≤ 256). An experiment with exclusive-oR logic operations with liquid-crystal-television spatial light modulators is used to show the feasibility of an optoelectronic implementation of the model. The behavior of terminal attractors in basins of energy space is illustrated by examples.     

Construction of Probabilistic Boolean Networks from a Prescribed Transition Probability Matrix: A Maximum Entropy Rate Approach

Modeling genetic regulatory networks is an important problem in genomic research. Boolean Networks (BNs) and their extensions Probabilistic Boolean Networks (PBNs) have been proposed for modeling genetic regulatory interactions. In a PBN, its steady-state distribution gives very important information about the long-run behavior of the whole network. However, one is also interested in system synthesis which requires the construction of networks. The inverse problem is ill-posed and challenging, as there may be many networks or no network having the given properties, and the size of the problem is huge. The construction of PBNs from a given transition-probability matrix and a given set of BNs is an inverse problem of huge size. We propose a maximum entropy approach for the above problem. Newton’s method in conjunction with the Conjugate Gradient (CG) method is then applied to solving the inverse problem. We investigate the convergence rate of the proposed method. Numerical examples are also given to demonstrate the effectiveness of our proposed method.     

Computational complexity of spin-glass three-dimensional(3D) Ising model

In this work, the computational complexity of a spin-glass three-dimensional(3 D) Ising model(for the lattice size N = lmn, where l, m, n are the numbers of lattice points along three crystallographic directions) is studied. We prove that an absolute minimum core(AMC) model consisting of a spin-glass 2 D Ising model interacting with its nearest neighboring plane, has its computational complexity O(2 mn). Any algorithms to make the model smaller(or simpler) than the AMC model will cut the basic element of the spin-glass3 D Ising model and lost many important information of the original model. Therefore, the computational complexity of the spin-glass 3 D Ising model cannot be reduced to be less than O(2 mn) by any algorithms,which is in subexponential time, superpolynomial.     

The decolorization and mineralization of acid orange 6 azo dye in aqueous solution by advanced oxidation processes: a comparative study

The comparison of different advanced oxidation processes (AOPs), i.e. ultraviolet (UV)/TiO(2), O(3), O(3)/UV, O(3)/UV/TiO(2), Fenton and electrocoagulation (EC), is of interest to determine the best removal performance for the destruction of the target compound in an Acid Orange 6 (AO6) solution, exploring the most efficient experimental conditions as well; on the other hand, the results may provide baseline information of the combination of different AOPs in treating industrial wastewater. The following conclusions can be drawn: (1) in the effects of individual and combined ozonation and photocatalytic UV irradiation, both O(3)/UV and O(3)/UV/TiO(2) processes exhibit remarkable TOC removal capability that can achieve a 65% removal efficiency at pH 7 and O(3) dose=45mg/L; (2) the optimum pH and ratio of [H(2)O(2)]/[Fe(2+)] found for the Fenton process, are pH 4 and [H(2)O(2)]/[Fe(2+)]=6.58. The optimum [H(2)O(2)] and [Fe(2+)] under the same HF value are 58.82 and 8.93mM, respectively; (3) the optimum applied voltage found in the EC experiment is 80V, and the initial pH will affect the AO6 and TOC removal rates in that acidic conditions may be favorable for a higher removal rate; (4) the AO6 decolorization rate ranking was obtained in the order of O(3)相似文献   

Influence of spinel substrate and over-layer for enhanced SAW and AO properties with KNbO3 thin film

Surface acoustic wave (SAW) propagation characteristics have been studied using modeling calculations for a potassium niobate (KNbO/sub 3/) thin film-layered structure with [001] and [110] orientation on a single crystal spinel (MgAl/sub 2/O/sub 4/) substrate, and a spinel buffer layer on silicon. Variation in the electromechanical coupling and acoustic attenuation has been compared. A significantly high value of coupling factor (k/sub max//sup 2/=23%) is obtained for the [001]KNbO/sub 3//spinel structure by introducing an optimum thickness of spinel over-layer for potential wide bandwidth SAW device applications. The dispersion characteristics with the [110] KNbO/sub 3/ orientation indicate an initial peak in the coupling coefficient value (k/sub max//sup 2/=8.8%) at a relatively low KNbO/sub 3/ film thickness that appears attractive for fabricating devices with thinner films. The KNbO/sub 3/ film with [001] orientation is found attractive for efficient acousto-optic (AO) device application with the formation of a symmetric waveguide structure (spinel(0.5 /spl mu/m)/KNbO/sub 3/(1.0 /spl mu/m)/spinel). A high value of k/sup 2/=23.5% with 50% diffraction efficiency has been obtained for the spinel(0.5 /spl mu/m)/KNbO/sub 3/(1.0 /spl mu/m)/spinel structure at 1 GHz SAW frequency and 633 nm optical wavelength at a very low input drive power of 15.4 mW.     

Stochastic assembly of sublithographic nanoscale interfaces

We describe a technique for addressing individual nanoscale wires with microscale control wires without using lithographic-scale processing to define nanoscale dimensions. Such a scheme is necessary to exploit sublithographic nanoscale storage and computational devices. Our technique uses modulation doping to address individual nanowires and self-assembly to organize them into nanoscale-pitch decoder arrays. We show that if coded nanowires are chosen at random from a sufficiently large population, we can ensure that a large fraction of the selected nanowires have unique addresses. For example, we show that N lines can be uniquely addressed over 99% of the time using no more than /spl lceil/2.2log/sub 2/(N)/spl rceil/+11 address wires. We further show a hybrid decoder scheme that only needs to address N=O(W/sub litho-pitch//W/sub nano-pitch/) wires at a time through this stochastic scheme; as a result, the number of unique codes required for the nanowires does not grow with decoder size. We give an O(N/sup 2/) procedure to discover the addresses which are present. We also demonstrate schemes that tolerate the misalignment of nanowires which can occur during the self-assembly process.     

On Generating Optimal Sparse Probabilistic Boolean Networks with Maximum Entropy from a Positive Stationary Distribution

To understand a genetic regulatory network, two popular mathematical models, Boolean Networks (BNs) and its extension Probabilistic Boolean Networks (PBNs) have been proposed. Here we address the problem of constructing a sparse Probabilistic Boolean Network (PBN) from a prescribed positive stationary distribution. A sparse matrix is more preferable, as it is easier to study and identify the major components and extract the crucial information hidden in a biological network. The captured network construction problem is both ill-posed and computationally challenging. We present a novel method to construct a sparse transition probability matrix from a given stationary distribution. A series of sparse transition probability matrices can be determined once the stationary distribution is given. By controlling the number of nonzero entries in each column of the transition probability matrix, a desirable sparse transition probability matrix in the sense of maximum entropy can be uniquely constructed as a linear combination of the selected sparse transition probability matrices (a set of sparse irreducible matrices). Numerical examples are given to demonstrate both the efficiency and effectiveness of the proposed method.     

基于复合形算子的基础支护桩优化设计智能算法研究

本文通过遗传算法和传统复合形搜索法相结合,基于对遗传算法算子计算结构的调整,并将遗传算法与神经网络相结合,提出并研究了一种新的优化设计方法,协同求解复杂工程中的优化问题。并针对悬臂式支护桩的优化设计的数学模型,采用该算法进行了优化设计分析;计算结果表明,该算法可克服遗传算法最终进化至最优解较慢和人工神经网络易陷入局部解的缺陷,具有较好的全局性和收敛速度。     

The dependence of the optoelectrical properties of silver nanowire networks on nanowire length and diameter

We have characterized the optoelectrical properties of networks of silver nanowires as a function of nanowire dimension by measuring transmittance (T) and sheet resistance (R(s)) for a large number of networks of different thicknesses fabricated from wires of different diameters (D) and lengths (L). We have analysed these data using both bulk-like and percolative models. We find the network DC conductivity to scale linearly with wire length while the optical conductivity is approximately invariant with nanowire length. The ratio of DC to optical conductivity, often taken as a figure of merit for transparent conductors, scales approximately as L/D. Interestingly, the percolative exponent, n, scales empirically as D2, while the percolative figure of merit, Π, displays large values at low D. As high T and low R(s) are associated with low n and high Π, these data are consistent with improved optoelectrical performance for networks of low-D wires. We predict that networks of wires with D = 25 nm could give sheet resistance as low as 25 Ω/□ for T = 90%.     

Agent-based computational modeling of wounded epithelial cell monolayers

Computational modeling of biological systems, or in silico biology, is an emerging tool for understanding structure and order in biological tissues. Computational models of the behavior of epithelial cells in monolayer cell culture have been developed and used to predict the healing characteristics of scratch wounds made to urothelial cell cultures maintained in low- and physiological [Ca/sup 2+/] environments. Both computational models and in vitro experiments demonstrated that in low exogenous [Ca/sup 2+/], the closure of 500-/spl mu/m scratch wounds was achieved primarily by cell migration into the denuded area. The wound healing rate in low (0.09 mM) [Ca/sup 2+/] was approximately twice as rapid as in physiological (2 mM) [Ca/sup 2+/]. Computational modeling predicted that in cell cultures that are actively proliferating, no increase in the fraction of cells in the S-phase would be expected, and this conclusion was supported experimentally in vitro by bromodeoxyuridine incorporation assay. We have demonstrated that a simple rule-based model of cell behavior, incorporating rules relating to contact inhibition of proliferation and migration, is sufficient to qualitatively predict the calcium-dependent pattern of wound closure observed in vitro. Differences between the in vitro and in silico models suggest a role for wound-induced signaling events in urothelial cell cultures.     

Dispersion of solute by electrokinetic flow through post arrays and wavy-walled channels

In this work, we simulate electrokinetically driven transport of unretained solute bands in a variety of two-dimensional spatially periodic geometries (post arrays as well as sinuous/varicose channels), in the thin Debye layer limit. Potential flow fields are calculated using either an inverse method or a Schwarz-Christoffel transform, and transport is modeled using a Monte Carlo method in the transformed plane. In this way, spurious "numerical diffusion" transverse to streamlines is completely eliminated, and streamwise numerical diffusion is reduced to arbitrary precision. Late-time longitudinal dispersion coefficients are calculated for Peclet numbers from 0.1 to 3162. In most geometries, a Taylor-Aris-like scaling law for the dispersion coefficient D(L)/D(L0) = 1 + Pe2/alpha underpredicts dispersion when Pe approximately O(alpha1/2) (here D(L0) is the effective axial diffusion coefficient in the periodic geometry). A two-parameter correlation widely used in the porous media literature, D(L)/D(L0) = 1 + Pe(n)/alpha, agrees slightly better, but much better agreement can be obtained using a new quadratic form: D(L)/D(L0) = 1 + Pe/alpha1 + Pe2/alpha2. A quasi-universal relationship for stream-wise dispersion is offered that predicts 96% of the simulation data to within a factor of 2 in all geometries studied. Comparison with previous work shows that in circular post arrays, the dispersion coefficient for electrokinetic flow is a factor of 3-10 less (depending on Pe and relative post size) than for pressure-driven flow.     

Asymmetrical spectral curvature algorithms: oceanic-constituents sensitivities

The asymmetrical spectral curvature algorithm for Morel case 1 waters has been characterized by application of the semianalytical radiance model of ocean color to post-Coastal Zone Color Scanner (CZCS) sensor bands. Results of the study suggest that the [L (490)/L (443)][L (490)/L (555)] asymmetrical spectral curvature algorithm has a higher pigment-retrieval sensitivity than does the [L (490)/L (443)][L (490)/L (510)] curvature algorithm that was initially identified for pigment recovery. When this [L (490)/L (443)][L (490)/L (555)] algorithm was highlighted for study, it was found to (a) xhibit pigment-retrieval sensitivity that is intermediate to the [L (443)/L (555)] and the [L (510)/L (555)] CZCS-type radiance-ratio algorithms, (b) have less sensitivity to nonabsorbing particulate backscatter (NAB) than the [L (443)/L (555)] radiance ratio, (c) display remarkable insensitivity to the absorption of dissolved organic material (DOM), and (d) possess a NAB invariance point at an algorithm value of ～1.8 (corresponding to a pigment concentration of ～0.35 mg/M(3)). At this invariance point the [L (490)/L (443)][L (490)/L (555)] algorithm is insensitive to a wide concentration range of coccolith-like backscatterers in addition to being insensitive to DOM. The dual DOM and NAB insensitivity of the algorithm at a specific curvature value and chlorophyllous-pigment concentration suggests that such invariance points should be further studied for possible use in (1) the validation of other chlorophyllouspigment algorithms or model inversions and (2) the computation of other inherent optical properties.     

On approximate stochastic control in genetic regulatory networks

The control of probabilistic Boolean networks as a model of genetic regulatory networks is formulated as an optimal stochastic control problem and has been solved using dynamic programming; however, the proposed methods fail when the number of genes in the network goes beyond a small number. There are two dimensionality problems. First, the complexity of optimal stochastic control exponentially increases with the number of genes. Second, the complexity of estimating the probability distributions specifying the model increases exponentially with the number of genes. We propose an approximate stochastic control method based on reinforcement learning that mitigates the curses of dimensionality and provides polynomial time complexity. Using a simulator, the proposed method eliminates the complexity of estimating the probability distributions and, because the method is a model-free method, it eliminates the impediment of model estimation. The method can be applied on networks for which dynamic programming cannot be used owing to computational limitations. Experimental results demonstrate that the performance of the method is close to optimal stochastic control.     

Hydrodynamics at the smallest scales: a solvability criterion for Navier-Stokes equations in high dimensions

Strong global solvability is difficult to prove for high-dimensional hydrodynamic systems because of the complex interplay between nonlinearity and scale invariance. We define the Ladyzhenskaya-Lions exponent α(L)(n)=(2+n)/4 for Navier-Stokes equations with dissipation -(-Δ)(α) in R(n), for all n≥2. We review the proof of strong global solvability when α≥α(L)(n), given smooth initial data. If the corresponding Euler equations for n>2 were to allow uncontrolled growth of the enstrophy (1/2)∥?u∥(L2)(2), then no globally controlled coercive quantity is currently known to exist that can regularize solutions of the Navier-Stokes equations for α<α(L)(n). The energy is critical under scale transformations only for α=α(L)(n).     

Thickness-dependent leakage current of (polyvinylidene fluoride/lead titanate) pyroelectric detectors

The novel pyroelectric IR detectors have been fabricated using the Polyvinylidene Fluoride (PVDF)/Lead Titanate (PT) pyroelectric bilayer thin films, which were deposited onto Pt(111)/SiO/sub 2//Si(100) substrates by a sol-gel process. The ceramic/polymer structure was constructed of the randomly oriented polycrystalline PT film (/spl sim/1 /spl mu/m) heated at 700/spl deg/C for 1 h and the /spl beta/-phase PVDF film crystallized at 65/spl deg/C for 2 h. The effects of PVDF thin film thickness (100 /spl sim/ 580 nm) on the pyroelectric response of IR detectors were studied. The results show that the depositions of PVDF thin films onto the PT films will cause the leakage current (J) of the detectors decrease from 6.37/spl times/10/sup -7/ A/cm/sup 2/ to 3.86/spl times/10/sup -7/ A/cm/sup 2/. The specific detectivity (D*) measured at 100 Hz decreased from 2.72/spl times/10/sup 7/ cm/spl middot/Hz/sup 1/2//W for detector without PVDF to 1.71/spl times/10/sup 7/ cm/spl middot/Hz/sup 1/2//W for detector with PVDF thickness of 580 nm. By optimizing the ratio of the specific detectivity (D*) to leakage current, D*/J, the detector with PVDF thickness of 295 nm exhibits the best performance.