Enhancing robustness and immunization in geographical networks

We find that different geographical structures of networks lead to varied percolation thresholds, although these networks may have similar abstract topological structures. Thus, strategies for enhancing robustness and immunization of a geographical network are proposed. Using the generating function formalism, we obtain an explicit form of the percolation threshold q(c) for networks containing arbitrary order cycles. For three-cycles, the dependence of q(c) on the clustering coefficients is ascertained. The analysis substantiates the validity of the strategies with analytical evidence.

Potential Landscape and Flux Framework of Nonequilibrium Networks: Robustness, Dissipation, and Coherence of Biochemical Oscillations

We established a theoretical framework for studying nonequilibrium networks with two distinct natures essential for characterizing the global probabilistic dynamics: the underlying potential landscape and the corresponding curl flux. We applied the idea to a biochemical oscillation network and found that the underlying potential landscape for the oscillation limit cycle has a distinct closed ring valley (Mexican hat-like) shape when the fluctuations are small. This global landscape structure leads to attractions of the system to the ring valley.

Robustness and dissipation of mitogen-activated protein kinases signal transduction network: Underlying funneled landscape against stochastic fluctuations

We uncovered the underlying energy landscape of the mitogen-activated protein kinases signal transduction cellular network by exploring the statistical natures of the Brownian dynamical trajectories. We introduce a dimensionless quantity: The robustness ratio of energy gap versus local roughness to measure the global topography of the underlying landscape. A high robustness ratio implies funneled landscape. The landscape is quite robust against environmental fluctuations and variants of the intrinsic chemical reaction rates.

Robustness and Coherence of a Three-Protein Circadian Oscillator: Landscape and Flux Perspectives

Three-protein circadian oscillations in cyanobacteria sustain for weeks. To understand how cellular oscillations function robustly in stochastic fluctuating environments, we used a stochastic model to uncover two natures of circadian oscillation: the potential landscape related to steady-state probability distribution of protein concentrations; and the corresponding flux related to speed of concentration changes which drive the oscillations. The barrier height of escaping from the oscillation attractor on the landscape provides a quantitative measure of the robustness and coherence for oscillations against intrinsic and external fluctuations. The difference between the locations of the zero total driving force and the extremal of the potential provides a possible experimental probe and quantification of the force from curl flux. These results, correlated with experiments, can help in the design of robust oscillatory networks.

Potential energy landscape and robustness of a gene regulatory network: Toggle switch

Finding a multidimensional potential landscape is the key for addressing important global issues, such as the robustness of cellular networks. We have uncovered the underlying potential energy landscape of a simple gene regulatory network: a toggle switch. This was realized by explicitly constructing the steady state probability of the gene switch in the protein concentration space in the presence of the intrinsic statistical fluctuations due to the small number of proteins in the cell. We explored the global phase space for the system. We found that the protein synthesis rate and the unbinding rate of proteins to the gene were small relative to the protein degradation rate; the gene switch is monostable with only one stable basin of attraction. When both the protein synthesis rate and the unbinding rate of proteins to the gene are large compared with the protein degradation rate, two global basins of attraction emerge for a toggle switch. These basins correspond to the biologically stable functional states. The potential energy barrier between the two basins determines the time scale of conversion from one to the other. We found as the protein synthesis rate and protein unbinding rate to the gene relative to the protein degradation rate became larger, the potential energy barrier became larger. This also corresponded to systems with less noise or the fluctuations on the protein numbers.

Quantifying robustness and dissipation cost of yeast cell cycle network: The funneled energy landscape perspectives

We study the origin of robustness of yeast cell cycle cellular network through uncovering its underlying energy landscape. This is realized from the information of the steady-state probabilities by solving a discrete set of kinetic master equations for the network. We discovered that the potential landscape of yeast cell cycle network is funneled toward the global minimum, G1 state. The ratio of the energy gap between G1 and average versus roughness of the landscape termed as robustness ratio ( RR) becomes a quantitative measure of the robustness and stability for the network. The funneled landscape is quite robust against random perturbations from the inherent wiring or connections of the network. There exists a global phase transition between the more sensitive response or less self-degradation phase leading to underlying funneled global landscape with large RR, and insensitive response or more self-degradation phase leading to shallower underlying landscape of the network with small RR. Furthermore, we show that the more robust landscape also leads to less dissipation cost of the network. Least dissipation and robust landscape might be a realization of Darwinian principle of natural selection at cellular network level. It may provide an optimal criterion for network wiring connections and design.

Funneled landscape leads to robustness of cellular networks: MAPK signal transduction

We uncover the underlying potential energy landscape for a cellular network. We find that the potential energy landscape of the mitogen-activated protein-kinase signal transduction network is funneled toward the global minimum. The funneled landscape is quite robust against random perturbations. This naturally explains robustness from a physical point of view. The ratio of slope versus roughness of the landscape becomes a quantitative measure of robustness of the network. Funneled landscape is a realization of the Darwinian principle of natural selection at the cellular network level. It provides an optimal criterion for network connections and design. Our approach is general and can be applied to other cellular networks.

Wave Propagation Analysis in a Pressure-Wave-Refrigerator

Pressure wave refrigerators (PWR) refrigerate the gas through periodical expansion waves. Due to its simple structure and robustness, PWR may have many potential applications if the efficiency becomes competitive with existing alternative devices. In order to improve the efficiency, the characteristics of wave propagation in a PWR are studied by experiment, numerical simulation and theoretical analysis. Based on the experimental results and numerical simulation, a simplified model is suggested, which includes the assumptions of flux-equilibrium and conservation of the free energy. This allows the independent analysis of the operation parameters and design specifics. Furthermore, the optimum operation condition can be deduced. Some considerations to improve the PWR efficiency are also given.

Perturbational Finite Volume Method For The Solution of 2-D Navier-Stokes Equations on Unstructured and Structured Colocated Meshes

Based on the first-order upwind and second-order central type of finite volume( UFV and CFV) scheme, upwind and central type of perturbation finite volume ( UPFV and CPFV) schemes of the Navier-Stokes equations were developed. In PFV method, the mass fluxes of across the cell faces of the control volume (CV) were expanded into power series of the grid spacing and the coefficients of the power series were determined by means of the conservation equation itself. The UPFV and CPFV scheme respectively uses the same nodes and expressions as those of the normal first-order upwind and second-order central scheme, which is apt to programming. The results of numerical experiments about the flow in a lid-driven cavity and the problem of transport of a scalar quantity in a known velocity field show that compared to the first-order UFV and second-order CFV schemes, upwind PFV scheme is higher accuracy and resolution, especially better robustness. The numerical computation to flow in a lid-driven cavity shows that the under-relaxation factor can be arbitrarily selected ranging from 0.3 to 0. 8 and convergence perform excellent with Reynolds number variation from 102 to 104.

Pattern Recognition With Weighted Complex Networks

In this paper we introduce a weighted complex networks model to investigate and recognize structures of patterns. The regular treating in pattern recognition models is to describe each pattern as a high-dimensional vector which however is insufficient to express the structural information. Thus, a number of methods are developed to extract the structural information, such as different feature extraction algorithms used in pre-processing steps, or the local receptive fields in convolutional networks. In our model, each pattern is attributed to a weighted complex network, whose topology represents the structure of that pattern. Based upon the training samples, we get several prototypal complex networks which could stand for the general structural characteristics of patterns in different categories. We use these prototypal networks to recognize the unknown patterns. It is an attempt to use complex networks in pattern recognition, and our result shows the potential for real-world pattern recognition. A spatial parameter is introduced to get the optimal recognition accuracy, and it remains constant insensitive to the amount of training samples. We have discussed the interesting properties of the prototypal networks. An approximate linear relation is found between the strength and color of vertexes, in which we could compare the structural difference between each category. We have visualized these prototypal networks to show that their topology indeed represents the common characteristics of patterns. We have also shown that the asymmetric strength distribution in these prototypal networks brings high robustness for recognition. Our study may cast a light on understanding the mechanism of the biologic neuronal systems in object recognition as well.

The Relationship between Decision Trees and the Scale of Train Data Set

Decision Trees need train samples in the train data set to get classification rules. If the number of train data was too small, the important information might be missed and thus the model could not explain the classification rules of data. While it is not affirmative that large scale of train data set can get well model. This Paper analysis the relationship between decision trees and the train data scale. We use nine decision tree algorithms to experiment the accuracy, complexity and robustness of decision tree algorithms. Some results are demonstrated.

Wave Propagation Analysis in a Pressure-Wave-Refrigerator

Pressure wave refrigerators (PWR) refrigerate the gas through periodical expansion waves. Due to its simple structure and robustness, PWR may have many potential applications if the efficiency becomes competitive with existing alternative devices. In order to improve the efficiency, the characteristics of wave propagation in a PWR are studied by experiment, numerical simulation and theoretical analysis. Based on the experimental results and numerical simulation, a simplified model is suggested, which includes the assumptions of flux-equilibrium and conservation of the free energy. This allows the independent analysis of the operation parameters and design specifics. Furthermore, the optimum operation condition can be deduced. Some considerations to improve the PWR efficiency are also given.

Developing A Microfluidic-Based System To Quantify Cell Capture Efficiency

Micro-fabrication technology has substantial potential for identifying molecular markers expressed on the surfaces of tissue cells and viruses. It has been found in several conceptual prototypes that cells with such markers are able to be captured by their antibodies immobilized on microchannel substrates and unbound cells are flushed out by a driven flow. The feasibility and reliability of such a microfluidic-based assay, however, remains to be further tested. In the current work, we developed a microfluidic-based system consisting of a microfluidic chip, an image grabbing unit, data acquisition and analysis software, as well as a supporting base. Specific binding of CD59-expressed or BSA-coupled human red blood cells (RBCs) to anti-CD59 or anti-BSA antibody-immobilized chip surfaces was quantified by capture efficiency and by the fraction of bound cells. Impacts of respective flow rate, cell concentration, antibody concentration and site density were tested systematically. The measured data indicated that the assay was robust. The robustness was further confirmed by capture efficiencies measured from an independent ELISA-based cell binding assay. These results demonstrated that the system developed provided a new platform to effectively quantify cellular surface markers effectively, which promoted the potential applications in both biological studies and clinical diagnoses.

Coherent population transfer with chirped few-cycle laser pulses in an excited-doublet four-level system

The behavior of population transfer in an excited-doublet four-level system driven by linear polarized few-cycle ultrashort laser pulses is investigated numerically. It is shown that almost complete population transfer can be achieved even when the adiabatic criterion is not fulfilled. Moreover, the robustness of this scheme in terms of the Rabi frequencies and chirp rates of the pulses is explored.

A reliable phase unwrapping algorithm based on the local fitting plane and quality map

A fast and reliable phase unwrapping (PhU) algorithm, based on the local quality-guided fitting plane, is presented. Its framework depends on the basic plane-approximated assumption for phase values of local pixels and on the phase derivative variance (PDV) quality map. Compared with other existing popular unwrapping algorithms, the proposed algorithm demonstrated improved robustness and immunity to strong noise and high phase variations, given that the plane assumption for local phase is reasonably satisfied. Its effectiveness is demonstrated by computer-simulated and experimental results.