Removable ears of 1-extendable graphs

<正> Carvalho,Lucchesi and Murty proved that any 1-extendable graph G different from K_2and C_(2n)has at least Δ(G)edge-disjoint removable ears,and any brick G distinct from K_4 and■hasat least Δ(G)-2 removable edges,where Δ(G)denotes the maximum degree of G.In this paper,weimprove the lower bounds for numbers of removable ears and removable edges of 1-extendable graphs.It is proved that any 1-extendable graph G different from K_2 and C_(2n)has at least χ′(G)edge-disjointremovable ears,and any brick G distinct from K_4 and■has at least χ′(G)-2 removable edges,whereχ′(G)denotes the edge-chromatic number of G.     

Network's Relationship Flow-Behavior Theorems — Structural Theory of General Systems Applied in Networks

On the basis of several new concepts, such as, the relationship flow and the basic level of a network, and by applying the Structural Theory of General Systems, this article conducts a study of the relationships and their laws between the relationship flows, including information flows, matter flows, energy flows, fund flows, personnel flows, and so on, and the behavior or function of a network, and mathematically obtains two theorems, namely the network's relationship flow-behavior theorem 1 and 2. It then proposes a new model of networks, called the relationship flow-behavior model of networks, which shows that for a network, its behavior or function is determined and governed only by its input flow Rf(t) and relationship flow set Rf_nb(t) on its so-called basic level H_b, that is, its total relationship flows TRf(t)= Rf(t) ∪ Rf_nb(t), especially by the relationship flow cycle(s) in TRf(t). By a further mathematical study of the model, it can be expected to obtain a series of inherent relationships and their laws between the relationship flows and the behavior or function of a network, as well as their derivates, for example, the issues, ideas, theories, methods, approaches, and tools of network research, which would make significant contributions to the advancement of network research.     

Participatory Sustainability Impact Assessment: Scientific Policy Advice as a Social Learning Process

This paper deals with the development of scientific policy advice by providing a methodology to foster a social learning process. The methodology, called participatory Sustainability Impact Assessment (pSIA), aims to structure complex problem situations, to clarify interests and basic assumptions, to interpret scientific studies, to develop impact assessment, and to explore sensitivity of uncertainty and lack of information. In pSIA workshops the participants are supposed to build conceptual models with different modelling methods, like System Dynamics, Value Chain Analysis, and Morphological Analysis. A case study is presented that describes a workshop series with political as well as academic actors, applying the pSIA approach to an impact assessment of Economic Partnership Agreements between the European Union and the Eastern and Southern Africa Region.

Dynamic price model based on transmission delay — Petroleum price fluctuation in China

Petroleum is a kind of fundamental energy resource. Its price fluctuation transmits from upper-stream industry to the lower-stream industry as the production factors price changes. And this leads to the price changes of final consumption. Meantime, due to the cycle of industrial chain, the price changes of lower-stream industry also affect the upper-stream industry in return. This price transmission path is quite complicated. Firstly, it includes both direct and indirect paths; secondly, the transmission process is accompanied with time delay. The traditional input-output price model based on cost-push theory can efficiently solve the first problem when estimating the impact of price fluctuation on the whole price system. However, it neither reflects the dynamic characteristics of price transmission with time nor solves the second problem. To solve this problem, this paper uses the directed weighted network to describe the price transmission among industrial sectors by taking the time-dimension into account, and dynamic price transmission network model is constructed. This model not only describes transmission time delay more accurately, but also calculates the price fluctuation dynamically. On this basis, by utilizing the 2007 Chinese input-output table, this paper conducts empirical analysis on the impact of petroleum price fluctuation on other sectors. The empirical results indicate that the price fluctuation transmission mainly depends on two factors, the orice reaction period Tk and the consumption relationship with petroleum aik. 1） If t 〈 Tk, then the price change of sector k at period t △pkt = 0, the petroleum price fluctuation has not transmitted to the sector k, so the price of sector k remains unchanged. 2） If t 〉 Tk, then Apt 〉 0, and the greater aik, the higher price change rate. 3） If t →∞, it is the same with that in traditional input-output price model. So it can be clearly seen that dynamic price transmission network model is more general than the traditional model, and the traditional model is just an asymptotical special case when time approaches to infinity. Keywords Directed weighted network, input-output price model, petroleum price, transmission time delay.     

Induced Subgraph in Random Regular Graph

Let Gn,d be a random d-regular graph with n vertices, where d = o（n）. Given a fixed graph H, YH denotes the number of induced copies of H in Gn d In this paper, the authors determine the threshold of the event ＂YH 〉 0＂, and also obtain the induced subgraph counts inside the threshold interval.     

Practicality, Positionality, and Emancipation: Reflections on Participatory Action Research with a Watershed Partnership

In the last few decades, there has been a trend towards increased stakeholder and public participation in natural resource management in North America. To a certain extent, the rationale for this trend is found in the complexity and uncertainty of environmental issues, which confront us with the coexistance of multiple legitimate values and perspectives in society. Recognizing this “epistemological plurality” has important implications for both policy and science. In this paper, I critically reflect on my experiences as a doctoral student engaged in participatory action research (PAR) with a watershed partnership in Ontario, Canada. In providing this biographical account, I seek to make a contribution to ongoing discussions regarding the nature, challenges and benefits of this methodological approach for academic research, as well as to emerging debates on PAR in the context of environmental governance and “post-normal” approaches to natural resource management.

Creating ‘Rhizomatic Systems’ for Understanding Complexity in Organizations

The article describes and demonstrates the use of a new research proposal for understanding the complexity in organizations in terms of a Deleuzian sense of an event. It creates the rhizome metaphor that allows the emergence of different ways of systems thinking, a legitimate challenge to the Modernist’s orthodoxy. For Deleuze and Guattari, micropolitics are the essence of what we call ‘rhizomatic systems.’ It is this concept of the organization, as a rhizome or rhizomatic systems that we want to focus from ‘problem solving’ in a real-world situation to the process of problematization, that is, the making or appreciating a series of events in the problematizing fields. The paper draws on the research experience in which participatory action research was carried out in a Korean distribution company. The participatory learning process happened to create a series of events in which ‘time-related research’ was conducted in order to facilitate the process of problematization within the organization.

Dealing with a Differentiated Whole: The Philosophy of the WSR Approach

This paper seeks to explore a philosophical ground for the formulation and practice of an Oriental systems methodology, the wuli–shili–renli approach (WSR). Drawing insights from ancient Chinese thought, WSR contends that, in sociotechnical systems design/management, we should investigate and follow wuli, shili, and renli, which constitute a differentiable, dynamic whole. Wuli, shili, and renli condition and determine the fate of our projects, meaning different methods are needed to deal with each differentiable aspect. It also points out that, to deal with wuli, shili, and renli properly, we need to engage in encounters with the "dark side" of Confucianism and with the contemporary tendency of scientism.     

Construction and comparisons of simultaneous confidence intervals for the mean difference of multivariate normal distributions

<正> In this paper,Scheffé and Simplified Scheffé simultaneous confidence intervals are firstconstructed for mean difference of several multivariate normal distributions.Then the authors theoreticallyprove that when there are only two populations,Bonferroni bounds and Simplified Scheffébounds are the same and they are shorter than Scheffé bounds for p10.In the case for 3k10and 2p10,there exists n(p,k)such that Bonferroni method is better than Simplified Schefféprocedure for nn(p,k),otherwise Simplified Scheffé procedure is better.Finally,the authors findout that neither of Scheffé critical values nor Simplified Scheffé critical values are always larger thananother through numerical calculation.     

An FE-Inexact Heterogeneous ADMM for Elliptic Optimal Control Problems with <Emphasis Type="Italic">L</Emphasis><Superscript>1</Superscript>-Control Cost

Elliptic PDE-constrained optimal control problems with L¹-control cost (L¹-EOCP) are considered. To solve L¹-EOCP, the primal-dual active set (PDAS) method, which is a special semismooth Newton (SSN) method, used to be a priority. However, in general solving Newton equations is expensive. Motivated by the success of alternating direction method of multipliers (ADMM), we consider extending the ADMM to L¹-EOCP. To discretize L¹-EOCP, the piecewise linear finite element (FE) is considered. However, different from the finite dimensional l1-norm, the discretized L¹-norm does not have a decoupled form. To overcome this difficulty, an effective approach is utilizing nodal quadrature formulas to approximately discretize the L¹-norm and L²-norm. It is proved that these approximation steps will not change the order of error estimates. To solve the discretized problem, an inexact heterogeneous ADMM (ihADMM) is proposed. Different from the classical ADMM, the ihADMM adopts two different weighted inner products to define the augmented Lagrangian function in two subproblems, respectively. Benefiting from such different weighted techniques, two subproblems of ihADMM can be efficiently implemented. Furthermore, theoretical results on the global convergence as well as the iteration complexity results o(1/k) for ihADMM are given. In order to obtain more accurate solution, a two-phase strategy is also presented, in which the primal-dual active set (PDAS) method is used as a postprocessor of the ihADMM. Numerical results not only confirm error estimates, but also show that the ihADMM and the two-phase strategy are highly efficient.     

Systemic Human Relations in Dynamic Equilibrium

This paper reports on a breakthrough in thinking based on 33 years of field practice-based inquiry and previously published studies. It brings together several bodies of established and emerging thought including systems thinking, epistemology, psychology and sociology, in a way of thinking about the living fabric of complex human systems-in-process. It is offered here as a kind of transdisciplinary ‘Rosetta stone’ to those working around the world with one or more of these bodies of thought as a way of making some critical connections between them. In summary, an integrating ‘mental architecture’ is proposed whereby inquiry (research as an evaluative dynamic act of seeking) may be seen as the way by which living (notably human) systems come alive, and which is incorporated, organ-ised, ‘structured’ and relationally embodied in an individual and their psychological mind as personal process, and in social collectivities and their sociological organisation as cultural process.

EXTENDED CLUSTERING COEFFICIENTS：GENERALIZATION OF CLUSTERING COEFFICIENTS IN SMALL-WORLD NETWORKS

The clustering coefficient C of a network, which is a measure of direct connectivity between neighbors of the various nodes, ranges from 0 （for no connectivity） to 1 （for full connectivity）. We define extended clustering coefficients C（h） of a small-world network based on nodes that are at distance h from a source node, thus generalizing distance-1 neighborhoods employed in computing the ordinary clustering coefficient C = C（1）. Based on known results about the distance distribution Pδ（h） in a network, that is, the probability that a randomly chosen pair of vertices have distance h, we derive and experimentally validate the law Pδ（h）C（h） ≤ c log N / N, where c is a small constant that seldom exceeds 1. This result is significant because it shows that the product Pδ（h）C（h） is upper-bounded by a value that is considerably smaller than the product of maximum values for Pδ（h） and C（h）. Extended clustering coefficients and laws that govern them offer new insights into the structure of small-world networks and open up avenues for further exploration of their properties.     

The limit theorem for dependent random variables with applications to autoregression models

This paper studies the autoregression models of order one, in a general time series setting that allows for weakly dependent innovations. Let {X _t } be a linear process defined by X _t = Σ _k=0^∞ψ _k ɛ _t−k , where {ψ _k , k ≥ 0} is a sequence of real numbers and {ɛ _k , k = 0, ±1, ±2, …} is a sequence of random variables. Two results are proved in this paper. In the first result, assuming that {ɛ _k , k ≥ 1} is a sequence of asymptotically linear negative quadrant dependent (ALNQD) random variables, the authors find the limiting distributions of the least squares estimator and the associated regression t statistic. It is interesting that the limiting distributions are similar to the one found in earlier work under the assumption of i.i.d. innovations. In the second result the authors prove that the least squares estimator is not a strong consistency estimator of the autoregressive parameter α when {ɛ _k , k ≥ 1} is a sequence of negatively associated (NA) random variables, and ψ ₀ = 1, ψ _k = 0, k ≥ 1.     

Analysis and verification of network profile

The elements of network profile are proposed. Based   on the network traffic distribution model, the network profile includes   the application request rate, the branch transfer probability,   the ratio of application requests, and the probability distribution of   the requested objects. Based on the evaluation method of network   performance reliability, four simulation cases are constructed in   OPNET software, and the results show the four elements of profile   have impacts on the network reliability.     

Improve Robustness and Accuracy of Deep Neural Network with L2,∞ Normalization

In this paper, the L_2,∞ normalization of the weight matrices is used to enhance the robustness and accuracy of the deep neural network(DNN) with Relu as activation functions. It is shown that the L_2,∞ normalization leads to large dihedral angles between two adjacent faces of the DNN function graph and hence smoother DNN functions, which reduces over-fitting of the DNN. A global measure is proposed for the robustness of a classification DNN, which is the average radius of th...     

Solutions for singular p-Laplacian equation in R n

In this paper, the authors study the existence and non-existence of positive solutions for singular p-Laplacian equation −∆ _p u = f(x)u ^−α + λg(x)u ^β in R ^N ; where N ≥ 3, 1 < p < N, λ > 0, 0 < α < 1, max(p, 2) < β + 1 < p* = \fracN_pN - p \frac{{{N_p}}}{{N - p}} . We prove that there exists a critical value ¤ such that the problem has at least two solutions if 0 < λ < Λ; at least one solution if λ = Λ; and no solutions if λ > Λ.     

DEGREE CONDITIONS FOR GRAPHS TO BE FRACTIONAL （a, b, n）-CRITICAL GRAPHS

Let G be a graph, and a and b be integers with a ≤ b. A graph G is called a fraetional （a, b, n）-critical graph if after any n vertices of G are deleted the remaining subgraph has a fractional [a, b]-factor. In this paper two degree conditions for graphs to be fractional （a, b, n）-eritical graphs are presented, and the degree conditions are sharp in some sense.     

NNMDS codes

C is an[n,k,d]_q linear code over F₉.And s（C）=n+1-k-d is the Singleton defect of C.An MDS code C with s（C）=0 has been studied extensively.Recently,a near-MDS code C with s（C）=s（C^⊥）=1 is studied by many scholars,where C^⊥denotes the dual code of C.This paper concentrates on the linear code C with s（C）=s（C^⊥）=2,and the author calls it an NNMDS code.A series of iff conditions of NNMDS codes are presented.And the author gives an upper bound on length of NNMDS codes.In the last,some examples of NNMDS are given.