An optimal algorithm for the weighted backup 2-center problem on a tree

In this paper, we are concerned with the weighted backup 2-center problem on a tree. The backup 2-center problem is a kind of center facility location problem, in which one is asked to deploy two facilities, with a given probability to fail, in a network. Given that the two facilities do not fail simultaneously, the goal is to find two locations, possibly on edges, that minimize the expected value of the maximum distance over all vertices to their closest functioning facility. In the weighted setting, each vertex in the network is associated with a nonnegative weight, and the distance from vertex $u$ to $v$ is weighted by the weight of $u$. With the strategy of prune-and-search, we propose a linear time algorithm, which is asymptotically optimal, to solve the weighted backup 2-center problem on a tree.Comment: 14 pages, 4 figure

A combinatorial proof of tree decay of semi-invariants

We consider finite range Gibbs fields and provide a purely combinatorial proof of the exponential tree decay of semi--invariants, supposing that the logarithm of the partition function can be expressed as a sum of suitable local functions of the boundary conditions. This hypothesis holds for completely analytical Gibbs fields; in this context the tree decay of semi--invariants has been proven via analyticity arguments. However the combinatorial proof given here can be applied also to the more complicated case of disordered systems in the so called Griffiths' phase when analyticity arguments fail

Maintaining Contour Trees of Dynamic Terrains

We consider maintaining the contour tree $\mathbb{T}$ of a piecewise-linear triangulation $\mathbb{M}$ that is the graph of a time varying height function $h: \mathbb{R}^2 \rightarrow \mathbb{R}$. We carefully describe the combinatorial change in $\mathbb{T}$ that happen as $h$ varies over time and how these changes relate to topological changes in $\mathbb{M}$. We present a kinetic data structure that maintains the contour tree of $h$ over time. Our data structure maintains certificates that fail only when $h(v)=h(u)$ for two adjacent vertices $v$ and $u$ in $\mathbb{M}$, or when two saddle vertices lie on the same contour of $\mathbb{M}$. A certificate failure is handled in $O(\log(n))$ time. We also show how our data structure can be extended to handle a set of general update operations on $\mathbb{M}$ and how it can be applied to maintain topological persistence pairs of time varying functions

Equalitarian Societies are Economically Impossible

The inequality of wealth distribution is a universal phenomenon in the civilized nations, and it is often imputed to the Matthew effect, that is, the rich get richer and the poor get poorer. Some philosophers unjustified this phenomenon and tried to put the human civilization upon the evenness of wealth. Noticing the facts that 1) the emergence of the centralism is the starting point of human civilization, i.e., people in a society were organized hierarchically, 2) the inequality of wealth emerges simultaneously, this paper proposes a wealth distribution model based on the hidden tree structure from the viewpoint of complex network. This model considers the organized structure of people in a society as a hidden tree, and the cooperations among human beings as the transactions on the hidden tree, thereby explains the distribution of wealth. This model shows that the scale-free phenomenon of wealth distribution can be produced by the cascade controlling of human society, that is, the inequality of wealth can parasitize in the social organizations, such that any actions in eliminating the unequal wealth distribution would lead to the destroy of social or economic structures, resulting in the collapse of the economic system, therefore, would fail in vain

Causality and Temporal Dependencies in the Design of Fault Management Systems

Reasoning about causes and effects naturally arises in the engineering of safety-critical systems. A classical example is Fault Tree Analysis, a deductive technique used for system safety assessment, whereby an undesired state is reduced to the set of its immediate causes. The design of fault management systems also requires reasoning on causality relationships. In particular, a fail-operational system needs to ensure timely detection and identification of faults, i.e. recognize the occurrence of run-time faults through their observable effects on the system. Even more complex scenarios arise when multiple faults are involved and may interact in subtle ways. In this work, we propose a formal approach to fault management for complex systems. We first introduce the notions of fault tree and minimal cut sets. We then present a formal framework for the specification and analysis of diagnosability, and for the design of fault detection and identification (FDI) components. Finally, we review recent advances in fault propagation analysis, based on the Timed Failure Propagation Graphs (TFPG) formalism.Comment: In Proceedings CREST 2017, arXiv:1710.0277

Towards an Analytical Framework for Assessing Property Rights to Natural Resources: A Case Study in the Communal Areas of Zimbabwe

A taxonomy for describing property rights to natural resources is described and applied in a Zimbabwean case study. The taxonomy allows: tenures to be systematically compared and contrasted; incentives for natural resource management to be identified; and the evolution of tenure to natural resources to be assessed. In the case study, we find: key differences between tenure types, all termed "communal"; a wide range of tenure arrangements that transcend concepts of "tree" and "land tenure"; information suggesting that the promotion of tree planting may work on some tenure types, but is likely to fail on others; and that the evolution of indigenous tenure to natural resources seems to have been somewhat immune from external changes in institutional systems. Prospects for further theoretical and empirical advances are discussed within the context of the property rights framework presented.incentives, natural resources, property rights framework/taxonomy, tenure, Zimbabwe, Resource /Energy Economics and Policy,