打分机制公平性评估的概率统计模型

针对评委聘请问题建立了综合评估模型,得出了各种评委的打分能力的评价分数,分析了评委淘汰的各种原因。就打分机制的公平性评价问题,定义了公平偏移度,建立概率统计模型,量化给出了几种打分机制的公平性的评价结果。     

K-causal structure of space-time in general relativity

Using K-causal relation introduced by Sorkin and Woolgar [1], we generalize results of Garcia-Parrado and Senovilla [2,3] on causal maps. We also introduce causality conditions with respect to K-causality which are analogous to those in classical causality theory and prove their inter-relationships. We introduce a new causality condition following the work of Bombelli and Noldus [4] and show that this condition lies in between global hyperbolicity and causal simplicity. This approach is simpler and more general as compared to traditional causal approach [5,6] and it has been used by Penrose et al [7] in giving a new proof of positivity of mass theorem. C ⁰-space-time structures arise in many mathematical and physical situations like conical singularities, discontinuous matter distributions, phenomena of topology-change in quantum field theory etc.      

图上合作博弈和图的边密度

1977年, Myerson建立了以图作为合作结构的可转移效用博弈模型(也称图博弈), 并提出了一个分配规则, 也即"Myerson 值", 它推广了著名的Shapley值. 该模型假定每个连通集合(通过边直接或间接内部相连的参与者集合)才能形成可行的合作联盟而取得相应的收益, 而不考虑连通集合的具体结构. 引入图的局部边密度来度量每个连通集合中各成员之间联系的紧密程度, 即以该连通集合的导出子图的边密度来作为他们的收益系数, 并由此定义了具有边密度的Myerson值, 证明了具有边密度的Myerson值可以由"边密度分支有效性"和"公平性"来唯一确定.     

Space-time singularities and microwave background radiation

A general relativistic space-time universe is considered together with a radiation such as the microwave background radiation. It is shown that if certain reasonable conditions are satisfied, then the presence of such a radiation would imply space-time singularities in the sense that all time-like curves will be incomplete in the past. The considerations provide an upperbound to the age of the universe, which is consistent with present data.     

On Flat Complete Causal Lorentzian Manifolds

We describe up to finite coverings causal flat affine complete Lorentzian manifolds such that the past and the future of any point are closed near this point. We say that these manifolds are strictly causal. In particular, we prove that their fundamental groups are virtually abelian. In dimension 4, there is only one, up to a scaling factor, strictly causal manifold which is not globally hyperbolic. For a generic point of this manifold, either the past or the future is not closed and contains a lightlike straight line     

Λ and the Heisenberg Principle

A time dependent “cosmological constant” Λ(t) is conjectured, in terms of the Gaussian curvature of the causal horizon. It is nonvanishing even in Minkowski space because of the lack of informations beyond the light cone. Using the Heisenberg Principle, the corresponding energy of the quantum fluctuations localized on the past or future null horizons is proportional to Λ^1/2. We compute Λ(t) for the (Lorenzian version) of the (conformally flat) Hawking wormhole geometry (written in static spherical Rindler coordinates) and for the de Sitter spacetime. A possible explanation of the Hawking temperature is proposed, in terms of a constant Λ.     

Computational Mechanics: Pattern and Prediction, Structure and Simplicity

Computational mechanics, an approach to structural complexity, defines a process's causal states and gives a procedure for finding them. We show that the causal-state representation—an -machine—is the minimal one consistent with accurate prediction. We establish several results on -machine optimality and uniqueness and on how -machines compare to alternative representations. Further results relate measures of randomness and structural complexity obtained from -machines to those from ergodic and information theories.     

A General Scheme for Shape Preserving Planar Interpolating Curves

This paper describes the application of the so-called Abstract Schemes (AS) for the construction of shape preserving interpolating planar curves. The basic idea behind AS is given by observing that when we interpolate some data points by a spline, we can dispose of several free parameters d ₀,d ₁,...,d _N (d _i R ^q ), which are associated with the knots. If we now express shape constraints as conditions relative to each interval between two knots, they can be rewritten as a sequences of inclusion conditions: ({d} _i ,d _i+1)D _i R ^2q , where the sets D _i are the corresponding feasible domains. In this setting the problems of existence, construction and selection of an optimal solution can be studied with the help of Set Theory in a general way. The method is then applied for the construction of shape preserving, planar interpolating curves.     

Finitary, Causal, and Quantal Vacuum Einstein Gravity

We continue recent work (Mallios and Raptis, International Journal of Theoretical Physics 40, 1885, 2001; in press) and formulate the gravitational vacuum Einstein equations over a locally finite space-time by using the basic axiomatics, techniques, ideas, and working philosophy of Abstract Differential Geometry. The main kinematical structure involved, originally introduced and explored in (Mallios and Raptis, International Journal of Theoretical Physics 40, 1885, 2001), is a curved principal finitary space-time sheaf of incidence algebras, which have been interpreted as quantum causal sets, together with a nontrivial locally finite spin-Loretzian connection on it which lays the structural foundation for the formulation of a covariant dynamics of quantum causality in terms of sheaf morphisms. Our scheme is innately algebraic and it supports a categorical version of the principle of general covariance that is manifestly independent of a background -smooth space-time manifold M. Thus, we entertain the possibility of developing a fully covariant path integral-type of quantum dynamical scenario for these connections that avoids ab initio various problems that such a dynamics encounters in other current quantization schemes for gravity—either canonical (Hamiltonian) or covariant (Lagrangian)—involving an external, base differential space-time manifold, namely, the choice of a diffeomorphism-invariant measure on the moduli space of gauge-equivalent (self-dual) gravitational spin-Lorentzian connections and the (Hilbert space) inner product that could in principle be constructed relative to that measure in the quantum theory—the so-called inner product problem, as well as the problem of time that also involves the Diff(M) structure group of the classical -smooth space-time continuum of general relativity. Hence, by using the inherently algebraico—sheaf—theoretic and calculus-free ideas of Abstract Differential Geometry, we are able to draw preliminary, albeit suggestive, connections between certain nonperturbative (canonical or covariant) approaches to quantum general relativity (e.g., Ashtekar's new variables and the loop formalism that has been developed along with them) and Sorkin et al.'s causal set program. As it were, we noncommutatively algebraize, differential geometrize and, as a result, dynamically vary causal sets. At the end, we anticipate various consequences that such a scenario for a locally finite, causal and quantal vacuum Einstein gravity might have for the obstinate (from the viewpoint of the smooth continuum) problem of -smooth space-time singularities.     

Coaxing a planar curve to comply

A long-standing problem in computer graphics is to find a planar curve that is shaped the way you want it to be shaped. A selection of various methods for achieving this goal is presented. The focus is on mathematical conditions that we can use to control curves while still allowing the curves some freedom. We start with methods invented by Newton (1643–1727) and Lagrange (1736–1813) and proceed to recent methods that are the subject of current research. We illustrate almost all the methods discussed with diagrams. Three methods of control that are of special interest are interpolation methods, global minimization methods (such as least squares), and (Bézier) control points. We concentrate on the first of these, interpolation methods.