arXiv subjects

Bin Xu

Publications and source records attributed to Bin Xu.

262 records · Page 15Linked to original sources

arXiv2012

Maxent in Experimental 2$\times$2 Population Games

In mixed strategy 2\times2 population games, the realization of maximum entropy (Maxent) is of the theoretical expectation. We evaluate this theoretical prediction in the experimental economics game data. The data includes 12 treatments and 108 experimental sessions in which the random match human subjects pairs make simultaneous strategy moves repeated 200 rounds. Main results are (1) We confirm that experimental entropy value fit the prediction from Maxent well; and (2) In small proportion samples, distributions are deviated from Maxent expectations; interesting is that, the deviated patterns are significant more concentrated. These experimental findings could enhance the understanding of social game behavior with the natural science rule --- Maxent.

stat.AP↗

arXiv2011

Test the Principle of Maximum Entropy in Constant Sum 2x2 Game:Evidence in Experimental Economics

Entropy serves as a central observable which indicates uncertainty in many chemical, thermodynamical, biological and ecological systems, and the principle of the maximum entropy (MaxEnt) is widely supported in natural science. Recently, entropy is employed to describe the social system in which human subjects are interacted with each other, but the principle of the maximum entropy has never been reported from this field empirically. By using laboratory experimental data, we test the uncertainty of strategy type in various competing environments with two person constant sum $2 \times 2$ game. Empirical evidence shows that, in this competing game environment, the outcome of human's decision-making obeys the principle of maximum entropy.

physics.soc-ph↗

arXiv2011

Measurement and Application of Entropy Production Rate in Human Subject Social Interaction Systems

This paper illustrates the measurement and the applications of the observable, entropy production rate (EPR), in human subject social interaction systems. To this end, we show (1) how to test the minimax randomization model with experimental economics' 2$\times$2 games data and with the Wimbledon Tennis data; (2) how to identify the Edgeworth price cycle in experimental market data; and (3) the relationship within EPR and motion in data. As a result, in human subject social interaction systems, EPR can be measured practically and can be employed to test models and to search for facts efficiently.

stat.ME↗

arXiv2010

Gradient estimate of a Dirichlet eigenfunction on a compact manifold with boundary

Let $e_ł(x)$ be an eigenfunction with respect to the Dirichlet Laplacian $Δ_N$ on a compact Riemannian manifold $N$ with boundary: $Δ_N e_ł=ł^2 e_ł$ in the interior of $N$ and $e_ł=0$ on the boundary of $N$. We show the following gradient estimate of $e_ł$: for every $ł\geq 1$, there holds $ł\|e_ł\|_\infty/C\leq \|\nabla e_ł\|_\infty\leq Cł\|e_ł\|_\infty$, where $C$ is a positive constant depending only on $N$. In the proof, we use a basic geometrical property of nodal sets of eigenfunctions and elliptic apriori estimates.

math.AP↗

arXiv2009

Gradient estimate of an eigenfunction on a compact Riemannian manifold without boundary

Let $e_ł(x)$ be an eigenfunction with respect to the Laplace-Beltrami operator $Δ_M$ on a compact Riemannian manifold $M$ without boundary: $Δ_M e_ł=ł^2 e_ł$. We show the following gradient estimate of $e_ł$: for every $ł\geq 1$, there holds $ł\|e_ł\|_\infty/C\leq \|\nabla e_ł\|_\infty\leq Cł\|e_ł\|_\infty$, where $C$ is a positive constant depending only on $M$.

math.SP↗

arXiv2009

The Riemannian manifolds with boundary and large symmetry

Sixty years ago, S. B. Myers and N. E. Steenrod ({\it Ann. of Math.} {\bf 40} (1939), 400-416) showed that the isometry group of a Riemannian manifold without boundary has a structure of Lie group. Recently A. V. Bagaev and N. I. Zhukova ({\it Siberian Math. J.} {\bf 48} (2007), 579-592) proved the same result for a Riemannian orbifold. In this paper, we firstly show that the isometry group of a Riemannian manifold $M$ with boundary has dimension at most ${1/2} \dim M (\dim M-1)$. Then we completely classify such Riemannian manifolds with boundary that their isometry groups attain the preceding maximal dimension.

math.DG↗

arXiv2008

Process Flow Diagram of an Ammonia Plant as a Complex Network

Complex networks have attracted increasing interests in almost all disciplines of natural and social sciences. However, few efforts have been afforded in the field of chemical engineering. We present in this work an example of complex technological network, investigating the process flow of an ammonia plant (AP). We show that the AP network is a small-world network with scale-free distribution of degrees. Adopting Newman's maximum modularity algorithm for the detection of communities in complex networks, evident modular structures are identified in the AP network, which stem from the modular sections in chemical plants. In addition, we find that the resultant AP tree exhibits excellent allometric scaling.

physics.bio-ph↗

arXiv2005

The Degree of Symmetry of Certain Compact Smooth Manifolds II

In this paper, we give the sharp estimates for the degree of symmetry and the semi-simple degree of symmetry of certain four dimensional fiber bundles by virtue of the rigidity theorem of harmonic maps due to Schoen and Yau. As a corollary of this estimate, we compute the degree of symmetry and the semi-simple degree of symmetry of ${\Bbb C}P^2\times V$, where $V$ is closed smooth manifold admitting a real analytic Riemannian metric of non-positive curvature. In addition, by the Albanese map, we obtain the sharp estimate of the degree of symmetry of a compact smooth manifold with some restrictions on its one dimensional cohomology.

math.GT↗

arXiv2005

Asymptotic behavior of $L^2$-normalized eigenfunctions of the Laplace-Beltrami operator on a closed Riemannian manifold

Let $e(x,y,ł)$ be the spectral function and $χ_ł$ the unit band spectral projection operator, with respect to the Laplace-Beltrami operator $\D_M$ on a closed Riemannian manifold $M$. We firstly review the one-term asymptotic formula of $e(x,x,ł)$ as $ł\to\infty$ by H{\" o}rmander (1968) and the one of $\p^\al_x\p^\bt_y e(x,y,ł)|_{x=y}$ as $ł\to\infty$ in a geodesic normal coordinate chart by the author (2004) and the sharp asymptotic estimates from above of the mapping norm $\|χ_ł\|_{L_2\to L_p}$ ($2\leq p\leq\infty$) by Sogge (1988 $&$ 1989) and of the mapping norm $\|χ_ł\|_{L_2\to {\rm Sobolev} L_p}$ by the author (2004). In the paper we show the one term asymptotic formula for $e(x,y,ł)$ as $ł\to\infty$, provided that the Riemannian distance between $x$ and $y$ is ${\rm O}(1/ł)$. As a consequence, we obtain the sharp estimate of the mapping norm $\|χ_ł\|_{L_2\to C^\d}$ ($0<\d<1$), where $C^\d(M)$ is the space of H{\" o}lder continuous functions with exponent $\d$ on $M$. Moreover, we show a geometric property of the eigenfunction $e_ł$: $\D_M e_ł+ł^2 e_ł=0$, which says that $1/ł$ is comparable to the distance between the nodal set of $e_ł$ (where $e_ł$ vanishes) and the concentrating set of $e_ł$ (where $e_ł$ attains its maximum or minimum) as $ł\to\infty$.

math.SP↗

arXiv2005

Compact Group Actions On Closed Manifolds of Non-positive Curvature

A. Borel proved that, if a finite group $F$ acts effectively and continuously on a closed aspherical manifold $M$ with centerless fundamental group $π_1(M)$, then a natural homomorphism $ψ$ from $F$ to the outer automorphism group ${\rm Out} π_1(M)$ of $π_1(M)$, called the associated abstract kernel, is a monomorphism. In this paper, we investigate to what extent Borel's theorem holds for a compact Lie group $G$ acting effectively and smoothly on a particular orientable aspherical manifold $N$ admitting a Riemannian metric $g_0$ of non-positive curvature in case that $π_1(N)$ has a non-trivial center. It turns out that if $G$ attains the maximal dimension equal to the rank of Center $π_1(N)$ and the metric $g_0$ is real analytic, then any element of $G$ defining a diffemorphism homotopic to the identity of $N$ must be contained in the identity component $G^0$ of $G$. Moreover, if the inner automorphism group of $π_1(N)$ is torsion free, then the associated abstract kernel $ψ: G/G^0\to {\rm Out} π_1(N)$ is a monomorphism. The same result holds for the non-orientable $N$'s under certain techical assumptions. Our result is an application of a theorem by Schoen-Yau (Topology, {\bf 18} (1979), 361-380) on harmonic mappings.

math.DG↗