6,156 research outputs found
Positive curvature operator, projective manifold and rational connectedness
In his recent work \cite{Y1}, X. Yang proved a conjecture raised by Yau in
1982 (\cite{Yau82}), which states that any compact K\"{a}hler manifold with
positive holomorphic sectional curvature must be projective. In this note, we
prove that any compact Hermitian manifold with positive real bisectional
curvature, its hodge number . In
particular, if in addition is K\"{a}hler, then is projective. Also, it
is rationally connected manifold when . This partially confirms the
conjecture 1.11 \cite{Y1} which is proposed by X. Yang.Comment: 9 pages. arXiv admin note: text overlap with arXiv:1708.06713,
arXiv:1610.07165, arXiv:1802.08732 by other author
On the Dirichlet Problem for Backward Parabolic Stochastic Partial Differential Equations in General Smooth Domains
Backward stochastic partial differential equations of parabolic type with
variable coefficients are considered in smooth domains. Existence and
uniqueness results are given in weighted Sobolev spaces allowing the
derivatives of the solutions to blow up near the boundary.Comment: 28 page
Strong Solution of Backward Stochastic Partial Differential Equations in Domains
This paper is concerned with the strong solution to the Cauchy-Dirichlet
problem for backward stochastic partial differential equations of parabolic
type. Existence and uniqueness theorems are obtained, due to an application of
the continuation method under fairly weak conditions on variable coefficients
and domains. The problem is also considered in weighted Sobolev spaces
which allow the derivatives of the solutions to blow up near the boundary. As
applications, a comparison theorem is obtained and the semi-linear equation is
discussed in the domain.Comment: 26 page
MacWilliams type identities on the Lee and Euclidean weights for linear codes over
Motivated by the works of Shiromoto [3] and Shi et al. [4], we study the
existence of MacWilliams type identities with respect to Lee and Euclidean
weight enumerators for linear codes over Necessary and
sufficient conditions for the existence of MacWilliams type identities with
respect to Lee and Euclidean weight enumerators for linear codes over
are given. Some examples about such MacWilliams type
identities are also presented
-Solution () of Linear Degenerate Backward Stochastic Partial Differential Equations in the Whole Space
In this paper, we consider the backward Cauchy problem of linear degenerate
stochastic partial differential equations. We obtain the existence and
uniqueness results in Sobolev space with both
and being arbitrary, without imposing the symmetry
condition for the coefficient of the gradient of the second
unknown---which was introduced by Ma and Yong [Prob. Theor. Relat. Fields 113
(1999)] in the case of . To illustrate the application, we give a maximum
principle for optimal control of degenerate stochastic partial differential
equations.Comment: 29 page
Theory for Super-parabolic Backward Stochastic Partial Differential Equations in the Whole Space
This paper is concerned with semi-linear backward stochastic partial
differential equations (BSPDEs for short) of super-parabolic type. An
-theory is given for the Cauchy problem of BSPDEs, separately for the case
of and for the case of . A comparison theorem is
also addressed
On the power of dominated players in team competitions
We investigate multi-round team competitions between two teams, where each
team selects one of its players simultaneously in each round and each player
can play at most once. The competition defines an extensive-form game with
perfect recall and can be solved efficiently by standard methods. We are
interested in the properties of the subgame perfect equilibria of this game.
We first show that uniformly random strategy is a subgame perfect equilibrium
strategy for both teams when there are no redundant players (i.e., the number
of players in each team equals to the number of rounds of the competition).
Secondly, a team can safely abandon its weak players if it has redundant
players and the strength of players is transitive.
We then focus on the more interesting case where there are redundant players
and the strength of players is not transitive. In this case, we obtain several
counterintuitive results. First of all, a player might help improve the payoff
of its team, even if it is dominated by the entire other team. We give a
necessary condition for a dominated player to be useful. We also study the
extent to which the dominated players can increase the payoff.
These results bring insights into playing and designing general team
competitions.Comment: 8pages, AAMAS201
Morley-Wang-Xu element methods with penalty for a fourth order elliptic singular perturbation problem
Two Morley-Wang-Xu element methods with penalty for the fourth order elliptic
singular perturbation problem are proposed in this paper, including the
interior penalty Morley-Wang-Xu element method and the super penalty
Morley-Wang-Xu element method. The key idea in designing these two methods is
combining the Morley-Wang-Xu element and penalty formulation for the Laplace
operator. Robust a priori error estimates are derived under minimal regularity
assumptions on the exact solution by means of some established a posteriori
error estimates. Finally, we present some numerical results to demonstrate the
theoretical estimates.Comment: 18 page
Decision Making with Machine Learning and ROC Curves
The Receiver Operating Characteristic (ROC) curve is a representation of the
statistical information discovered in binary classification problems and is a
key concept in machine learning and data science. This paper studies the
statistical properties of ROC curves and its implication on model selection. We
analyze the implications of different models of incentive heterogeneity and
information asymmetry on the relation between human decisions and the ROC
curves. Our theoretical discussion is illustrated in the context of a large
data set of pregnancy outcomes and doctor diagnosis from the Pre-Pregnancy
Checkups of reproductive age couples in Henan Province provided by the Chinese
Ministry of Health
Effects of Weak Ties on Epidemic Predictability in Community Networks
Weak ties play a significant role in the structures and the dynamics of
community networks. Based on the susceptible-infected model in contact process,
we study numerically how weak ties influence the predictability of epidemic
dynamics. We first investigate the effects of different kinds of weak ties on
the variabilities of both the arrival time and the prevalence of disease, and
find that the bridgeness with small degree can enhance the predictability of
epidemic spreading. Once weak ties are settled, compared with the variability
of arrival time, the variability of prevalence displays a diametrically opposed
changing trend with both the distance of the initial seed to the bridgeness and
the degree of the initial seed. More specifically, the further distance and the
larger degree of the initial seed can induce the better predictability of
arrival time and the worse predictability of prevalence. Moreover, we discuss
the effects of weak tie number on the epidemic variability. As community
strength becomes very strong, which is caused by the decrease of weak tie
number, the epidemic variability will change dramatically. Compared with the
case of hub seed and random seed, the bridgenss seed can result in the worst
predictability of arrival time and the best predictability of prevalence. These
results show that the variability of arrival time always marks a complete
reversal trend of that of prevalence, which implies it is impossible to predict
epidemic spreading in the early stage of outbreaks accurately.Comment: 8 pages, 6 figure
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