Research Interests: Mechanical Engineering, Mathematics, Computer Science, Graph Theory, Cognitive Robotics, and 12 moreNavigation, Robots, Manufacturing Engineering, ROBOT, Competitive Analysis, Graph, Correctness, Electrical And Electronic Engineering, Performance Measure, Solid Modeling, Relative Orientation, and Homogeneous
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Abstract Background: Survivors of intensive care unit (ICU) transfer to the common ward are often accompanied by psychological distress, negative emotions, fatigue, and sleep disturbances that affect recovery. Mindfulness-based stress... more
Abstract Background: Survivors of intensive care unit (ICU) transfer to the common ward are often accompanied by psychological distress, negative emotions, fatigue, and sleep disturbances that affect recovery. Mindfulness-based stress reduction (MBSR) has achieved reliable results in improving physical and mental health. However, no clinical study has been conducted to evaluate the effects of MBSR on negative emotions, fatigue and sleep quality of patients who survived ICU and were transferred to general wards. Methods: This is a prospective randomized controlled trial (RCT) examining the effects of MBSR on negative emotions, fatigue, and sleep quality in inpatients transferred from ICU to general ward. Participants were randomly divided into the treatment group and the control group in a ratio of 1:1. On the basis of the same nursing plan and health education, the treatment group received MBSR therapy, while the control group received no other interventions, and all the patients were followed up for 3 months after 2 weeks of continuous treatment. The indicators included negative mood indicators [Self-rating Depression Scale (SDS) and Self-Rating Anxiety Scale (SAS)], fatigue index [Fatigue Severity Scale (FSS) and Brief Fatigue Inventory (BFI)], and sleep quality index [Pittsburgh Sleep Quality Index (PSQI)]. Finally, SPSS 20.0 software was used for statistical analysis of the data. Discussion: This study will evaluate the effects of MBSR on negative emotions, fatigue, and sleep quality in hospitalized patients transferred from ICU to general ward. The results of this study will provide a reference for MBSR to improve psychological distress in ICU survivors transferred to general ward. Trial registration: This study protocol was registered in the Open Science Framework (OSF) (registration number: DOI 10.17605/OSF.IO/PD7SU).
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Research Interests: Applied Mathematics, Computer Science, Parallel Algorithms, Computational Geometry, Combinatorial Optimization, and 13 moreGraph Theory, Computer Networks, Pure Mathematics, Local Area Networks, Implementation, Parallel Algorithm, Numerical Analysis and Computational Mathematics, Shortest Path Problem, Communication Complexity, Parallel Computer, Graph Algorithm, Coarse Grained Soil, and Communication Cost
Research Interests: Mathematics, Applied Mathematics, Computer Science, Combinatorial Optimization, Mathematical Programming, and 11 moreLinear Programming, Integer Programming, Cooperative Games, Duality Theory, Bipartite Graph, Numerical Analysis and Computational Mathematics, Duality, Non-Cooperative Game Theory, Vertex Cover, LINEAR PROGRAM, and Cooperative game
We discuss an integer programming formulation for a class of cooperative games. We focus on algorithmic aspects of the core, one of the most important solution concepts in cooperative game theory. Central to our study is a simple (but... more
We discuss an integer programming formulation for a class of cooperative games. We focus on algorithmic aspects of the core, one of the most important solution concepts in cooperative game theory. Central to our study is a simple (but very useful) observation that the core for this class is nonempty if and only if an associated linear program has an integer optimal solution. Based on this, we study the computational complexity and algorithms to answer important questions about the cores of various games on graphs, such as maximum flow, connectivity, maximum matching, minimum vertex cover, minimum edge cover, maximum independent set, and minimum coloring.
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The Fisher market model is one of the most fundamental resource allocation models in economics. In a Fisher market, the prices and allocations of goods are determined according to the preferences and budgets of buyers to clear the market.... more
The Fisher market model is one of the most fundamental resource allocation models in economics. In a Fisher market, the prices and allocations of goods are determined according to the preferences and budgets of buyers to clear the market. In a Fisher market game, however, buyers are strategic and report their preferences over goods; the market-clearing prices and allocations are then determined based on their reported preferences rather than their real preferences. We show that the Fisher market game always has a pure Nash equilibrium, for buyers with linear, Leontief, and Cobb-Douglas utility functions, which are three representative classes of utility functions in the important Constant Elasticity of Substitution (CES) family. Furthermore, to quantify the social efficiency, we prove Price of Anarchy bounds for the game when the utility functions of buyers fall into these three classes respectively.
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We introduce a general integer programming formulation for a class of combinatorial op-timization games, which include many interesting problems on graphs. The formulation im-mediately allows us to improve the algorithmic result for... more
We introduce a general integer programming formulation for a class of combinatorial op-timization games, which include many interesting problems on graphs. The formulation im-mediately allows us to improve the algorithmic result for finding imputations in the core (an important solution concept in cooperative game theory) of the network flow game on unit networks. An important result is a general theorem that the core for this class of games is nonempty if and only if a related linear program has an integer optimal solution. We study the properties for this mathematical condition to hold for several problems on graphs, and apply them to resolve algorithmic and complexity issues for their cores: decide whether the core is empty; if the core is empty, find an imputation in the core; given an imputation $x $ , test whether $x $ is in the core. 1
We consider the problem of finding a fully colored base triangle on the 2-dimensional Mobius band under the standard boundary condition, proving it to be PPA-complete. The proof is based on a construction for the DPZP problem, that of... more
We consider the problem of finding a fully colored base triangle on the 2-dimensional Mobius band under the standard boundary condition, proving it to be PPA-complete. The proof is based on a construction for the DPZP problem, that of finding a zero point under a discrete version of continuity condition. It further derives PPA-completeness for versions on the Mobius band of other related discrete fixed point type problems, and a special version of the Tucker problem, finding an edge such that if the value of one end vertex is x, the other is --x, given a special anti-symmetry boundary condition. More generally, this applies to other non-orientable spaces, including the projective plane and the Klein bottle. However, since those models have a closed boundary, we rely on a version of the PPA that states it as to find another fixed point giving a fixed point. This model also makes it presentationally simple for an extension to a high dimensional discrete fixed point problem on a non-or...
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We resolve the complexity of n-dimensional Octahedral Tucker (a special case of the celebrated Tucker problem), a classical statement from algebraic topology, by proving it PPA− Complete. For this, we define a new problem called General... more
We resolve the complexity of n-dimensional Octahedral Tucker (a special case of the celebrated Tucker problem), a classical statement from algebraic topology, by proving it PPA− Complete. For this, we define a new problem called General Octahedral Tucker, and prove that it is PPA− Complete and that Octahedral Tucker is a special case of the same. The proof involves two folding techniques, Fold and Wrap. First, using Fold, we reduce 2-D Tucker, a known PPA− Complete problem, to an instance of General Octahedral Tucker, and then successively reduce General Octahedral Tucker to higher dimensional instances of the same problem. Once we obtain instances that have constant side length, application of the Wrap technique results in an instance of Octahedral Tucker. This result settles a decade old open question from [13], also raised in [1, 11]. ∗School of EECS, Peking University, Beijing, China. Email: xiaotie@pku.edu.cn. Research results reported in this work are partially supported by th...
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In this paper, we consider the popular proportional sharing mechanism and discuss the incentives and opportunities of an agent to lie for personal gains in resource exchange game. The main result is a proof that an agent manipulating the... more
In this paper, we consider the popular proportional sharing mechanism and discuss the incentives and opportunities of an agent to lie for personal gains in resource exchange game. The main result is a proof that an agent manipulating the proportional sharing mechanism by misreporting its resource amount will not benefit its own utility eventually. This result establishes a strategic stability property of the resource exchange protocol. We further illustrate and confirm the result via network examples.
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Studies on games in coalition form deal with the power of cooperation among its participants. In this sense it is often referred to as cooperative game theory. In a simple mathematical formulation, we have a set N of agents, and a value... more
Studies on games in coalition form deal with the power of cooperation among its participants. In this sense it is often referred to as cooperative game theory. In a simple mathematical formulation, we have a set N of agents, and a value function v: 2N-> R where, for each subset SC TV, v (S) represents the value obtained by the coalition of agents of the subset S without assistance of other agents, with w (0)= 0. Individual income can be represented by a vector x: N—> R. We consider games with side payments. The main ...
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We prove a new discrete fixed point theorem for direction-preserving functions defined on integer points, based on a novel characterization of boundary conditions for the existence of fixed points. The theorem allows us to derive an... more
We prove a new discrete fixed point theorem for direction-preserving functions defined on integer points, based on a novel characterization of boundary conditions for the existence of fixed points. The theorem allows us to derive an improved algorithm for finding such a fixed point. We also develop a new lower bound proof technique. Together, they allow us to derive an asymptotic matching bound for the problem of finding a fixed point in a hypercube of any constantly bounded finite dimension. Exploring a linkage with the approximation version of the continuous fixed point problem, we obtain asymptotic matching bounds for the complexity of the approximate Brouwer fixed point problem in the continuous case for Lipschitz functions. It settles a fifteen-years-old open problem of Hirsch, Papadimitriou, and Vavasis by improving both the upper and lower bounds. Our characterization for the existence of a fixed point is also applicable to functions defined on nonconvex domains, which makes ...
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We prove that Bimatrix, the problem of finding a Nash equilibrium in a two-player game, is complete for the complexity class PPAD (Polynomial Parity Argument, Directed version) introduced by Papadimitriou in 1991. Our result, building... more
We prove that Bimatrix, the problem of finding a Nash equilibrium in a two-player game, is complete for the complexity class PPAD (Polynomial Parity Argument, Directed version) introduced by Papadimitriou in 1991. Our result, building upon the work of Daskalakis et al. [2006a] on the complexity of four-player Nash equilibria, settles a long standing open problem in algorithmic game theory. It also serves as a starting point for a series of results concerning the complexity of two-player Nash equilibria. In particular, we prove the following theorems: —Bimatrix does not have a fully polynomial-time approximation scheme unless every problem in PPAD is solvable in polynomial time. —The smoothed complexity of the classic Lemke-Howson algorithm and, in fact, of any algorithm for Bimatrix is not polynomial unless every problem in PPAD is solvable in randomized polynomial time. Our results also have a complexity implication in mathematical economics: —Arrow-Debreu market equilibria are PPA...
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Nash equilibrium has traditionally been one of the most influential tools in the study of many disciplines involved with strategies, such as Political Science and Economics. The rise of the Internet and the study of its anarchical... more
Nash equilibrium has traditionally been one of the most influential tools in the study of many disciplines involved with strategies, such as Political Science and Economics. The rise of the Internet and the study of its anarchical environment have made Nash equilibrium an ...
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ABSTRACT
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... price during the pre-opening period of a computerized trading system, such as Oskar Lange had advocated since the dawn of the ... complexity of non-cooperative game in bimatrix form has been a long standing open problem known since... more
... price during the pre-opening period of a computerized trading system, such as Oskar Lange had advocated since the dawn of the ... complexity of non-cooperative game in bimatrix form has been a long standing open problem known since Lemke-Howson's algorithm was first ...
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The paper presents theoretical analysis of the deterministic complexity of the load balancing problem (LBP). Because of difficulty of the general problem, research in the area mostly restricts itself to probabilistic or approximation... more
The paper presents theoretical analysis of the deterministic complexity of the load balancing problem (LBP). Because of difficulty of the general problem, research in the area mostly restricts itself to probabilistic or approximation algorithms, or to the average behavior of a network. The paper provides deterministic analysis of the problem for general networks. It focuses on the worst-case complexity analysis
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ABSTRACT Recently, much work has been done in game theory towards understanding the bounded rationality of players in infinite games. This requires the strategies of realistic players to be restricted to have bounded resources of... more
ABSTRACT Recently, much work has been done in game theory towards understanding the bounded rationality of players in infinite games. This requires the strategies of realistic players to be restricted to have bounded resources of reasoning. We discuss infinite two-person games, focusing on the case where our player follows a computable strategy and the adversary may use any strategy, which formulates the notion of computer against extremely formidable nature. In this context, we say that an infinite game is semicomputably determinate if either the adversary has a winning strategy or our player has a computable winning strategy. We show that, whereas all open games are semicomputably determinate, there is a semicomputably indeterminate closed game. Since we want to prove an indeterminacy result for closed games and since the adversary’s strategy set is uncountable and our player’s strategy set is countable, our proof for the indeterminacy result requires a new diagonalization technique, which might be useful in other similar cases. Our study of semicomputable games was inspired by online computing problems. In this direction, we discuss several possible applications to derandomization in online computing, with the restriction that the strategies of our player should be computable. We also study the power of randomization for the classical case where our player is allowed to play according to unrestricted strategies. An indeterminate game is obtained for which both players have a simple randomized winning strategy against all of the deterministic strategies of the opponent.
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Our main result is a linear-time (that is, time $O(m + n)$) algorithm to recognize and represent proper circular-arc graphs. The best previous algorithm, due to A. Tucker, has time complexity $O(n^2 )$. We take advantage of the fact that... more
Our main result is a linear-time (that is, time $O(m + n)$) algorithm to recognize and represent proper circular-arc graphs. The best previous algorithm, due to A. Tucker, has time complexity $O(n^2 )$. We take advantage of the fact that (among connected graphs) proper ...
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This paper presents a theoretical analysis of the Load Balancing Problem (LBP) in a network of processing units. The performance objective is to minimize the makespan, i.e., the time spent to finish all jobs in a network of processing... more
This paper presents a theoretical analysis of the Load Balancing Problem (LBP) in a network of processing units. The performance objective is to minimize the makespan, i.e., the time spent to finish all jobs in a network of processing units. Because of the communication delay that results from the network topology, it is impossible to have a strategy which obtains
Research Interests: Computer Science, Distributed Computing, Software Engineering, Modeling, Scheduling, and 15 moreDistributed System, Algorithm, Computer Network, Network Design, Competitive Analysis, Load distribution, Simulation Study, Network Topology, Load Balance, Network Flow, Communication Delay, Optimal Solution, Distributed Algorithm, Approximate solution, and Informational Efficiency
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ABSTRACT We discuss the potential function introduced in D. Coppersmith, P. Doyle, P. Raghvan and M. Suir [Random walks on weighted graphs, Proc. 22nd annual ACM Symp. on Theory of Computing, 369-378 (1990)] for analysis of the online... more
ABSTRACT We discuss the potential function introduced in D. Coppersmith, P. Doyle, P. Raghvan and M. Suir [Random walks on weighted graphs, Proc. 22nd annual ACM Symp. on Theory of Computing, 369-378 (1990)] for analysis of the online algorithm for k-server problems in resistive space. We show that the potential function for the randomized algorithm is an equivalent characterization of resistive spaces, which explains the reason that approach cannot cover the general k-server problem P. Berman, H. Karloff and G. Tardos [A competitive 3-server algorithm, Proc. 1st annual ACM-SIAM Symp. on Discrete Algorithms, 280- 290 (1989)] and A. Fiat, Y. Rabani and Y. Ravid [Competitive k-server algorithms, Proc. 31st annual Symp. on Foundations of Computer Sciences, 454-463], while it applies to all the special cases of the server problem which are known to have k-competitive algorithms.