We consider the problem of semi-supervised graph-based learning upon multimodal and mixmodal data. Since in semi-supervised settings, the labeled information is very limited, we first propose a non-convex sparse-coding based label propagation (αα-SLP) method to estimate the soft labels, and thereby to enrich the supervised information. By considering the structural properties of multimodal and mixmodal data, we present a semi-supervised graph-based embedding (SGE) approach that incorporates the soft label information with the hierarchical local geometric information of within-class, between-class, and overall-class data. Based on this, subspaces characterizing the multimodal and mixmodal data structure can be derived by maximizing the weighted between-class separability and minimizing the locality-preserved within-class as well as overall-class distances of the training samples. We further extend SGE into semi-supervised sparse subspace learning scenarios and present an αα-structural-regularization-induced SGE (αα-SSGE) model, which can give better results in extracting discriminative groups of features by utilizing the non-convex structural regularization techniques. Experiments for multimodal and mixmodal digit as well as face recognition verify the validity and effectiveness of the proposed models.

Probabilistic Boolean networks (PBNs) have been proved to be a useful tool for modeling genetic regulatory interactions. The study of the steady-state probability distribution may help to understand the essential long-run behavior of a PBN. In this paper we focus on a type of PBNs derived from gene expression data collected in a study of metastatic melanoma. The metastatic melanoma model is usually described by a PBN containing seven genes among which WNT5A plays a significant role in the development of melanoma and is known to induce the metastasis of melanoma when highly active. This paper investigates the issue of how to drive the corresponding PBN towards desired steady-state probability distributions so as to reduce the WNT5A's ability to induce a metastatic phenotype.

Increasingly influential leadership is significant to the cooperation and success of human societies. However, whether and how leaders emerge among evolutionary game players still remain less understood. Here, we study the evolution of potential leaders in the framework of evolutionary game theory, adopting the prisoner's dilemma and snowdrift game as metaphors of cooperation between unrelated individuals. We find that potential leaders can spontaneously emerge from homogeneous populations along with the evolution of cooperation, demonstrated by the result that a minority of agents spread their strategies more successfully than others and guide the population behavior, irrespective of the applied games. In addition, the phenomenon just described can be observed more notably in populations situated on scale free networks, and thus implies the relevance of heterogeneous networks for the possible emergence of leadership in the proposed system. Our results underscore the importance of the study of leadership in the population indulging in evolutionary games.

We provide a general approach for the design of a response Boolean network (BN) to achieve complete synchronization with a given drive BN. The approach is based on the algebraic representation of BNs in terms of the semi-tensor product of matrices. Instead of designing the logical dynamic equations of a response BN directly, we first construct its algebraic representation and then convert the algebraic representation back to the logical form. The results are applied to a three-neuron network in order to illustrate the effectiveness of the proposed approach.

We examine complete synchronization of two deterministic Boolean networks (BNs) coupled unidirectionally in the drive-response configuration. A necessary and sufficient criterion is presented in terms of algebraic representations of BNs. As a consequence, we show that complete synchronization can occur only between two conditionally identical BNs when the transition matrix of the drive network is nonsingular. Two examples are worked out to illustrate the obtained results.

Cooperation among unrelated individuals is pervasive in human societies, while natural selection favors the survival of the fittest. The theoretical explanation for this puzzle is a challenge across disciplines. Among other mechanisms that can promote cooperation is costly punishment, in which altruistic individuals privately bear the cost to punish defection. But it decreases the welfare of both the punisher and the punished, and defectors are hard and costly to be caught in many cases. Moreover, punishment may trigger a chain of retaliation between the punisher and the punished and induce second-order free riding - those who never punish will be better off than punishers. In this article we aim to get rid of these drawbacks by refining the mechanism of punishment. First we define an extended Public Goods game in which the defector is caught and punished with a certain probability and the cost of punishment is equally shared between the remainder of the group. Then we derive the fixation probability for one mutant cooperator to invade and take over the whole population. Our analysis shows that, when the probability for punishment is above a threshold, natural selection favors cooperating replacing defecting. Both analytical results and computer simulations show that severe punishment for a small fraction of defectors is enough for one mutant cooperator to become fixed with an advantageous probability in the population of defectors. In addition, this way of punishment can considerably decrease the total cost of inhibiting defection, especially for large populations.

This paper considers the flocking problem of a group of autonomous agents moving in the space with a virtual leader. We investigate the dynamic properties of the group for the case where the state of the virtual leader may be time-varying and the topology of the neighboring relations between agents is dynamic. To track such a leader, we introduce a set of switching control laws that enable the entire group to generate the desired stable flocking motion. The control law acting on each agent relies on the state information of its neighboring agents and the external reference signal (or "virtual leader"). Then we prove that, if the acceleration input of the virtual leader is known, then each agent can follow the virtual leader, and moreover, the convergence rate of the center of mass (CoM) can be estimated; if the acceleration input is unknown, then the velocities of all agents asymptotically approach the velocity of the CoM, and thus the flocking motion can be obtained, however in this case, the final velocity of the group may not be equal to the desired velocity. Numerical simulations are worked out to further illustrate our theoretical results

We study the coordinated motion of a group of vehicles with a leader based on nearest neighbor rules. The leader may be a special vehicle in the group or an external signal (virtual leader) to steer the vehicle group. The control law consists of two parts: a potential field force that makes the vehicles attract to each other and at the same time avoid collision in the group, and an alignment force that makes all vehicles' headings and speeds to converge respectively to common values. We assume that the interaction patterns are either fixed or switching based on the information topologies of the leader and member vehicles. Our approach is based on the Lyapunov theory and basic graph theory. We also consider the effect of noise on the collective dynamics of the group. Numerical simulations are worked out to illustrate the analytical results

This paper considers a group of mobile autonomous agents moving in the space with a virtual leader. We investigate the dynamic properties of the group for the case where the topology of the neighboring relations between agents varies with time and the coupling matrix is asymmetric. We introduce a set of switching control laws that enable the group to generate the desired stable flocking motion. The control laws are a combination of attractive/repulsive and alignment forces, and the control law acting on each agent relies on the state information of its neighbors and the external reference signal (or "virtual leader"). When the velocity damping is taken into account, we can appropriately modify the control laws to generate the same stable flocking motion. Numerical simulations are worked out to further illustrate our theoretical results

This paper considers an anisotropic swarm model with an attraction/repulsion function. We study its aggregation properties and show that the swarm members aggregate and eventually form a cohesive cluster of finite size around their weighted center in a finite time. Numerical simulations demonstrate that all agents eventually enter and remain in a bounded region around the weighted center. The swarm may eventually stop moving or exhibit complex spiral motion due to asymmetry of the coupling structure. The model in this paper is more general than isotropic swarms and our results provide further insight into the effect of the interaction pattern on individual motion in a swarm system

In this paper we study the property of controllability for a class of interconnected systems with a leader in switching networks. We obtain necessary and sufficient conditions for the interconnected systems using neighbor rules, to be controllable by one of them acting as a leader. Here, we take the control laws to be an attractive force, and we assume the topology of the control interconnections is variant, that is, each swarm individual (agent) updates is current state based on the current information from neighboring individuals and the leader. Results show that the interconnected systems can be completely controllable even though every subsystem cannot be controllable by selecting one of the as a leader and neighbor interaction rules. Moreover, the swarm can begin from the given initial configuration and reach a desired final configuration while satisfying certain conditions. The model and results of this paper present a novel method to investigate a class of swarms via switching systems and provide further insight into the effect of the interaction pattern on self-organized motion in a swarm system. Numerical simulations are also worked out to illustrate the analytical results.

In this paper, we consider a group of mobile agents moving in the space with point mass dynamics. We investigate the dynamic properties of the group for the case where the topology of the neighboring relations between agents varies with time. Under the assumption that the neighboring graph is always connected, we show that stable flocking motion can be achieved by using a set of switching control laws. The control laws are a combination of attractive/repulsive and alignment forces. Using the control laws, all agent velocities become asymptotically the same, collisions can be avoided between the agents, and the final tight formation minimizes all agent potentials. Moreover, we show that the velocity of the center of mass is invariant and is equal to the final common velocity. Subsequently, we study the motion of the group when the velocity damping is taken into account. In this case, we can appropriately modify the control laws to generate the same stable flocking motion. Finally, we provide some numerical simulations to further illustrate our theoretical results.

This paper considers a group of mobile autonomous agents moving in the space with point mass dynamics and with asymmetric coupling matrix. We investigate the dynamic properties of the group for the case that the topology of the neighboring relations between agents varies with time. Under the assumption that the neighboring graphs are always connected, we show that stable flocking motion can be achieved by using a set of switching control laws. The control laws are a combination of attractive/repulsive and alignment forces. By using the control laws, all agent velocities become asymptotically the same, collisions can be avoided between the agents, and the final tight formation minimizes all agent potentials. Moreover, we show that the velocity of the center of mass is invariant and is equal to the final common velocity. Finally, we study the motion of the group when the velocity damping is taken into account. We prove that the common velocity asymptotically approaches zero. In this case, we can properly modify the control laws to generate the same stable flocking motion.

In the paper, commuting and stable feedback design for switched linear systems is investigated. This problem is formulated as to build up state feedback controller for each subsystem such that the closed-loop systems are not only asymptotically stable but also commuting each other. A new concept, common admissible eigenvector set (CAES), is introduced to establish necessary/sufficient conditions for such feedback controllers. For second-order systems, a equivalent condition is established. Moreover, a parametrization of the CAES is also obtained. The motivation comes from stabilization of switched linear systems which consist of a family of LTI systems and a switching law specifying the switching between them, where if all the subsystems are stable and commuting each other, then the total system is stable under arbitrary switching.

The problems of Extended Strict Positive Realness (ESPR) analysis and synthesis for a class of discrete-time systems with polytopic uncertainty are considered. An equivalent condition of ESPR for discrete-time systems is first given in terms of linear matrix inequalities (LMIs). Moreover, a sufficient condition for the uncertain systems to be robustly stable with ESPR is established by stability with ESPR of vertex systems. Furthermore, a condition on robust stability with ESPR for the uncertain systems is obtained in terms of linear matrix inequalities. Based on this result, a simple approach to the design of a linear state-feedback controller which stabilizes robustly the uncertain systems and achieves ESPR is proposed. A numerical example is worked out to illustrate the efficiency of the proposed approach.

The control problem of networked control systems via output feedback is considered in this paper. In the system, a sensor is connected to a linear controller/actuator via a network. The plant is controlled alternately by an open loop controller and a closed loop controller. Necessary and sufficient conditions for the exponential stability of such systems are derived in terms of the network dwell times and the system parameters. Based on the results, a simple procedure for designing the output feedback controller is presented. Numerical simulation shows the feasibility and efficiency of the proposed method.