Wireless channels in the networked control systems are vulnerable to intentional interference, such as jamming attacks. This paper investigates jamming attacks on the wireless controller actuator channel of a control system that can tolerate occasional control inputs from the controller. We start with a worst case scenario for the jammer where the controller knows its channel state. We develop an adaptive jamming strategy in which the jammer, observing the success or failure of each controller transmission, forms beliefs about its own and the controller actuator channel states. Using this belief, it optimizes its actions under a limited jamming budget. To counter this, we develop an event-triggered defense scheme for the controller in two settings: with and without the knowledge of its channel state. Simulation results show that optimal adaptive jamming attacks can significantly degrade control performance, even with a limited budget, while the defense scheme, even without channel state knowledge, can effectively reduce this impact.

We prove that if a finite group G acts outerly on a McDuff II_1 factor M, then 𝖱𝖾𝗉(G/KL) is a braided monoidal full subcategory of the categorical Connes' (M⋊ G) defined in arXiv:2111.06378, where K and L are the centrally trivial and approximately inner parts in G respectively. When L is trivial, we give an explicit formula for the G/K-gauging procedure on (M⋊ G). This is the categorical generalization of Connes' short exact sequence on χ(M⋊ G). Using this machinery, for any finite group G, we construct a McDuff II_1 factor M, whose (M) is braided equivalent to 𝖱𝖾𝗉(G). This is the first example of a braided fusion category which is not modular as .

Hyper-redundant manipulators based on bionic structures offer superior dexterity due to their large number of degrees of freedom (DOFs) and slim bodies. However, controlling these manipulators is challenging because of infinite inverse kinematic solutions. In this paper, we present a novel reinforcement learning-based control method for hyper-redundant manipulators, integrating path and configuration planning. First, we introduced a deep reinforcement learning-based control method for a multi-target approach, eliminating the need for complicated reward engineering. Then, we optimized the network structure and joint space target points sampling to implement precise control. Furthermore, we designed a variable-reset cycle technique for a continuous multi-target approach without resetting the manipulator, enabling it to complete end-effector trajectory tracking tasks. Finally, we verified the proposed control method in a dynamic simulation environment. The results demonstrate the effectiveness of our approach, achieving a success rate of 98.32% with a 134% improvement using the variable-reset cycle technique.

We introduce a K-theoretic invariant for actions of unitary fusion categories on unital C^* -algebras. We show that for inductive limits of finite dimensional actions of fusion categories on AF-algebras, this is a complete invariant. In particular, this gives a complete invariant for inductive limit actions of finite groups on unital AF-algebras. We apply our results to obtain a classification of finite depth, strongly AF-inclusions of unital AF-algebras.

This paper investigates distributed detection of sparse stochastic signals with quantized measurements under Byzantine attacks, where sensors may send falsified data to the Fusion Center (FC) to degrade system performance. Here, the Bernoulli-Gaussian (BG) distribution is used to model sparse stochastic signals. Several detectors with significantly improved detection performance are proposed by incorporating estimates of attack parameters into the detection process. In the case of unknown sparsity degree and attack parameters, we propose the generalized likelihood ratio test with reference sensors (GLRTRS) as well as the locally most powerful test with reference sensors (LMPTRS). Our simulation results show that these detectors outperform the LMPT and GLRT detectors designed in attack-free environments and achieve detection performance close to the benchmark likelihood ratio test (LRT) detector. In the case of unknown sparsity degree and known fraction of Byzantine nodes in the network, we further propose enhanced LMPTRS (E-LMPTRS) and enhanced GLRTRS (E-GLRTRS) detectors by filtering out potential malicious sensors in the network, resulting in improved detection performance compared to GLRTRS and LMPTRS detectors.

In this article, we construct a 2-shaded rigid ${\rm C}^*$ multitensor category with canonical unitary dual functor directly from a standard $\lambda$-lattice. We use the notions of traceless Markov towers and lattices to define the notion of module and bimodule over standard $\lambda$-lattice(s), and we explicitly construct the associated module category and bimodule category over the corresponding 2-shaded rigid ${\rm C}^*$ multitensor category. As an example, we compute the modules and bimodules for Temperley-Lieb-Jones standard $\lambda$-lattices in terms of traceless Markov towers and lattices. Translating into the unitary 2-category of bigraded Hilbert spaces, we recover DeCommer-Yamshita's classification of $\mathcal{TLJ}$ modules in terms of edge weighted graphs, and a classification of $\mathcal{TLJ}$ bimodules in terms of biunitary connections on square-partite weighted graphs. As an application, we show that every (infinite depth) subfactor planar algebra embeds into the bipartite graph planar algebra of its principal graph.

In this article, we construct a 2 -shaded rigid \mathrm{C}^{*} multitensor category with canonical unitary dual functor directly from a standard \lambda -lattice. We use the notions of traceless Markov towers and lattices to define the notion of module and bimodule over standard \lambda -lattice(s), and we explicitly construct the associated module category and bimodule category over the corresponding 2 -shaded rigid \mathrm{C}^{*} multitensor category. As an example, we compute the modules and bimodules for Temperley–Lieb–Jones standard \lambda -lattices in terms of traceless Markov towers and lattices. Translating into the unitary 2-category of bigraded Hilbert spaces, we recover De Commer–Yamashita’s classification of \mathcal{T LJ} module categories in terms of edge weighted graphs, and a classification of \mathcal{T LJ} bimodule categories in terms of biunitary connections on square-partite weighted graphs. As an application, we show that every (infinite depth) subfactor planar algebra embeds into the bipartite graph planar algebra of its principal graph.

The ordered transmission based (OT-based) schemes reduce the number of transmissions needed in a distributed detection network without any loss in the probability of error performance. In this paper, we investigate the performance of a conventional OT-based system in the presence of additive Byzantine attacks in Gaussian shift in mean problems. In this work, by launching additive Byzantine attacks, attackers are able to alter the order as well as the data for the binary hypothesis testing problem. We also determine the optimal attack strategy for the Byzantine sensors. Furthermore, we analyze a communication efficient OT-based (CEOT-based) scheme in the presence of additive Byzantine attacks. We obtain the probabilities of error for both the OT-based system and the CEOT-based system under attack and evaluate the number of transmissions they save. We also derive analytical bounds for the number of transmissions saved in both systems under attack. Simulation results show that the additive Byzantine attacks have significant impact on the number of transmissions saved even when the signal strength is sufficiently large. A comparison of detection performance between the conventional OT-based system and the CEOT-based system reveals that the CEOT-based system is more robust to additive Byzantine attacks.

This paper proposes a belief-updating scheme in a human-machine collaborative decision-making network to combat Byzantine attacks. A hierarchical framework is used to realize the network where local decisions from physical sensors act as reference decisions to improve the quality of human sensor decisions. During the decision-making process, the belief that each physical sensor is malicious is updated. The case when humans have side information available is investigated, and its impact is analyzed. Simulation results substantiate that the proposed scheme can significantly improve the quality of human sensor decisions, even when most physical sensors are malicious. Moreover, the performance of the proposed method does not necessarily depend on the knowledge of the actual fraction of malicious physical sensors. Consequently, the proposed scheme can effectively defend against Byzantine attacks and improve the quality of human sensors' decisions so that the performance of the human-machine collaborative system is enhanced.

Popa introduced the tensor category χ̃(M) of approximately inner, centrally trivial bimodules of a II_1 factor M, generalizing Connes’ χ (M) . We extend Popa’s notions to define the W^* -tensor category End_loc(𝒞) of local endofunctors on a W^* -category 𝒞 . We construct a unitary braiding on End_loc(𝒞) , giving a new construction of a braided tensor category associated to an arbitrary W^* -category. For the W^* -category of finite modules over a II_1 factor, this yields a unitary braiding on Popa’s χ̃(M) , which extends Jones’ κ invariant for χ (M) . Given a finite depth inclusion M_0⊆ M_1 of non-Gamma II_1 factors, we show that the braided unitary tensor category χ̃(M_∞) is equivalent to the Drinfeld center of the standard invariant, where M_∞ is the inductive limit of the associated Jones tower. This implies that for any pair of finite depth non-Gamma subfactors N_0⊆ N_1 and M_0⊆ M_1 , if the standard invariants are not Morita equivalent, then the inductive limit factors N_∞ and M_∞ are not isomorphic.

In distributed detection systems, energy-efficient ordered transmission (EEOT) schemes are able to reduce the number of transmissions required to make a final decision. In this work, we investigate the effect of data falsification attacks on the performance of EEOT-based systems. We derive the probability of error for an EEOT-based system under attack and find an upper bound (UB) on the expected number of transmissions required to make the final decision. Moreover, we tighten this UB by solving an optimization problem via integer programming (IP). We also obtain the FC's optimal threshold which guarantees the optimal detection performance of the EEOT-based system. Numerical and simulation results indicate that it is possible to reduce transmissions while still ensuring the quality of the decision with an appropriately designed threshold.

In this paper, two reputation based algorithms called Reputation and audit based clustering (RAC) algorithm and Reputation and audit based clustering with auxiliary anchor node (RACA) algorithm are proposed to defend against Byzantine attacks in distributed detection networks when the fusion center (FC) has no prior knowledge of the attacking strategy of Byzantine nodes. By updating the reputation index of the sensors in cluster-based networks, the system can accurately identify Byzantine nodes. The simulation results show that both proposed algorithms have superior detection performance compared with other algorithms. The proposed RACA algorithm works well even when the number of Byzantine nodes exceeds half of the total number of sensors in the network. Furthermore, the robustness of our proposed algorithms is evaluated in a dynamically changing scenario, where the attacking parameters change over time. We show that our algorithms can still achieve superior detection performance.

The ordered transmission (OT) scheme reduces the number of transmissions needed in the network to make the final decision, while it maintains the same probability of error as the system without using OT scheme. In this paper, we investigate the performance of the system using OT scheme in the presence of Byzantine attacks for binary hypothesis testing problem. We analyze the probability of error for the system under attack and evaluate the number of transmissions saved using Monte Carlo method. We also derive the bounds for the number of transmissions saved in the system under attack. The optimal attacking strategy for the OT-based system is investigated. Simulation results show that the Byzantine attacks have significant impact on the number of transmissions saved even when the signal strength is sufficiently large.

This paper employs an audit bit based mechanism to mitigate the effect of Byzantine attacks on distributed Bayesian detection systems. In this framework, the optimal attacking strategy for strategic attackers is investigated for the traditional audit bit based scheme (TAS) to evaluate the robustness of the system. We show that it is possible for a strategic attacker to degrade the performance of TAS to the system without audit bits. To enhance the robustness of the system in the presence of strategic attackers, we propose an enhanced audit bit based scheme (EAS). The optimal fusion rule for the proposed scheme is derived and the detection performance of the system is evaluated via the probability of error for the system. Simulation results show that the proposed EAS improves the robustness and the detection performance of the system. Moreover, based on EAS, another new scheme called the reduced audit bit based scheme (RAS) is proposed which further improves system performance. We derive the new optimal fusion rule and the simulation results show that RAS outperforms EAS and TAS in terms of both robustness and detection performance of the system. Then, we extend the proposed RAS for a wide-area cluster based distributed wireless sensor networks (CWSNs). Simulation results show that the proposed RAS significantly reduces the communication overhead between the sensors and the FC, which prolongs the lifetime of the network.

This work considers a Bayesian signal processing problem where increasing the power of the probing signal may cause risks or undesired consequences. We employ a market based approach to solve energy management problems for signal detection while balancing multiple objectives. In particular, the optimal amount of resource consumption is determined so as to maximize a profit-loss based expected utility function. Next, we study the human behavior of resource consumption while taking individuals' behavioral disparity into account. Unlike rational decision makers who consume the amount of resource to maximize the expected utility function, human decision makers act to maximize their subjective utilities. We employ prospect theory to model humans' loss aversion towards a risky event. The amount of resource consumption that maximizes the humans' subjective utility is derived to characterize the actual behavior of humans. It is shown that loss attitudes may lead the human to behave quite differently from a rational decision maker.

A Q-system in a C⁎ 2-category is a unitary version of a separable Frobenius algebra object and can be viewed as a unitary version of a higher idempotent. We define a higher unitary idempotent completion for C⁎ 2-categories called Q-system completion and study its properties. We show that the C⁎ 2-category of right correspondences of unital C⁎-algebras is Q-system complete by constructing an inverse realization †-2-functor. We use this result to construct induced actions of group theoretical unitary fusion categories on continuous trace C⁎-algebras with connected spectra.

For multi-area interconnected power networks, energy interchange among subareas is benefit to improve energy utilization. The regulators of different subareas are generally incapable to access the private system information from others, which makes the information barriers. Then, the conventional integrated Power Flow (PF) method based on complete network information show incapability in analyzing operation state for multi-area systems. To generate the same PF solution as that by integrated method, an optional approach is to separately run PF Calculation (PFC) for each subarea alternated with the adjustment of state variables for boundary buses. Thus, this study proposes a decomposition-coordination PF model with two layers of coordination. Moreover, incorporated with the Ridge Regression, an improved Locally Weighted Linear Regression (LWLR) approach is established in treating the adjustment of boundary variables. Case studies based on IEEE300 and IEEE RTS-1996 test systems demonstrate the efficiency of the proposed method, which generates PF results with high accuracy and convergence in case of less data requirement compared to conventional Newton's method. Furthermore, the proposed PF method is capable to identify the subarea with potential questionable data in case of PFC divergence, contributing to analyzing the cause of numerical ill-conditions.

Power grid interconnection is an effective way for energy interchange among subareas to improve energy utilization. The conventional integrated Power Flow (PF) method is effective to analyze system operation state under the circumstance of complete power network information. However, for multi-area interconnected networks, the independent regulator for each subarea is generally incapable to access the private system information from others, which makes the information barriers. To generate the same PF solution as that by integrated method, an optional approach is to separately run PF Calculation (PFC) for each subarea alternated with the adjustment of state variables for boundary buses. Thus, this study proposes a decomposition-coordination PF model with two layers of coordination. Moreover, incorporated with the Ridge Regression, an improved Locally Weighted Linear Regression (LWLR) approach is established in treating the adjustment of boundary variables. Case studies based on IEEE300 and IEEE RTS-1996 test systems demonstrate the efficiency of the proposed method to generate PF results with high accuracy and convergence. Furthermore, the proposed PF method is capable to identify the subarea with potential questionable data i n case of PFC divergence, contributing to analyzing the cause of numerical ill-conditions.

Two-dimensional generalized XY spin model on a triangular lattice is studied by means of Monte-Carlo simulations. The critical temperatures of Berezinskii-Kosterlitz-Thouless (BKT) phase transition are obtained by the method of helicity modulus. It is found that the results are consistent with those obtained by other methods. The vortex density and the vortex-antivortex pair formation energy are also obtained. The result shows that the critical temperature decreases with the increase of the generalization parameter q. While the vortex-antivortex pair formation energy increases with the increase of q when q>1.

The system of the extradosed cable-stayed bridge constantly changed during construction. In order to obtain the reasonable finished dead state and ensure the structural safety during construction, it is necessary to deeply investigate the construction stages. A finite element model of a real long- span railway extradosed cable-stayed bridge built in China was established by using MIDAS/Civil finite element software to analyze the stress and deformation of the bridge based on reasonable construction state. The results show that it should be paid attention to the longitudinal displacement at the top of the tower after the middle-span closure stage, and the vertical displacement of the girder in the longest single cantilever stage. The maximum compressive stresses of the tower appeared after the cable tensioning and the girder appeared when the bridge is in the longest single cantilever state are less than the design compressive strength of concrete C55. The maximum tensile stress of the girder appeared when the bridge is in the longest double cantilever state is less than the design tensile strength of concrete C55.