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Seidel switching is a classical operation on graphs which plays a central role in the theory of two-graphs, signed graphs, and switching classes. In this paper we focus on those switches which leave a given graph invariant up to isomorphism. We call such subsets of the vertex set \emph{identity Seidel switches}. After recalling basic properties of Seidel switching and the associated abelian group structure, we introduce Seidel equivalence classes of graphs and then study the structure of the family of identity Seidel switches of a fixed graph. We show that this family forms a 14 pages; 2--group under composition, and we obtain structural constraints on graphs in which many vertices or edges give rise to identity switches. In particular, we derive necessary conditions in terms of degree parameters, and we characterize certain edge-identity switches via an automorphism of an induced subgraph. Several constructions and examples are presented, and some open problems are proposed.

This paper investigates the optimal co-design of logical and continuous controls for switched linear systems governed by controlled logical switching dynamics. Unlike traditional switched systems with arbitrary or state-dependent switching, the switching signals here are generated by an internal logical dynamical system and explicitly integrated into the control synthesis. By leveraging the semi-tensor product (STP) of matrices, we embed the coupled logical and continuous dynamics into a unified algebraic state-space representation, transforming the co-design problem into a tractable linear-quadratic framework. We derive Riccati-type backward recursions for both deterministic and stochastic logical dynamics, which yield optimal state-feedback laws for continuous control alongside value-function-based, state-dependent decision rules for logical switching. To mitigate the combinatorial explosion inherent in logical decision-making, a hierarchical algorithm is developed to decouple offline precomputation from efficient online execution. Numerical simulations demonstrate the efficacy of the proposed framework.

Compute Express Link (CXL) switch allows memory extension via PCIe physical layer to address increasing demand for larger memory capacities in data centers. However, CXL attached memory introduces 170ns to 400ns memory latency. This becomes a significant performance bottleneck for applications that host data in persistent memory as all updates, after traversing the CXL switch, must reach persistent domain to ensure crash consistent updates. We make a case for persistent CXL switch to persist updates as soon as they reach the switch and hence significantly reduce latency of persisting data. To enable this, we presented a system independent persistent buffer (PB) design that ensures data persistency at CXL switch. Our PB design provides 12\% speedup, on average, over volatile CXL switch. Our \textit{read forwarding} optimization improves speedup to 15\%.

With a growing number of quantum networks in operation, there is a pressing need for performance analysis of quantum switching technologies. A quantum switch establishes, distributes, and maintains entanglements across a network. In contrast to a classical switching fabric, a quantum switch is a two sided queueing network. The switch generates Link Level Entanglements (LLEs), which are then fused to process the networks entanglement requests. Our proof techniques analyse a two time scale separation phenomenon at the fluid scale for a general switch topology. This allows us to demonstrate that the optimal fluid dynamics are given by a scheduling algorithm that solves a certain average reward Markov Decision Process.

We show that each (r, lambda)-design yields a class of switching methods that can be used produce cospectral graphs. We use this to explain several specific switching methods such as Godsil-McKay (GM) switching and Wang-Qiu-Hu (WQH) switching.

This paper studies cone-preserving linear discrete-time switched systems whose switching is governed by an automaton. For this general system class, we present performance analysis conditions for a broadly usable performance measure. In doing so, we generalize several known results for performance and stability analysis for switched and positive switched systems, providing a unifying perspective. We also arrive at novel $\ell_1$-performance analysis conditions for positive switched systems with constrained switching, for which we present an application-motivated numerical example. Further, the cone-preserving perspective provides insights into appropriate Lyapunov function selection.

R. Shorten, F. Wirth, O. Mason, K. Wulff and C. King have asked whether a linear switched system is guaranteed to be globally uniformly stable under arbitrary switching if it is known that every trajectory induced by a periodic switching law converges exponentially to the origin. Positive answers to this question have previously been announced for linear switched systems of order two and three. We answer this question negatively in all higher orders by constructing a fourth-order linear switched system with four switching states which is not uniformly exponentially stable but which has the property that every trajectory defined by a periodic switching law converges exponentially to the origin. We argue informally that positive linear systems with this combination of properties are likely to exist in sufficiently high dimensions.

This paper deals with input/output-to-state stability (IOSS) of switched nonlinear systems whose switching signals obey pre-specified restrictions on admissible switches between the subsystems and admissible dwell times on the subsystems. We present sufficient conditions on the subsystems, admissible switches between them and admissible dwell times on them, such that a switched system generated under all switching signals obeying the given restrictions is IOSS. Multiple Lyapunov-like functions and graph theory are the key apparatuses for our analysis. A numerical example is presented to demonstrate our results.

Reinforcement learning (RL) -- finding the optimal behaviour (also referred to as policy) maximizing the collected long-term cumulative reward -- is among the most influential approaches in machine learning with a large number of successful applications. In several decision problems, however, one faces the possibility of policy switching -- changing from the current policy to a new one -- which incurs a non-negligible cost, and in the decision one is limited to using historical data without the availability for further online interaction. Despite the inevitable importance of this offline learning scenario, to our best knowledge, very little effort has been made to tackle the key problem of balancing between the gain and the cost of switching in a flexible and principled way. Leveraging ideas from the area of optimal transport, we initialize the systematic study of policy switching in offline RL. We establish fundamental properties and design a Net Actor-Critic algorithm for the proposed novel switching formulation. Numerical experiments demonstrate the efficiency of our approach on multiple robot control benchmarks of the Gymnasium and traffic light control from SUMO-RL.

We demonstrate that epitaxial thin film antiferromagnet Mn2As exhibits the quench-switching effect, which was previously reported only in crystallographically similar antiferromagnetic CuMnAs thin films. Quench switching in Mn2As shows stronger increase in resistivity, reaching hundreds of percent at 5K, and significantly longer retention time of the metastable high-resistive state before relaxation towards the low-resistive uniform magnetic state. Qualitatively, Mn2As and CuMnAs show analogous parametric dependence of the magnitude and relaxation of the quench-switching signal. Quantitatively, relaxation dynamics in both materials show direct proportionality to the Néel temperature. This confirms that the quench switching has magnetic origin in both materials. The presented results suggest that the antiferromagnets crystalizing in the Cu2Sb structure are well suited for exploring and exploiting the intriguing physics of highly non-uniform magnetic states associated with the quench switching.

The asymmetric switch process is a binary stochastic process that alternates between the values one and minus one, where the distributions of the time in these states may differ. Two versions of the process are considered: a non-stationary version that starts with a switch at time zero and a stationary one constructed from the non-stationary one. Characteristics of these two processes, such as the expected values and covariance, are investigated. The main results show an equivalence between the monotonicity of the expected value functions and the distribution of the intervals having a stochastic representation in the form of a sum of random variables, where the number of terms follows a geometric distribution. This representation has a natural interpretation as a model in which switching attempts may fail at random. From these results, conditions are derived when these characteristics lead to valid interval distributions, which is vital in applications.

In this paper, we extend nonlinear negative imaginary (NI) systems theory to switched systems. Switched nonlinear NI systems and switched nonlinear output strictly negative imaginary (OSNI) systems are defined. We show that the interconnection of two switched nonlinear NI systems is still switched nonlinear NI. The interconnection of a switched nonlinear NI system and a switched nonlinear OSNI system is asymptotically stable under some assumptions. This stability result is then illustrated using a numerical example.

This paper deals with the analysis of input/output-to-state stability (IOSS) and construction of state-norm estimators for continuous-time switched nonlinear systems under restricted switching. Our contributions are twofold. First, given a family of systems, possibly containing unstable dynamics, a set of admissible switches between the subsystems and admissible minimum and maximum dwell times on the subsystems, we identify a class of switching signals that obeys the given restrictions and preserves IOSS of the resulting switched system. Second, we design a class of state-norm estimators for switched systems under our class of stabilizing switching signals. These estimators are switched systems themselves with two subsystems -- one stable and one unstable. The key apparatus for our analysis is multiple Lyapunov-like functions. A numerical example is presented to demonstrate the results.

Dynamic algorithm selection aims to exploit the complementarity of multiple optimization algorithms by switching between them during the search. While these kinds of dynamic algorithms have been shown to have potential to outperform their component algorithms, it is still unclear how this potential can best be realized. One promising approach is to make use of landscape features to enable a per-run trajectory-based switch. Here, the samples seen by the first algorithm are used to create a set of features which describe the landscape from the perspective of the algorithm. These features are then used to predict what algorithm to switch to. In this work, we extend this per-run trajectory-based approach to consider a wide variety of potential points at which to perform the switch. We show that using a sliding window to capture the local landscape features contains information which can be used to predict whether a switch at that point would be beneficial to future performance. By analyzing the resulting models, we identify what features are most important to these predictions. Finally, by evaluating the importance of features and comparing these values between multiple algorithms, we

The dynamical behavior of switched affine systems is known to be more intricate than that of the well-studied switched linear systems, essentially due to the existence of distinct equilibrium points for each subsystem. First, under arbitrary switching rules, the stability analysis must be generally carried out with respect to a compact set with non-empty interior rather than to a singleton. We provide a novel proof technique for existence and outer approximation of attractive invariant sets of a switched affine system, under the hypothesis of global uniform stability of its linearization. On the other hand, considering dwell-time switching signals, forward invariant sets need not exist for this class of switched systems, even for stable ones. Hence, more general notions of stability/boundedness are introduced and studied, highlighting the relations of these concepts to the uniform stability of the linear part of the system under the same class of dwell-time switching signals. These results reveal the main differences and specificities of switched affine systems with respect to linear ones, providing a first step for the analysis of switched systems composed by subsystems not sharin

For the identification of switched systems with a measured switching signal, this work aims to analyze the effect of switching strategies on the estimation error. The data for identification is assumed to be collected from globally asymptotically or marginally stable switched systems under switches that are arbitrary or subject to an average dwell time constraint. Then the switched system is estimated by the least-squares (LS) estimator. To capture the effect of the parameters of the switching strategies on the LS estimation error, finite-sample error bounds are developed in this work. The obtained error bounds show that the estimation error is logarithmic of the switching parameters when there are only stable modes; however, when there are unstable modes, the estimation error bound can increase linearly as the switching parameter changes. This suggests that in the presence of unstable modes, the switching strategy should be properly designed to avoid the significant increase of the estimation error.

The control properties of discrete-time switched linear systems (SLS) with switching signals generated by logical dynamic systems are studied using the semi-tensor product (STP) approach. With the algebraic state space representation (ASSR), the linear modes and the logical generators are aggregated as a hybrid system, leading to the criteria of reachability, controllability, observability, and reconstructibility of the SLSs. Algorithms for checking these properties are given. Then, two kinds of realization problems concerning whether the logical dynamic systems can generate the desired switching signals are investigated, and necessary and sufficient conditions for the realisability of the required switching signals are given with respect to the cases of fixed operating time switching and finite reference signal switching.

In this paper, we introduce a type switching mechanism for the Contact Process on the lattice $\mathbb{Z}^d$. That is, we allow the individual particles/sites to switch between two (or more) types independently of one another, and the different types may exhibit specific infection and recovery dynamics. Such type switches can eg.\ be motivated from biology, where 'phenotypic switching' is common among micro-organisms. Our framework includes as special cases systems with switches between 'active' and 'dormant' states (the Contact Process with dormancy, CPD), and the Contact Process in a randomly evolving environment (CPREE) introduced by Broman (2007). The 'standard' multi-type Contact Process (without type-switching) can also be recovered as a limiting case. After constructing the process from a graphical representation, we establish several basic properties that are mostly analogous to the classical Contact Process. We then provide couplings between several variants of the system, which in particular yield the existence of a phase transition. Further, we investigate the effect of the switching parameters on the critical value of the system by providing rigorous bounds obtained fro

This paper presents an analytical method to predict the delayed switching dynamics of nonlinear shallow arches while switching from one state to another state for different loading cases. We study an elastic arch subject to static loading and time-dependent loading separately. In particular, we consider a time-dependent loading that evolves linearly with time at a constant rate. In both cases, we observed that the switching does not occur abruptly when the load exceeds the static switching load, rather the time scale of the dynamics drastically slows down; hence there is a delay in switching. For time-independent loading, this delay increases as the applied load approach the static switching load. Whereas for a time-dependent loading, the delay is proportional to the rate of the applied load. Other than the loading parameters, the delay switching time also depends on the local curvature of the force-displacement function at the static switching point and the damping coefficient of the arch material. The delay switching occurs due to the flatness of the energy curve at static switching load. Therefore, we linearize the arch near the static switching point and get a reduced nonlinear