Recent advancements in Neural Combinatorial Optimization (NCO) have shown promise in solving routing problems like the Traveling Salesman Problem (TSP) and Capacitated Vehicle Routing Problem (CVRP) without handcrafted designs. Research in this domain has explored two primary categories of methods: iterative and non-iterative. While non-iterative methods struggle to generate near-optimal solutions directly, iterative methods simplify the task by learning local search steps. However, existing iterative methods are often limited by restricted neighborhood searches, leading to suboptimal results. To address this limitation, we propose a novel approach that extends the search to larger neighborhoods by learning a destroy-and-repair strategy. Specifically, we introduce a Destroy-and-Repair framework based on Hyper-Graphs (DRHG). This framework reduces consecutive intact edges to hyper-edges, allowing the model to pay more attention to the destroyed part and decrease the complexity of encoding all nodes. Experiments demonstrate that DRHG achieves stateof-the-art performance on TSP with up to 10,000 nodes and shows strong generalization to real-world TSPLib and CVRPLib problems.
Randomized compiling (RC) is the standard technique for converting coherent (systematic) gate errors into stochastic noise. The prevailing view is that the twirl destroys coherent-error information. An exact Fisher-information conservation law shows the opposite: the coherent-error information RC removes from the averaged output is preserved in full in the twirl labels -- the per-shot random gate choices that standard RC discards. Retaining the labels and forming a label-outcome correlation recovers the coherent error parameters at the quantum Fisher-information limit, unbiased under all standard incoherent channels, at zero additional circuit cost. Two theorems are proved, the conservation law is verified to machine precision across 12 circuit families, and recovery is confirmed on a 127-qubit IBM Quantum processor (ibm_marrakesh). The labeled estimator recovers injected coherent phases to within 0.0063 rad of the true value across all depths tested, while the standard marginal estimator returns near-zero signal at every depth.
A fundamental step in the patent application process is the determination of whether there exist prior patents that are novelty destroying. This step is routinely performed by both applicants and examiners, in order to assess the novelty of proposed inventions among the millions of applications filed annually. However, conducting this search is time and labor-intensive, as searchers must navigate complex legal and technical jargon while covering a large amount of legal claims. Automated approaches using information retrieval and machine learning approaches to detect novelty destroying patents present a promising avenue to streamline this process, yet research focusing on this space remains limited. In this paper, we introduce a novel data pipeline, ClaimCompare, designed to generate labeled patent claim datasets suitable for training IR and ML models to address this challenge of novelty destruction assessment. To the best of our knowledge, ClaimCompare is the first pipeline that can generate multiple novelty destroying patent datasets. To illustrate the practical relevance of this pipeline, we utilize it to construct a sample dataset comprising of over 27K patents in the electroche
Motility-Induced Phase Separation (MIPS) is a distinctive phenomenon in active matter that arises from its inherent non-equilibrium nature. Despite recent progress in understanding MIPS in dry active systems, it has been debated whether MIPS can be observed in wet systems in which fluid-mediated hydrodynamic interactions (HI) are present. We use theory and large-scale {\it Active Fast Stokesian Dynamics} simulations of the so-called squirmer model to show that collision-induced pusher force dipoles, which are present even for the simplest neutral squirmers (stealth swimmers), destroy MIPS when HI are included. Both rotational and translational HI independently suppress phase separation: rotation by shortening a swimmer's persistence length (and thus reducing the swim pressure), translation by a confinement-scale advective fluid flow. We further clarify that collisional dipoles between swimmers and boundaries can generate attractive flows that promote particle aggregation observed in some previous simulations and experiments. Finally, we show how to recover MIPS in fluidic environments by tuning the magnitude of the HI through brush-like surface coatings on the active particles.
In arXiv:2410.21850, I proved that the quantum coherence between the mass eigenstates of a neutrino will be destroyed if they are correlated with different momenta. In arXiv:2411.01190, James M. Cline claimed that I had made the unrealistic assumption that the neutrino is always in a nearly exact energy eigenstate, and ignored the spatial dependence of the wavefunction in my paper. However, I did not assume that the neutrino is in a nearly exact eigenstate of energy anywhere in my paper, and the wavefunction I wrote in the position representation has a spatial dependence. The argumentation of arXiv:2411.01190 is based on misinterpreting my claim, and on ignoring the critical fact that the neutrino's wavepacket has a finite size and the detector has a large volume.
For a rotating black hole to be nonsingular, it means that there are no spacetime singularities at its center. The destruction of the event horizon of such a rotating black hole is not constrained by the weak cosmic censorship conjecture, which may provide possibilities to understand the internal structure of black hole event horizons. In this paper, we employ test particles with large angular momentum and a scalar field with large angular momentum to investigate the potential of destroying the event horizon of rotating Black-Bounce black holes. Additionally, we investigate the possibility of destroying the event horizon of a rotating Black-Bounce black hole by considering test particles with large angular momentum and scalar fields with large angular momentum, covering the entire range of the rotating Black-Bounce black hole. We analyze the influence of the parameter m on the possibility of destroying the event horizon in this spacetime. Our analysis reveals that under extreme or near-extreme conditions, the event horizon of this spacetime can potentially be destroyed after the absorption of particles energy and angular momentum, as well as the scattering of scalar fields. Additio
In the paper we first characterize three-dimensional Kolmogorov systems possessing a two-dimensional invariant sphere in $\mathbb{R}^3$, then establish a global attracting criterion for this invariant sphere in $\mathbb{R}^3$ except the origin, and give global dynamics with isolated equilibria on the sphere. Finally, we consider the persistence of the attractive invariant sphere under the perturbation induced by linear multiplicative Wiener noise. It is shown that suitable noise intensity can destroy the sphere and lead to bifurcation of stationary measures.
Strengthening or destroying a network is a very important issue in designing resilient networks or in planning attacks against networks including planning strategies to immunize a network against diseases, viruses etc.. Here we develop a method for strengthening or destroying a random network with a minimum cost. We assume a correlation between the cost required to strengthen or destroy a node and the degree of the node. Accordingly, we define a cost function c(k), which is the cost of strengthening or destroying a node with degree k. Using the degrees $k$ in a network and the cost function c(k), we develop a method for defining a list of priorities of degrees, and for choosing the right group of degrees to be strengthened or destroyed that minimizes the total price of strengthening or destroying the entire network. We find that the list of priorities of degrees is universal and independent of the network's degree distribution, for all kinds of random networks. The list of priorities is the same for both strengthening a network and for destroying a network with minimum cost. However, in spite of this similarity there is a difference between their p_c - the critical fraction of node
We investigate a gedanken experiment to destroy an extremally charged black hole by dropping a test particle, provided that there are multiple $U(1)$ gauge fields coupled with each other through higher derivative interactions. In the absence of higher derivative corrections, it is known that the Coulomb repulsion prevents a test particle that would break the extremal condition from falling into an extremal black hole and therefore the black hole cannot be destroyed. We extend this observation to include higher derivative corrections. Although the extremal condition is modified by the higher derivative interactions, we find that the repulsive force induced by the higher derivative couplings is responsible for preventing a test particle that would break the modified extremal condition to reach the event horizon. Thus, we confirm that the weak cosmic censorship conjecture holds for extremally charged black holes even in the presence of higher derivative corrections, as long as the test particle approximation is justified.
If a neutrino or antineutrino produced in the decay of an unstable particle is not entangled to its accompanying particles, its mass is necessarily correlated with its momentum. In this manuscript, I illustrate that this entanglement would destroy the quantum coherence between the neutrino's mass eigenstates in both the momentum and position representations, which was overlooked by other authors in previous investigations of entanglement and coherence associated with neutrino oscillations. I further point out that the states of a neutrino and an electron become nonseparable after their charged-current interaction. This nonseparability leads to decoherence for neutrinos propagating in matter, but was not taken into consideration in previous investigations of the matter effect.
We use magneto-hydrodynamical simulations of Milky Way-mass haloes from the Auriga project to examine the properties of surviving and destroyed dwarf galaxies that are accreted by these haloes over cosmic time. We show that the combined luminosity function of surviving and destroyed dwarfs at infall is similar in the various Auriga haloes, and is dominated by the destroyed dwarfs. There is, however, a strong dependence on infall time: destroyed dwarfs have typically early infall times, $t_{infall}<6$ Gyr, whereas the majority of dwarfs accreted at $t_{infall}>10$ Gyr have survived to the present day. Because of their late infall the surviving satellites today had higher metallicites at infall than their destroyed counterparts of similar infall mass; the difference is even more pronounced for the present-day metallicites of satellites, many of which continue to form stars after infall. In agreement with previous work, we find that a small number of relatively massive destroyed dwarf galaxies dominate the mass of the stellar haloes. However, there is a significant radial dependence: while 90 per cent of the mass in the inner regions ($<\,20\,$kpc) is contributed, on average,
We propose a new form of entanglement called the dormant entanglement that can be activated or destroyed by the basis choice of measurements on an external system. The dormant entanglement without activation cannot be used as a quantum communication resource and has reduced correlation as compared to the Bell states. A particular form of the dormant entanglement is so weak that, without activation, no correlation in any basis can be observed between the entangled qubits. The dormant entanglement showcases a unique quantum behavior that the physical description of a local system remains incomplete until the information on all external systems entangled with the local system becomes available. For a potential application, we propose an n-party collective quantum communication channel that allows any 2 out of the n parties to activate an entanglement pair with the complete consensus of all other parties.
For prohibitively large-scale Travelling Salesman Problems (TSPs), existing algorithms face big challenges in terms of both computational efficiency and solution quality. To address this issue, we propose a hierarchical destroy-and-repair (HDR) approach, which attempts to improve an initial solution by applying a series of carefully designed destroy-and-repair operations. A key innovative concept is the hierarchical search framework, which recursively fixes partial edges and compresses the input instance into a small-scale TSP under some equivalence guarantee. This neat search framework is able to deliver highly competitive solutions within a reasonable time. Fair comparisons based on nineteen famous large-scale instances (with 10,000 to 10,000,000 cities) show that HDR is highly competitive against existing state-of-the-art TSP algorithms, in terms of both efficiency and solution quality. Notably, on two large instances with 3,162,278 and 10,000,000 cities, HDR breaks the world records (i.e., best-known results regardless of computation time), which were previously achieved by LKH and its variants, while HDR is completely independent of LKH. Finally, ablation studies are performed
The destruction of the event horizon of a nonsingular black hole, which is not prevented by the weak cosmic censorship conjecture, might provide us the possibility to access quantum regime of gravity inside black hole. We investigate the possibility of overspinning a nonsingular rotating quantum-corrected black hole by a test particle and a scalar field in this paper, and analyse the effect of the quantum parameter on the destruction of the event horizon. For the test particle injection, both extremal and near-extremal black holes cannot be overspun due to the existence of the quantum parameter. And the larger the quantum parameter the harder the black hole to be overspun. It seems that the quantum parameter acts as a protector to prevent the black hole to be destroyed. However, for the test scalar field scattering, both extremal and near-extremal black holes can be destroyed. Due to the loop quantum gravity correction, the angular velocity of the extremal black hole shifts from that of the extremal Kerr black hole. This provides a small range of wave modes to destroy the event horizon of the quantum-corrected black hole.
Given an abelian group $G$, it is natural to ask whether there exists a permutation $π$ of $G$ that "destroys" all nontrivial 3-term arithmetic progressions (APs), in the sense that $π(b) - π(a) eq π(c) - π(b)$ for every ordered triple $(a,b,c) \in G^3$ satisfying $b-a = c-b eq 0$. This question was resolved for infinite groups $G$ by Hegarty, who showed that there exists an AP-destroying permutation of $G$ if and only if $G/Ω_2(G)$ has the same cardinality as $G$, where $Ω_2(G)$ denotes the subgroup of all elements in $G$ whose order divides $2$. In the case when $G$ is finite, however, only partial results have been obtained thus far. Hegarty has conjectured that an AP-destroying permutation of $G$ exists if $G = \mathbb{Z}/n\mathbb{Z}$ for all $n eq 2,3,5,7$, and together with Martinsson, he has proven the conjecture for all $n > 1.4 \times 10^{14}$. In this paper, we show that if $p$ is a prime and $k$ is a positive integer, then there is an AP-destroying permutation of the elementary $p$-group $(\mathbb{Z}/p\mathbb{Z})^k$ if and only if $p$ is odd and $(p,k) ot\in \{(3,1),(5,1), (7,1)\}$.
Recently, several authors have studied the possibility of overspinning or overcharging an existing black hole to destroy its event horizon and make the central singularity naked. When all the effects are properly taken into account, any attempt to destroy the black hole seems to be doomed to fail, in agreement with the weak cosmic censorship conjecture. In this letter, we study the possibility of destroying the event horizon of regular black holes. These objects have no central singularity and therefore they are not protected by the cosmic censorship hypothesis. Our results strongly support the conclusion that regular black holes can be destroyed. If we believe that the central singularity in astrophysical black holes is solved by quantum gravity effects, we might have a chance to see the black hole's internal region and observe quantum gravity phenomena. As our finding implies the violation of the black hole's area theorem, the collision of two black holes may release an amount of energy exceeding the Hawking bound, which can be experimentally tested by gravitational wave detectors.
Resource theory is a widely-applicable framework for analyzing the physical resources required for given tasks, such as computation, communication, and energy extraction. In this paper, we propose a general scheme for analyzing resource theories based on resource destroying maps, which leave resource-free states unchanged but erase the resource stored in all other states. We introduce a group of general conditions that determine whether a quantum operation exhibits typical resource-free properties in relation to a given resource destroying map. Our theory reveals fundamental connections among basic elements of resource theories, in particular, free states, free operations, and resource measures. In particular, we define a class of simple resource measures that can be calculated without optimization, and that are monotone nonincreasing under operations that commute with the resource destroying map. We apply our theory to the resources of coherence and quantum correlations (e.g., discord), two prominent features of nonclassicality.
We report theoretical investigations on how edge states are destroyed in disordered mesoscopic samples by calculating a "phase diagram" in terms of energy versus disorder strength $(E,W)$, and magnetic field versus disorder strength $(B,W)$, in the integer quantum Hall regime. It is found that as the disorder strength $W$ increases, edge states are destroyed one by one if transmission eigen-channels are used to characterize the edge states. Near the insulating regime, transmission eigen-channels are closed one by one in the same order as edges states are destroyed. To identify those edge states which have survived disorder, we introduce a generalized current density that can be calculated and visualized.
The emerging quantum technologies rely on our ability to establish and control quantum systems in nonclassical states, exhibiting entanglement and quantum coherence. It is thus crucial to understand how entanglement and coherence can be created in the most efficient way. In this work we study optimal ways to create a large amount of quantum coherence via quantum channels. For this, we compare different scenarios, where the channel is acting on an incoherent state, on states which have coherence, and also on subsystems of multipartite quantum states. We show that correlations in multipartite systems do not enhance the ability of a quantum channel to create coherence. We also study the ability of quantum channels to destroy coherence, proving that a channel can destroy more coherence when acting on a subsystem of a bipartite state. Crucially, we also show that the destroyed coherence on multipartite system can exceed the upper bound of those on the single system when the total state is entangled. Our results significantly simplify the evaluation of coherence generating capacity of quantum channels, which we also discuss.
We combined mapping-mode mid-infrared Spitzer spectra with complementary infrared imaging to perform a spatially resolved study of polycyclic aromatic hydrocarbons (PAHs) emission from the central regions of 66 nearby galaxies, roughly evenly divided into star-forming systems and low-luminosity active galactic nuclei (AGNs). In conjunction with similar measurements available for quasars, we aim to understand the physical properties of PAHs across a broad range of black hole accretion power, with the goal of identifying observational diagnostics that can be used to probe the effect of AGNs on the host galaxy. Whereas the PAH emission correlates tightly with far-ultraviolet luminosity in star-forming regions, the spatially resolved regions of AGNs tend to be PAH-deficient. Moreover, AGN regions exhibit on average smaller PAH 6.2 μm/7.7 μm and larger PAH 11.3 μm/7.7 μm band ratios. Although the current data are highly restrictive, they suggest that these anomalous PAH band ratios cannot be explained by the effects of the AGN radiation field alone. Instead, they hint that small grains may be destroyed by the combined effects of radiative processes and shocks, which are plausibly linked