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The robustness of complex networks against node failure and malicious attack has been of interest for decades, while most of the research has focused on random attack or hub-targeted attack. In many real-world scenarios, however, attacks are neither random nor hub-targeted, but localized, where a group of neighboring nodes in a network are attacked and fail. In this paper we develop a percolation framework to analytically and numerically study the robustness of complex networks against such localized attack. In particular, we investigate this robustness in Erd s-Rényi networks, random-regular networks, and scale-free networks. Our results provide insight into how to better protect networks, enhance cybersecurity, and facilitate the design of more robust infrastructures.

Absolute Concentration Robustness (ACR) was introduced by Shinar and Feinberg (Science 327:1389-1391, 2010) as robustness of equilibrium species concentration in a mass action dynamical system. Their aim was to devise a mathematical condition that will ensure robustness in the function of the biological system being modeled. The robustness of function rests on what we refer to as empirical robustness —the concentration of a species remains unvarying, when measured in the long run, across arbitrary initial conditions. Even simple examples show that the ACR notion introduced in Shinar and Feinberg (Science 327:1389-1391, 2010) (here referred to as static ACR ) is neither necessary nor sufficient for empirical robustness. To make a stronger connection with empirical robustness, we define dynamic ACR , a property related to long-term, global dynamics, rather than only to equilibrium behavior. We discuss general dynamical systems with dynamic ACR properties as well as parametrized families of dynamical systems related to reaction networks. We find necessary and sufficient conditions for dynamic ACR in complex balanced reaction networks, a class of networks that is central to the theory of reaction networks.

In quantum mechanics performing a measurement is an invasive process which generally disturbs the system. Due to this phenomenon, there exist incompatible quantum measurements, i.e. measurements that cannot be simultaneously performed on a single copy of the system. It is then natural to ask what the most incompatible quantum measurements are. To answer this question, several measures have been proposed to quantify how incompatible a set of measurements is, however their properties are not well-understood. In this work, we develop a general framework that encompasses all the commonly used measures of incompatibility based on robustness to noise. Moreover, we propose several conditions that a measure of incompatibility should satisfy, and investigate whether the existing measures comply with them. We find that some of the widely used measures do not fulfil these basic requirements. We also show that when looking for the most incompatible pairs of measurements, we obtain different answers depending on the exact measure. For one of the measures, we analytically prove that projective measurements onto two mutually unbiased bases are among the most incompatible pairs in every dimension. However, for some of the remaining measures we find that some peculiar measurements turn out to be even more incompatible.

Numerics converging on stripes The Hubbard model (HM) describes the behavior of interacting particles on a lattice where the particles can hop from one lattice site to the next. Although it appears simple, solving the HM when the interactions are repulsive, the particles are fermions, and the temperature is low—all of which applies in the case of correlated electron systems—is computationally challenging. Two groups have tackled this important problem. Huang et al. studied a three-band version of the HM at finite temperature, whereas Zheng et al. used five complementary numerical methods that kept each other in check to discern the ground state of the HM. Both groups found evidence for stripes, or one-dimensional charge and/or spin density modulations. Science, this issue p. 1161, p. 1155 Upon doping, Mott insulators often exhibit symmetry breaking where charge carriers and their spins organize into patterns known as stripes. For high–transition temperature cuprate superconductors, stripes are widely suspected to exist in a fluctuating form. We used numerically exact determinant quantum Monte Carlo calculations to demonstrate dynamical stripe correlations in the three-band Hubbard model, which represents the local electronic structure of the copper-oxygen plane. Our results, which are robust to varying parameters, cluster size, and boundary conditions, support the interpretation of experimental observations such as the hourglass magnetic dispersion and the Yamada plot of incommensurability versus doping in terms of the physics of fluctuating stripes. These findings provide a different perspective on the intertwined orders emerging from the cuprates’ normal state.

Animal morphogenesis arises from the complex interplay between multiple mechanical and biochemical processes with mutual feedback. Developing an effective, coarse-grained description of morphogenesis is essential for understanding how these processes are coordinated across scales to form robust, functional outcomes. Here we show that the nematic order of the supracellular actin fibres in regenerating Hydra defines a slowly varying field, whose dynamics provide an effective description of the morphogenesis process. We show that topological defects in this field, which are long-lived yet display rich dynamics, act as organization centres with morphological features developing at defect sites. These observations suggest that the nematic orientation field can be considered a ‘mechanical morphogen’ whose dynamics, in conjugation with various biochemical and mechanical signalling processes, result in the robust emergence of functional patterns during morphogenesis. Topological defects in the nematic order of actin fibres in a regenerating organism are shown to be tied to key feature formation. Fibre alignment sets the regenerated body axis and defect sites form organizing centres for the developing body plan.

We study the robust double auction mechanisms, that is, the double auction mechanisms that satisfy dominant strategy incentive compatibility, ex-post individual rationality and ex-post budget balance. We first establish that the price in any robust mechanism does not depend on the valuations of the trading players. We next establish that, with a non-bossiness assumption, the price in any robust mechanism does not depend on players' valuations at all, whether trading or non-trading. Our main result is the characterization result that, with a non-bossy assumption along with other assumptions on the properties of the mechanism, the generalized posted mechanism in which a constant price is posted for each possible set of traders is the only robust double auction mechanism. We also show that, even without the non-bossiness assumption, it is quite difficult to find a reasonable robust double auction mechanism other than the generalized posted price mechanism.

Optical knots and links have attracted great attention because of their exotic topological characteristics. Recent investigations have shown that the information encoding based on optical knots could possess robust features against external perturbations. However, as a superior coding scheme, it is also necessary to achieve a high capacity, which is hard to be fulfilled by existing knot-carriers owing to the limit number of associated topological invariants. Thus, how to realize the knot-based information coding with a high capacity is a key problem to be solved. Here, we create a type of nested vortex knot, and show that it can be used to fulfill the robust information coding with a high capacity assisted by a large number of intrinsic topological invariants. In experiments, we design and fabricate metasurface holograms to generate light fields sustaining different kinds of nested vortex links. Furthermore, we verify the feasibility of the high-capacity coding scheme based on those topological optical knots. Our work opens another way to realize the robust and high-capacity optical coding, which may have useful impacts on the field of information transfer and storage.

I construct a novel random double auction as a robust bilateral trading mechanism for a profit-maximizing intermediary who facilitates trade between a buyer and a seller. It works as follows. The intermediary publicly commits to charging a fixed commission fee and randomly drawing a spread from a uniform distribution. Then the buyer submits a bid price and the seller submits an ask price simultaneously. If the difference between the bid price and the ask price is greater than the realized spread, then the asset is transacted at the midpoint price, and each pays the intermediary half of the fixed commission fee. Otherwise, no trade takes place, and no one pays or receives anything. I show that the random double auction maximizes the worst-case expected profit across all dominant-strategy incentive compatible and ex-post individually rational mechanisms for the symmetric case. I also construct a robust trading mechanism with similar properties for the asymmetric case.

Abstract Person Re-Identification(ReID) is developing rapidly these years powered by deep learning. However most existing methods with state-of-the-art performance are highly dependent on “heavy” CNN backbones, which are hard to deploy on lightweight computing devices. In this paper, we propose a novel feature distillation method called Relevance Transfer, which aims to transfer the knowledge hidden inside the relation of different feature parts from teacher network to tiny student network. And we conduct a Multi-Granularity Horizontal Partition (MGHP) strategy to make training more efficient and robust. As results on two mainstream ReID datasets show, our method achieves competitive performance with original logits Knowledge Distillation (logits KD), and gains even more aggressive performance when works along with logits KD.

Recently, several quantum machine learning algorithms have been proposed that may offer quantum speed-ups over their classical counterparts. Most of these algorithms are either heuristic or assume that data can be accessed quantum-mechanically, making it unclear whether a quantum advantage can be proven without resorting to strong assumptions. Here we construct a classification problem with which we can rigorously show that heuristic quantum kernel methods can provide an end-to-end quantum speed-up with only classical access to data. To prove the quantum speed-up, we construct a family of datasets and show that no classical learner can classify the data inverse-polynomially better than random guessing, assuming the widely believed hardness of the discrete logarithm problem. Furthermore, we construct a family of parameterized unitary circuits, which can be efficiently implemented on a fault-tolerant quantum computer, and use them to map the data samples to a quantum feature space and estimate the kernel entries. The resulting quantum classifier achieves high accuracy and is robust against additive errors in the kernel entries that arise from finite sampling statistics. Many quantum machine learning algorithms have been proposed, but it is typically unknown whether they would outperform classical methods on practical devices. A specially constructed algorithm shows that a formal quantum advantage is possible.