In this paper, we develop a new method to classify abelian automorphism groups of hypersurfaces. We use this method to classify (Theorem 4.2) abelian groups that admit a liftable action on a smooth cubic fourfold. A parallel result (Theorem 5.1) is obtained for quartic surfaces.
Quantum sensing employs quantum resources of a sensor to attain a smaller estimation error of physical quantities than the limit constrained by classical physics. To measure a quantum reservoir, which is significant in decoherence control, a nonunita
ry-encoding sensing scheme becomes necessary. However, previous studies showed that the reservoir-induced degradation to quantum resources of the sensor makes the errors divergent with the increase of encoding time. We here propose a scheme to use $N$ two-level systems as the sensor to measure a quantum reservoir. A threshold, above which the shot-noise-limited sensing error saturates or even persistently decreases with the encoding time, is uncovered. Our analysis reveals that it is due to the formation of a bound state of the total sensor-reservoir system. Solving the outstanding error-divergency problem in previous studies, our result supplies an insightful guideline in realizing a sensitive measurement of quantum reservoirs.
To take full advantage of fast-growing unlabeled networked data, this paper introduces a novel self-supervised strategy for graph representation learning by exploiting natural supervision provided by the data itself. Inspired by human social behavior
, we assume that the global context of each node is composed of all nodes in the graph since two arbitrary entities in a connected network could interact with each other via paths of varying length. Based on this, we investigate whether the global context can be a source of free and effective supervisory signals for learning useful node representations. Specifically, we randomly select pairs of nodes in a graph and train a well-designed neural net to predict the contextual position of one node relative to the other. Our underlying hypothesis is that the representations learned from such within-graph context would capture the global topology of the graph and finely characterize the similarity and differentiation between nodes, which is conducive to various downstream learning tasks. Extensive benchmark experiments including node classification, clustering, and link prediction demonstrate that our approach outperforms many state-of-the-art unsupervised methods and sometimes even exceeds the performance of supervised counterparts.
The richness in the content of various information networks such as social networks and communication networks provides the unprecedented potential for learning high-quality expressive representations without external supervision. This paper investig
ates how to preserve and extract the abundant information from graph-structured data into embedding space in an unsupervised manner. To this end, we propose a novel concept, Graphical Mutual Information (GMI), to measure the correlation between input graphs and high-level hidden representations. GMI generalizes the idea of conventional mutual information computations from vector space to the graph domain where measuring mutual information from two aspects of node features and topological structure is indispensable. GMI exhibits several benefits: First, it is invariant to the isomorphic transformation of input graphs---an inevitable constraint in many existing graph representation learning algorithms; Besides, it can be efficiently estimated and maximized by current mutual information estimation methods such as MINE; Finally, our theoretical analysis confirms its correctness and rationality. With the aid of GMI, we develop an unsupervised learning model trained by maximizing GMI between the input and output of a graph neural encoder. Considerable experiments on transductive as well as inductive node classification and link prediction demonstrate that our method outperforms state-of-the-art unsupervised counterparts, and even sometimes exceeds the performance of supervised ones.
It is becoming widely accepted that very early in the origin of life, even before the emergence of genetic encoding, reaction networks of diverse small chemicals might have manifested key properties of life, namely self-propagation and adaptive evolu
tion. To explore this possibility, we formalize the dynamics of chemical reaction networks within the framework of chemical ecosystem ecology. To capture the idea that life-like chemical systems are maintained out of equilibrium by fluxes of energy-rich food chemicals, we model chemical ecosystems in well-mixed containers that are subject to constant dilution by a solution with a fixed concentration of food chemicals. Modelling all chemical reactions as fully reversible, we show that seeding an autocatalytic cycle (AC) with tiny amounts of one or more of its member chemicals results in logistic growth of all member chemicals in the cycle. This finding justifies drawing an instructive analogy between an AC and the population of a biological species. We extend this finding to show that pairs of ACs can show competitive, predator-prey, or mutualistic associations just like biological species. Furthermore, when there is stochasticity in the environment, particularly in the seeding of ACs, chemical ecosystems can show complex dynamics that can resemble evolution. The evolutionary character is especially clear when the network architecture results in ecological precedence (survival of the first), which makes the path of succession historically contingent on the order in which cycles are seeded. For all its simplicity, the framework developed here is helpful for visualizing how autocatalysis in prebiotic chemical reaction networks can yield life-like properties. Furthermore, chemical ecosystem ecology could provide a useful foundation for exploring the emergence of adaptive dynamics and the origins of polymer-based genetic systems.
In this paper, we study how the Pruned Landmark Labeling (PPL) algorithm can be parallelized in a scalable fashion, producing the same results as the sequential algorithm. More specifically, we parallelize using a Vertex-Centric (VC) computational mo
del on a modern SIMD powered multicore architecture. We design a new VC-PLL algorithm that resolves the apparent mismatch between the inherent sequential dependence of the PLL algorithm and the Vertex- Centric (VC) computing model. Furthermore, we introduce a novel batch execution model for VC computation and the BVC-PLL algorithm to reduce the computational inefficiency in VC-PLL. Quite surprisingly, the theoretical analysis reveals that under a reasonable assumption, BVC-PLL has lower computational and memory access costs than PLL and indicates it may run faster than PLL as a sequential algorithm. We also demonstrate how BVC-PLL algorithm can be extended to handle directed graphs and weighted graphs and how it can utilize the hierarchical parallelism on a modern parallel computing architecture. Extensive experiments on real-world graphs not only show the sequential BVC-PLL can run more than two times faster than the original PLL, but also demonstrates its parallel efficiency and scalability.
Quantum metrology employs quantum effects to attain a measurement precision surpassing the limit achievable in classical physics. However, it was previously found that the precision returns the shot-noise limit (SNL) from the ideal Zeno limit (ZL) du
e to the photon loss in quantum metrology based on Mech-Zehnder interferometer. Here, we find that not only the SNL can be beaten, but also the ZL can be asymptotically recovered in long-encoding-time condition when the photon dissipation is exactly studied in its inherent non-Markovian manner. Our analysis reveals that it is due to the formation of a bound state of the photonic system and its dissipative noise. Highlighting the microscopic mechanism of the dissipative noise on the quantum optical metrology, our result supplies a guideline to realize the ultrasensitive measurement in practice by forming the bound state in the setting of reservoir engineering.
Inspired by findings of sensorimotor coupling in humans and animals, there has recently been a growing interest in the interaction between action and perception in robotic systems [Bogh et al., 2016]. Here we consider perception and action as two ser
ial information channels with limited information-processing capacity. We follow [Genewein et al., 2015] and formulate a constrained optimization problem that maximizes utility under limited information-processing capacity in the two channels. As a solution we obtain an optimal perceptual channel and an optimal action channel that are coupled such that perceptual information is optimized with respect to downstream processing in the action module. The main novelty of this study is that we propose an online optimization procedure to find bounded-optimal perception and action channels in parameterized serial perception-action systems. In particular, we implement the perceptual channel as a multi-layer neural network and the action channel as a multinomial distribution. We illustrate our method in a NAO robot simulator with a simplified cup lifting task.
In this paper, we will consider derived equivalences for differential graded endomorphism algebras by Kellers approaches. First we construct derived equivalences of differential graded algebras which are endomorphism algebras of the objects from a tr
iangle in the homotopy category of differential graded algebras. We also obtain derived equivalences of differential graded endomorphism algebras from a standard derived equivalence of finite dimensional algebras. Moreover, under some conditions, the cohomology rings of these differential graded endomorphism algebras are also derived equivalent. Then we give an affirmative answer to a problem of Dugas cite{Dugas2015} in some special case.
