Finding pythons in unexpected places

We argue that novel (highly nonclassical) quantum extremal surfaces play a crucial role in reconstructing the black hole interior even for isolated, single-sided, non-evaporating black holes (i.e. with no auxiliary reservoir). Specifically, any code subspace where interior outgoing modes can be excited will have a quantum extremal surface in its maximally mixed state. We argue that as a result, reconstruction of interior outgoing modes is always exponentially complex. Our construction provides evidence in favor of a strong Python’s lunch proposal: that nonminimal quantum extremal surfaces are the exclusive source of exponential complexity in the holographic dictionary. We also comment on the relevance of these quantum extremal surfaces to the geometrization of state dependence in the typicality arguments for firewalls.

Efficient distributed discovery of bidirectional order dependencies

Bidirectional order dependencies (bODs) capture order relationships between lists of attributes in a relational table. They can express that, for example, sorting books by publication date in ascending order also sorts them by age in descending order. The knowledge about order relationships is useful for many data management tasks, such as query optimization, data cleaning, or consistency checking. Because the bODs of a specific dataset are usually not explicitly given, they need to be discovered. The discovery of all minimal bODs (in set-based canonical form) is a task with exponential complexity in the number of attributes, though, which is why existing bOD discovery algorithms cannot process datasets of practically relevant size in a reasonable time. In this paper, we propose the distributed bOD discovery algorithm DISTOD, whose execution time scales with the available hardware. DISTOD is a scalable, robust, and elastic bOD discovery approach that combines efficient pruning techniques for bOD candidates in set-based canonical form with a novel, reactive, and distributed search strategy. Our evaluation on various datasets shows that DISTOD outperforms both single-threaded and distributed state-of-the-art bOD discovery algorithms by up to orders of magnitude; it can, in particular, process much larger datasets.

Energy-Delay-Balanced Load Dispatching in Cloud-Assisted Edge Computing of Smart City

As smart city develops, Cloud Assisted Mobile Edge computing (CAME) framework is popular because it has the advantage of low delay and cost. But the computing capacity of mobile users is constrained in energy consumption, especially how to overcome the tradeoff between system latency and energy. In this article, an energy-delay-balanced load dispatching algorithm is suggested by exploiting the Karush-Kuhn-Tucker (KKT) conditions. Its exponential complexity is circumvented by taking the advantage of the linear property of constraints, rather than directly figuring out the KKT conditions. Compared to the fair ratio algorithm and the greedy algorithm, our suggested one is proved to provide better performance by simulation, which can decrease the delay by 35% and 49% respectively on the basis of the same energy consumption. The results indicate that the designed algorithm provides desirable tradeoff between system latency and energy.

A Formula for the Möbius Function of the Permutation Poset Based on a Topological Decomposition

International audience The poset P of all permutations ordered by pattern containment is a fundamental object of study in the field of permutation patterns. This poset has a very rich and complex topology and an understanding of its Möbius function has proved particularly elusive, although results have been slowly emerging in the last few years. Using a variety of topological techniques we present a two term formula for the Mo ̈bius function of intervals in P. The first term in this formula is, up to sign, the number of so called normal occurrences of one permutation in another. Our definition of normal occurrences is similar to those that have appeared in several variations in the literature on the Möbius function of this and other posets, but simpler than most of them. The second term in the formula is (still) complicated, but we conjecture that it equals zero for a significant proportion of intervals. We present some cases where the second term vanishes and others where it is nonzero. Computing the Möbius function recursively from its definition has exponential complexity, whereas the computation of the first term in our formula is polynomial and the exponential part is isolated to the second term, which seems to often vanish. This is thus the first polynomial time formula for the Möbius function of what appears to be a large proportion of all intervals of P.

Replication of Quantum Computing towards an Unconventional Environment using QuIDE

Current quantum computer simulation strategies are inefficient in simulation and their realizations are also failed to minimize those impacts of the exponential complexity for simulated quantum computations. We proposed a Quantum computer simulator model in this paper which is a coordinated Development Environment – QuIDE (Quantum Integrated Development Environment) to support the improvement of algorithm for future quantum computers. The development environment provides the circuit diagram of graphical building and flexibility of source code. Analyze the complexity of algorithms shows the performance results of the simulator and used for simulation as well as result of its deployment during simulation

Exponentially Complex “Classically Entangled” States in Arrays of One-Dimensional Nonlinear Elastic Waveguides

We demonstrate theoretically, using multiple-time-scale perturbation theory, the existence of nonseparable superpositions of elastic waves in an externally driven elastic system composed of three one-dimensional elastic wave guides coupled via nonlinear forces. The nonseparable states span a Hilbert space with exponential complexity. The amplitudes appearing in the nonseparable superposition of elastic states are complex quantities dependent on the frequency of the external driver. By tuning these complex amplitudes, we can navigate the state’s Hilbert space. This nonlinear elastic system is analogous to a two-partite two-level quantum system.

Pricing Personal Data Based on Data Provenance

Data have become an important asset. Mining the value contained in personal data, making personal data an exchangeable commodity, has become a hot spot of industry research. Then, how to price personal data reasonably becomes a problem we have to face. Based on previous research on data provenance, this paper proposes a novel minimum provenance pricing method, which is to price the minimum source tuple set that contributes to the query. Our pricing model first sets prices for source tuples according to their importance and then makes query pricing based on data provenance, which considers both the importance of the data itself and the relationships between the data. We design an exact algorithm that can calculate the exact price of a query in exponential complexity. Furthermore, we design an easy approximate algorithm, which can calculate the approximate price of the query in polynomial time. We instantiated our model with a select-joint query and a complex query and extensively evaluated its performances on two practical datasets. The experimental results show that our pricing model is feasible.

Robot Mission Planning using Co-evolutionary Optimization

SummaryMission planning is a complex motion planning problem specified by using Temporal Logic constituting of Boolean and temporal operators, typically solved by model verification algorithms with an exponential complexity. The paper proposes co-evolutionary optimization thus building an iterative solution to the problem. The language for mission specification is generic enough to represent everyday missions, while specific enough to design heuristics. The mission is broken into components which cooperate with each other. The experiments confirm that the robot is able to outperform the search, evolutionary and model verification techniques. The results are demonstrated by using a Pioneer LX robot.

Efficient Algorithms for Coded Multicasting in Heterogeneous Caching Networks

Coded multicasting has been shown to be a promising approach to significantly improve the performance of content delivery networks with multiple caches downstream of a common multicast link. However, the schemes that have been shown to achieve order-optimal performance require content items to be partitioned into several packets that grows exponentially with the number of caches, leading to codes of exponential complexity that jeopardize their promising performance benefits. In this paper, we address this crucial performance-complexity tradeoff in a heterogeneous caching network setting, where edge caches with possibly different storage capacity collect multiple content requests that may follow distinct demand distributions. We extend the asymptotic (in the number of packets per file) analysis of shared link caching networks to heterogeneous network settings, and present novel coded multicast schemes, based on local graph coloring, that exhibit polynomial-time complexity in all the system parameters, while preserving the asymptotically proven multiplicative caching gain even for finite file packetization. We further demonstrate that the packetization order (the number of packets each file is split into) can be traded-off with the number of requests collected by each cache, while preserving the same multiplicative caching gain. Simulation results confirm the superiority of the proposed schemes and illustrate the interesting request aggregation vs. packetization order tradeoff within several practical settings. Our results provide a compelling step towards the practical achievability of the promising multiplicative caching gain in next generation access networks.

Approximating Ground States by Neural Network Quantum States

The many-body problem in quantum physics originates from the difficulty of describing the non-trivial correlations encoded in the exponential complexity of the many-body wave function. Motivated by the Giuseppe Carleo's work titled solving the quantum many-body problem with artificial neural networks [Science, 2017, 355: 602], we focus on finding the NNQS approximation of the unknown ground state of a given Hamiltonian $H$ in terms of the best relative error and explore the influences of sum, tensor product, local unitary of Hamiltonians on the best relative error. Besides, we illustrate our method with some examples.