success probability
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Chun-Yan Zhao ◽  
Yan-Rong Fu ◽  
Jin-Hua Zhao

Abstract Message passing algorithms, whose iterative nature captures well complicated interactions among interconnected variables in complex systems and extracts information from the fixed point of iterated messages, provide a powerful toolkit in tackling hard computational tasks in optimization, inference, and learning problems. In the context of constraint satisfaction problems (CSPs), when a control parameter (such as constraint density) is tuned, multiple threshold phenomena emerge, signaling fundamental structural transitions in their solution space. Finding solutions around these transition points is exceedingly challenging for algorithm design, where message passing algorithms suffer from a large message fluctuation far from convergence. Here we introduce a residual-based updating step into message passing algorithms, in which messages varying large between consecutive steps are given a high priority in updating process. For the specific example of model RB, a typical prototype of random CSPs with growing domains, we show that our algorithm improves the convergence of message updating and increases the success probability in finding solutions around the satisfiability threshold with a low computational cost. Our approach to message passing algorithms should be of value for exploring their power in developing algorithms to find ground-state solutions and understand the detailed structure of solution space of hard optimization problems.

Gabriel Anzer ◽  
Pascal Bauer

AbstractPasses are by far football’s (soccer) most frequent event, yet surprisingly little meaningful research has been devoted to quantify them. With the increase in availability of so-called positional data, describing the positioning of players and ball at every moment of the game, our work aims to determine the difficulty of every pass by calculating its success probability based on its surrounding circumstances. As most experts will agree, not all passes are of equal difficulty, however, most traditional metrics count them as such. With our work we can quantify how well players can execute passes, assess their risk profile, and even compute completion probabilities for hypothetical passes by combining physical and machine learning models. Our model uses the first 0.4 seconds of a ball trajectory and the movement vectors of all players to predict the intended target of a pass with an accuracy of $$93.0\%$$ 93.0 % for successful and $$72.0\%$$ 72.0 % for unsuccessful passes much higher than any previously published work. Our extreme gradient boosting model can then quantify the likelihood of a successful pass completion towards the identified target with an area under the curve (AUC) of $$93.4\%$$ 93.4 % . Finally, we discuss several potential applications, like player scouting or evaluating pass decisions.

2022 ◽  
Vol 22 (1&2) ◽  
pp. 53-85
Thomas G. Wong

The task of finding an entry in an unsorted list of $N$ elements famously takes $O(N)$ queries to an oracle for a classical computer and $O(\sqrt{N})$ queries for a quantum computer using Grover's algorithm. Reformulated as a spatial search problem, this corresponds to searching the complete graph, or all-to-all network, for a marked vertex by querying an oracle. In this tutorial, we derive how discrete- and continuous-time (classical) random walks and quantum walks solve this problem in a thorough and pedagogical manner, providing an accessible introduction to how random and quantum walks can be used to search spatial regions. Some of the results are already known, but many are new. For large $N$, the random walks converge to the same evolution, both taking $N \ln(1/\epsilon)$ time to reach a success probability of $1-\epsilon$. In contrast, the discrete-time quantum walk asymptotically takes $\pi\sqrt{N}/2\sqrt{2}$ timesteps to reach a success probability of $1/2$, while the continuous-time quantum walk takes $\pi\sqrt{N}/2$ time to reach a success probability of $1$.

2021 ◽  
Vol 1 (4) ◽  
pp. 1-28
Denis Antipov ◽  
Benjamin Doerr

To gain a better theoretical understanding of how evolutionary algorithms (EAs) cope with plateaus of constant fitness, we propose the n -dimensional \textsc {Plateau} _k function as natural benchmark and analyze how different variants of the (1 + 1)  EA optimize it. The \textsc {Plateau} _k function has a plateau of second-best fitness in a ball of radius k around the optimum. As evolutionary algorithm, we regard the (1 + 1)  EA using an arbitrary unbiased mutation operator. Denoting by \alpha the random number of bits flipped in an application of this operator and assuming that \Pr [\alpha = 1] has at least some small sub-constant value, we show the surprising result that for all constant k \ge 2 , the runtime  T follows a distribution close to the geometric one with success probability equal to the probability to flip between 1 and k bits divided by the size of the plateau. Consequently, the expected runtime is the inverse of this number, and thus only depends on the probability to flip between 1 and k bits, but not on other characteristics of the mutation operator. Our result also implies that the optimal mutation rate for standard bit mutation here is approximately  k/(en) . Our main analysis tool is a combined analysis of the Markov chains on the search point space and on the Hamming level space, an approach that promises to be useful also for other plateau problems.

Entropy ◽  
2021 ◽  
Vol 24 (1) ◽  
pp. 18
Jinhua Zhang ◽  
Fulin Zhang ◽  
Zhixi Wang ◽  
Hui Yang ◽  
Shaoming Fei

We investigate the discrimination of pure-mixed (quantum filtering) and mixed-mixed states and compare their optimal success probability with the one for discriminating other pairs of pure states superposed by the vectors included in the mixed states. We prove that under the equal-fidelity condition, the pure-pure state discrimination scheme is superior to the pure-mixed (mixed-mixed) one. With respect to quantum filtering, the coherence exists only in one pure state and is detrimental to the state discrimination for lower dimensional systems; while it is the opposite for the mixed-mixed case with symmetrically distributed coherence. Making an extension to infinite-dimensional systems, we find that the coherence which is detrimental to state discrimination may become helpful and vice versa.

John S. Van Dyke ◽  
Edwin Barnes ◽  
Sophia Economou ◽  
Rafael I Nepomechie

Abstract The open spin-1/2 XXZ spin chain with diagonal boundary magnetic fields is the paradigmatic example of a quantum integrable model with open boundary conditions. We formulate a quantum algorithm for preparing Bethe states of this model, corresponding to real solutions of the Bethe equations. The algorithm is probabilistic, with a success probability that decreases with the number of down spins. For a Bethe state of L spins with M down spins, which contains a total of (L M) 2M M! terms, the algorithm requires L + M2+ 2M qubits.

Electronics ◽  
2021 ◽  
Vol 10 (24) ◽  
pp. 3169
Khaled F. Hayajneh

The next-generation networks (5G and beyond) require robust channel codes to support their high specifications, such as low latency, low complexity, significant coding gain, and flexibility. In this paper, we propose using a fountain code as a promising solution to 5G and 6G networks, and then we propose using a modified version of the fountain codes (Luby transform codes) over a network topology (Y-network) that is relevant in the context of the 5G networks. In such a network, the user can be connected to two different cells at the same time. In addition, the paper presents the necessary techniques for analyzing the system and shows that the proposed scheme enhances the system performance in terms of decoding success probability, error probability, and code rate (or overhead). Furthermore, the analyses in this paper allow us to quantify the trade-off between overhead, on the one hand, and the decoding success probability and error probability, on the other hand. Finally, based on the analytical approach and numerical results, our simulation results demonstrate that the proposed scheme achieves better performance than the regular LT codes and the other schemes in the literature.

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3241
Jan Lansky ◽  
Amir Masoud Rahmani ◽  
Saqib Ali ◽  
Nasour Bagheri ◽  
Masoumeh Safkhani ◽  

In this paper, targeting efficient authentication and key agreement in an IoT environment, we propose an Elliptic Curve Cryptography- (ECC) based lightweight authentication protocol called BCmECC which relies on a public blockchain to validate the users’ public key to provide desired security. We evaluate the security of the proposed protocol heuristically and validate it formally, which demonstratse the high level of the security. For the formal verification we used the widely accepted formal methods, i.e., BAN logic and the Scyther tool. In this paper we also analyse the security of recently proposed blockchain-based authentication protocols and show that this protocol does not provide the desired security against known session-specific temporary information attacks in which the adversary has access to the session’s ephemeral values and aims to retrieve the shared session key. In addition, the protocol lacks forward secrecy, in which an adversary with access to the server’s long-term secret key can retrieve the previous session keys, assuming that the adversary has already eavesdropped the transferred messages over a public channel in the target session. The proposed attacks are very efficient and their success probability is `1’, while the time complexity of each attack could be negligible. Besides, we show that BCmECC is secure against such attacks.

S. Salimian ◽  
Mohammad K. Tavassoly ◽  
N. Sehati

Abstract An efficient scheme is proposed to teleport an entangled state of two superconducting (SC) qubits from Alice's to Bob's lab. This type of two-level systems has recently attracted a lot of attention due to the possible tunability of the coupling strength of the qubits with each other. To achieve the purpose, we first generate the GHZ state as the necessary teleportation channel. Then, appropriate interactions are performed in two processes between two of the five qubits, each with a certain frequency modulative external magnetic field which is applied on specific one of the qubits. Next, via applying proper gates and measurements in each lab, we observe that the teleportation can be successfully performed with maximum possible values of fidelity and success probability. At last, to make the protocol close to reality, decay rates of SC qubits are also taken into account, showing that our protocol still works well, satisfactorily.

2021 ◽  
Subin narayanan ◽  
Dimitris Tsolkas ◽  
Nikos Passas ◽  
Andreas Höglund ◽  
Olof Liberg

<div>The effective support of 5G-Internet of Things (IoT) requires cellular service in deep coverage areas while providing long battery life for IoT devices which perform infrequent small data transmission towards the base station. Relaying is a promising solution to extend the coverage while at the same time meeting the battery life requirements of the IoT devices. Considering this, we analyze the suitability of layer-3 relaying over the 3GPP Release 16 NR-PC5 interface to support massive IoT applications. More precisely, we study the unicast connection establishment mechanism over the NR PC5 interface in a partial coverage scenario. Further, a set of optimizations on the Release 16 NR-PC5 procedure to effectively support massive IoT applications are proposed and analyzed. The obtained performance evaluation results which are presented in terms of data success probability, device power consumption, and signaling overhead, quantify how effectively the Release 16 NR-PC5 interface can support the requirement of IoT in the 5G and beyond era. The proposed sidelink small data transmission and frame-level access provides the largest gain overall and can reduce the device power consumption by an average of 68%, and signaling overhead by 15% while maintaining a data success probability of more than 90% in an IMT-2020 defined IoT traffic scenario.</div>

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