Time Algorithm Research Articles

Computational complexity of normalizing constants for the product of determinantal point processes

We consider the product of determinantal point processes (DPPs), a point process whose probability mass is proportional to the product of principal minors of multiple matrices, as a natural, promising generalization of DPPs. We study the computational complexity of computing its normalizing constant, which is among the most essential probabilistic inference tasks. Our complexity-theoretic results (almost) rule out the existence of efficient algorithms for this task unless the input matrices are forced to have favorable structures. In particular, we prove the following:•Computing ∑Sdet⁡(AS,S)p exactly for every (fixed) positive even integer p is UP-hard and Mod3P-hard, which gives a negative answer to an open question posed by Kulesza and Taskar [51].•∑Sdet⁡(AS,S)det⁡(BS,S)det⁡(CS,S) is NP-hard to approximate within a factor of 2O(|I|1−ε) or 2O(n1/ε) for any ε>0, where |I| is the input size and n is the order of the input matrix. This result is stronger than the #P-hardness for the case of two matrices derived by Gillenwater [36].•There exists a kO(k)nO(1)-time algorithm for computing ∑Sdet⁡(AS,S)det⁡(BS,S), where k is the maximum rank of A and B or the treewidth of the graph formed by nonzero entries of A and B. Such parameterized algorithms are said to be fixed-parameter tractable. These results can be extended to the fixed-size case. Further, we present two applications of fixed-parameter tractable algorithms given a matrix A of treewidth w:•We can compute a 2n2p−1-approximation to ∑Sdet⁡(AS,S)p for any fractional number p>1 in wO(wp)nO(1) time.•We can find a 2n-approximation to unconstrained maximum a posteriori inference in wO(wn)nO(1) time.

Strategic Recommendation: Revenue Optimal Matching for Online Platforms (Student Abstract)

We consider a platform in a two-sided market with unit-supply sellers and unit-demand buyers. Each buyer can transact with a subset of sellers it knows off platform and another seller that the platform recommends. Given the choice of sellers, transactions and prices form a competitive equilibrium. The platform selects one seller for each buyer, and charges a fixed percentage of prices to all transactions that it recommends. The platform seeks to maximize total revenue. We show that the platform's problem is NP-hard, even when each buyer knows at most two buyers off platform. Finally, when each buyer values all sellers equally and knows only one buyer off platform, we provide a polynomial time algorithm that optimally solves the problem.

Parameterization of (Partial) Maximum Satisfiability above Matching in a Variable-Clause Graph

In the paper, we study the Maximum Satisfiability and the Partial Maximum Satisfiability problems. Using Gallai–Edmonds decomposition, we significantly improve the upper bound for the Maximum Satisfiability problem parameterized above maximum matching in the variable-clause graph. Our algorithm operates with a runtime of O*(2.83^k'), a substantial improvement compared to the previous approach requiring O*(4^k' ), where k' denotes the relevant parameter. Moreover, this result immediately implies O*(1.14977^m) and O*(1.27895^m) time algorithms for the (n, 3)-MaxSAT and (n, 4)-MaxSAT where m is the overall number of clauses. These upper bounds improve prior-known upper bounds equal to O*(1.1554^m) and O*(1.2872^m). We also adapt the algorithm so that it can handle instances of Partial Maximum Satisfiability without losing performance in some cases. Note that this is somewhat surprising, as the existence of even one hard clause can significantly increase the hardness of a problem.

Theoretical Aspects of Generating Instances with Unique Solutions: Pre-assignment Models for Unique Vertex Cover

The uniqueness of an optimal solution to a combinatorial optimization problem attracts many fields of researchers' attention because it has a wide range of applications, it is related to important classes in computational complexity, and the existence of only one solution is often critical for algorithm designs in theory. However, as the authors know, there is no major benchmark set consisting of only instances with unique solutions, and no algorithm generating instances with unique solutions is known; a systematic approach to getting a problem instance guaranteed having a unique solution would be helpful. A possible approach is as follows: Given a problem instance, we specify a small part of a solution in advance so that only one optimal solution meets the specification. This paper formulates such a ``pre-assignment'' approach for the vertex cover problem as a typical combinatorial optimization problem and discusses its computational complexity. First, we show that the problem is ΣP2-complete in general, while the problem becomes NP-complete when an input graph is bipartite. We then present an O(2.1996^n)-time algorithm for general graphs and an O(1.9181^n)-time algorithm for bipartite graphs, where n is the number of vertices. The latter is based on an FPT algorithm with O*(3.6791^τ) time for vertex cover number τ. Furthermore, we show that the problem for trees can be solved in O(1.4143^n) time.

Impact Analysis of Different Trajectory Shapes on Optimization Based on Original Natural Algorithm

In this paper, the reentry phase of the Aerospaceplane is taken as the research object, and the performance parameters of the reusable rocket of a private company are analyzed. Aiming at the guidance and control scheme of the spacecraft returning to the reentry trajectory in the real environment, the original natural algorithm is optimized by considering various reentry flight constraints, and the improved original natural algorithm is used to optimize the reentry trajectory of the Aerospaceplane. We obtained two types of reentry trajectories in the presence of large flight-restricted areas, the “S-type” trajectory and the “spiral-type” trajectory, and obtained data on various influencing factors. The results showed that the basic state parameters of the spiral trajectory optimized using the improved original natural algorithm after adding constraints met the constraint conditions. The aerodynamic heating rate and overload of the spiral reentry trajectory were to some extent greater than those of the S-type trajectory. Under the increasingly stringent requirements of the aerospace environment, new requirements were put forward for the thermal protection system to meet the wider environmental situation. This paper uses the improved original natural algorithm for the first time and applies it to the field of aerospace reentry and entry and adds more constraints to this algorithm for computation. Besides, for the first time, the macroscopic nature of trajectory types is used as a comparative element for parameter comparison, providing a reference basis for selecting trajectory optimization directions from the macroscopic perspective of trajectory types.

An Adjustable Wireless Backhaul Link Selection Algorithm for LEO-UAV-Sensor-Based Internet of Remote Things Network.

Internet of Remote Things (IoRT) networks utilize the backhaul links between unmanned aerial vehicles (UAVs) and low-earth-orbit (LEO) satellites to transfer the massive data collected by sensors. However, the backhaul links change rapidly due to the fast movement of both the UAVs and the satellites, which is different from conventional wireless networks. Additionally, due to the various requirements of IoRT multiservices, the system performance should be comprehensively considered. Thus, an adjustable wireless backhaul link selection algorithm for a LEO-UAV-sensor-based IoRT network is proposed. Firstly, an optimization model for backhaul link selection is proposed. This model uses Q, which integrates the remaining service time and capacity as the objective function. Then, based on the snapshot method, the dynamic topology is converted into the static topology and a heuristic optimization algorithm is proposed to solve the backhaul link selection problem. Finally, the proposed algorithm is compared with two traditional algorithms, i.e., maximum service time and maximum capacity algorithms. Numerical simulation results show that the proposed model can achieve better system performance, and the overload of the satellites is more balanced. The algorithm can obtain a trade-off between remaining service time and capacity by dynamically adjusting model parameters. Thus, the adjustable backhaul link selection algorithm can apply to multiservice IoRT scenarios.

Grouped domination parameterized by vertex cover, twin cover, and beyond

A dominating set S of graph G is called an r-grouped dominating set if S can be partitioned into S1,S2,…,Sk such that the size of each unit Si is r and the subgraph of G induced by Si is connected. The concept of r-grouped dominating sets generalizes several well-studied variants of dominating sets with requirements for connected component sizes, such as the ordinary dominating sets (r=1), paired dominating sets (r=2), and connected dominating sets (r is arbitrary and k=1). In this paper, we investigate the computational complexity of r-Grouped Dominating Set, which is the problem of deciding whether a given graph has an r-grouped dominating set with at most k units. For general r, r-Grouped Dominating Set is hard to solve in various senses because the hardness of the connected dominating set is inherited. We thus focus on the case in which r is a constant or a parameter, but we see that r-Grouped Dominating Set for every fixed r>0 is still hard to solve. From the observations about the hardness, we consider the parameterized complexity concerning well-studied graph structural parameters. We first see that r-Grouped Dominating Set is fixed-parameter tractable for r and treewidth, which is derived from the fact that the condition of r-grouped domination for a constant r can be represented as monadic second-order logic (MSO2). This fixed-parameter tractability is good news, but the running time is not practical. We then design an O⁎(min⁡{(2τ(r+1))τ,(2τ)2τ})-time algorithm for general r≥2, where τ is the twin cover number, which is a parameter between vertex cover number and clique-width. For paired dominating set and trio dominating set, i.e., r∈{2,3}, we can speed up the algorithm, whose running time becomes O⁎((r+1)τ). We further argue the relationship between FPT results and graph parameters, which draws the parameterized complexity landscape of r-Grouped Dominating Set.

A novel mitochondrial unfolded protein response-related risk signature to predict prognosis, immunotherapy and sorafenib sensitivity in hepatocellular carcinoma.

Hepatocellular carcinoma (HCC) is a common cause of cancer-associated death worldwide. The mitochondrial unfolded protein response (UPRmt) not only maintains mitochondrial integrity but also regulates cancer progression and drug resistance. However, no study has used the UPRmt to construct a prognostic signature for HCC. This work aimed to establish a novel signature for predicting patient prognosis, immune cell infiltration, immunotherapy, and chemotherapy response based on UPRmt-related genes (MRGs). Transcriptional profiles and clinical information were obtained from the TCGA and ICGC databases. Cox regression and LASSO regression analyses were applied to select prognostic genes and develop a risk model. The TIMER algorithm was used to investigate immunocytic infiltration in the high- and low-risk subgroups. Here, two distinct clusters were identified with different prognoses, immune cell infiltration statuses, drug sensitivities, and response to immunotherapy. A risk score consisting of seven MRGs (HSPD1, LONP1, SSBP1, MRPS5, YME1L1, HDAC1 and HDAC2) was developed to accurately and independently predict the prognosis of HCC patients. Additionally, the expression of core MRGs was confirmed by immunohistochemistry (IHC) staining, single-cell RNA sequencing, and spatial transcriptome analyses. Notably, the expression of prognostic MRGs was significantly correlated with sorafenib sensitivity in HCC and markedly downregulated in sorafenib-treated HepG2 and Huh7 cells. Furthermore, the knockdown of LONP1 decreased the proliferation, invasion, and migration of HepG2 cells, suggesting that upregulated LONP1 expression contributed to the malignant behaviors of HCC cells. To our knowledge, this is the first study to investigate the consensus clustering algorithm, prognostic potential, immune microenvironment infiltration and drug sensitivity based on the expression of MRGs in HCC. In summary, the UPRmt-related classification and prognostic signature could assist in determining the prognosis and personalized therapy of HCC patients from the perspectives of predictive, preventative and personalizedmedicine.

The Constrained 2-Maxian Problem on Cycles

This paper deals with p-maxian problem on cycles with an upper bound on the distances of all facilities. We consider the case of p=2 and show that, in the worst case, the optimal solution contains at least one vertex of the underlying cycle, which helps to develop an efficient algorithm to solve the constrained 2-maxian problem. Based on this property, we develop a linear time algorithm for the constrained 2-maxian problem on a cycle. We also discuss the relations between the constrained and unconstrained 2-maxian problems on which the underlying graphs are cycles.

Coordinating scheduling and rejection decisions in a two-machine flow shop scheduling problem

We study a two-machine flow shop scheduling problem where any operation can be rejected at a certain cost. A solution for such a problem requires two sets of decisions. The first involves the partition of the set of operations into two subsets: the set of operations that are accepted for scheduling in the shop, and the set of rejected operations. The second decision involves scheduling the set of accepted operations in the shop. The objective is to find a solution that minimizes the sum of the makespan and the total rejection cost. We prove that the problem is NP-hard even if all processing operations have identical processing times and identical rejection costs on either one of the two machines. We show, however, that the problem is fixed parameterized tractable with respect to a parameter that combine the number of different processing times on both machines with the number of different rejection costs on one out of the two machines. We also provide a pseudo-polynomial time algorithm for the problem, which we then convert into a fully polynomial time approximation scheme. This is achieved by dividing the problem into a set of subproblems and deriving a fully polynomial time approximation scheme for each one of them, separately. Finally, we present an integer linear programming formulation of the problem and two simple 2-approximation algorithms.

New data on distribution of Miramiola pusilla (Miram, 1927) (Orthoptera: Tettigoniidae

The rare bush-cricket Miramiola pusilla (Miram, 1925) is distributed over the dry steppe and semi-desert territories of Eurasia from the southern parts of East European Plain up to the southern parts of West Siberian Plain and the Tarbagatai Mts. (E Kazakhstan). The species is strongly associated with short grass vegetation. Its abundance is usually low. The ecologo-geographic models of the species distribution over the eastern parts of its range are generated by the Maxent algorithm for the first time. The species conservation status is discussed.

A Security-Enhanced Energy Conservation with Enhanced Random Forest Classifier for Low Execution Time Framework (S-2EC-ERF) for Wireless Sensor Networks

Wireless sensor networks (WSNs) play a pivotal role in diverse applications such as environmental monitoring, industrial automation, healthcare, and smart cities. The motivation behind the development of WSNs stems from their impact in providing real-time data on various environmental parameters. The challenge for WSNs is to achieve strong security and efficient energy saving together. Traditional methods sought to find solutions either through security or energy. In response, this study proposed a secure and energy-efficient framework for enhancing security measures in WSNs while minimizing the impact on energy resources by using the Enhanced Consumed Energy Leach (ECP-LEACH) protocol and the Enhanced Random Forest Classifier for Low Execution Time (ERF-LET) algorithm for attack detection named Security-Enhanced Energy Conservation with ERF-LET (S-2EC-ERF). The integration of the detection algorithm at the node level played a pivotal role in fortifying the security posture of individual nodes by detecting and mitigating potential security threats. Leveraging a comprehensive dataset obtained from NS3 simulations, the ERF-LET algorithm demonstrated its proficiency in differentiating between normal and attack packets, thereby laying a strong foundation for subsequent evaluations, where it achieved an accuracy of 98.193%. The proposed methodology was further validated through real-time simulations conducted on the NS3. The results demonstrated the superiority of the proposed S-2EC-ERF in terms of the packet delivery ratio (PDR), average throughput, end-to-end delay, and mean energy consumption compared to the Security-Enhanced Energy Conservation with Logistic Regression (S-2EC-LR), Security-Enhanced Energy Conservation with Decision Tree (S-2EC-DT), and Security-Enhanced Energy Conservation with AdaBoost (S-2EC-Ada) algorithms.

Multi-distribution bi-deniable inner product encryption based on Decision-LWE

Bi-deniable Encryption scheme means that when the sender and the receiver are coerced, the coercer can obtain fake plaintext, random numbers, and secret keys. It’s a solution strategy in the case of information leakage. Compared with traditional encryption, deniable encryption can provide secret communications in situations of coercion in the Post-Quantum era. Compared with sender-deniable encryption and receiver-deniable encryption, bi-deniable encryption can achieve secret communications in the situation that both sender and receiver are coerced by the coercer. So, we propose to design a bi-deniable encryption scheme under the multi-distribution model. In our bi-deniable encryption scheme, we construct a bi-deniable encryption scheme based on the assumption of Decision-Learning With Errors (DLWE) under the multi-distribution model. Firstly, the principle of Inner Product Predicate Encryption (IPPE) is applied in our scheme. Secondly, we apply the framework of Bi-Translucent Set (BTS), combined with inner product predicate encryption. Thirdly, we construct a series of probabilistic polynomial time algorithms, which apply linear transformation between different lattice structures, and Regev dual encryption. Fourthly, the statistical indistinguishability between the sampling algorithm with discrete Gaussian sampling algorithm, and the computational indistinguishability between LWE’s ciphertext samples with uniform samples, the property of indistinguishability is applied in theorem proving, which obtain Indistinguishability under Chosen Plaintext Attacks (IND-CPA) security and the property of bi-deniability. Given the value range of the Gaussian parameter and security parameter in our scheme, the correctness of the bi-deniable encryption scheme is guaranteed. We also give the security proof of IND-CPA and bi-deniability’s property by a series of games. The ‘Inner-Product Bi-Translucent Set’ Bi-Deniable Encryption scheme under the multi-distribution model is based on Decision-LWE assumption, and can avoid quantum-resistant attacks. The bi-deniable encryption scheme is firstly constructed by the inner product with the Decision-LWE assumption, which can provide better properties of security and deniability.

Solving polynomial systems over non-fields and applications to modular polynomial factoring

We study the problem of solving a system of m polynomials in n variables over the ring of integers modulo a prime-power pk. The problem over finite fields is well studied in varied parameter settings. For small characteristic p=2, Lokshtanov et al. (SODA'17) initiated the study, for degree d=2 systems, to improve the exhaustive search complexity of O(2n)⋅poly(m,n) to O(20.8765n)⋅poly(m,n); which currently is improved to O(20.6943n)⋅poly(m,n) in Dinur (SODA'21). For large p but constant n, Huang and Wong (FOCS'96) gave a randomized poly(d,m,log⁡p) time algorithm. Note that for growing n, system-solving is known to be intractable even with p=2 and degree d=2.We devise a randomized poly(d,m,log⁡p)-time algorithm to find a root of a given system of m integral polynomials of degrees bounded by d, in n variables, modulo a prime power pk; when n+k is constant. In a way, we extend the efficient algorithm of Huang and Wong (FOCS'96) for system-solving over Galois fields (i.e., characteristic p) to system-solving over Galois rings (i.e., characteristic pk); when k>1 is constant. The challenge here is to find a lift of singularFp-roots (exponentially many); as there is no efficient general way known in algebraic-geometry for resolving singularities.Our algorithm has applications to factoring univariate polynomials over Galois rings. Given f∈Z[x] and a prime-power pk (k≥2), finding factors of fmodpk has a curious state-of-the-art. It is solved for large k by p-adic factoring algorithms (von zur Gathen, Hartlieb, ISSAC'96); but unsolved for small k. In particular, no nontrivial factoring method is known for k≥5 (Dwivedi, Mittal, Saxena, ISSAC'19). One issue is that degree-δ factors of f(x)modpk could be exponentially many, as soon as k≥2. We give the first randomized poly(deg⁡(f),log⁡p)-time algorithm to find a degree-δ factor of f(x)modpk, when k+δ is constant. Our method has potential application in algebraic coding theory. In particular, extending algebraic geometric and Reed-Solomon codes to Galois rings could enable new and improved bounds on their underlying efficiency parameters.

Deep Learning Promotes Profiling of Multiple miRNAs in Single Extracellular Vesicles for Cancer Diagnosis.

Extracellular vesicle microRNAs (EV miRNAs) are critical noninvasive biomarkers for early cancer diagnosis. However, accurate cancer diagnosis based on bulk analysis is hindered by the heterogeneity among EVs. Herein, we report an approach for profiling single-EV multi-miRNA signatures by combining total internal reflection fluorescence (TIRF) imaging with a deep learning (DL) algorithm for the first time. This innovative technique allows for the precise characterization of EV miRNAs at the single-vesicle level, overcoming the challenges posed by EV heterogeneity. TIRF with high resolution and a signal-to-noise ratio can simultaneously detect multi-miRNAs in situ in individual EVs. DL algorithm avoids complicated and inaccurate artificial feature extraction, achieving automated high-resolution image analysis. Using this approach, we reveal that the main variation of EVs from 5 cancer cells and normal plasma is the triple-positive EV subpopulation, and the classification accuracy of single triple-positive EVs from 6 sources can reach above 95%. In the clinical cohort, 20 patients (5 lung cancer, 5 breast cancer, 5 cervical cancer, and 5 colon cancer) and 5 healthy controls are predicted with an overall accuracy of 100%. This single-EV strategy provides new opportunities for exploring more specific EV biomarkers to achieve cancer diagnosis and classification.

SparseRNAfolD: optimized sparse RNA pseudoknot-free folding with dangle consideration

MotivationComputational RNA secondary structure prediction by free energy minimization is indispensable for analyzing structural RNAs and their interactions. These methods find the structure with the minimum free energy (MFE) among exponentially many possible structures and have a restrictive time and space complexity (O(n3)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$O(n^3)$$\\end{document} time and O(n2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$O(n^2)$$\\end{document} space for pseudoknot-free structures) for longer RNA sequences. Furthermore, accurate free energy calculations, including dangle contributions can be difficult and costly to implement, particularly when optimizing for time and space requirements.ResultsHere we introduce a fast and efficient sparsified MFE pseudoknot-free structure prediction algorithm, SparseRNAFolD, that utilizes an accurate energy model that accounts for dangle contributions. While the sparsification technique was previously employed to improve the time and space complexity of a pseudoknot-free structure prediction method with a realistic energy model, SparseMFEFold, it was not extended to include dangle contributions due to the complexity of computation. This may come at the cost of prediction accuracy. In this work, we compare three different sparsified implementations for dangle contributions and provide pros and cons of each method. As well, we compare our algorithm to LinearFold, a linear time and space algorithm, where we find that in practice, SparseRNAFolD has lower memory consumption across all lengths of sequence and a faster time for lengths up to 1000 bases.ConclusionOur SparseRNAFolD algorithm is an MFE-based algorithm that guarantees optimality of result and employs the most general energy model, including dangle contributions. We provide a basis for applying dangles to sparsified recursion in a pseudoknot-free model that has the potential to be extended to pseudoknots.

Bounded scheduling two-component jobs simultaneously or hierarchically

This paper studies the multi-objective problem of scheduling n two-component jobs on a fabrication machine with bounded batch capacity in terms of the number of jobs. Each job consists of two components, one is common among all jobs (called standard component) and the other is unique to itself (called specific component). The machine processes all components so that it might become a capacitated bottleneck machine. Standard components have equal processing times. They are fabricated in batches sequentially on the machine, and a setup time is required to fabricate a batch. Each batch contains the standard components of at most b(b < n) jobs. Specific components are manufactured individually, therefore their associated setup times could be absorbed into their processing times. Standard components in a batch are not available until all these components are completed (meaning that the processing time of a batch is equal to the total processing time of the standard components in it), whereas a specific component is available on completion of its processing. A job is completed when both its two components are completed and available. For simultaneous optimization of makespan and maximum lateness, an O(n3)-time algorithm is obtained. Through a careful use of the heap data structure, the time bound can be improved to O(n2 log n). For hierarchical optimization of two maximum lateness objectives and makespan, an O(n5)-time algorithm is obtained, which can be improved to run in time O(n4).

Tensor Recurrent Neural Network With Differential Privacy

Recurrent neural network (RNN), a branch of deep learning, is a powerful model for sequential data that has outstanding performance on a wide range of important Internet of Things (IoT) tasks. This unprecedented growth of RNN model has however encountered both heterogeneous IoT data and privacy issues. Existing RNN model can not deal with heterogeneous sequential data; often the larger datasets used in training of RNN model contain sensitive information. To tackle these challenges and for the first time, this research proposes a novel differentially private tensor-based RNN (DPTRNN) that can be applied in many challenging deep learning sequence tasks for IoT systems. Specifically, to process heterogeneous sequential data, we propose a tensor-based RNN model. To guarantee privacy, we develop a tensor-based back-propagation through time algorithm with perturbation to avoid exposing the sensitive information for training the tensor-based RNN model within the framework of differential privacy. Thorough security analysis shows that the differential private tensor-based RNN efficiently protects the confidentiality of sensitive user information for IoT. Our results from extensive experiments on two challenging large video datasets suggest that our proposed scheme is practical with guarantee of data privacy preservation and acceptable accuracy loss.

Improving the accuracy of wind speed spatial interpolation: A pre-processing algorithm for wind speed dynamic time warping interpolation

Wind power is one of the most vital renewable energy resources in the world. Wind energy production is directly correlated with the quality and quantity of wind speed data. Interpolation techniques can be employed to fill in the gaps in the current wind speed observation data series. However, existing methods for obtaining blank data do not pre-regulate the regional spatial wind speed sequence and instead rely on direct interpolation, which leads to low accuracy in the interpolation. This is not a problem with the model itself, but rather with the wind speed flowing in space and exhibiting sequence misalignment on the timeline. To address this issue, this study proposes a Wind Speed Dynamic Time Warping (WSDTW) algorithm based on Dynamic Time Warping (DTW) to match similar wind speed reduction sequences in terms of time error. We used the shape context descriptor to encode wind speed and introduced wind rose descriptors to represent wind direction initially. The matching cost of DTW was then optimized. Finally, five common interpolation methods were selected to evaluate the method. The research results indicate that interpolation after WSDTW matching and warping can significantly improve the accuracy of wind speed interpolation and reduce the spatial dependence of wind speed. This method demonstrates good stability and generalization, performing exceptionally well in situations where there are gaps in regional wind speed data or missing data.

Single-Shot Decoding of Good Quantum LDPC Codes

Quantum Tanner codes constitute a family of quantum low-density parity-check codes with good parameters, i.e., constant encoding rate and relative distance. In this article, we prove that quantum Tanner codes also facilitate single-shot quantum error correction (QEC) of adversarial noise, where one measurement round (consisting of constant-weight parity checks) suffices to perform reliable QEC even in the presence of measurement errors. We establish this result for both the sequential and parallel decoding algorithms introduced by Leverrier and Zémor. Furthermore, we show that in order to suppress errors over multiple repeated rounds of QEC, it suffices to run the parallel decoding algorithm for constant time in each round. Combined with good code parameters, the resulting constant-time overhead of QEC and robustness to (possibly time-correlated) adversarial noise make quantum Tanner codes alluring from the perspective of quantum fault-tolerant protocols.