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**A**: In practice it is the generating set produced by the constructive recognition algorithms from [10, 11] as implemented in MAGMA**B**: Consequently, algorithms in the composition tree data structure, both in MAGMA and in GAP, store elements in classical groups as words in the LGO generators. Moreover, the LGO gene...
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Selection 3
**A**: We remark that in this case, our method is similar to that of [MR3591945], with some differences. First we consider that T~~𝑇\tilde{T}over~ start_ARG italic_T end_ARG can be nonzero**B**: Of course, the numerical scheme and the estimates developed in Section 3.1 hold. However, several simplifications are possib...
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**A**: Moreover, Alg-A is more stable than the alternatives. During the iterations of Alg-CM, the coordinates of three corners and two midpoints of a P-stable triangle (see Figure 37) are maintained**B**: Alg-CM uses an involved subroutine (far more complicated than ours given in Algorithm 1) to update the coordinates ...
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Selection 1
**A**: For the latter, we select the baselines from NN-based variations, inspired by state-of-the-art short-text classification models, i.e., Basic tanh-RNN , 1-layer GRU-RNN, 1-layer LSTM, 2-layer GRU-RNN, FastText [14] and CNN+LSTM [33] model. The hybrid model CNN+LSTM is adapted in our work for tweet classification....
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Selection 4
**A**: We might improve the validation and test errors even when when the decrease in the training loss is tiny and even when the validation loss itself increases. **B**: We should not rely on plateauing of the training loss or on the loss (logistic or exp or cross-entropy) evaluated on a validation data, as measures t...
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**A**: We observe that at certain points in time, the volume of rumor-related tweets (for sub-events) in the event stream surges. This can lead to false positives for techniques that model events as the aggregation of all tweet contents; that is undesired at critical moments**B**: It can be seen that although the cred...
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**A**: For this part, we first focus on evaluating the performance of single L2R models that are learned from the pre-selected time (before, during and after) and types (Breaking and Anticipate) set of entity-bearing queries**B**: We then evaluate our ensemble ranking model (results from the cascaded evaluation) and sh...
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Selection 1
**A**: 3 times the average insulin dose of others in the morning.**B**: The insulin intakes tend to be more in the evening, when basal insulin is used by most of the patients**C**: The only difference happens to patient 10 and 12 whose intakes are earlier at day. Further, patient 12 takse approx
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**A**: The first line separates deep learning approaches with architectures pre-trained on image classification (the superscript ††{}^{\dagger}start_FLOATSUPERSCRIPT † end_FLOATSUPERSCRIPT represents models with a VGG16 backbone) from shallow networks and other machine learning methods**B**: Entries between the second ...
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**A**: In this work, we have answered several open questions about the string parameter of the locality number**B**: As an additional result, our reductions also pointed out an interesting relationship between these classical graph parameters and the locality number for strings, with implications for approximating thes...
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Selection 3
**A**: In the best case of Freeway, our method is more than 10x more sample-efficient, see Figure 3. Since the publication of the first preprint of this work, it has been shown in van Hasselt et al. (2019); Kielak (2020) that Rainbow can be tuned to have better results in low data regime**B**: In our empirical evaluati...
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**A**: Compared to step negotiation purely in rolling locomotion mode, the proposed strategy demonstrated significant enhancements in energy performance, particularly for taller steps**B**: The implementation of the energy criterion strategy has proven effective in facilitating autonomous locomotion mode transitions f...
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**A**: The algorithm classifies items according to their size. Tiny items have their size in the range (0,1/3]013(0,1/3]( 0 , 1 / 3 ], small items in (1/3,1/2]1312(1/3,1/2]( 1 / 3 , 1 / 2 ], critical items in (1/2,2/3]1223(1/2,2/3]( 1 / 2 , 2 / 3 ], and large items in (2/3,1]231(2/3,1]( 2 / 3 , 1 ]. In addition, the al...
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**A**: Vectorization was done with the TfidfVectorizer class, with the standard English stop words list**B**: Additionally, terms having a document frequency lower than 20 were ignored. Finally, classifiers were coded using their corresponding sklearn built-in classes, e.g. LogisticRegression, KNeighborsClassifier, Mul...
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**A**: More details about the convergence performance of GMC are provided in Section 5.**B**: Note that we impose a constraint on the momentum coefficient β𝛽\betaitalic_β during the theoretical proof**C**: But in practice, even when the constraint is relaxed, e.g., β=0.9𝛽0.9\beta=0.9italic_β = 0.9, GMC still converge...
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**A**: Using cross-correlation would produce the same results and would not require flipping the kernels during visualization**B**: operation.**C**: , where ∗*∗ is the convolution333We use convolution instead of cross-correlation only as a matter of compatibility with previous literature and computational frameworks
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**A**: In this scenario, there are N=50𝑁50N=50italic_N = 50 channels, and the number of UAVs should be limited to M≤250𝑀250M\leq 250italic_M ≤ 250. **B**: Since the demanding channel’s capacity should not be more than the channel’s size we provide, we limit the number of UAVs in the tolerance range which satisfies th...
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**A**: For this shot (and simulation), Vc⁢o⁢m⁢p=12subscript𝑉𝑐𝑜𝑚𝑝12V_{comp}=12italic_V start_POSTSUBSCRIPT italic_c italic_o italic_m italic_p end_POSTSUBSCRIPT = 12kV and tc⁢o⁢m⁢p=45⁢μsubscript𝑡𝑐𝑜𝑚𝑝45μt_{comp}=45\upmuitalic_t start_POSTSUBSCRIPT italic_c italic_o italic_m italic_p end_POSTSUBSCRIPT = 45 roman...
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**A**: The results in Figure 3 show that using DQN with different Dropout methods result in better-preforming policies and less variability as the reduced standard deviation between the variants indicate to**B**: In table 1, Wilcoxon Sign-Ranked test was used to analyze the effect of Variance before applying Dropout (...
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Selection 1
**A**: In contrast to natural images, it is difficult to tabulate and summarize the performance of medical image segmentation methods because of the vast number of (a) medical imaging modalities and (b) medical image segmentation datasets. Figure 15 presents a breakdown of the various attributes of the medical image se...
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**A**: Current state-of-the-art methods directly map random forests into neural networks**B**: The overall performance is shown in the last column. Due to the stochastic process when training the random forests, the results can vary marginally.**C**: The number of parameters of the resulting network is evaluated on all...
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**A**: In comparison, existing algorithms based on value iteration, e.g., optimistic least-squares value iteration (LSVI) (Jin et al., 2019), do not allow adversarially chosen reward functions**B**: Such a notion of robustness partially justifies the empirical advantages of KL-regularized policy optimization (Neu et al...
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**A**: Most of these methods focus on the quadratic complexity of the self-attention heads and use low-rank matrix operations, downsampling or exploit pre-set or learned sparsity patterns.**B**: Sparse attention mechanisms and approximations have been proposed to address this issue and improve the efficiency of transfo...
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**A**: We thank Prof. Henry Adams and Dr. Johnathan Bush for very useful feedback about a previous version of this article**B**: We thank Dr. Qingsong Wang for bringing to our attention the paper [76] which was critical for the proof of Theorem 1. Finally, we thank Dr. Alexey Balitsky for pointing out an imprecision in...
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**A**: Performance   There are two reasons why we decided to use the Barnes-Hut implementation of the original t-SNE algorithm [52], instead of a newer and faster implementation [53, 54]**B**: Second, in this phase of the research, we were mainly concerned with designing and validating the system with the right set of ...
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**A**: Authors conclude that it “is unnecessary, misleading and based on unconvincing assumptions of river dynamics and soil erosion that lack a real scientific rationale”. **B**: They also examine the natural metaphor of “water drops flowing in rivers removing the soil from the riverbed”, which is the source of inspir...
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**A**: The main contributions are listed as follows:**B**: Since a large proportion of clustering methods are based on the graph, it is reasonable to consider how to employ GCN to promote the performance of graph-based clustering methods. In this paper, we propose an Adaptive Graph Auto-Encoder (AdaGAE) to extend graph...
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Selection 1
**A**: We summarise the limitations of the previous studies below and in Table 1, and compare to SMap. **B**: The key requirements for conducting Internet studies upon which conclusions can be drawn include scalable measurement infrastructure, good coverage of the Internet and a representative selection of measurement’...
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**A**: If the context layer can process unlabeled data, then it is no longer necessary to include every class in every batch. The full six-gas sensor drift dataset can be used, as well as other unbalanced and therefore realistic datasets.**B**: This design introduces variation in training inputs, which makes it harder ...
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**A**: The version for automaton semigroups does not follow directly from 8, as the free monogenic semigroup is not a complete automaton semigroup [4, Proposition 4.3] or even a (partial) automaton semigroup (see [8, Theorem 18] or [20, Theorem 1.2.1.4]). **B**: The construction used to prove Theorem 6 can also be used...
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**A**: We proposed a simple regularization scheme which, despite not requiring additional annotations, rivals state-of-the-art accuracy. Future visual grounding methods should be tested with a more comprehensive experimental setup and datasets for proper evaluation. **B**: We found that the accuracy improvements stem f...
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**A**: Sathyendra et al. (2017) presented a dataset and developed a model to automatically identify and label opt-out choices offered in privacy policies. Similarly, Zimmeck et al**B**: Other corpora similar to OPP-115 Corpus have enabled research on privacy practices. The PrivacyQA corpus contains 1,750 questions and ...
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**A**: StackGenVis: Alignment of Data, Algorithms, and Models for Stacking Ensemble Learning Using Performance Metrics(b, \raisebox{-.0pt} {\tiny\bfS6}⃝)).**B**: The same MDS projection is observable in varying stages with different legend ranges and diverse colors for each instance, depending on the selected performan...
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**A**: small data sets) to get a parameter initialization which is easy to adapt to target tasks with a few samples. As a model-agnostic framework, MAML is successfully employed in different NLP applications. Some works use MAML for few-shot text classification, such as relation classification [Obamuyide and Vlachos, 2...
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Selection 2
**A**: Then the TE estimation algorithm which exploits the MSI prediction error is proposed in Section IV-B. The TE-aware CCA codebook based 3D beamwidth selection algorithm is developed based on the TE estimation to achieve effective beam tracking in Section IV-C.**B**: The position and attitude compose the UAV’s moti...
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**A**: We**B**: Note that the 1111-color case with the completeness requirement is not very interesting, and also not useful for the general case: completeness states that every node on the left must be connected, via the unique edge relation, to every node on the right – regardless of the matrix**C**: This will be boo...
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**A**: In particular, we aim to characterize how an overparameterized two-layer neural network and its induced feature representation evolve in TD and Q-learning, especially their rate of convergence and global optimality**B**: A fundamental obstacle, however, is that such an evolving feature representation possibly le...
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**A**: (2016) with 32⁢k32𝑘32k32 italic_k merging operations on all data sets to address the unknown word issue**B**: We only kept sentences with a maximum of 256256256256 subword tokens for training. For fair comparison, we did not tune any hyperparameters but followed Vaswani et al. (2017) for all experiment settings...
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Selection 4
**A**: In particular, as b∈W⊆V2(a′,y′)𝑏𝑊superscriptsubscript𝑉2superscript𝑎′superscript𝑦′b\in W\subseteq V_{2}^{(a^{\prime},y^{\prime})}italic_b ∈ italic_W ⊆ italic_V start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT ( italic_a start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT , italic_y start_POSTSUPERSCRIPT...
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**A**: The proposed ordinal distortion is a learning-friendly representation for neural networks, which is explicit and homogeneous compared with the implicit and heterogeneous distortion parameters**B**: Thus, our learning model gains sufficient distortion perception of features and shows faster convergence. Moreover,...
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**A**: In this paper, we first review the convergence property of MSGD, one of the most widely used variants of SGD, and analyze the failure of MSGD in large-batch training from an optimization perspective**B**: Then, we propose a novel method, called stochastic normalized gradient descent with momentum (SNGM), for lar...
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**A**: Unfortunately, standard SAA approaches [26, 7] do not directly apply to radius minimization problems**B**: See Appendix A for an in-depth discussion.**C**: On a high level, the obstacle is that radius-minimization requires estimating the cost of each approximate solution; counter-intuitively, this may be harder...
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Selection 2
**A**: Then we substitute this upper bound into the Lyapunov function difference inequality of the consensus error, and obtain the estimated convergence rate of mean square consensus (Lemma 3.3)**B**: Further, the estimations of these rates are substituted into the recursive inequality of the conditional mean square er...
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Selection 1
**A**: Furthermore, the QI values of individuals can be easily exposed that increases the background knowledge of adversary to learn the pattern of QI values and sensitive values in the released table [13, 30].**B**: However, most existing approaches cannot prevent identity disclosure, and the existence of individuals ...
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**A**: Due to limited mask representation of HTC, we move on to SOLOv2, which utilizes much larger mask to segment objects. It builds an efficient yet simple instance segmentation framework, outperforming other segmentation methods like TensorMask Chen et al**B**: (2020) on COCO. In SOLOv2, the unified mask feature br...
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**A**: For the significance of this conjecture we refer to the original paper [FK], and to Kalai’s blog [K] (embedded in Tao’s blog) which reports on all significant results concerning the conjecture**B**: [KKLMS] establishes a weaker version of the conjecture**C**: Its introduction is also a good source of information...
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Selection 4
**A**: We compare the cumulative rewards of the proposed algorithms with five baseline algorithms: Epsilon-Greedy (Watkins, 1989), Random-Exploration, LSVI-UCB (Jin et al., 2020), OPT-WLSVI (Touati & Vincent, 2020), and MASTER (Wei & Luo, 2021)**B**: As discussed before, we are the first one to perform numerical experi...
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Selection 2
**A**: Trust is built on transparency and truthfulness, and the presence of fake news, which is deceptive and usually meant to serve hidden agendas, may erode trust. It is worthwhile to consider whether the trust in media items is due to people’s own encounters with fake news, or because of secondary factors**B**: The...
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Selection 3
**A**: As depicted in 2b, each layer in DAN consists of two steps, similar to a multi-layer GAT**B**: Alternatively, we can implement the decentralized approach using a second-order attention mechanism**C**: The computation involves the previous two layers and can be formulated using the following equation:
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Selection 1
**A**: Following this principle, we implement an ensemble-based dynamics model with three probabilistic neural networks for Noisy-Mnist. Each network outputs a 512d diagonal Gaussian to model the mean and variance of each pixel. We train such an ensemble-based model by supervised learning for 200 epochs to predict the ...
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**A**: Further, we recognize that the Vandermonde approach is inaccurate and even becomes numerically unstable (rising errors) for higher degrees**B**: As expected, (Chebyshev) polynomial interpolation on uniform grids (uniform) and multi-linear interpolation also do not converge.**C**: It is therefore inappropriate fo...
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Selection 1
**A**: the disentangled factors) and correlated components Z𝑍Zitalic_Z, a.k.a as nuisance variables, which encode the details information not stored in the independent components. A series of works starting from [beta] aims to achieve that via regularizing the models by up-weighting certain terms in the ELBO formulati...
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**A**: As mentioned above, the search is carried out and the results are expressed by the unique number of each vertex. The result is as shown in Table. 1. The result of moving from the K2 peak to the K1 peak is the same as that of the XNOR, and the result of moving from the K2 peak to the K3 peak is the same as that o...
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**A**: There has been extensive study about a family of polynomial maps defined through a parameter a∈𝔽𝑎𝔽a\in\mathbb{F}italic_a ∈ blackboard_F over finite fields**B**: Some well-studied families of polynomials include the Dickson polynomials and reverse Dickson polynomials, to name a few**C**: Conditions for such fa...
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Selection 2
**A**: Note that we are primarily interested in the extent to which differences between the meta-learners are moderated by the experimental factors of sample size, view size, number of views, and correlation structure**B**: The values of partial η2superscript𝜂2\eta^{2}italic_η start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRI...
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Selection 3
**A**: Given that there has been an extensive collection of feature selection and prediction techniques available, a meaningful and effective way for anomaly detection is to make use of off-the-shelf supervised techniques, instead of reinventing the wheel by developing new methods. **B**: Thus, dependency-based approac...
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Selection 4
**A**: [2021] recently proposed the idea of convex relaxation of the confidence set for the more straightforward logistic bandit setting. Our work can be viewed as an extension of their construction to the MNL setting. **B**: Comparison with Abeille et al**C**: [2021]  Abeille et al
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**A**: It progressively aggregates features from cross scales as well as from the same scale at multiple network levels via a hybrid module of a temporal branch and a graph branch**B**: Inspired by FPN [22], which computes multi-scale features with different levels, we propose a cross-scale graph pyramid network (xGPN...
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Selection 1
**A**: If not, then more stages should be involved in the process until his/her expectations are met**B**: This entire process should be trackable and manageable from the user’s side. The best models (according to the user) are accumulated in a final bucket, forming a majority-voting ensemble. **C**: Li et al. [LCW∗18]...
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**A**: In this section, we introduce a shortest-path algorithm that is proposed as a modification to the Metropolis-Hastings algorithm in [7, Section V-E] and integrated with the Markov chain synthesis methods described in [14] and [15]**B**: Our approach begins by categorizing the states of the desired distribution.*...
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**A**: Our algorithm is efficient, straightforward to implement, and montonically increases the objective function. Experimentally we have demonstrated that our method outperforms recent state-of-the-art techniques in terms of matching quality, while producing cycle-consistent results and being efficient.**B**: We pre...
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**A**: In Section 4 we present our recognition algorithm for path graphs, we prove its correctness, we report some implementation details and we compute its time complexity. Finally, in Section 5 we provide a similar analysis for directed path graphs. **B**: The paper is organized as follows**C**: In Section 2 we prese...
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**A**: DCSBM is widely used for community detection for non-mixed membership networks (zhao2012consistency, ; SCORE, ; cai2015robust, ; chen2018convexified, ; chen2018network, ; ma2021determining, ). MMSB constructed a mixed membership stochastic blockmodel (MMSB) which is an extension of SBM by letting each node have...
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**A**: (2018); Boumal et al. (2018); Bécigneul and Ganea (2018); Zhang and Sra (2018); Sato et al. (2019); Zhou et al. (2019); Weber and Sra (2019) and the references therein. Also see recent reviews (Ferreira et al., 2020; Hosseini and Sra, 2020)**B**: (2017); Agarwal et al. (2018); Zhang et al. (2018); Tripuraneni et...
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Selection 2
**A**: We run the experiments under three traffic flow configurations: real traffic flow, mixed low traffic flow and mixed high traffic flow. The real traffic flow is real-world hourly statistical data with slight variance in vehicle arrival rates, as shown in Tab**B**: II. A detailed description of traffic flow config...
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**A**: Concerning the application of frequency predictions in competitive online optimization, we note that, perhaps surprisingly, such predictions have not been used widely, despite their simplicity and effectiveness**B**: (?) gave improved competitive ratios for a generalized online matching problem motivated by adve...
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Selection 4
**A**: We present Locally Conditioned Atlas (LoCondA), a framework for generating and reconstructing meshes of objects using an atlas of localized charts that leverage the introduced notion of the continuous atlas. It consists of two parts**B**: Firstly, we map the target object into a known prior distribution (trainin...
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Selection 1
**A**: However, in the Section 3 we obtained results in a general setup without additional knowledge about cost functions and sets. On the contrary, in this section we utilize the special structure of the WB problem and introduce slightly different norms. After that, we get a convergence guarantee by applying Theorem 3...
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**A**: We proceed by trying to find a counterexample based on our previous observations**B**: In the first part, we focus on the complete analysis of small graphs, that is: graphs of at most 9 nodes. In the second part, we analyze larger families of graphs by random sampling instances.**C**: In this section we present ...
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**A**: of Patáková [35, Theorem 2.3] into: **B**: One immediate application of Theorem 1.2 is the reduction of fractional Helly numbers**C**: For instance, it easily improves a theorem444[35, Theorem 2.3] was not phrased in terms of (K,b)𝐾𝑏(K,b)( italic_K , italic_b )-free covers but readily generalizes to that setti...
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**A**: T3: Analyze the effect of diverse feature transformations. When some features’ distributions are skewed left or right, logarithmic or exponential transformations respectively could further boost each feature’s contribution**B**: A user should be competent in judging the influence of feature transformations befor...
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**A**: The performance metrics evaluating infinitytracking accuracy and time are summarized in the table for unconstrained and constrained BO.**B**: The right panel shows the evolution of BO iterations, until optimization terminates**C**: Figure 5: Position, velocity, acceleration, and maximal contour error resulting ...
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**A**: For instance, the widely used Colored MNIST dataset, where colors and digits are spuriously correlated with each other, is setup differently across papers. Some use it as a binary classification task (class 0: digits 0-4, class 1: digits: 5-9) [5, 50], whereas others use a multi-class setting (10 classes) [37, 4...
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Selection 3
**A**: Due to the diversity of human eyes, 3D eye models are usually person-specific.**B**: These methods can be broadly categorized into three groups: 3D eye model recovery-based, 2D eye feature regression-based, and appearance-based methods. 3D eye model recovery-based methods construct a geometric 3D eye model and e...
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**A**: Moreover, dealing with only the unmasked regions, the high generalization of the proposed method makes it applicable in real-time applications**B**: Other methods, however, aim to unmask the masked face using generative networks such as in din2020novel . This strategy is a greedy task and not preferable for real...
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**A**: Connectives that have noninvertible right rules are positive and those that have noninvertible left rules are negative. The key innovation of SAX is to replace the noninvertible rules with their axiomatic counterparts in a Hilbert-style system. Consider the following right rule for implication as well as the ori...
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Selection 1
**A**: [27] aimed to achieve differential access control and access history hiding on the cloud while enabling fair redistribution tracing by embedding watermarks homomorphically. However, the computing overhead on the cloud side would be onerous due to the need of performing re-encryption operations and homomorphic op...
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**A**: It is worth mentioning that we have also tried to set a threshold to select the edges in the graph, i.e., setting a minimum value for the edge probability of cutting edges off**B**: But the performance is not as good as using a fixed-degree graph. This is reasonable as the edge weights of different nodes’ neighb...
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**A**: [2022] when computing the step size according to the strategy from Pedregosa et al**B**: [2020]; see 5 in Algorithm 4. The remaining two variants ensure that 𝐱∈dom⁢(f)𝐱dom𝑓\mathbf{x}\in\mathrm{dom}(f)bold_x ∈ roman_dom ( italic_f ) by using second-order information about f𝑓fitalic_f, which we explicitly do n...
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**A**: Informal description: Extend-Active-Paths can be seen as performing a Depth First Search (DFS) along active paths**B**: The backtracking is not applied to the structures that are on hold, as those structures did not attempt extending their active paths in the corresponding streaming pass. **C**: When an active p...
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**A**: We provide necessary notation and assumptions in Section II**B**: The rest of this paper is organized as follows**C**: CPP is introduced and analyzed in Section III. In Section IV, we consider the algorithm B-CPP. Numerical examples are presented in Section V, and we conclude the paper in Section VI.
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**A**: It is worth considering the use of the variance reduction technique in accelerated sliding to develop an algorithm that is highly efficient in terms of communication and number of iterations**B**: Possible interesting areas for further research are related to the practical features that arise in the federated le...
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**A**: Kuhn Poker (Kuhn, 1950; Southey et al., 2009; Lanctot, 2014) is a zero-sum poker game with only two actions per player**B**: The two-player variant is solvable with PSRO, however the three-player version benefits from JPSRO**C**: The results in Figure 2(a) show rapid convergence to equilibrium.
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**A**: However, its optimality is for worst-case adaptive queries, and the guarantees that it offers only beat the naive intervention—of splitting a dataset so that each query gets fresh data—when the input dataset is quite huge (Jung et al., 2020)**B**: Differential privacy essentially provides the optimal asymptotic...
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Selection 1
**A**: We generate a set of colorings that is guaranteed to contain at least one such coloring**B**: Using the previous lemmas the problem of finding a reducible single-tree FVC reduces to finding a coloring that properly colors a simple reducible FVC**C**: To generate this set we use the concept of a universal set.
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Selection 3
**A**: Nonetheless, it is very difficult to obtain paired data, i.e., a composite image without foreground shadow and a ground-truth image with foreground shadow, which are required by supervised deep learning methods on shadow generation [203, 92, 52]**B**: Some works [203, 92] construct rendered datasets with paired ...
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Selection 4
**A**: By leveraging this transferable knowledge across domains with this multi-city, multi-task data, CityNet can help researcher alleviate the data scarcity problems that arise in newly-built or under-developed cities. **B**: Transfer learning: Firstly, it can serve as an ideal testbed for transfer learning algorithm...
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Selection 3
**A**: All experimental results were obtained by evaluating the models on 50 different train/test-splits of the data sets in Table 2**B**: If a calibration set was needed for post-hoc calibration, the training set was further divided into two equal-sized sets. Because the models were tested both with and without post-h...
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Selection 2
**A**: homophonic or polyphonic music. Utilising the POP909 dataset \textcitepop909, we can develop a model that classifies each Pitch event into vocal melody, instrumental melody or accompaniment, with classification accuracy (ACC) serving as the evaluation metric.111111We note that there is a task closely related to ...
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Selection 3
**A**: As it was stated in the proof of Lemma 2.2, while searching for a central vertex we always jump from a vertex to its neighbor in a way that decreases the largest remaining component by one**B**: Thus, if in the next iteration we start at exactly the neighbor of the previous central vertex, there can be only O⁢(n...
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Selection 1
**A**: The mechanism behind this is that semantic information takes into account the meaning and veracity of source data because they can be both informative and factual[7], besides, the semantic data can be compressed to a proper size by employing a lossless method[8]. However, it is very challenging to define the sem...
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Selection 1
**A**: However, the cross-branch can still produce reasonable scores as the network is learned to only propagate features from the same category for each point. The intra branch produces better results than the cross branch, but still lower than the basic branch**B**: Performance of different branches: Table IV compare...
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Selection 3
**A**: Figure 5: Qualitative results of our method for multi-class 3D object detection**B**: All illustrated images are from the KITTI test set. Zoom in the image for more details.**C**: We use orange box for cars, purple box for pedestrians, and green box for cyclists
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Selection 2
**A**: It contains 1,000 training and 500 testing images. MSRA-TD500 [45] is dedicated to detecting multi-oriented long non-Latin texts**B**: ICDAR2015 [44] includes multi-orientated and small-scale text instances. Its ground truth is annotated with word-level quadrangles**C**: It contains 300 training images and 200 ...
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Selection 2
**A**: Hence, we present an alternative pre-allocation strategy for the memory blocks. A memory block will be allocated only when the first three parts of an initial IP address have been given. In particular, pre-allocating a big memory block of size 128 MB containing 256×256256256256\times 256256 × 256 contiguous memo...
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Selection 3
**A**: The authors would like to thank Mingjian Ding, and Baoxuan Zhu for providing an alternative proof of the Hurwitz stability of polynomials (25). They also thank Jarle Sogn for communicating on Schur complement based preconditioners. The work of M. Cai is partially supported by the NIH-RCMI grant through 347 U54MD...
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Selection 3
**A**: In this case, the data is vertically partitioned across different applications of the different companies.**B**: At the same time, the users do not wish to share raw personal data with the companies**C**: As a motivating example, we consider two smartphone application providers who wish to train a global model o...
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Selection 3
**A**: We present four different definitions of tensor ε𝜀\varepsilonitalic_ε-pseudospectra (cf**B**: The second main contribution of this paper is the development of pseudospectra theory for third-order tensors**C**: Definitions 9 and 10) and establish their equivalence under certain conditions. We also provide variou...
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Selection 1
**A**: This work is partly supported by the National Natural Science Foundation of China (No**B**: 2019M660406), the Research Program of State Key Laboratory of Software Development Environment (SKLSDE-2021ZX-04), and the Fundamental Research Funds for the Central Universities. We also give specical thanks to Alibaba ...
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Selection 2
**A**: In a binary erasure channel (BEC), a binary symbol is either received correctly or totally erased with probability ε𝜀\varepsilonitalic_ε**B**: The concept of BEC was first introduced by Elias in 1955 InfThe **C**: Together with the binary symmetric channel (BSC), they are frequently used in coding theory and in...
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Selection 2