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**A**: The LGO generating set offers a variety of advantages**B**: In practice it is the generating set produced by the constructive recognition algorithms from [10, 11] as implemented in MAGMA**C**: Consequently, algorithms in the composition tree data structure, both in MAGMA and in GAP, store elements in classical g...
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**A**: From now on, we concentrate on approximating P𝑃Pitalic_P so that (25) can be accurately and efficiently solved. **B**: Solving (25) on the other hand involves computing the hℎhitalic_h-dependent, global operator P𝑃Pitalic_P, leading to a dense matrix in (25)**C**: Except for (ii), all steps above above can be ...
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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**: We call them “debunking words” e.g., hoax, rumor or not true. Our intuition is, that the attitude of doubting or denying events is in essence sufficient to distinguish rumors from news. What is more, this generalization augments the size of the crowd (covers more ’voting’ tweets), which is crucial, and thus cont...
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**A**: Instead, we should look at the 00–1111 error on the validation dataset**B**: 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. **C**: We should not rely on plateauing of the training loss or on the loss (lo...
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**A**: Others user-based features like UserReputationScore and UserJoinDate also have a better performance in the first fews hours. That means the sources (the posters in the first few hours) of news and rumors are quite different with each other**B**: The performance of user features is similar with the Twitter featur...
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**A**: We then bin the entities in the two datasets chronologically into 10 different parts. We set up 4 trials with each of the last 4 bins (using the history bins for training in a rolling basic) for testing; and report the results as average of the trials.**B**: In total, our training dataset for AOL consists of 1,7...
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**A**: Only one of the patients suffers from diabetes type 2 and all are in ICT therapy. In terms of time since being diagnosed with diabetes, patients vary from inexperienced (2 years) to very experienced (35 years), with a mean value of 13.9 years.**B**: Table 1 shows basic patient information. Half of the patients ...
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**A**: Table 4: The results after evaluating our model with respect to its computational efficiency. We tested five versions trained on different eye tracking datasets, each receiving input images of their preferred sizes in pixels (px)**B**: The minimal GPU memory utilization was measured with TensorFlow in megabytes ...
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**A**: Addressing these questions is the main purpose of this paper.**B**: For Loc, only exact exponential-time algorithms are known and whether it can be solved in polynomial-time, or whether it is at least fixed-parameter tractable is mentioned as open problems in [15]**C**: Approximation algorithms have not yet bee...
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**A**: Section 6.4)**B**: The world model is trained for 45454545K steps in the first iteration and for 15151515K steps in each of the following ones. Shorter training in later iterations does not degrade the performance because the world model after first iteration captures already part of the game dynamics and only n...
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**A**: During the step negotiation simulations, it was noticed that the rolling locomotion mode encountered constraints when attempting to cross steps with a height greater than thrice the track height (h being the track height as shown in Fig. 3)**B**: This limitation originates from the traction forces generated by ...
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**A**: First, we show that the randomized algorithm of Purohit et al. [29] for the ski rental problem Pareto-dominates any deterministic algorithm, even when the latter is allowed unbounded advice.**B**: All the above results pertain to deterministic online algorithms**C**: In Section 6, we study the power of randomiz...
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**A**: those caused by not using other information than text for classification, another limitation in the present work is that we used words as the basic building blocks (i.e**B**: Besides the limitations described in Subsection 5.2, e.g**C**: each writing was processed as a Bag of Words) on which our approach begins ...
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**A**: Note that the convergence guarantee of DEF-A and its momentum variant for non-convex problems is lacking in (Xu and Huang, 2022)**B**: We provide the convergence analysis for GMC+, which can be seen as a global momentum variant of DEF-A**C**: We eliminate the assumption of ring-allreduce compatibility from (Xu a...
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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**: The topological structure of Multi-UAV network is shown in Fig. 1 (a).**B**: All the UAVs have the same volume of battery E𝐸Eitalic_E and communication capability**C**: We construct a UAV ad-hoc network in a post-disaster scenario with M𝑀Mitalic_M identical UAVs being randomly deployed, in which M𝑀Mitalic_M ...
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**A**: italic_e **B**: has no component perpendicular to the boundary (i.e.,𝐩⟂|Γ=0)(i.e.,\,\mathbf{p_{\perp}}|_{\Gamma}=0)( italic_i **C**: , bold_p start_POSTSUBSCRIPT ⟂ end_POSTSUBSCRIPT | start_POSTSUBSCRIPT roman_Γ end_POSTSUBSCRIPT = 0 ). In the following, we will refer to these conditions as the natural
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**A**: A fully connected neural network architecture was used**B**: It was composed of two hidden layers of 128 neurons and two Dropout layers between the input layer and the first hidden layer and between the two hidden layers**C**: ADAM optimizer for the minimization[25].
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**A**: Next, we briefly discuss the most popular and widely used datasets for the semantic segmentation of natural images**B**: For a comprehensive review of the natural image datasets that segmentation models are usually benchmarked upon, we direct the interested readers to Lateef and Ruichek (2019). **C**: These data...
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**A**: Each of the neurons is connected to all split nodes on the path from the root node to the leaf node to evaluate if the data is routed to the respective leaf node**B**: The second hidden layer has a neuron per leaf node in the decision tree**C**: Finally, the output layer is connected to all leaf neurons and aggr...
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**A**: As a result, such a lack of statistical understanding hinders the development of more sample-efficient policy optimization algorithms beyond heuristics. In fact, empirically, vanilla policy gradient is known to exhibit a possibly worse sample complexity than random search (Mania et al., 2018), even in basic sett...
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**A**: (2019a) and Cai et al. (2019). They introduce gates for every layer that determine the number of bits used for quantization, and they perform continuous stochastic optimization of probability parameters associated with each of these gates.**B**: Wu et al**C**: (2018a) performed mixed-precision quantization using...
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**A**: To avoid that, we will invoke a result due to Liu [64]. **B**: However, if FillRad⁢(M)FillRad𝑀\mathrm{FillRad}(M)roman_FillRad ( italic_M ) were small, one would not be able to apply Wilhelm’s theorem**C**: The proof strategy for Propositions 9.8 and 9.9 is to invoke Wilhelm’s result [82, Main Theorem 2] and Le...
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**A**: In our Dimension Correlation tool, the user also draws a polyline to identify a shape, but our intention is exactly the opposite of AxiSketcher: we want to capture dimension contributions in an easy and accessible way. For this, we project low-dimensional points into the line (not high-dimensional ones, as in Ax...
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**A**: Authors annotate that this novel mechanism is capable of checking that if the algorithm is biased towards exploration, it will shift towards exploitation in subsequent iterations and vice versa. This strategy obtains the dispersion degree of the population by calculating the standard deviation of the historical ...
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**A**: The adaptive learning will induce the model to exploit the high-level information. In particular, AdaGAE is stable on all datasets. **B**: Classical clustering models work poorly on large scale datasets. Instead, DEC and SpectralNet work better on the large scale datasets**C**: Although GAE-based models (GAE, MG...
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**A**: Although a valuable complementary technique for active probes with vantage points, this approach has significant limitations: in the absence of loops ingress filtering cannot be inferred, alternately a forwarding loop in traceroute does not imply absence of filtering at the edge, since a loop resulting from a tr...
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**A**: TABLE I: Mean generalization accuracy**B**: Listed is the classification accuracy (correct / total) of various models evaluated on the unseen testing data, i.e., batch T𝑇Titalic_T**C**: The values represent the average accuracy over 30 trials. The final column lists the mean of the values for batches 3 through ...
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**A**: In fact, the construction to generate these semigroups is quite simple [4, Proposition 4.1] (compare also to 3). The same construction can also be used to generate free monoids as automaton semigroups or monoids. Here, the main difference is that the free monoid in one generator can indeed be generated by an aut...
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**A**: Table A4 shows VQA accuracy for each answer type on VQACPv2’s test set. HINT/SCR and our regularizer show large gains in ‘Yes/No’ questions**B**: However, in the test set, answer ‘yes’ is more frequent. Regularization effects caused by HINT/SCR and our method cause the models to weaken this prior i.e., reduce th...
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**A**: (2016) followed a bottom-up approach and identified different categories from analysis of data practices in privacy policies, we followed a top-down approach and applied topic modelling to the corpus in order to extract common themes for paragraphs. The categories identified in the OPP-115 Corpus can be found in...
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**A**: To illustrate how to choose different metrics (and with which weights), we start our exploration by selecting the heart disease data set in StackGenVis: Alignment of Data, Algorithms, and Models for Stacking Ensemble Learning Using Performance Metrics(a). Knowing that the data set is balanced, we pick accuracy ...
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**A**: We first study the effects of data quantity and distribution on the training strategy: RQ1. Since the parameter initialization learned by MAML can be seen as a general language model of training tasks, when the training and testing tasks have different data distributions, how can the general language model train...
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**A**: If an inappropriate subarray is activated, the beam angle may go beyond the radiation range of certain subarray elements, degrading the beam gain and SE.**B**: Due to the directivity, the DREs of the CCA subarray at different positions are anisotropic, and this phenomenon is different from the UPA**C**: Activat...
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**A**: 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**B**: This will be bootstrapped...
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**A**: (2019); Chen et al. (2019b) study the convergence of Q-learning. When the value function approximator is nonlinear, TD possibly diverges (Baird, 1995; Boyan and Moore, 1995; Tsitsiklis and Van Roy, 1997). Bhatnagar et al. (2009) propose nonlinear gradient TD, which converges but only to a locally optimal solutio...
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**A**: However, even with only one layer for the hidden state computation and with 27.77%percent27.7727.77\%27.77 % fewer parameters (45.0545.0545.0545.05M against 62.3762.3762.3762.37M), depth-wise LSTM (Equation 5) still slightly outperforms the vanilla Transformer baseline in BLEU (27.8427.8427.8427.84 against 27.55...
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**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**: Based on the above limitations and the presented solutions, we plan to achieve a more comprehensive and robust distortion rectification framework in future work. **B**: The second limitation is that the distortion needs to be radially symmetric**C**: This problem may be addressed by the grid optimization techniq...
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**A**: Then, we propose a novel method, called stochastic normalized gradient descent with momentum (SNGM), for large-batch training**B**: 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 optimiz...
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**A**: We also consider the polynomial-scenarios model [23, 15, 21, 10], where the distribution 𝒟𝒟\mathcal{D}caligraphic_D is listed explicitly**B**: We use the suffixes BB and Poly to distinguish these settings. For example, 2S-Sup-BB is the previously defined 2S-Sup in the black-box model. **C**: The most general w...
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**A**: Motivated by distributed statistical learning over uncertain communication networks, we study the distributed stochastic convex optimization by networked local optimizers to cooperatively minimize a sum of local convex cost functions. The network is modeled by a sequence of time-varying random digraphs which ma...
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**A**: However, most existing approaches cannot prevent identity disclosure, and the existence of individuals in published table is likely to be disclosed [27]**B**: Comparing to generalization, bucketization technique [33, 18] maintains excellent information utility because it preserves all the original QI values**C*...
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**A**: It produces smooth object boundaries with much finer details than previously two-stage detectors like MaskRCNN, which naturally benefits large object instances and complex scenes**B**: PointRend performs point-based segmentation at adaptively selected locations and generates high-quality instance mask**C**: Furt...
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**A**: This solves a question raised by Gady Kozma some time ago (see [K], comment from April 2, 2011)**B**: More specifically, we proved**C**: In version 1 of this note, which can still be found on the ArXiv, we showed that the analogous version of the conjecture for complex functions on {−1,1}nsuperscript11𝑛\{-1,1\...
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**A**: Section 6 shows our experiment results. Section 7 concludes the paper and discusses some future directions. All detailed proofs can be found in Appendices.**B**: Section 3 establishes the minimax regret lower bound for nonstationary linear MDPs. Section 4 and Section 5 present our algorithms LSVI-UCB-Restart, Ad...
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**A**: That respondents show strong trust and reliance on government communication platforms, such as official websites and hotlines, signifies the relatively strong faith that Singapore residents have in the Singapore Government to provide truthful and helpful information and to debunk fake news. This may be attribute...
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**A**: However, this input embedding can still accumulate knowledge by participating in the aggregations of its neighbors. The acquired information may not necessarily reside in the same dimension for a pair of aligned entities at this layer, which accounts for the comparatively lower performance of this layer**B**: T...
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**A**: Before training, the agent interacts with the environments for 104superscript10410^{4}10 start_POSTSUPERSCRIPT 4 end_POSTSUPERSCRIPT steps to estimate the mean and standard deviation of the states. We further normalize the observed states for training by the estimated mean and standard deviation before training....
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**A**: As expected, (Chebyshev) polynomial interpolation on uniform grids (uniform) and multi-linear interpolation also do not converge.**B**: Further, we recognize that the Vandermonde approach is inaccurate and even becomes numerically unstable (rising errors) for higher degrees**C**: It is therefore inappropriate fo...
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**A**: Prior work in unsupervised DR learning suggests the objective of learning statistically independent factors of the latent space as means to obtain DR. The underlying assumption is that the latent variables H𝐻Hitalic_H can be partitioned into independent components C𝐶Citalic_C (i.e**B**: They aren’t really sepa...
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**A**: In other words, operating a structural computer with a minimal lead is also a task to be addressed by this study because one of the most important factors in computer hardware design is aggregation. Let’s look at the role of the four pins that transmit signals in a 4 pin based signal system. Four pins are paired...
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**A**: Conditions for such families of maps to define a permutation of the field 𝔽𝔽\mathbb{F}blackboard_F are well studied and established for special classes like Dickson polynomials [20], linearized polynomials [21] and few other specific forms [13, 14] to name a few. **B**: There has been extensive study about a f...
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**A**: The results of two meta-learners do not align with this pattern, namely those for the interpolating predictor and NNFS**B**: Since feature selection often comes at a cost in terms of stability (Xu \BOthers., \APACyear2012), it is to be expected that view selection stability (Φ^^Φ\hat{\Phi}over^ start_ARG roman_...
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**A**: Notably, IEPC shows the longest average running time, particularly for large-sized datasets like Ads, Census, and Backdoor. As for the five prediction models, their computational costs are moderate, ranging from 8.8 to 21 seconds on average. **B**: Comparing the five methods, FBED is the most efficient, with an ...
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**A**: Comparison with Oh & Iyengar [2019] The Thompson Sampling based approach is inherently different from our Optimism in the face of uncertainty (OFU) style Algorithm CB-MNL**B**: However, the main result in Oh & Iyengar [2019] also relies on a confidence set based analysis along the lines of Filippi et al**C**: [...
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**A**: Besides evaluating all actions in general, we also provide average mAPs of short actions for VSGN as well as other methods that have detection results available**B**: Here, we refer to action instances that are shorter than 30 seconds as short actions**C**: On ActivityNet, there are 54.4% short actions, whereas...
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**A**: The use of parallel coordinates plots [ID87] is rather prominent for the visualization of automatic hyperparameter tuners such as HyperOpt [BKE∗15]**B**: Most of the time, less interactive visualizations have been developed for monitoring automatic frameworks [ASY∗19, GSM∗17, KKP∗18, LLN∗18, LTKS19, TBCT∗18]**C*...
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**A**: The decentralized state-dependent Markov matrix synthesis (DSMC) algorithm is introduced in Section III. Section IV introduces the probabilistic swarm guidance problem formulation, and presents numerical simulations of swarms converging to desired distributions. The paper is concluded in Section V.**B**: The pap...
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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**: A clique is a clique separator if its removal disconnects the graph in at least two connected components**B**: For example, every cycle has no clique separator, and the butterfly/hourglass graph has two cliques and it is an atom. In [18] it is proved that an atom is a path graph and/or a directed path graph if ...
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**A**: Subfigure 1(k) suggests that Mixed-SLIM, Mixed-SCORE, and GeoNMF share similar performances and they perform better than OCCAM under the MMSB setting**B**: the proposed Mixed-SLIM significantly outperforms the other three methods under the DCMM setting.**C**: The numerical results are given by the last two pane...
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**A**: (2018); Cheng and Bartlett (2018); Chatterji et al. (2018); Wibisono (2018); Bernton (2018); Dalalyan and Karagulyan (2019); Baker et al. (2019); Ma et al. (2019a, b); Mou et al. (2019); Vempala and Wibisono (2019); Salim et al. (2019); Durmus et al. (2019); Wibisono (2019) and the references therein. Among thes...
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**A**: MetaLight [14] is a value-based meta RL method via parameter initialization based on MAML [73]**B**: Here we extend it to a multi-agent scenario without considering neighbor information. **C**: MetaLight is originally a single-agent approach for meta-learning on multiple separate tasks
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**A**: Previous work on this problem has assumed ideal and error-free predictions that must be provided by a very powerful oracle, without any learnability considerations, as we discuss in more detail in Section 1.2**B**: We give the first theoretical and experimental study of online bin packing with machine-learned pr...
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**A**: Finally, we empirically show the proposed framework produces high-fidelity and watertight meshes**B**: To evaluate the continuity of output surfaces, we propose to use the following metric.**C**: It means that it solves the initial problem of disjoint patches occurring in the original AtlasNet (Groueix et al., ...
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**A**: By using batching technique, the results can be generalized to stochastic saddle-point problems [15, 23]**B**: Instead of the smooth convex-concave saddle-point problem we can consider general sum-type saddle-point problems with common variables in more general form. For each group of common variable, we introdu...
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**A**: The length of a cycle is its number of edges. The minimum cycle basis (MCB) problem is the problem of finding a cycle basis such that the sum of the lengths (or edge weights) of its cycles is minimum**B**: In [5] a unified perspective of the problem is presented. The authors show that the MCB problem is differe...
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**A**: A major part of this paper, all of Sections 3 and 4, is devoted to adapt it to handle the k𝑘kitalic_k-partite structure of colorful intersection patterns.**B**: This technique, which we briefly outline here, was specifically designed for complete intersection patterns**C**: The proof of Theorem 2.1 is quite in...
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**A**: For the latter, mutual information is used in our VA system (also used by May et al. [26], for instance). Features are added to capture the missing information and improve the classifier’s performance [34]. The magnitude of correlation with the dependent variable and in-between features is key to such decisions ...
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**A**: We compare three schemes: manual tuning of the MPCC parameters for fixed low level controller gains, Tuning of MPCC parameters through Bayesian optimization, and joint tuning of the MPCC- and the low-level cascade controller parameters using Bayesian optimization.**B**: We have implemented the simulations in Mat...
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**A**: In this set of experiments, we compare the resistance to explicit and implicit biases**B**: To ease analysis, we compute the accuracy gap between the majority and minority groups i.e., majority/minority difference (MMD). Majority/minority groups are defined per variable e.g., for foreground color, green 1’s, red...
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**A**: **B**: Eye image-based methods typically use head pose vectors as an additional input [17, 55]. \addedNevertheless, the impact of head pose appears to be marginal [49], particularly when the basic network has already achieved high accuracy**C**: One possible rationale for this observation lies in the fact that a...
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**A**: The comparison of the computation times between the proposed method and Almabdy et al.’s method almabdy2019deep shows that the use of the BoF paradigm decreases the time required to extract deep features and to classify the masked faces (See Table 4)**B**: AlexNet is lowest training and testing time compared t...
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**A**: Moreover, we take the liberty to nest values (boxed and highlighted yellow), which can be expanded into SAX [PP20].**B**: Since they are not recursive, we do not bother tracking the size superscript of the typing judgment, since they can be inlined**C**: First, we define head and tail observations on streams of...
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**A**: The whole FairCMS-II scheme is summarized as follows. First, suppose an owner rents the cloud’s resources for media sharing, the owner and the cloud execute Part 1 as shown in Fig**B**: 5. Then, suppose the k𝑘kitalic_k-th user makes a request indicating that he/she wants to access one of the owner’s media conte...
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**A**: (2017) concatenates the node features and introduces three**B**: (2013), the learning process of graph convolutional networks (GCN) Kipf and Welling (2017) also can be considered as a mean-pooling neighborhood aggregation. GraphSAGE Hamilton et al**C**: Though based on graph spectral theory Bruna et al
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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**: This 2222-approximate maximum matching is our starting matching**B**: In the first pass, we apply a simple greedy algorithm to find a maximal matching, hence a 2222-approximation**C**: The rest of our algorithm is divided into multiples phases. In each phase, we iteratively improve the approximation ratio of ou...
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**A**: CPP enjoys large flexibility in both the compression method and the network topology**B**: In this paper, we consider decentralized optimization over general directed networks and propose a novel Compressed Push-Pull method (CPP) that combines Push-Pull/𝒜⁢ℬ𝒜ℬ\mathcal{A}\mathcal{B}caligraphic_A caligraphic_B wi...
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**A**: In addition, we present Algorithm 3 which used the randomized local method from [30]. This algorithm is used to compare Algorithm 1 with Local randomized methods (like Algorithm 3) in practice.**B**: We develop multiple novel algorithms to solve decentralized personalized federated saddle-point problems**C**: T...
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**A**: We evaluate a number of (C)CE MSs in JPSRO on pure competition, pure cooperation, and general-sum games (Section H)**B**: More thorough descriptions of the games used can be found in Section F. We use an exact BR oracle, and exactly evaluate policies in the meta-game by traversing the game tree to precisely isol...
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**A**: One cluster of works that steps away from this worst-case perspective focuses on giving privacy guarantees that are tailored to the dataset at hand (Nissim et al., 2007; Ghosh and Roth, 2011; Ebadi et al., 2015; Wang, 2019)**B**: In  Feldman and Zrnic (2021) in particular, the authors elegantly manage to track t...
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**A**: After such reduction steps, the size of the entire structure we are trying to find can be bounded in terms of the parameter k𝑘kitalic_k. We then use color coding [6] to identify antler structures. A significant amount of effort goes into proving that the reduction steps preserve antler structures and the optima...
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**A**: Inspired by [129], they adapt a pretrained diffusion model to a subject by finetuning on a few reference images of this subject, so that a rare token is associated with this subject**B**: The existing generative image composition methods can be divided into two groups: token-to-object methods and object-to-objec...
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**A**: Problem Statement**B**: At every timestamp τ𝜏\tauitalic_τ, we use this policy to dispatch available taxis to current passengers, with the aim of maximizing the total revenue of all taxis in the long run. To achieve this, we divide the city into uniform hexagonal grids, as opposed to square grids used in previou...
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Selection 3
**A**: It was found that for some models the coverage decreased sharply. Both of these observations should not come as a surprise. The amount by which the intervals are scaled can be interpreted as a hyperparameter of the model. In general it is better to use more data to train than to validate, as long as the validati...
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Selection 4
**A**: Being inspired by the Bi-LSTM-Attn model \parencitelin2017structured, we employ an attention-based weighting average mechanism to convert the sequence of 512 hidden vectors for an input sequence to one single vector before feeding it to the classifier layer, which comprises two dense layers. We note that, unlike...
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Selection 3
**A**: This description draws a comparison e.g**B**: to L⁢(k,1)𝐿𝑘1L(k,1)italic_L ( italic_k , 1 )-labeling problem (see e.g**C**: [10] for a survey), where the colors of any two adjacent vertices have to differ by at least k𝑘kitalic_k and the colors of any two vertices within distance 2222 have to be distinct.
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Selection 3
**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 2
**A**: For One-Thing-One-Click[48] and MulPro[8], we use the results reported from the MulPro[8] paper**B**: Comparison with existing 3D WSSS methods: We compare our proposed method with existing 3D WSSS methods[13, 51, 41]**C**: [10] utilizes 2D dense labels on 2D projections of the 3D point clouds and [13] utilize t...
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**A**: A quantitative investigation is conducted by replacing the depth predictions with the ground-truth depth values on a baseline model**B**: However, the performance gap between LiDAR-based and monocular image-based approaches remains significant, mainly because of the lack of reliable depth information**C**: The d...
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**A**: For shape approximation (SAp), we first draw the text segments on a blank image and then use the contour of these overlapping text segments to approximate the original text contour**B**: To connect text segments with each other more closely, an opening operation with a kernel size of 3×3333\times 33 × 3 is perf...
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**A**: The remainder of this paper is organized as follows**B**: We briefly describe some of the original sorting techniques as well as various parallel sorting algorithms in Section 2**C**: In Section 3, we introduce the proposed method. The experimental results are presented in Section 4. Finally, we draw the conclus...
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Selection 2
**A**: For example, when the system matrix in (1) is extended to the n𝑛nitalic_n-tuple case, it is the block tridiagonal systems discussed in [37]**B**: The above 3333-by-3333 block linear problems (1) and (2) can be naturally extended to the n𝑛nitalic_n-tuple cases**C**: When the system matrix in (2) is extended to ...
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**A**: Other works have analyzed versions of horizontal federated learning for hierarchical or multi-tier networks where data is partitioned horizontally across all clients participating in the process (Liu et al., 2020b; Wang et al., 2020b; Castiglia et al., 2021; Abad et al., 2020).**B**: Federated averaging methods ...
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Selection 4
**A**: The pseudospectra of finite-dimensional matrices and their extension to linear operators in Banach space have been extensively investigated and summarized in the classical book by Trefethen and Embree trefethen2005spectra . In the book, four different definitions of matrix pseudospectra are introduced and shown ...
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Selection 4
**A**: 10 volunteers with image processing expertise are involved in this evaluation. They are invited to choose the most realistic image from those inpainted by the proposed method and the representative state-of-the-art approaches**B**: User Study. We further perform subjective user study**C**: Specifically, each pa...
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**A**: Together with the binary symmetric channel (BSC), they are frequently used in coding theory and information theory because they are among the simplest channel models, and many problems in communication theory can be reduced to problems in a BEC. Here we consider more generally a q𝑞qitalic_q-ary erasure channel ...
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