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In Section 8, we assess the performance of the proposed algorithm. <|MaskedSetence|> These empirical findings consistently align with our theoretical analysis.
To evaluate the efficacy of our contraction algorithm, we conduct experiments on various tensor network structures. <|MaskedSetence|> Notably, our algorithm outperforms both the CATN algorithm proposed in [61] and the SweepContractor proposed in [14] when considering tensor networks defined on lattices representing the classical Ising model. Specifically, our approach achieves an order of magnitude
speed-up in execution time while maintaining the same level of accuracy. <|MaskedSetence|>
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**A**: Regarding the sub-problem of approximating a general tensor network into a tree tensor network, our experimental results show the superior efficiency of the density matrix algorithm compared to the canonicalization-based algorithm when applied to multiple input tensor network structures.
**B**: The results demonstrate that by leveraging environments and employing the density matrix algorithm, we achieve significant reductions in overall execution time and improvements in accuracy when dealing with tensor networks defined on lattices and random regular graphs.
**C**: This.
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We evaluate the results of our proposed method on publicly available external datasets to verify that the model trained with Diff4MMLiTS can effectively generalize to out-of-distribution data without the need for retraining on the new dataset. All methods are trained on mmLiTs and tested on lesion samples selected from LiTS. The comparison results as shown in Table II. <|MaskedSetence|> This implies that training models with such reliable synthetic images can effectively mitigate the risk of overfitting to in-distribution samples, thereby enhancing their ability to generalize to out-of-distribution samples. <|MaskedSetence|> The findings indicate that our framework adapts seamlessly to all backbones, achieving notable performance improvements. <|MaskedSetence|> This identifies the adaptability of our framework to different backbone models and the effectiveness of the hybrid training strategy in enhancing segmentation performance.
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**A**: This underscores the potential of the proposed method as a promising solution for liver tumor screening.
To further evaluate the adaptability of Diff4MMLiTS, we use three backbone models in the MS module, namely U-Net, AttentionUNet, and nnUNet, with results presented in Table III.
**B**: Compared to nnUNet fully trained on real data, Diff4MMLiTS with the synthesis strategy achieves a 16.12% improvement in DSC.
**C**: Compared to segmentation models trained solely on real data, those employing the hybrid training strategy show improvements of 1.95%, 6.58%, and 2.68% in DSC.
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As shown in Figure 8, the total number of Gaussian points decreases rapidly after
the stop of densification
when using the volume mask, while the PSNR remains stable, indicating that the mask pruning technique effectively removes redundant Gaussians. <|MaskedSetence|> <|MaskedSetence|> 30.48) and decreasing the number of Gaussian points from 2.62M to 1.26M. <|MaskedSetence|> Given that the mask pruning technique introduces minimal additional computational overhead, we choose to use it with a threshold of 0.05 as the default method for reducing the number of Gaussians..
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**A**: A higher opacity threshold eliminates floaters in the scene, leading to a higher PSNR (33.46 vs.
**B**: Additionally, applying mask pruning further reduces the number of redundant Gaussians while preserving similar rendering quality.
**C**: This results in a 2.47×2.47\times2.47 × reduction in the total number of points, from 1.26M to 0.51M.
Table V provides the detailed quantitative results.
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These questions form the core of our investigation, delving into the potential impact of counterfactual learning on the identification of significant document segments, and its broader integration into the pretraining process to improve document retrieval model capabilities.
Table 1. The retrieval effectiveness of retrieving passage within the document according to δrelsubscript𝛿rel\delta_{\text{rel}}italic_δ start_POSTSUBSCRIPT rel end_POSTSUBSCRIPT with difference window size and different type of counterfactual construction methods. Window size of 128 reaches the best performance. <|MaskedSetence|> <|MaskedSetence|> <|MaskedSetence|>
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**B**: The best performance among various counterfactual document construction methods for a model is boldfaced.
**C**: ∗∗\ast∗ indicates significant improvements(p ¡ 0.05)..
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<|MaskedSetence|> <|MaskedSetence|> The decoder sequentially produces hidden features. <|MaskedSetence|> Notably, given the absence of text input in the video captioning task, we rely on single-modal representations instead of reconstructed representations during inference. However, it is worth noting that the reconstructed representations are still utilized for video-language alignment purposes during training..
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**A**: Subsequently, we employ a linear projection layer to map these hidden features to the vocabulary dictionary.
**B**:
For video-question answering, due to the established video-text fine-grained alignment from the hierarchical Banzhaf Interaction module, we can adopt a simplified answer prediction head, without the need for sophisticated multi-modal fusion/reasoning stages like many previous VideoQA models.
**C**: For the question-answering prediction head, we concatenate the video representation and text representation followed by an MLP to predict the answer.
For video captioning, we utilize a single-layer transformer decoder as the generator of the caption.
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<|MaskedSetence|> There is no such criteria for ranking the contributions of the different DMD modes. <|MaskedSetence|> The DMD modes can then be selected based on their amplitude or based on their frequency/growth rate. The amplitude criterion is also not perfect because there exist modes with very high amplitudes but which are very fast damped. <|MaskedSetence|>
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**A**: The selection based on frequency/growth rate has also disadvantages because it relies on a priori physical knowledge.
Additionally, spatial non-orthogonality of the DMD modes
may introduce a poor quality of approximation.
**B**:
In POD the modes are ranked by energy level through the POD singular values.
**C**: Different criteria are developed depending on what can be considered important for the models used.
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First set visited[x]:=1assignvisiteddelimited-[]𝑥1\textsf{visited}[x]:=1visited [ italic_x ] := 1. <|MaskedSetence|> For every vertex v∈C𝑣𝐶v\in Citalic_v ∈ italic_C, the algorithm sets visited[v]:=1assignvisiteddelimited-[]𝑣1\textsf{visited}[v]:=1visited [ italic_v ] := 1 if there is a path from a marked vertex to v𝑣vitalic_v such that the internal vertices of that path all belong to only one component Iisubscript𝐼𝑖I_{i}italic_I start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT. Similarly, for each edge e=(u,v)𝑒𝑢𝑣e=(u,v)italic_e = ( italic_u , italic_v ) of C𝐶Citalic_C, the algorithm sets visited[e]:=u′assignvisiteddelimited-[]𝑒superscript𝑢′\textsf{visited}[e]:=u^{\prime}visited [ italic_e ] := italic_u start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT if (i) there exists an edge f=(u′,v′)𝑓superscript𝑢′superscript𝑣′f=(u^{\prime},v^{\prime})italic_f = ( italic_u start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT , italic_v start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT ) which crosses e𝑒eitalic_e, (ii) there is a path from a marked vertex to u′superscript𝑢′u^{\prime}italic_u start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT such that the internal vertices of that path all belong to only one component Iisubscript𝐼𝑖I_{i}italic_I start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT and, (iii) f𝑓fitalic_f is the closest such edge to u𝑢uitalic_u. <|MaskedSetence|> We use the procedure AuxReach recursively to check if there is a path between two vertices in a single connected component of H⋄C⋄𝐻𝐶H\diamond Citalic_H ⋄ italic_C. <|MaskedSetence|>
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**A**: A formal description of AuxReach is given in \exprefAlgorithmalg:psgreach.
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**B**: Finally we output true if visited[y]=1visiteddelimited-[]𝑦1\textsf{visited}[y]=1visited [ italic_y ] = 1 else output false.
**C**: We then perform an outer loop with hℎhitalic_h iterations and in each iteration update certain entries of the array visited as follows.
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One of the most well-known concepts for the extraction of low-dimensional features is principal curves (Hastie and Stuetzle, 1989), which generalized PCA in the nonlinear setting. The principal curve is a smooth curve that passes through the middle of a data set. Any point on a principal curve is defined as the conditional expectation of all the data that project to that point, which is a property called self-consistency. Following this concept, a lot of research work has been generated to investigate the properties and algorithms for principal curves. See, for example, Banfield and Raftery (1992), Tibshirani (1992), Stanford and Raftery (2000) and Verbeek et al. (2002). The fact that principal curves do not always exist, motivated a related line of work on modified principal curves, which started with Kégl et al. (2000). See also Biau and Fischer (2011) and Delattre and Fischer (2020) and references therein.
If the idea of local averaging in the original definition of principal curves is replaced by that of taking a local maximum in the orthogonal subspace, then we obtain the concept of ridges, which first appears in the literature of image analysis. <|MaskedSetence|> Ridges have a mathematical definition using derivatives up to second order and they come with intuitive geometric interpretation (see Section 2.1). <|MaskedSetence|> <|MaskedSetence|>
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**A**: As shown in Ozertem and Erdogmus (2011), the ridge estimators can perform well even when there are loops, bifurcations, and self intersections in data, while these are difficult to handle for the principal curve method..
**B**: See Eberly (1996).
**C**: In practice, ridges can be used to estimate filaments with flexible shapes and structures without strong requirements on the starting points of algorithms for ridge extraction.
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Furthermore, in the scenario (d), if it is possible to draw artificial data according the observation model, sometimes is preferable to generate fake data (given some parameters) and to measure the discrepancy between the generated data and the actual data, instead of evaluating the costly likelihood function [12, 57]. This approach is known as Approximate Bayesian Computation (ABC). This area has generated much activity in the literature (see, e.g., [77]). The discrepancy measure plays the role a surrogate model and, due to the stochastic generation of the artificial data, it also adds uncertainty (i.e., as a noise perturbation) in the internal evaluations within the ABC-Monte Carlo methods [57]. Finally, The last scenario (e) is intrinsically noisy, so that it also requires specific computational solutions.
The three different cases above, intractable, costly and noisy evaluations of a posterior distribution can appear and/or can be addressed separately [53, 2, 57]. <|MaskedSetence|> <|MaskedSetence|> The challenge posed by these contexts has led to the development of recent theoretical and methodological advances in the literature. Furthermore, surrogate models have been considered as an alternative to Monte Carlo for approximating complicated integrals. <|MaskedSetence|> A cubature rule is subsequently obtained, which makes a more efficient use of the posterior evaluations [16, 46, 48].
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**A**: As described above, these cases also appear jointly in real-world applications (specially, if we consider the algorithms designed to address those issues): ‘intractable and costly’, ‘intractable and noisy’, or ‘costly and noisy’ posterior evaluations, etc.
**B**: Here, the surrogate is substituted directly into the integral of interest, instead of the original density (e.g., a posterior).
**C**: In all of these cases, a surrogate model can accelerate the Monte Carlo method or approximate the posterior distribution [20, 68, 84, 44].
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In [49], the authors show that, in the voter model, the presence of stubborn agents with opposite opinions precludes the convergence to consensus. The work [42] studies the asynchronous voter rule and the asynchronous majority rule dynamics with Poisson clocks when the opinion set is binary.
The authors use mean-field techniques, and focus on two different scenarios: In the first, some agents have a probability (which depends on their current opinion) not to update when the clock ticks. <|MaskedSetence|> <|MaskedSetence|> If the two sizes are close to each other and not too large, then agreement on both opinions is possible. <|MaskedSetence|> The case in which the two stubborn communities have equal size corresponds to the uniform communication noise model.
We remark, however, that in our work we consider a different setting: First, we consider the synchronous version of the 3-Majority dynamics, which cannot be analyzed with the same tools of the asynchronous version..
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**A**: Otherwise, either no agreement is possible, or the process converges to an agreement towards a single opinion, which is that of the largest stubborn community.
**B**: In the second, there are stubborn agents.
**C**: In the second case, which directly relates to our work, they show that for the 3-Majority dynamics, there are either one or two possible stable equilibria, depending on the sizes of the stubborn communities, which are reached in logarithmic time.
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<|MaskedSetence|> Any bounded kernel satisfies (3) [Fischer and Steinwart, 2020, Lemma 10]. <|MaskedSetence|> <|MaskedSetence|> The empirical eigenvalues are simple to compute, so it is simple to validate this assumption with a diagnostic plot. Figure 2 verifies polynomial decay of the empirical eigenvalues in the real world application of Section 6; the Project STAR data have a low effective dimension as required by Assumptions 5.2 and 5.3.222Specifically, we divide each empirical eigenvalue by the trace of the corresponding matrix, to convey the fraction of variation explained.
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**A**: A higher value of b𝑏bitalic_b corresponds to a lower effective dimension, better control of the variance of our estimator, and hence a faster rate.
**B**: The limit b→∞→𝑏b\rightarrow\inftyitalic_b → ∞ gives an RKHS with finite dimension [Caponnetto and De Vito, 2007].
**C**: (3)
The eigenvalues decay at least polynomially.
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<|MaskedSetence|> <|MaskedSetence|> The second contribution is a novel coded distributed learning architecture for DARL1N called Coded DARL1N, which allows individual agents to be trained by multiple compute nodes simultaneously, enabling resilience to stragglers. <|MaskedSetence|> Four codes including Maximum Distance Separable (MDS), Random Sparse, Repetition, and Low Density Generator Matrix (LDGM) codes are investigated to introduce redundant computation. Moreover, we conduct comprehensive experiments comparing DARL1N with four state-of-the-art MARL methods, including MADDPG, MFAC, EPC and SAC, and evaluating their performance in different RL environments, including Ising Model, Food Collection, Grassland, Adversarial Battle, and Multi-Access Wireless Communication. We also conduct experiments to evaluate the resilience of Coded DARL1N to stragglers when trained under different coding schemes.
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**A**: Our analysis shows that introducing redundant computations via coding theory does not introduce bias in the value and policy gradient estimates, and the training converges similarly to stochastic gradient descent-based methods.
**B**:
Contributions:
The primary contribution of this paper is a new MARL algorithm called DARL1N, which employs one-hop neighborhood factorization of the value and policy functions, allowing distributed training with each compute node simulating a small number of agent transitions.
**C**: DARL1N supports highly-efficient distributed training and generates high-quality multi-agent policies for large agent teams.
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<|MaskedSetence|> We propose a policy which appropriately deflates the price selected by SAA, and show that this policy achieves a worst-case regret which has a ϵitalic-ϵ\sqrt{\epsilon}square-root start_ARG italic_ϵ end_ARG dependence in the radius of heterogeneity. We also show that this performance is rate-optimal.
To our understanding, analyzing these non-SAA policies (which are required for good performance in pricing) deviates from standard analyses used in learning theory and critically requires the reduction we derive in Theorem 1, as we elaborate on in Section 5.1. <|MaskedSetence|> We combine this observation with a critical relation between the Wasserstein distance (in 1 dimension) of two probability measures and their associated cumulative distribution functions to obtain the desired result. <|MaskedSetence|>
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**A**:
Analyzing policies beyond SAA to achieve rate-optimality.
In Section 5.1 we complete the picture for the pricing problem under Wasserstein heterogeneity.
**B**: We believe that this problem-specific analysis may be of independent interest.
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**C**: To derive our result, we leverage the structure of the objective function in pricing: while it is not continuous in general, it is ensured to be one-sided Lipschitz-continuous (when deflating the price).
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We used the MSAs constructed by Infernal 46 and rMSA (https://github.com/pylelab/rMSA) to capture co-evolutionary information of the sequence as an additional input. Using Infernal, it is possible to locate homologous sequences with conserved secondary structures; on the other hand, rMSA employs an iterative search strategy based on RNA sequence databases. <|MaskedSetence|> In AlphaFold2, a similar approach was used with different alignment tools and sequence databases. <|MaskedSetence|> Subsequently, during the inference phase, 256 MSAs were either randomly selected or chosen through clustering, and then fed into RhoFold+. We implemented clustering with conserved secondary structure or sequence embeddings from our pre-trained RNA language model. Different sampled and clustered results can be thus used for multiple predictions, as marked by Top5, Top10, etc. <|MaskedSetence|> RhoFold+ (TopK) refers to the optimal model selected from K different models generated using distinct sampled MSAs.
RNA-FM language model.
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**A**: By default, the top 256 MSAs are chosen as input features for predicting the standard structure, which we refer to as standard RhoFold+.
**B**: We utilized the nucleic acid sequence databases Rfam and RNAcentral 47.
**C**: Given the need to produce several models and the constraints imposed by hardware memory, we reduced our fully extracted MSAs to a maximum of 256 sequences during the training phase.
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Finally, we want to summarize the main idea of MAZE. As the previous methods using self-play may not capture the cooperation behaviors between AI and humans well in heterogeneous settings, MAZE uses two different policies to represent the agent and partner, respectively. The simplest implementation is to train them directly without changing training partners, called Vanilla-MAZE (V-MAZE). <|MaskedSetence|> <|MaskedSetence|> Inspired by previous works [18, 31, 62, 9], MAZE further tries to improve the diversity of partners to obtain better ZSC agents through three different ways: 1) maintaining a population and changing the paired policies in the sub-process of pairing; 2) adding diversity terms into the objective function rather than just maximizing rewards in the sub-process of updating; 3) actively selecting diverse partners from an archive for the next generation in the sub-process of selection. <|MaskedSetence|>
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**A**: In fact, V-MAZE has already performed well on heterogeneous tasks, which will be shown in RQ1 of experiments.
**B**: To verify the necessity and effectiveness of the above-proposed components, we will conduct ablation studies, starting from the simplest V-MAZE and adding these components gradually until the complete MAZE, which will be shown in RQ3 of experiments.
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**C**: That is, V-MAZE simply takes heterogeneity into account.
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<|MaskedSetence|> As a stand-alone model LPJmL has been mainly calibrated with respect to reanalysis, and a similarly accurate precipitation output within CM2Mc-LPJmL would hence be favorable to maintain consistency and to obtain realistic surface fluxes from LPJmL. <|MaskedSetence|> <|MaskedSetence|> (\APACyear2021)]. After a 5000-year stand-alone LPJmL spin-up, a second fully coupled spin-up under pre-industrial conditions without land use was performed for 1250 model years. In this way we ensure that the model starts from a consistent equilibrium between the long-term soil carbon pool, vegetation, ocean, and climate.
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**A**: This motivates the work presented below, where we use a specific kind of GAN to transform the AM2 precipitation fields toward fields that are indistinguishable from ERA5 precipitation fields (see below).
The model experiments of this paper are consistent with [Drüke, von Bloh\BCBL \BOthers.
**B**: For the overall performance of CM2Mc-LPJmL, realistically simulated precipitation fields are therefore crucial.
**C**: In CM2Mc-LPJmL, the fluxes simulated by LPJmL depend, of course, on the precipitation modelled by AM2.
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PCB assembly planning is a multi-level optimisation problem which consists of several interdependent problems (refer to Figs. 2 and 3 in Mumtaz et al. <|MaskedSetence|> Each of the problems in the PCB assembly planning is an NP-hard problem. The complexity of these problems is exacerbated by their large scale, involving a large number of components and a diverse range of PCBs, making it challenging to comprehensively address all sub-problems and achieve an integrated solution for optimal outcomes (Gao et al. (2021)). In fact, despite being studied for several decades (Drezner and Nof (1984); Ahmadi et al. <|MaskedSetence|> <|MaskedSetence|>
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**A**: (2019) and Ji and Wan (2001)).
**B**: (2018)).
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**C**: (1988)), even individual machine-level problems are solved approximately using heuristic methods (Li et al.
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Next location prediction is essentially about sequence modeling since the next location visit is usually dependent on the previous one [23, 24]. Traditional Mc-based methods often incorporate other techniques, such as matrix factorization [4] and activity-based modeling [5], for enhanced prediction performance. However, they are limited in capturing long-term dependencies or predicting explorative human mobility.
Rnn-based models regard the next location prediction problem as a sequence-to-sequence task and have shown superior performance. <|MaskedSetence|> Building on this, Stgn [26] introduces spatial and temporal gates to Long Short-Term Memory (Lstm) networks to better capture users’ interests, while Flashback [8] leverages spatial and temporal intervals to aggregate past RNN hidden states for improved predictions. <|MaskedSetence|> Attention mechanisms are also utilized to enhance model performance. DeepMove [7] combines attention mechanisms with Rnn modules to effectively capture users’ long- and short-term preferences. <|MaskedSetence|> Furthermore, Stan [10] extracts relative spatial-temporal information between both consecutive and non-consecutive locations through a spatio-temporal attention network. These approaches collectively highlight the importance of integrating spatial-temporal dynamics and attention mechanisms to improve the accuracy of human mobility predictions. In addition, some efforts incorporate contextual information [28] such as geographical information [29], dynamic-static [30], text content about locations [31] into sequence modeling.
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**A**: Additionally, Lstpm [27] employs a non-local network and a geo-dilated Lstm to model both long- and short-term user preferences.
**B**: Similarly, Arnn [11] uses a knowledge graph to identify related neighboring locations and employs attentional Rnns to model the sequential regularity of check-ins.
**C**: Strnn [25] is a pioneering work that integrates spatial-temporal characteristics between consecutive human visits into Rnns, laying the groundwork for subsequent studies.
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<|MaskedSetence|> An example of resourceful states are the absolutely maximally entangled (AME) states which maximized the entanglement in the bipartitions, but are notoriously difficult to characterize Scott (2004); Facchi et al. (2008); Reuvers (2018); Gour and Wallach (2010); Huber et al. <|MaskedSetence|> (2022); Rather et al. <|MaskedSetence|>
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For many important applications entanglement has been proven to be a powerful resource.
**B**: (2022).
However, multiparticle entanglement offers a complex and rich structure resulting in the impossibility of quantification by means of a single number..
**C**: (2017, 2018); Contreras and Goyeneche (2022).
Still, the analysis of AME states is important for understanding quantum error correction and regarded as one of the central problems in the field Horodecki et al.
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<|MaskedSetence|> <|MaskedSetence|> <|MaskedSetence|> The limitation of the technique used to prove Theorem 1 is clear from [efx_3]. At each step, our allocation Pareto dominates the previous allocations. As shown in [efx_3], even for three agents, there could be a partial allocation that Pareto dominates all complete allocations. So one cannot hope to reach a complete allocation using this technique..
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**A**: We give an EFX allocation with at most k−2𝑘2k-2italic_k - 2 unallocated goods such that no agent envies the bundle of unallocated goods.
**B**:
5 Conclusion
In this paper, we generalize the existing results in literature on EFX allocations to the setting when the number of distinct valuations is k𝑘kitalic_k, but the number of agents can be arbitrary.
**C**: We also show the existence of a complete EFX allocation under MMS-feasible valuations when all but two agents have identical valuations.
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<|MaskedSetence|> 2014) and ADE20K (Zhou et al. <|MaskedSetence|> Therefore, training with such OoD samples allows models foresee the anomalous objects, resulting in their good performance. Moreover, training in this manner also results in a large gap between these methods and ours in performance on the FS Lost & Found and Lost & Found datasets since anomalous objects in the FS Lost & Found dataset are more realistic. Finally, though our SLEEG performs inferior on FS Static dataset, since the anomaly segmentation task targets at real-world automatic driving scenarios, the ability of tackling realistic unexpected samples is more essential for our SLEEG. <|MaskedSetence|>
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**A**: 2019).
**B**: As shown in the Table 1 of the manuscript and Fig. 7, our SLEEG performs inferior to SOTA methods that utilize auxiliary OoD data on the FS Static dataset.
This mainly accounts for that the synthetic anomalous objects in FS Static are similar to the instances in the auxiliary dataset that these methods use, i.e., COCO (Lin et al.
**C**: Therefore, we focus on utilizing the inherent spatial context to improve the ability of tackling with the distribution discrepancy of normal and anomalies without requiring extra OoD data.
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In this work, we utilise the peculiar properties of the RCDT to capture geometric and spatial variations within a parameterised input and use this to produce an approximate solution for system parameters in a model order reduction methodology. Initially, we investigate the properties of the RCDT with simplified test cases to gauge the strengths and weaknesses of the potential use of the transform in the ROM and CFD communities. The RCDT is then applied to a POD-based ROM workflow and later tested on a number of computational fluid dynamics (CFD) data sets. This allows for the preservation of the flow features when transformed between spaces, alongside the accuracy of ROM’s flow reconstruction at reduced order. We finally introduce interpolation and study the error in predicting flows, giving an initial qualitative gauge of RCDTs’ applicability to fluid dynamics and advection-dominated problems.
Both the implementation of the RCDT and ROM workflows have been written in Python 3.9.7, making use of two packages, PyTransKit [27] and EZyRB [28]; implementing the discretised form of RCDT – with subsequent forward/inverse transforms – and model order reduction functionality, respectively. <|MaskedSetence|> EZyRB, model reduction is approached using proper orthogonal decomposition (POD), see [29, 30], for example, in applying EZyRB towards shape optimization problems. All the code developed for the preparation of this article is available open-source [31]. <|MaskedSetence|> <|MaskedSetence|> Three distinct workflows have been implemented: the RCDT transform upon a single snapshot image/flow followed by the inverse transformation to observe the intrinsic error induced by the discretisation and implementation of the non-linear transform; the RCDT-POD reconstruction/projection error to evaluate the effect of the non-linear transformation in the POD modes; and, the complete RCDT-POD ROM workflow consisting of the RCDT-POD on a series of snapshots, and the subsequent interpolation (with respect to time or other parameters) to predict unseen scenarios..
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**A**: Specifically, the singular value decomposition (SVD) – discussed more in section 2.5 – is used to determine the POD modes for the reduced-order model.
**B**: For the ROM side, i.e.
**C**: SVD is not the only way to compute the POD, though an alternative approach is given by the method of snapshots [6, 32].
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In this note, we showed how the tensor CUR (TCUR) approximation can be extended to tensor pairs and tensor triplets. <|MaskedSetence|> <|MaskedSetence|> We established connections between some special cases of the GTCUR and the classical TCUR approximation. <|MaskedSetence|> We are investigating the theoretical and numerical aspects of the presented GTCUR approaches for tensor pairs and tensor triplets in a practical setting.
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**A**: Efficient algorithms are presented to compute the GTCUR approximation for both tensor pairs and tensor triplets.
**B**: We use the tensor Discrete Interpolatory Empirical Method (TDEIM) to generalize the TCUR to tensor pairs and tensor triplets.
**C**: This extension is called the generalized TCUR (GTCUR) method.
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<|MaskedSetence|> We assess the realism of noise distributions synthesized by different methods using the public evaluation metrics AKLD and PGap on the SIDD validation set. We compare RNSD with baseline techniques including GRDN (Kim, Chung, and Jung 2019), C2N (Jang et al. 2021), sRGB2Flow (Kousha et al. 2022), DANet (Yue et al. 2020), PNGAN (Cai et al. 2021) and NeCA (Fu, Guo, and Wen 2023). As shown in Table 1, our method outperforms the state-of-the-art (SOTA) with a PGap reduced by 0.30 and an AKLD improved by 0.027, indicating more realistic and stable noise synthesis.
Additionally, we evaluate our method using another publicly available metric (Jang et al. 2021) by training the DnCNN network (Zhang et al. 2017) from scratch with synthetic noise generated by RNSD. We compare its performance with C2N (Jang et al. 2021), NoiseFlow (Abdelhamed, Brubaker, and Brown 2019), sRGB2Flow (Kousha et al. <|MaskedSetence|> 2023), and NeCA (Fu, Guo, and Wen 2023). As shown in Table 2, our synthetic noise improves DnCNN’s denoising PSNR by 0.75 dB compared to the SOTA, approaching the performance of real-data training (38.11 dB vs. <|MaskedSetence|>
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**B**: 2022), GMDCN (Song et al.
**C**: 38.40 dB)..
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<|MaskedSetence|> This is in line with what factorization machines are commonly used for - CTR prediction. For binary labels we use the cross-entropy loss, whereas for real-valued labels we use the L2 loss. For tuning the step-size, batch-size, the number of intervals, and the embedding dimension we use Optuna (Akiba et al., 2019). <|MaskedSetence|> In addition, 20% of the data was held out for validation, and regression targets were standardized. <|MaskedSetence|>
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**A**: Finally, for the adult income data-set, 0 has a special meaning for two columns, and was treated as a categorical value.
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**C**: For binning, we also tuned the choice of uniform or quantile bins.
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Paper organization
In §2 we review related work in the field of strategic information retrieval. <|MaskedSetence|> In §4 we discuss the publishers’ game model. §5 provides a theoretical analysis of learning dynamics in our model, and studies stability under different ranking schemes (PRP, softmax and linear).
In §6 we provide experimental results of simulating learning dynamics under the different ranking schemes. <|MaskedSetence|> <|MaskedSetence|>
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**B**: §3 provides preliminary definitions and results from game theory.
**C**: We then conclude and present future work directions in §7.
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<|MaskedSetence|> The current paper reformulates these ideas in a visual CFFG framework, which explicates the role of backward messages in GFE optimisation (see also our companion paper (Koudahl et al., 2023)). Inspired by (Winn and Bishop, 2005), prior work by (Champion et al., 2021) derives variational message passing updates for AIF by augmenting variational message updates with an Expected Free Energy (EFE) term. <|MaskedSetence|> <|MaskedSetence|> Implications of message passing in deep temporal models on neural connectivity are further explored by (Friston et al., 2017). An operational framework and simulation environment for AIF by message passing on FFGs is described by (van de Laar and.
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**A**: In contrast, the current paper takes a constrained optimisation approach, augmenting the variational objective itself, and deriving message update expressions by variational optimisation.
Message passing formulations of AIF allow for modular extension to hierarchical structures.
**B**:
Towards a message passing formulation of Active Inference (AIF), (Parr and Friston, 2019) proposed a Generalised Free Energy (GFE) objective, which incorporates prior beliefs on future outcomes as part of the Generative Model (GM).
**C**: Temporal thickness in the context of message passing is explored by (de Vries and Friston, 2017), which formulates deep temporal AIF by message passing on an FFG representation of a hierarchical GM.
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Empirical validation on a real-world dataset. <|MaskedSetence|> Specifically, we utilize more than a million interaction data points of users on the Glance333Please note that the dataset we use is not publicly available. However, it can be provided by Glance upon request for verification purposes only. For further information about Glance, we refer the reader to their website: https://glance.com/us. platform – a smart lock-screen that aims to personalize user experience through recommending dynamic lock screens (also called glances). <|MaskedSetence|> <|MaskedSetence|>
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**A**: We find that MNN can improve the mean-squared error by 28x compared to a standard matrix completion method (see Table 1).
**B**: We also report empirical performance using a synthetic dataset to discuss nuanced properties of MNN that are not necessarily captured by theoretical results (see Section 6).
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**C**: To establish relevance of the model and subsequently resulting algorithm, MNN, we consider a real-world setting.
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<|MaskedSetence|> <|MaskedSetence|> If the chunk size is smaller than the layer size, then all the weights of a layer may not be generated together. <|MaskedSetence|> However, overall chunk-wise weight generation leads to reducing complexity and improving the scalability of hypernets. For example, Chauhan et al., 2024c [14], Oswald et al., [49] used chunk-wise weight generation.
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**A**: This can lead to not using some of the generated weights because the weights are generated as per the chunk size, which may not match the layer sizes.
**B**: Moreover, these hypernets need additional embeddings to distinguish different chunks and to produce specific weights for the chunks.
**C**:
Generate Chunk-wise: Chunk-wise hypernetworks generate weights of the target network in chunks.
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<|MaskedSetence|> <|MaskedSetence|> Sec. 4 shows how to obtain a Prob-solvable loop using our approximation method and hence how to automatically compute moment-based invariants of all orders for the program state variables. Sec. 5 presents the exact method leveraging the theory in (Jasour et al., 2021) to compute the exact moments of PPs with trigonometric and exponential updates. <|MaskedSetence|> We conclude in Sec. 7.
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**A**:
Outline.
Sec. 2 provides the necessary background on Prob-solvable Loops and the theory of general Polynomial Chaos Expansion (gPCE).
**B**: Sec. 3 introduces our gPCE-based approximation method presenting the conditions that are necessary to accurately approximate general non-polynomial updates in a probabilistic loop.
**C**: Sec. 6 evaluates the accuracy and feasibility of the proposed approaches over several benchmarks comparing them with the state-of-the-art.
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In low-density networks, while the attack has an impact on performance, the effects might be comparatively less severe due to the sparser node distribution. However, flooding attacks exert a pronounced impact on high-density networks, exacerbating congestion and severely compromising network performance, resulting in a reduction of up to 31%. Moreover, the excessive transmission of RREQ messages intensifying increased the network overhead to almost more than double, thereby creating a bottleneck. <|MaskedSetence|> Sinkhole and dropping attacks, conducted by randomly selected attackers, seem to exert minimal impact on network performance. Indeed, in the case of a sinkhole attack, the primary objective is to deceive network nodes by providing false routing information and redirecting traffic through malicious nodes. These attacks aim to mislead rather than directly interfere with data packets, potentially resulting in their impact being less pronounced compared to other attacks. Similarly, dropping attacks attempted by randomly chosen attackers might indeed have a limited impact on network performance due to their positional constraints within the network. On the other hand, deliberate placement of attackers on active routes in dropping attacks allows them to strategically receive and drop packets passing through these active routes. <|MaskedSetence|> <|MaskedSetence|>
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**A**: The contrast between these two scenarios underscores the pivotal role of attackers’ placement within a highly dynamic network..
**B**: This bottleneck leads to significant increases in E2E metrics, differentiating it from other attacks and hindering the timely delivery of remaining data across the network.
Summary of Lessons Learned from Attack Analysis:
The effects of all attacks on PDR are comparatively illustrated in Figure 8.
**C**: This interference significantly disrupts the transmission process, leading to a reduction in PDR.
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<|MaskedSetence|> Screeners chose the ISO. The choice was restricted by the sorting fields of the hiring platform, such as using the candidates’ last name.
G2 Two ways to search the candidate pool. Two search practices became apparent: full or partial search of the candidate pool.
G3 Meeting the set of minimum basic requirements. <|MaskedSetence|> <|MaskedSetence|>
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**A**: G1 Varying ISOs.
**B**: Fairness goals already existed in the form of representation quotas, often around gender, that were enforced by the screeners..
**C**: Screeners were able to differentiate candidates relative to each other, but their focus was on finding candidates that met these requirements.
Order within the selected k𝑘kitalic_k candidates was not necessarily important.
G4 Diverse suitable candidates.
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6.3 Comparisons
We compare our results with seven methods, including SRIE [15], LIME [19], EnlightenGAN [23], Zero-DCE [17], URetinex [56], SNRANet [59], UHDFour [26], RetinexFormer [5], LLDiffusion [52], and ACCA [78], on LOL-V2 dataset. As shown in Table 3, we outperform other comparison methods in PSNR and SSIM. <|MaskedSetence|> 1. <|MaskedSetence|> 1, LIME and URetinex over-enhance the low-light images. <|MaskedSetence|> UHDFour encounters the color cast in the first-line image. Our method yields visual-pleased results. It demonstrates the advantages of WDT and LAT.
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**A**: Visual comparisons are shown in Fig.
**B**: Zero-DCE produces under-enhanced results.
**C**: As shown in Fig.
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This paper employs methods from economic theory to model and analyze this interaction. <|MaskedSetence|> <|MaskedSetence|> Crucially, the producers must decide how to distribute the surplus, and engage in a bargaining process in advance of making their investment decisions. An immediate intuition might be to divide the surplus based on contribution to the technology — however, this is one of many potential bargaining solutions, each with different normative assumptions and implications for the technology’s performance and the distribution of utility.
Through this analysis, we uncover several general principles that apply not just to today’s AI technologies, but to a potentially wide swath of models that exhibit a similar structure — i.e., developed for general use and adapted to one or more domains to produce revenue. <|MaskedSetence|> For example, cloud computing infrastructure enables a number of consumer-facing services that use web hosting, database services, and other on-demand computing resources. Additive manufacturing (e.g., 3D printing) requires the production of a general-purpose technology that other entities use to create valuable products in particular domains. Digital marketplaces, too, are general market-making technologies that enable specialists (vendors) to sell goods, subject to an agreement over surplus..
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**A**: Thus, even as these technologies improve and develop, our proposed model of fine-tuning may continue to describe how they may be adapted for real-world use(s).
Further, some of our findings apply to other general-purpose technologies outside the AI context.
**B**: We put forward a model of fine-tuning where the interaction between two agents, a generalist and a domain-specialist, determines how they’ll bring a general-purpose technology to market (Figure 1).
**C**: The result of this interaction is a domain-adapted product that offers a certain level of performance to consumers, in exchange for a certain level of surplus revenue for the producers.
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In frame 2536, the motion level of the bee No. 510 falls below the threshold α=0.5𝛼0.5\alpha=0.5italic_α = 0.5. <|MaskedSetence|> <|MaskedSetence|> <|MaskedSetence|> This indicates the limitations of the adopted motion model.
In frame 2539, the motion level of the bee No. 510 suddenly increases, leading the association metric to primarily rely on appearance cues. At this point, the two bees are highly distinguishable in appearance. This helps TOPICTrack to accurately resume tracking bee No. 510.
This demonstrates that our proposed algorithm heuristically exploits motion levels to adaptively select the most appropriate association metrics at each instant, thereby providing the algorithm with automatic error correction capabilities and achieving long-term robust tracking.
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**A**: At this point, however, bees No. 477 and 510 are very close to each other, resulting in the motion model erroneously assigning trajectories to both bees and causing ID switches.
**B**: In frame 2537, the motion level of bee ID 510 reaches the α𝛼\alphaitalic_α, prompting the algorithm to automatically switch to appearance cues as the primary assignment metric, thereby continuing to track the bee successfully.
In frame 2538, the motion level of bee No. 510 drops below the α𝛼\alphaitalic_α, causing the algorithm to revert to using motion cues as the primary assignment metric.
**C**: Consequently, TOPICTrack utilizes motion cues as the primary assignment metric, successfully maintaining the tracking of this bee.
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Zero-shot and Fine-tuned Performance using LLMs and Vision-LLMs. We explored the potential of multimodal and language foundation models, known for their impressive zero-shot question-answering performance, for predicting emotions and generating corresponding explanations on our newly proposed dataset. Specifically, we evaluated the performance of LLaMa2-7b [59], the latest API of GPT-4 [1], and recently released MiniGPT-4-v2 [13] with our designed prompts, as inputs to enable these models to generate emotions and their explanations. Table 5 presents results for models in zero-shot emotion explanation generation. The trend observed indicates that incorporating dialogs as input improves the results. Emotion F1 scores improved from 23.46 to 25.28 and from 24.28 and 29.79 for MiniGPT-4-v2 and GPT-4, respectively. <|MaskedSetence|> <|MaskedSetence|> These limitations highlight the significance of our dataset in advancing emotion-aware AI systems for future applications. In addition, we fine-tuned the open-source LlaMa2-7b [59] and MiniGPT-4-v2 [13] models on our dataset using instruction fine-tuning and assessed their performance. Table 5 shows that fine-tuning enhances the performance of these models, as evidenced by higher Emotion F1 scores. <|MaskedSetence|> Further details about prompts and generated examples are provided in the supplementary.
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**A**: This outcome underscores the significance of our dataset in improving model understanding and generation capabilities in terms of affective explanation.
**B**: Despite being powerful models trained on massive data, their performance lags behind our trained baselines, suggesting the need for considering emotional alignment with humans.
**C**: For example, our baselines trained on our dataset showed superior results, yielding more than 40404040 in F1 score.
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<|MaskedSetence|> <|MaskedSetence|> Consequently, these duplicate issues inherently serve as a source of the STS task. It is also worth noting that most issues contain long texts because of the inclusion of extensive code within the issues.
To compile the dataset, we extracted duplicated issues from 55555555 popular open-source projects (see A.1) on GitHub using GitHub API 222https://docs.github.com/en/rest. <|MaskedSetence|> Table 4 presents statistics of the GitHub Issues Similarity Dataset, while Figure 4 shows a violin plot illustrating the token-level text length distribution. The visualization reveals a substantial number of long texts. Specifically, the proportion of long texts (token length >512absent512>512> 512) for the train, validation, and test sets is at 61.03%percent61.0361.03\%61.03 %, 60.85%percent60.8560.85\%60.85 %, and 60.50%percent60.5060.50\%60.50 %, respectively.
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**A**: The duplicated issues were used as positive samples, while the remaining issues were considered negative samples.
**B**: We observed the presence of many duplicate issues on GitHub.
**C**: Typically, the maintainers of open source organizations tend to mark these duplicate issues as closed with a comment like “closing as a duplicate of #id”.
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<|MaskedSetence|> <|MaskedSetence|> This would result in astronomically high number of flows. Consequently, flagging those flows would take unrealistic time. Even if achievable, the number of cases would make it practically impossible to investigate. <|MaskedSetence|>
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The trends shown in Fig.
**B**: This is because most of the flows will have repeated accounts and transactions.
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**C**: 10 clearly indicate that, for DBJ* to achieve a coverage score close to FaSTM∀for-all\forall∀N, it would have to be run with numerous different motif configurations.
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<|MaskedSetence|> In the first condition, a constant input voltage of 24 V is maintained. <|MaskedSetence|> On the other hand, the second condition involves a dynamic scenario where the input voltage fluctuates between 24 V and 26 V. <|MaskedSetence|> Notably, to induce the input variation, a step change is introduced precisely at 0.5 s of the simulation. This comprehensive experimental design enables a thorough examination of the proposed method’s adaptability and control performance under both stable and dynamic operating conditions. For each condition, three scenarios are being taken into account. Each of those scenarios corresponds to a distinct reference voltage (48 V, 54 V, and 60 V). The objective of this experiment is to evaluate whether the suggested controller can achieve the desired voltage level while exhibiting precise step response characteristics.
Figure 5: Output voltage of boost converter using proposed control method (Condition II)
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**A**: The experimentation is conducted under two distinct conditions to evaluate the performance of the proposed method.
**B**: This specific setting allows for the observation and assessment of the control capability inherent in the traditional application of a boost converter.
**C**: The primary objective here is to scrutinize the controller’s efficacy in managing the variable input behavior.
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<|MaskedSetence|> Left: Proportion of users based on the varying number of historical prompts they have. Note that each user has a minimum of 18 historical prompts, as we have excluded those with fewer prompts from the dataset. <|MaskedSetence|> Best view in color.
Figure 2 illustrates the process of creating the dataset. <|MaskedSetence|> The purpose of using random selection instead of the most recent generated prompts is to enhance the diversity of our test data. Subsequently, we employ ChatGPT to condense the test prompts, ensuring they only include the primary object or scene, as depicted in Figure 2. We shorten the prompts into three scales, i.e., contain only nouns, noun phases or short sentences respectively. .
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Figure 3: Dataset statistics and distribution.
**B**: For each individual user, we randomly choose two prompts to serve as test prompts, with the remaining prompts allocated as training prompts (historical user query).
**C**: Right: Proportion of prompts based on their varying lengths.
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<|MaskedSetence|> The loss function is motivated by the intuition that nodes densely interconnected with edges in a given network are likely to exhibit similar labels. It is intended to incentivize nodes in a hyperedge (a clique) to have the same label by imposing a natural penalty when nodes within the hyperedge have diverse labels. It is worth noting that the intuition is consistent with SBM’s general assumption that nodes with the same label are more likely to be connected in a network. In conjunction with the objective function, we use discrete potential theory to initialize the node probability distribution, specifically the solution to an appropriate Dirichlet boundary value problem on graphs, which can be effectively solved using the concept of equilibrium measures [25].
We also propose a novel graph generation model, Stochastic Block Tensor Model (SBTM). <|MaskedSetence|> Specifically, when comparing networks of equivalent density (that is, networks with an identical count of nodes and edges), SBM-based models typically exhibit far fewer higher-order polyhedrons (simplices or cliques), than what is observed in real-world graphs. This limitation of SBM stems from its nature as an edge-generation model. For example, in social networks, while two people might form a friendship, it is also possible for three or more individuals to simultaneously establish a friendship. <|MaskedSetence|>
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In this study, we propose a novel probability-based objective (loss) function for the semi-supervised node classification (community detection) task using higher-order networks.
**B**: In light of this, we suggest that edge-generation models (SBM) have limits in producing network data that is similar to what is observed in the real world, and we offer a revised model capable of incorporating higher-order structures such as triangles and tetrahedrons into the network..
**C**: In general, traditional SBM-generated networks differ significantly from many real-world networks.
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Table I summarizes the model performance of the detection experiments with different lengths of input data. <|MaskedSetence|> It also shows that model accuracy is not sensitive to the increase in the input data length. The experiments show that the proposed model can effectively detect abnormal traffic with only 2 seconds of observed data. <|MaskedSetence|> Note that the model has a lower precision than recall (recall is 1 in most of the experiments), meaning that it can detect all the three types of attacks at various input lengths. <|MaskedSetence|>
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**A**: However, lower precision indicates that the model could misclassify some normal traffic as being attacked.
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**B**: Observe that the model performs similarly well across the three scenarios.
**C**: Generally, higher values of accuracy and F1subscript𝐹1F_{1}italic_F start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT score indicate better model performance in detecting attacked traffic.
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It’s worth noting that multi-structure data does not imply that each sample corresponds to multiple causal structures. <|MaskedSetence|> <|MaskedSetence|> <|MaskedSetence|> However, in multi-structure data, we observed the influence of the variable “Brain region A” on the variable “Brain region B”. Since different patient samples have different symptoms, these symptoms cause different electrical signal response rules between brain areas, i.e., different causal structures.
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**A**: In Figure 2, we list three samples of single-structure data and multi-structure data respectively.
**B**: As a physical law, it does not change with the sample.
**C**: In single-structure data, we observe the influence of the variable “Altitude” on the variable “Temperature”.
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Text Truncation discard the parts of the text that the model cannot handle, for example, anything more than 512 (or the max limit) tokens. The cut-short is done broadly in three ways: (i) Process the maximum length tokens from the beginning and discard the rest (ii) Process the maximum length tokens from the end and discard the tokens before (iii) Systematically select the most important tokens from the text and discarding the rest. Text Aggregation splits texts into multiple segments (each with a length equal to the maximum allowed input length) and then classifies each segment separately. Then aggregates the results using different strategies such as hard voting, majority voting, soft voting, averaging, or weighted averaging. Text Chunking with sliding window splits long texts into multiple segments by keeping overlaps between segments to drag the information from one segment to another. Then, each segment is classified separately or aggregates their outputs using various strategies. <|MaskedSetence|> However, the problem persists as many records may exceed this fixed length.
Although these three techniques have various advantages and benefits, they only partially solve the problem. We identify some crucial shortcomings and limitations here. (a) Critical Information Loss: Methods like truncation and using pre-trained language models like Longformer and BigBird may discard important information in the text’s truncated parts. This leads to information loss since the text is truncated beyond 512 or 4096 tokens. Clinical texts and admission notes usually contain more than the mentioned number of tokens, hence being prone to critical information loss during training and inference. <|MaskedSetence|> If significant information strides the boundary between two segments, the model might fail to recognize the relationship between the two pieces of information. (c) Annotation Challenges: Handling long clinical texts requires high-quality annotations for training supervised models. The sheer length and complexity of these texts can make the annotation process cumbersome, time-consuming, and prone to errors, affecting the overall quality of the trained model. (d) Domain-specific Challenges: Clinical language is laden with domain-specific terminologies and abbreviations and often presents itself in a non-standard form. <|MaskedSetence|>
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**A**: (b) Contextual Discontinuity: Techniques such as text chunking with a sliding window, while aiming to preserve continuity, can introduce breaks in the contextual flow of information.
**B**: Techniques that work well on general texts might not necessarily perform effectively on clinical notes, exacerbating the problem of long-text handling in clinical NLP.
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**C**: Language Models like Longformer and BigBird extend the maximum input sequence length from 512 to 4096 tokens.
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