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τ(G)=1|V|∏i=2|V|λi=12|E|∏i=1|V|di∏i=2|V|λ̄i⋅\displaystyle\tau(G)=\frac{1}{|V|}\prod\limits_{i=2}^{|V|}\lambda_{i}=\frac{1}%
{2|E|}\prod\limits_{i=1}^{|V|}d_{i}\prod\limits_{i=2}^{|V|}\lambdabar_{i}\cdotitalic_τ ( italic_G ) = divide start_ARG 1 end_ARG start_ARG | italic_V | end_ARG ∏ start_POSTSUBSCRIPT italic_i = 2 ... | We obtain the formulae for the total count of spanning trees of Pnsubscript𝑃𝑛P_{n}italic_P start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT and Pn′subscriptsuperscript𝑃′𝑛P^{\prime}_{n}italic_P start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT using the Theorem 4 as follows.
| As both of the structural descriptors have important applications in graph theory, networking systems, molecular chemistry, and other related fields, researchers have taken a strong interest in the Kirchhoff indices and degree-Kirchhoff indices of graphs in recent years. Finding the explicit formulae for the Kirchhoff ... |
The formulae of the degree-Kirchhoff index of linear hexagonal chains [9], hexagonal Möbius chains [16], linear crossed hexagonal chains [18], linear polyomino chains [8], cylinder phenylene chains [17], random polygonal chains [13], generalized phenylenes [25], cylinder, and Möbius octagonal chain [15], linear pentag... | Being motivated by the success of the Wiener index, nearly after four decades, in 1993,19931993,1993 , Klein and Randić put forward a novel structure-descriptor topological index, known as the Kirchhoff index [11]. The Kirchhoff index of a graph G𝐺Gitalic_G is calculated using the formula Kf(G)=12∑i=1|V|∑j=1|V|rijK... | B |
In this section we explore the power of ambiguity when the agent is allowed to select a mixed action and the principal is allowed to implementing mixed actions. Our main result (Theorem 6) is that in this case, the principal cannot gain from using an ambiguous contract. | Dai and Toikka, (2022) examine a principal who writes contracts to shape the actions of a team of agents, with the principal holding ambiguous beliefs about the actions available to the agents.
Dütting et al., (2019) examine moral hazard problems in which the principal has ambiguous beliefs about the distribution of ou... |
A flourishing literature examines design problems in the face of non-Bayesian uncertainty. One branch of this literature examines models in which the principal entertains non-Bayesian uncertainty about the agents. Bergemann and Schlag, (2011) examine monopoly pricing on the part of a principal with ambiguous beliefs a... | An implication of our results is that in the context of moral hazard problems, ambiguity and max-min utility drive optimal designs towards simplicity. We thus join a literature, with Holmström and Milgrom, (1987) as a key early entry, endeavoring to explain why actual contracts in moral hazard settings tend to be simpl... | Bade, (2023) obtains a similarly-spirited result in a mechanism design context, showing that if agents are dynamically consistent, meaning that they update their beliefs in response to information so as to make it optimal to continue with their ex-ante optimal plan of action, then ambiguity does not expand the set of i... | D |
In the conference version of the paper [Bla23], Theorem 2 was weaker by a multiplicative logn𝑛\log nroman_log italic_n factor, which similarly affects Theorems 1, 8 and 9. As a result, the statistical query mechanism described in Figure 1 was not known to be state of the art. To get around this, the conference versi... | To remove this multiplicative logn𝑛\log nroman_log italic_n factor, we revamped many of the proofs. Most notably, this involved developing a new notion of stability. The conference version used average leave-one-out KL stability (Definition 2.1), which this version generalizes to average leave-many-out KL stability (... | The starting point of our analysis is a new notion of algorithmic stability. We require the algorithm’s output to be stable even if a large portion of the dataset is removed. This definition generalizes [FS18]’s notion of “Average leave-one-out KL stability,” which is equivalent to the below with m=1𝑚1m=1italic_m = 1.... |
In the conference version of the paper [Bla23], Theorem 2 was weaker by a multiplicative logn𝑛\log nroman_log italic_n factor, which similarly affects Theorems 1, 8 and 9. As a result, the statistical query mechanism described in Figure 1 was not known to be state of the art. To get around this, the conference versi... | Generalizing the ideas from Section 2.1 to subsampling queries that take as input more than one point requires a fair bit of work. Instead, we give a technically simpler and quantitatively stronger proof that relies on a natural generalization of ALOOKL stability, which we call average leave-many-out KL stability (ALMO... | A |
A recurring theme in this context is accounting for additional symmetries.
The variables yIsubscript𝑦𝐼y_{I}italic_y start_POSTSUBSCRIPT italic_I end_POSTSUBSCRIPT of the Lasserre system of equations, cf. Definition 2.8, are indexed by sets of vertex pairs rather than by tuples of such. | Using techniques from [grohe_homomorphism_2022], we finally establish a characterisation of when the level-t𝑡titalic_t Lasserre relaxation of ISO(G,H)ISO𝐺𝐻\operatorname{ISO}(G,H)roman_ISO ( italic_G , italic_H ) is feasible in terms of homomorphism indistinguishability of G𝐺Gitalic_G and H𝐻Hitalic_H. In order to ... | In the first part of the paper (Section 3), linear algebraic tools developed in [mancinska_relaxation_2017, mancinska_quantum_2019] are generalised to yield reformulations of the entire Lasserre hierarchy with and without non-negativity constraints.
Section 4 is concerned with the graph theoretic properties of the grap... | In the subsequent sections, Theorems 3.1 and 3.2 will be proven in parallel. The equivalence of items 1 and 2, 2 and 3, and 3 and 4 are established in Section 3.3, Section 3.2, and Section 3.4, respectively. The statements on homomorphism indistinguishability are proven in Section 4.
| Theorems 3.1 and 3.2 summarise our results. The notions in items 2–4 and the graph classes ℒtsubscriptℒ𝑡\mathcal{L}_{t}caligraphic_L start_POSTSUBSCRIPT italic_t end_POSTSUBSCRIPT and ℒt+superscriptsubscriptℒ𝑡\mathcal{L}_{t}^{+}caligraphic_L start_POSTSUBSCRIPT italic_t end_POSTSUBSCRIPT start_POSTSUPERSCRIPT + end_P... | C |
After going through all conditions, participants filled out a final questionnaire. Besides the orientations and gaze as variables, we also included the familiarity of the participant with robots. This extra information was collected using the questionnaires. | Sideway orientation is the most special condition in all three moving cases because it gives participants the sense of moving in a vertical direction instead of the original path.
The head of the Spot points vertically toward the participant’s trajectory so that the Spot will move orthogonally to its orientation. Peopl... |
Our robot in this experiment is the Spot from Boston Dynamics. It comes with built-in autonomous walking, inspecting, and avoidance functions. Compared to the general model, this one is mounted with a robotic arm on its back, which gives it the appearance of a dog with the gripper as its head (see in Figure 1). There ... | Before the experiment design, we had initial thoughts that all moving conditions should result in longer personal distances than stationary cases. But in Figure 7 (c) we found that stationary condition (M=1.33,SD=0.36formulae-sequence𝑀1.33𝑆𝐷0.36M=1.33,SD=0.36italic_M = 1.33 , italic_S italic_D = 0.36) has even high... | The participant should start from position C and move towards the Table in position D to deliver the yellow cup, during which a non-contact interaction between the participant and the Spot was recorded by the motion capture cameras. In the non-stationary conditions, the Spot robot started moving from B to A the moment ... | A |
This section presents a simulation study of human inverse kinematics (IK) using the methods described above. To generate a trajectory, it is essential to ensure that both the starting and final points are within the workspace of the lower limb, as illustrated in Figure 4. According to [24], the average walking speed f... | Cyclic Coordinate Descent (CCD) is an iterative algorithm used to solve inverse kinematics problems. Yotchon et al. [13] proposed a hybrid approach combining the CCD method with a differential evolution algorithm, a metaheuristic optimization technique, to tackle inverse kinematics challenges. This combined method reli... |
This subsection explores the use of neural networks to find inverse kinematics (IK) solutions for the human leg. Shah et al. [22] applied deep artificial neural networks to solve the IK problem for a 5-axis serial link robotic manipulator. They achieved an accuracy where the deviation between the end effector and the ... |
The results of the inverse kinematics simulation for the lower limbs using the Cyclic Coordinate Descent (CCD) method are shown in Figure 5. To determine the position error illustrated in Figure 6, we used these results along with the forward kinematics described in Equation (5) to generate the end effector trajectory... |
Regarding the Levenberg-Marquardt Damped Least Squares (LMDLS) technique, the simulation results are shown in Figures 9 and 10. This method incurs a high computational cost, primarily due to the complexity of the human leg’s structure. Figure 11 displays the angular joint values obtained using the optimization algorit... | C |
A property of digraphs is a set of finite digraphs closed under isomorphism. A digraph G𝐺Gitalic_G is ε𝜀\varepsilonitalic_ε-far from having a property ΦΦ\Phiroman_Φ if any digraph G′superscript𝐺′G^{\prime}italic_G start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT on the vertex set V(G)𝑉𝐺V(G)italic_V ( italic_G ) that d... | The relationship between local and global properties of structures is a central theme in combinatorics and computer science. Since the work of Rubinstein and Sudan [25], testing properties by sampling a small number of elements is an emerging research area.
A classical result of this kind is the triangle removal lemma ... | The goal of this paper is to study testability of finite posets as special digraphs. By a poset, we mean a set equipped with a partial order ≺precedes\prec≺ that is anti-reflexive and transitive. Alon, Ben-Eliezer and Fischer [1] proved that hereditary (closed under induced subgraphs) classes of ordered graphs are stro... | Alon and Shapira [4] proved that every monotone property of undirected graphs (that is, closed under the removal of edges and vertices) is strongly testable, see Lovász and Szegedy for an analytic approach [22], while Rödl and Schacht generalized this to hypergraphs [23], see also Austin and Tao [8]. Similar results ha... |
Unfortunately, the dependence on ε𝜀\varepsilonitalic_ε can be quite bad already in the case of undirected graphs: the known upper bounds in the Alon-Shapira theorem are wowzer functions due to the iterated involvement of Szemerédi’s regularity lemma. Following Alon and Fox [7], we call a property easily testable if f... | C |
Concerning aspects of domain coverage and succinctness, additional processes are applicable that increase the final quality of the KG.
In addition to type and relation prediction, domain knowledge could possibly be extended by loading completing entity information from external (open accessible) knowledge bases. | This approach is different to the process of integrating an entire external data collection but only focuses on loading necessary domain information that relates to the already integrated entities.
For enhancing KG data with additional relevant domain entities information external knowledge bases can be requested based... | Regarding enrichment with external knowledge: While dstlr links entities to Wikidata, it also fetches stored properties from this external source. However, SLOGERT only adds links to external information based on previously extracted identifiers (PIDs).
| The approach utilizes Stanford CoreNLP for all their knowledge extraction steps: Named-entity extraction, relation extraction and linking the extracted mentions to Wikidata. The framework keeps the provenance of those mentions w.r.t to the source documents. The resulting KG is enriched with facts from an external KG by... | Concerning aspects of domain coverage and succinctness, additional processes are applicable that increase the final quality of the KG.
In addition to type and relation prediction, domain knowledge could possibly be extended by loading completing entity information from external (open accessible) knowledge bases. | A |
Furthermore, to minimize energy expenditure and combat fatigue, humans ideally produce motion characterized by low energy output. This energy constraint on the angular joints corresponds to the third derivative, aligning with the minimum jerk criterion. Figure 8 demonstrates that the cumulative energy of θ1subscript𝜃... |
This section focuses on the dynamic description of the lower limb shown in Figure 2 using the Dual Quaternion-based recursive Newton-Euler method. This method involves calculating the velocities and accelerations of the center of mass of each link, known as twists, based on the positions, velocities, and accelerations... | In this paper, the dual quaternion-based theory is applied to the kinematics and dynamics study of the 7-DOF human lower limbs in 3D space. Subsequently, the artificial neural networks method is used to solve the inverse kinematics problem. The efficiency of the artificial neural networks method is verified using the j... | Compared to classical methods such as Cardan, Fick, and Euler angles, which are based on homogeneous transformation, dual quaternions [1] offer an advantageous representation of rigid transformations in 3D space in many aspects. Dual quaternions require less computer memory, using only 8 elements to describe a rotatio... |
The primary objective of this paper was to leverage dual quaternions algebra for describing the kinematics, encompassing position and orientation, as well as the dynamics modeling of an anthropomorphic leg in 3D-space, thereby circumventing the high computational costs associated with homogeneous transformation method... | D |
We consider the variance-reduced cubic Newton method from (Zhou et al., 2019) (referred to as “full VR”), its lazy version where we do not update the snapshot Hessian (“Lazy VR”), the stochastic Cubic Newton method (“SCN”),
the Cubic Newton algorithm (“CN”), Gradient Descent with line search (“GD") and Stochastic Gradi... | Figure 1 shows that the lazy version saves both time and arithmetic computations without sacrificing the convergence precision. In these graphs, Gradcost is computed using the convention that computing one hessian is d𝑑ditalic_d times as expensive as computing one gradient.
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Figure 6: (left) times needed to compute the gradient, the Hessian, decompose the Hessian and solve the cubic subproblem for a diagonal neural network with n=10000𝑛10000n=10000italic_n = 10000 and different values of the dimension d𝑑ditalic_d. (right) average time for computing the Hessian divided by the average tim... | second-order optimization algorithms.
We take into account that the cost of one stochastic Hessian is proportional to d𝑑ditalic_d times the cost of the stochastic gradient, where d𝑑ditalic_d is the problem dimension, which holds for general dense problems. | We consider again a diagonal neural network and estimate the time costs needed for computing its gradient, Hessian, decomposing the Hessian, and solving the cubic subproblem. Figure 6 shows that the average cost of computing the Hessian is significantly higher than the cost of computing one gradient, and the quotient g... | A |
In practice, multiple network operators co-exist in a given geographical area, each operating in different frequency band. As a consequence, at a given point in time, multiple UEs are served by different operators in the system. In such a scenario, if an IRS is optimized to cater to the needs of one of the operators, i... | which represents the difference in the SNR/channel gain at a UE q𝑞qitalic_q (OOB-UE) served by BS-Y with and without the IRS in the environment. In Fig. 4, we plot the CCDF of ZN(Y)subscriptsuperscript𝑍𝑌𝑁Z^{(Y)}_{N}italic_Z start_POSTSUPERSCRIPT ( italic_Y ) end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_N end_POST... | We derive the ergodic sum spectral efficiencies (SE) of the two operators as a function of the number of IRS elements, under round-robin scheduling of UEs. We show that the ergodic sum-SE scales quadratically and linearly with the number of IRS elements for the in-band and OOB networks, respectively, even when the OOB ... | We provide an exact characterization of the complementary cumulative distribution function (CCDF) of the difference in the channel gain at an OOB UE with and without the IRS. We determine the probability with which the difference is non-negative as a function of the number of IRS elements, and show that the channel gai... |
In order to study the impact on the OOB performance, we consider the scheduling of UEs in a round-robin (RR) fashion at both BS-X and BS-Y. We note that the performance under opportunistic scheduling at either or both BSs can also be derived along similar lines, e.g., following the approach in [7]. Since the BSs are e... | B |
In the three extreme cases, DNNs may either collapse to simple models close to linear regressions, or learn non-transferable indiscriminative concepts, although the network output can still be represented as the sum of interaction effects of these concepts.
| Besides, Fig. 7(right) shows the average discrimination power β¯¯𝛽\bar{\beta}over¯ start_ARG italic_β end_ARG of the extracted concepts also decreased when we assigned more training samples with random labels.
This verified that the DNN usually could not learn transferable and discriminative concepts from samples that... | Furthermore, if a DNN encodes faithful symbolic concepts, then these concepts are supposed to exhibit certain discrimination power in the classification task.
In other words, for each concept S𝑆Sitalic_S, if the concept is saliently activated on a set of samples, then interaction effects I(S)𝐼𝑆I(S)italic_I ( italic... | If the ground-truth label for classification is incorrectly annotated on some samples, then the DNN usually has to memorize each incorrectly-labeled training sample for classification without summarizing many common features from such chaotic annotations.
Thus, in this case, the DNN usually encodes more non-transferabl... | To be precise, if a classification task can be conducted with some shortcut solutions without requiring the DNN to encode complex concepts, then the DNN probably converges to the shortcut solution.
For example, in an image classification task, if pixel-wise colors are sufficient to conduct the image-classification task... | C |
Interactive concepts vs. cognitive concepts and other interaction metrics. Although the Harsanyi interactive concept seems partially aligned with humans’ cognition to some extent (Cheng et al. 2021b), we do not think such interactive concepts exactly fit humans’ cognition. More crucially, the mathematical generalizati... |
Although there is a common intuition that more complex representations usually lead to over-fitting, this study uses an analytic inconsistency of concepts to explain the connection between the complexity of interactive concepts and their generalization power. The complexity of an interactive concept S𝑆Sitalic_S is de... | Therefore, a high-order interactive concept contains a large number of input variables, and represents a complex concept.
In this way, we use the high inconsistency to noises of high-order concepts to explain the high over-fitting risk of high-order concepts. | Complexity (order) of interactive concepts.
The complexity of the interactive concept S𝑆Sitalic_S is defined as the number of input variables contained in the concept, which is also termed as the order of the concept, i.e., order(S)=|S|order𝑆𝑆\textit{order}(S)=|S|order ( italic_S ) = | italic_S |. | In general, a DNN’s representation complexity is different from the cognitive complexity. For example, let us consider a small ball concept consisting of a few pixels (low-order concept) and a large ball concept consisting of massive pixels (high-order concept) in images. These two balls have similar cognitive difficul... | D |
We conducted experiments with MNIST, the most commonly used datasets in the field of image classification. We used MNIST datasets in torchvision and used 2 layered Networks which is optimized using SGD on a batch size of 64 with a learning rate of 0.001 and a momentum of 0.5 with random seed of 10. We confirmed that ou... |
The robust property of MoLU is to approach rapidly to the value of minimum of a loss function without losing stability. This is a truly useful characteristic when training long time-series data by using NeuralODEs(Neural Ordinary Differential Equations). To prove the performance of MoLU, we conducted experiment on Neu... |
We conducted experiment on CIFAR10 which is more challenging model than MNIST in classification fields. ResNet18 which is optimized using SGD on a batch size of 32 with a learning rate of 0.001, momentum of 0.9 is used for the experiment with random seed of 10. Our activation function converges rapidly with respect to... | We conducted experiments with MNIST, the most commonly used datasets in the field of image classification. We used MNIST datasets in torchvision and used 2 layered Networks which is optimized using SGD on a batch size of 64 with a learning rate of 0.001 and a momentum of 0.5 with random seed of 10. We confirmed that ou... | ReLU (Rectified Linear Units) is mainly used in the fields of vision classification. In classification, ordinarilly more layers is better in deep learning. On datasets such as MNIST, even simple CNNs with three layers can achieve high classification performance. However, for more challenging datasets such as CIFAR10, s... | B |
It is, of course, an open problem to establish if functional digraphs can be generated with a smaller delay. That would require us to somehow avoid testing O(n)𝑂𝑛O(n)italic_O ( italic_n ) possible merges in order to construct the next candidate digraph, or to avoid spending linear time in order to check for valid i... |
Notice how the isomorphism code for a functional digraph resembles a PQ-tree, a data structure representing permutations of a given set of elements which, incidentally, is used to efficiently check isomorphic graphs of certain classes [5]. However, for our application we need to represent the equivalence of all permut... | Another interesting line of research is to find variations of the tree-merging approach suitable for the efficient generation either of restricted classes of functional digraphs (for instance, with cycles of given lengths or trees of given heights, which is sometimes useful in applications related to the decomposition ... |
Enumeration problems for several classes of graphs have been analysed in the literature. For instance, efficient isomorphism-free generation algorithms for rooted, unordered trees are well known, even requiring only amortised constant time per solution [2], and there exist polynomial delay algorithms for the isomorphi... |
The synchronous execution of two dynamical systems A𝐴Aitalic_A and B𝐵Bitalic_B gives a dynamical system A⊗Btensor-product𝐴𝐵A\otimes Bitalic_A ⊗ italic_B, whose transition digraph is the direct product [15] of the transition digraphs of A𝐴Aitalic_A and B𝐵Bitalic_B. This product, together with a disjoint union ope... | B |
Then, to apply the approximation theory result (20), we recall that, by the hypotheses of this lemma, and (18), T†∈Hηk+1(Ω;Ω)superscript𝑇†superscriptsubscript𝐻𝜂𝑘1ΩΩT^{\dagger}\in H_{\eta}^{k+1}(\Omega;\Omega)italic_T start_POSTSUPERSCRIPT † end_POSTSUPERSCRIPT ∈ italic_H start_POSTSUBSCRIPT italic_η end_POSTSUBSCR... |
To derive analogous error bounds to those for pushforward measures in Section 4, we first present an abstract result to bound the KL divergence between a target measure and an approximate pullback measure. An application of this theorem to derive convergence results for an increasing class of monotone and triangular m... |
In this section we numerically validate the approximation results obtained in Section 4 for various realizations of the abstract algorithm of Section 2. Sections 5.1–5.2 investigate the algorithm that minimizes the Wasserstein distance, while Section 5.3 investigates the Kullback-Leibler divergence between pullback me... | and C>0𝐶0C>0italic_C > 0 is a constant independent of 𝒯^^𝒯\widehat{\mathcal{T}}over^ start_ARG caligraphic_T end_ARG. We note that T†superscript𝑇†T^{\dagger}italic_T start_POSTSUPERSCRIPT † end_POSTSUPERSCRIPT can be taken to be any transport map that satisfies the exact pushforward relation T♯†η=νsubscriptsupersc... | the applied analysis of the backward transport for triangular maps on unbounded domains by minimizing the KL
divergence. Our analysis for triangular maps relies on a specialized stability result, Theorem 8.3, which is analogous to the general Theorem 2.1 for the backward transport problem. However, due to the triangula... | A |
MMA-MRNNet comprises two primary components: the Multiple Models of Affect (MMA) extractor and the Masked RNN and Routing Network (MRNN). The MMA component is a Multi-Task Learning (MTL) CNN that extracts affective representations from each frame by concurrently estimating valence-arousal (VA), recognizing the 7 basic ... |
The extracted representations are then passed to the MRNN component, which consists of an RNN designed to capture temporal dependencies across the sequence of frames. To handle the varying lengths of input videos, a Mask layer is employed within the MRNN. This layer dynamically selects relevant RNN outputs based on th... | Figure 1:
Overview of the proposed MMA-MRNNet for dynamic multi-output Facial Expression Intensity Estimation. MMA-MRNNet comprises two main components: the Multiple Models of Affect (MMA) extractor, which generates affective representations (valence-arousal, basic expressions, and action units) for each video frame, ... |
These embeddings (corresponding to all video frames) are concatenated into a single vector embedding z′∈ℜd′⋅tsuperscriptz′superscript⋅superscript𝑑′𝑡\textbf{{z}}^{\prime}\in\Re^{d^{\prime}\cdot t}z start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT ∈ roman_ℜ start_POSTSUPERSCRIPT italic_d start_POSTSUPERSCRIPT ′ end_POSTSUP... | To the best of our knowledge, MMA-MRNNet is the first architecture to leverage valence-arousal, AUs, and basic expressions as intermediate representations for the task of Facial Expression Intensity Estimation. This approach not only enhances the model’s ability to capture the nuanced dynamics of emotional expressions ... | A |
A conformity function is a mapping ρ:ℝd×𝒴×Ω→ℝ:𝜌→superscriptℝ𝑑𝒴Ωℝ\rho:\mathbb{R}^{d}\times\mathscr{Y}\times\Omega\to\mathbb{R}italic_ρ : blackboard_R start_POSTSUPERSCRIPT italic_d end_POSTSUPERSCRIPT × script_Y × roman_Ω → blackboard_R such that ρ(x,y)=ρ(x,y,⋅)𝜌𝑥𝑦𝜌𝑥𝑦bold-⋅\rho(x,y)=\rho(x,y,\,\boldsymbol{\... | In general, the coverage indicators Zisubscript𝑍𝑖Z_{i}italic_Z start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT are dependent random variables, since for all future observables the corresponding conformal prediction sets in Definition 3 are defined in terms of the same calibration sample conformity score S(⌈(1−α)(n+1)... |
Conformity functions are agnostic to the choice of the specific models or algorithms used to construct μ^^𝜇\hat{\mu}over^ start_ARG italic_μ end_ARG, ξ^psubscript^𝜉𝑝\hat{\xi}_{p}over^ start_ARG italic_ξ end_ARG start_POSTSUBSCRIPT italic_p end_POSTSUBSCRIPT, and π^^𝜋\hat{\pi}over^ start_ARG italic_π end_ARG in Exa... |
Note that the regularity of a specific conformity function ρ𝜌\rhoitalic_ρ is contextual, being inherently dependent on the distribution of the underlying data sequence. Technically, we can always avoid ties among the sequence of conformity scores almost surely by introducing a properly constructed ancillary tie-break... | Under the data exchangeability assumption, the sequence of conformity scores {Si}i≥1subscriptsubscript𝑆𝑖𝑖1\{S_{i}\}_{i\geq 1}{ italic_S start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT } start_POSTSUBSCRIPT italic_i ≥ 1 end_POSTSUBSCRIPT is exchangeable.
| C |
This line of work first converts events within a time interval into dense frames and then processes them using off-the-shelf learning models tailored for images. Frame-based methods mainly focus on designing suitable representations to integrate the spatial semantics embedded in event streams. An example of the event ... |
As listed in Table I, we report the accuracy of our model and state-of-the-art methods on four event-based object classification datasets. To conduct a comprehensive analysis, both point-based [30, 9, 11, 10, 12, 24] and frame-based [4, 28, 5, 8, 6] methods are our comparison models. For these frame-based methods (i.e... |
Existing event-based learning models can be summarized into two main categories: frame-based and point-based methods. Frame-based methods [4, 5, 7, 8] first convert events into dense frame-based representations and then process them using learning models designed for images, such as convolutional neural networks (CNNs... | The conversion of dense frames sacrifices the sparse and asynchronous nature of events. Although frame-based methods outperform point-based ones in terms of accuracy, they usually require heavy-weight models to process dense input, leading to high computational complexity and latency. Some sparse frame-based solutions ... |
We compare our model with state-of-the-art point-based and frame-based methods on event-based action recognition. Motion-based SNN (MotionSNN) [17] and graph-based VMV-GCN are selected as representative point-based methods. The experimental results are evaluated with their default settings. Moreover, we re-implement s... | C |
It was proven by Takashi [33] that a given function f(𝐱)𝑓𝐱f(\mathbf{x})italic_f ( bold_x ) that meets the condition of the Eikonal Equation ∥∇𝐱f(𝐱)∥=1delimited-∥∥subscript∇𝐱𝑓𝐱1\left\lVert\nabla_{\mathbf{x}}f(\mathbf{x})\right\rVert=1∥ ∇ start_POSTSUBSCRIPT bold_x end_POSTSUBSCRIPT italic_f ( bold_x ) ∥ = 1 on... | In Fig. 6, the results for the precision of the reconstruction are shown. The single-object experiments are shown in black. We can see that the trends of both JS and CD are the same as for the simulation, even though we can notice noise in some touches. In yellow, the results for multi-object experiments are shown. Aga... | Points with a high loss from Eq. 8 are not on the estimated surface. And, intuitively, if all points were certain, the loss would be zero for all of them. However, this was not the case in our experiments. Therefore, we compute the Eikonal loss from Eq. 8 for all points on our current shape O𝑂Oitalic_O and take it as ... |
The first group of improvements concerns the process of shape completion performed by Implicit Geometric Regularization for Learning Shapes (IGR), which we modified as follows. We use a new, theoretically grounded, method to determine the points with highest uncertainty. In addition, we changed the sampling of points... |
We will first describe the module for the shape creation itself. In [1] the IGR network was used as a standalone library. To perform more efficiently and to be able to handle more objects at once, we modified it to be more compatible with the whole ecosystem (under Robot Operating System (ROS)). The module contains t... | B |
Infinitary ω𝜔\omegaitalic_ω-clones have been mainly studied with respect to both local topology and global topology. However, to extend the previous results to ω𝜔\omegaitalic_ω-clones that are not necessarily infinitary, we require a new concept of polymorphism. | In this section we introduce the ω𝜔\omegaitalic_ω-relation clones and prove that Inv𝒢ω(C)𝐼𝑛subscriptsuperscript𝑣𝜔𝒢𝐶Inv^{\omega}_{\mathcal{G}}(C)italic_I italic_n italic_v start_POSTSUPERSCRIPT italic_ω end_POSTSUPERSCRIPT start_POSTSUBSCRIPT caligraphic_G end_POSTSUBSCRIPT ( italic_C ) is an ω𝜔\omegaitalic_... | To describe ω𝜔\omegaitalic_ω-clones that are not necessarily infinitary through invariant relations, in Section 7.3 we introduce the notion of matrical polymorphisms. The main result characterising X𝑋Xitalic_X-closed ω𝜔\omegaitalic_ω-clones is presented in Theorem 7.13. As a corollary, we obtain a characterisation o... | In this section, we aim to introduce and explore this new notion of polymorphism that will allow us to generalise Theorem 7.3 to a wider class of ω𝜔\omegaitalic_ω-clones, and to
characterise trace (resp. uniform) closed sets of ω𝜔\omegaitalic_ω-operations. | In order to characterise the ω𝜔\omegaitalic_ω-relation clones of locally closed ω𝜔\omegaitalic_ω-relations (cω𝑐𝜔c\omegaitalic_c italic_ω-relation clones)
we define the notion of decreasing sequence of finitary relations. Each of these sequences has a locally closed ω𝜔\omegaitalic_ω-relation as a limit and we show... | C |
An illustrating example is the so-called synthesis problem in the field of system identification, where (under special conditions) the Minimum s𝑠sitalic_s-t𝑡titalic_t Cut problem can be used to determine an optimal placement of input and output signals in a physical system (modeled as a directed graph) to gather info... | This section is devoted to proving Theorem 1.1 by reducing SUM-k𝑘kitalic_k-DMC and COV-k𝑘kitalic_k-DMC to SMF on distributive lattices. First, we show that the domain of solutions of SUM-k𝑘kitalic_k-DMC and COV-k𝑘kitalic_k-DMC can be restricted to the set of k𝑘kitalic_k-tuples that satisfy a particular order, as o... |
We now briefly motivate why finding diverse minimum s𝑠sitalic_s-t𝑡titalic_t cuts in a graph can be of interest. In general, to solve a real-world problem, one typically formulates the problem as an instance of a computational problem and proceeds to find a solution with the help of an optimization algorithm. However... | One way of dealing with this issue is to present all optimal solutions of the simplified model and let a user choose between them based on external factors ignored by the mathematical model. Such an approach is useful when the number of optimal solutions is small, but in most cases (as in the Minimum s𝑠sitalic_s-t𝑡ti... | An illustrating example is the so-called synthesis problem in the field of system identification, where (under special conditions) the Minimum s𝑠sitalic_s-t𝑡titalic_t Cut problem can be used to determine an optimal placement of input and output signals in a physical system (modeled as a directed graph) to gather info... | C |
We also show how to lower bound information between probabilities over general spaces with information between probabilities over finite sequences using uniformly enumerable disjoint open sets. We provide an means to upper bound the probabilities between general spaces using computable non-probabilistic measure covers... | The average information between probability measures is small, less than the complexity of the averaging. This is true in the discrete and continuous case. For the discrete case, an enumerable sequence of uniformly computable probability measures over a general space is a sequence of measures {μi}subscript𝜇𝑖\{\mu_{i}... | We extend conservation to Borel measures over T0subscript𝑇0T_{0}italic_T start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT, second countable topologies. We restrict our attention to such topologies which can be represented by a tuple (X,ℬ,ν)𝑋ℬ𝜈(X,\mathcal{B},\nu)( italic_X , caligraphic_B , italic_ν ) where X𝑋Xitalic_X is a ... | We prove conservation of probabilities over successively general spaces. This includeds finite sequences, infinite sequences, and T0subscript𝑇0T_{0}italic_T start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT, second countable topologies. Conservation of probabilities over the case of finite and infinite sequences follow directly... | The advantage to the topological approach used in this paper is that a very general topology can be used. The only assumption needed is that the topology needs to have the T0subscript𝑇0T_{0}italic_T start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT property and a computable countable basis. Typical requirements in computability... | D |
Table VII demonstrates the significant performance improvement of context normalization over batch normalization (BN) when using the ViT architecture trained from scratch on CIFAR-100. Both CN-Patches and CN-Channels approaches outperform BN by approximately 10% and 18% in terms of accuracy and top-5 accuracy. The trai... | In this experiment, we show that due to its strength in local representation, context normalization can yield substantial gains in domain adaptation. Domain adaptation [28] is a technique for using knowledge learned by a model from a related domain with sufficient labeled data to improve the performance of the model in... | Different normalization techniques, including activation normalization, weight normalization, and gradient normalization, are employed to enhance the training performance of DNNs.
To normalize activations, the most common technique is Batch Normalization (BN) [4]. BN has been proposed to solve the problem caused by the... |
CN transform is a differentiable operation in deep neural networks that normalizes input data. By applying CN, the model can continuously learn from input distributions and adapt its representations to the target task, leading to improved performance. This normalization helps mitigate the influence of variations in in... | As deep neural networks require a certain amount of labeled data for effective training, it is well known that the lack of a large enough corpus of accurately labeled high-quality data can produce disappointing results. Data augmentation [23] is one way to overcome this problem. However, current approaches generate the... | D |
Comparison to SotA Methods.
DFB is also compared with five very recent SotA methods, including MaxLogit (Hendrycks et al., 2022), KL-Matching (Hendrycks et al., 2022), ReAct (Sun et al., 2021), MaSF (Haroush et al., 2022) and DML+ (Zhang and Xiang, 2023) , with their results reported at the top of Tabs. 1 and 2. Among ... | The Reasons behind the Effectiveness of DFB. We aim to understand the effectiveness of DFB from two perspectives, including the foreground and background OOD scoring, and the latent features learned in DFB, with the results on the Textures dataset reported in Figs. 4 and 5 respectively. We can see in Fig. 4 that the ba... | As depicted in Fig. 1, the proposed DFB effectively disentangles foreground and background features. In the ID data CIFAR10, DFB can more accurately locate the ID objects than the vanilla classifier. In the OOD data CIFAR100, which contains significant foreground objects, DFB successfully disentangle between the foregr... | This paper considers the importance of disentangling foreground and background features in OOD detection and proposes to leverage background features to enhance the OOD detection methods that are based on foreground features. To this end, we introduce a novel generic framework, called DFB, that can Disentangle the Fore... |
Using semantic of foreground objects only to detect OOD samples can often be successful when the OOD samples have some dominant semantics that are different from the ID images. However, approaches of this type would fail to work effectively when the OOD samples do not have clear object semantics and/or exhibit some si... | A |
In addition to the above conclusions, the choices of s=15𝑠15s=15italic_s = 15 and s=30𝑠30s=30italic_s = 30 may not necessarily be the optimal values for each LLIE method. Therefore, there may be larger improvements for a different choice of s𝑠sitalic_s which can be determined empirically. We fix s𝑠sitalic_s in ord... | Section V-A describes the datasets used in this study; Section V-B defines the configuration of LPDM and the training parameters used for all experiments; Section V-C provides detail on the LLIE models selected for comparison with LPDM; in order to achieve a fair comparison, we compare our approach to alternative denoi... | An ablation study is necessary in order to demonstrate that the improvements of LPDM can be attributed specifically to our proposed approach and that the results are not arbitrary. In Section V-F1 we examine the effect of predicting ϵbold-italic-ϵ\bm{\epsilon}bold_italic_ϵ, and in Section V-F2 we compare unconditional ... |
The results of the DLPDM experiment are summarized in Table III, which includes the other ablation results from Section V-F2. Our proposed LPDM approach performs better on SSIM and LPIPS and DLPDM performs better on PSNR and MAE (although the variance of DLPDM is higher). LPDM largely outperforms DLPDM on LPIPS which ... |
The experimental results in Table III show that LPDM significantly outperforms ULPDM across all metrics. Therefore, we conclude that conditioning is necessary in order for the LPDM to detect the wide variety of artifacts that can be present in 𝒙^0ηsuperscriptsubscriptbold-^𝒙0𝜂\bm{\hat{x}}_{0}^{\eta}overbold_^ start... | B |
Online technologies have fundamentally changed information provision and acquisition in our societies. While, in principle, the digital information ecosystem is horizontal, easy to navigate, and egalitarian in providing access to information, in practice, the networks of information repositories have become so complex... | Previous research has shown that individuals exhibit distinct cognitive patterns and abilities when engaging in online information-seeking activities, with several characteristics identified as influential factors. For instance, it has been demonstrated that information-seeking performance is not solely contingent upon... | In addition, our observations indicate that individual characteristics, including sex, ethnicity, native language, political stance, and reported spatial navigation skills, significantly influence navigation performance in one type of game (with time or distance constraints) but not the other. To fully understand these... | To gain insights into online navigation behaviors, researchers conducted a series of studies using Wikipedia as an observational setting [19, 20, 21, 22, 23] and utilized its well-documented network of articles as the framework for navigation studies [24, 25]. The wide range of topics represented in Wikipedia (https://... |
Online technologies have fundamentally changed information provision and acquisition in our societies. While, in principle, the digital information ecosystem is horizontal, easy to navigate, and egalitarian in providing access to information, in practice, the networks of information repositories have become so complex... | A |
The simulation software of the LHCb experiment is built upon two main projects named Gauss and Boole [3], both based on the Gaudi framework [4].
The Gauss framework implements the so-called generation and simulation phases, while the Boole application is responsible for the digitization phase. | The first step of any simulation production is the generation phase in which the high-energy collisions are simulated with Monte Carlo generators such as Pythia8 [5] and EvtGen [6].
The output of the generation phase is the set of long-lived particles able to traverse partially or entirely, depending on the particle sp... | The radiation-matter interactions occurring within the detector by the traversing long-lived particles are reproduced during the simulation phase that aims to compute the energy deposited in the active volumes relying on Geant4 [7].
Lastly, during the digitization phase, the energy deposits are converted into raw data ... | The simulation software of the LHCb experiment is built upon two main projects named Gauss and Boole [3], both based on the Gaudi framework [4].
The Gauss framework implements the so-called generation and simulation phases, while the Boole application is responsible for the digitization phase. |
The simulation of high-energy collisions, of the decays of the generated particles, and of the physics processes occurring within the detector by the decay products are a key necessity of analysis, typically for separating the signal from background sources or for selection efficiency studies. | A |
Figure 4: Pipeline for reconstructing the contact map based on Cβ atoms with length L𝐿Litalic_L: First, attention maps are extracted from each layer of the self-attention blocks. These maps undergo symmetrization and average product correction (APC) along the amino acid dimensions to produce an L×L𝐿𝐿L\times Litalic... | Structural Reconstruction Constraint.
As previously mentioned, the GVP layers encode the core structural features using N, Cα, and O atoms (These three types of atoms are called backbone atoms). To further enhance the structural constraints, we introduce a self-supervised structure reconstruction task. While predicting... |
Figure 2: Schematic diagram of the GVP module: Protein backbone atoms (C, Cα, and N) form the basis for generating graphs with node and edge features based on k-nearest neighbor relationships. These graphs are fed into the vector and scalar channels of the GVP module to produce vector and scalar features. These primar... | Virtual Cβ Atom Generation.
The virtual Cβ atoms are derived coordinates that may not physically exist in every residue. However, their positions can be inferred from the spatial relationships among protein backbone atoms: N, Cα𝛼\alphaitalic_α, and O atoms. The positions are calculated as follows: |
Figure 4: Pipeline for reconstructing the contact map based on Cβ atoms with length L𝐿Litalic_L: First, attention maps are extracted from each layer of the self-attention blocks. These maps undergo symmetrization and average product correction (APC) along the amino acid dimensions to produce an L×L𝐿𝐿L\times Litalic... | C |
As the results show, the LiftNet-based methods save 68.4%percent68.468.4\%68.4 % to 96.9%percent96.996.9\%96.9 % model parameters or the original models. Since the parameter size of LiftNet is negligible (324 parameters), the level of parameter efficiency is mainly affected by the ratio of entities to relations in the ... | We further discuss the impact of LiftNet on training complexity since it introduces additional neural layers to obtain entity representations. Specifically, we train each method for 100 epochs and then provide the average training time taken per epoch. As shown in Table VII, by adopting LiftNet, the ratio of training t... | We adjust the setups of TC layers by increasing/decreasing the kernel size accordingly to ensure the output dimensions are always 512. The results with respect to link prediction accuracy (H@10) are shown in Table VIII. We see that the results of LN-TransE and LN-TransH are relatively stable, introducing more TC layers... | The results of LiftNet-based methods for knowledge graph link prediction (accuracy measured by H@10 and MRR) are shown in Fig. 3. Generally, on WN18RR datasets, we observe the link prediction accuracy increases with higher input dimension, and the increase is significant from 4-dimension to 16-dimension. However, after... | We show the sensitivity of the performance of LiftNet-based methods regarding the output dimensions on WN18RR dataset. To do that, we vary the output dimensions from 128 to 1024 and adjust the setups of the two TC layers in LiftNet accordingly. The results in Fig. 4 show two different trends. First, LN-TransE and LN-Tr... | A |
The proposal outlined so far can be integrated with the work developed in [6], which focused on establishing simultaneous entanglement among more than two nodes. Specifically, we will target the distribution of three-partite entanglement, for which the scheme proposed in [6] is exact. Because the bipartite metrics con... |
The proposal outlined so far can be integrated with the work developed in [6], which focused on establishing simultaneous entanglement among more than two nodes. Specifically, we will target the distribution of three-partite entanglement, for which the scheme proposed in [6] is exact. Because the bipartite metrics con... | The second step is to demonstrate that the multipartite metrics (specifically, the fidelity and rate metrics for the multipartite state) are monotonic and label-isotonic with respect to the paths. For these metrics, instead of adding links to extend paths, one should combine paths to form trees. In the particular case ... | Since the ebits’ end-to-end fidelity decays with distance, one has to reduce the entanglement distribution rate as the distance increases. In general, the fidelity of each ebit in a path decays with its capacity, and the end-to-end rate of entanglement generation is bottlenecked by the smallest capacity among its links... |
It is known that if a routing metric is both isotonic and monotonic, a multi-objective optimization algorithm will always converge to the set of optimal solutions [6, 10]. Monotonicity means that when a path is extended, our metric will either always increase or always decrease. To introduce isotonicity, consider two ... | B |
The designed Eb/N0subscript𝐸𝑏subscript𝑁0E_{b}/N_{0}italic_E start_POSTSUBSCRIPT italic_b end_POSTSUBSCRIPT / italic_N start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT of the ECBS algorithm are 1.51.51.51.5dB and 2.572.572.572.57dB for (512,256)512256\left(512,256\right)( 512 , 256 ) and (512,384)512384\left(512,384\right)( 5... |
In this paper, the construction methods based on MWD are proposed to improve the performance of polar codes under SCL decoding. We first prove that the ML performance can approach the MWUB as the SNR goes to infinity. Then, we design the ordered and nested MWD sequence to apply fast construction without channel inform... | In Fig. 8(a), the information sets obtained by RM-polar [36] and MWD sequence are identical.
Then, the RM-polar and the MWD sequence have the optimum MWUB among these construction methods but a large performance gap between the MWUB and the performance, since the entropy constraint is unsatisfied. | Then, in Lemma 5, we prove the polar codes obeying the PO with the MWD sequence have the optimum performance evaluated by the MWUB in the high SNR region.
In Lemma 6, we prove the MWD sequence is nested, which means that the MWD sequence can be used similarly to the polar sequence in 5G [4]. | In Fig. 5(a), we observe that the required SNRs of polar sequence [4], GA algorithm [7] and MWD sequence are close to the required SNRs of corresponding MWUB.
Then, since the polar codes constructed by the MWD sequence have the optimum MWUB, the required SNRs are less than or equal to those of the polar sequence and GA... | B |
The solution for the Searcher will have the following structure. At every branch node j𝑗jitalic_j there is a favored branch Q1subscript𝑄1Q_{1}italic_Q start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT and a positive probability β𝛽\betaitalic_β (the favoring bias) for it to be chosen before looking at the signal.
With the rema... |
We can now state and prove our main theorem, which includes an expression for the value of the game. We describe the optimal strategy for the Searcher by giving the favoring bias β𝛽\betaitalic_β of searching the favored branch first (without needing to observe the signal) when at a branch node. | The solution for the Searcher will have the following structure. At every branch node j𝑗jitalic_j there is a favored branch Q1subscript𝑄1Q_{1}italic_Q start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT and a positive probability β𝛽\betaitalic_β (the favoring bias) for it to be chosen before looking at the signal.
With the rema... | So in particular the Searcher will never choose the unfavored arc (branch) when the signal is for the favored one. The use of biased depth-first Searcher strategies (random choices at every branch node) of the Searcher was introduced in another context in Alpern (2010) and Alpern and Lidbetter (2014), but those distrib... |
This paper has addressed the question of how to optimally search for an adversarially hidden target on a tree network in the presence of unreliable signals. We have found optimal solutions for both the Searcher and the Hider that can be calculated recursively, and a closed form expression for the value of the game. Fu... | C |
Several other works studied text-to-image latent diffusion models for medical imaging Chambon et al. (2022a); Akrout et al. (2023).
Closest to our work is Chambon et al. (2022b), where the authors explore various methods to adapt a pre-trained Stable Diffusion model to chest X-ray generation. | Figure 1: The Textual Inversion fine-tuning process for diffusion models trains a text conditioning embedding for a new token using a small set of images while keeping the rest of the architecture frozen. We show that this allows the adaption of latent diffusion models to a variety of medical imaging modalities, using ... | They performed experiments with both Textual Inversion and fine-tuning the U-net component of Stable Diffusion, similar to Ruiz et al. (2022).
They find that Textual Inversion works, but fine-tuning the U-net is more effective, especially with more complex prompts. | Several other works studied text-to-image latent diffusion models for medical imaging Chambon et al. (2022a); Akrout et al. (2023).
Closest to our work is Chambon et al. (2022b), where the authors explore various methods to adapt a pre-trained Stable Diffusion model to chest X-ray generation. | For these reasons, especially in the medical domain, it is essential to have computationally feasible methods that can fine-tune existing models towards a smaller set of a specific modality or disease.
In this paper, we pick one such method, Textual Inversion, and rigorously explore its capacities for adapting Stable D... | B |
Composition Correctness Evaluation. In this task, we assess the consistency of the generated 3D assets across two views, focusing on both semantic consistency and multi-view consistency. We collected four groups of samples, each comprising 3D assets generated by Latent-NeRF, SJC, and our method, using the same text pro... |
In our study, we employ the CLIP score as the primary evaluation metric to assess the congruence between the generated 3D assets and the associated text prompts. This score, commonly used in text-to-image generation research as noted in studies [38, 65, 55], is derived from the cosine similarity between the embeddings... | Object Identification. For this task, we selected four samples of 3D assets generated using our method, comprising a total of seven objects. Participants were then asked to identify the objects depicted in these assets. To evaluate the multi-object generation and combination capabilities of our approach, we calculated ... | Generative Quality Evaluation. We provided four groups of generated 3D assets (refer to the supplementary material) to each participant. For each group, the 3D assets were created using Latent-NeRF, SJC, and our method, all based on the same text prompt. Participants were then asked to assess the quality of these gener... | Composition Correctness Evaluation. In this task, we assess the consistency of the generated 3D assets across two views, focusing on both semantic consistency and multi-view consistency. We collected four groups of samples, each comprising 3D assets generated by Latent-NeRF, SJC, and our method, using the same text pro... | C |
The goal of clustering is to separate data points into groups such that points within a group a more similar to each other than to those outside the group (Cormack, (1971)). In practice, it is often not clear what constitutes a cluster (Hennig, (2015)). As a result, many practitioners evaluate cluster analysis algorith... | The generators OCLUS (Steinley and Henson, (2005)) and GenRandomClust (Qiu and Joe, (2006)) focus on providing more sophisticated overlap control compared to previous generators. GenRandomClust extends the generator of Milligan and Cooper, (1985) by managing overlaps between clusters with different ellipsoidal shapes a... |
MDCGen (Iglesias et al., (2019) is a feature-rich generator that supports many desiderata in cluster analysis, such as overlap control, different probability distributions, subspace clusters, and the ability to add noise points. In particular, it is nice to be able to place noise points away from the clusters, which i... |
OCLUS (Steinley and Henson, (2005)) quantifies cluster overlap in terms of the shared density between two clusters. The generator uses analytical formulas for integrals of several interesting probability distributions (including exponential, gamma, and chi-square), thereby effectively managing overlaps between non-nor... |
Synthetic data is valuable for two reasons. First, it clearly stipulates which data points belong to which cluster, allowing objective evaluation. Second, it allows independently manipulating different aspects of the data (such as the overlap between clusters or the variability of cluster shapes), which is critical fo... | D |
Given the input context 𝐜𝐜\mathbf{c}bold_c, which is a sequence of tokens [c1,⋯,cn]subscript𝑐1⋯subscript𝑐𝑛[c_{1},\cdots,c_{n}][ italic_c start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT , ⋯ , italic_c start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT ], the conventional event extraction task aims to identify the trigger words... |
For this conventional event extraction task, the current state-of-the-art generation-based approaches rely on manual templates, which require trigger words or event types to be given, to simplify this task (Hsu et al., 2022; Lu et al., 2021). However, in a realistic scenario, although argument roles are event-specific... | The event extraction task aims to identify events and their arguments from the given textual input context Nguyen et al. (2016); Wadden et al. (2019); Yang et al. (2019). Conventionally, this task can be decomposed into four sub-tasks Nguyen et al. (2016): (i) detecting the trigger word that most directly describes the... | The introduction of pre-trained language models revolutionized event extraction. Fine-tuning these models achieved state-of-the-art performance across various benchmarks (Lin et al., 2020; Ramponi et al., 2020; Wadden et al., 2019; Yang et al., 2021). These models captured deep contextual information and benefited from... |
While impressive results are reported, we identify two major limitations of the current generation-based event extraction methods. Firstly, most of these methods rely on heuristic templates and extensive human knowledge engineering. According to the experiments conducted by Hsu et al. (2022), a slight change in the te... | A |
This improvement is mainly due to the Lqsuperscript𝐿𝑞L^{q}italic_L start_POSTSUPERSCRIPT italic_q end_POSTSUPERSCRIPT-embedding property of the interpolation space [ℋ]ssuperscriptdelimited-[]ℋ𝑠[\mathcal{H}]^{s}[ caligraphic_H ] start_POSTSUPERSCRIPT italic_s end_POSTSUPERSCRIPT proved in Theorem 5 and a truncation ... |
The outline of the rest of the paper is as follows. In Section 2, we introduce basic concepts including priori knowledge of RKHS, integral operators and the definition of the interpolation space. In addition, we formally define the spectral algorithm, which is the main interest of this paper, and provide three example... | As mentioned in Fischer and Steinwart (2020), the empirical process and the integral operator techniques are the two main techniques used to derive the learning rates of kernel methods. Steinwart et al. (2009) firstly introduced the embedding property of RKHS for the empirical process technique. Fischer and Steinwart (... | Since the convergence rates and the minimax optimality of spectral algorithms in the well specified case are clear, a large amount of literature studied the misspecified spectral algorithms. Among these work, Steinwart et al. (2009); Dicker et al. (2017); Pillaud-Vivien et al. (2018); Fischer and Steinwart (2020); Celi... |
Compared with the line of work which considers the embedding index (Steinwart and Christmann, 2008; Pillaud-Vivien et al., 2018; Fischer and Steinwart, 2020, etc.), this paper removes the boundedness assumption, i.e., ‖fρ∗‖L∞(𝒳,μ)≤B∞<∞subscriptnormsuperscriptsubscript𝑓𝜌superscript𝐿𝒳𝜇subscript𝐵\|f_{\rho}^{*}\|_... | B |
HC and Potamias et al. are the only baselines with shorter runtimes than our method, and obtain maximum Hausdorff distances comparable to those obtained by our approach. However, as discussed in Section 2, tuning the user-specified HC parameters make striking a balance between feature preservation and retaining a suffi... |
Overall, these results show that our approach provides a computationally efficient option for performing point cloud simplification in settings where the user wishes to strike a balance between preserving high fidelity around sharp features in the cloud, and ensuring that the simplified cloud covers the manifold defin... |
Another widely-used technique is Weighted Locally Optimal Projection (WLOP) proposed by Huang et al. [14]. In this work, the authors modified the existing parameterization-free denoising simplification scheme termed Locally Optimal Projection (LOP) [22], which is unsuitable for non-uniformly distributed point clouds. ... | HC and Potamias et al. are the only baselines with shorter runtimes than our method, and obtain maximum Hausdorff distances comparable to those obtained by our approach. However, as discussed in Section 2, tuning the user-specified HC parameters make striking a balance between feature preservation and retaining a suffi... |
Since results and inference times for the Potamias et al. approach were provided by the author of the paper, we do not have knowledge of the exact details of their experimental setup, especially the time required in hours to train the model. As mentioned in Section 2, their learning-based approach demands huge dataset... | D |
Training on full resolution (FullRes):
We implemented a distributed version of the proposed architecture that splits the task to two GPUs if necessary. This allows for training directly on full resolution (2563superscript2563256^{3}256 start_POSTSUPERSCRIPT 3 end_POSTSUPERSCRIPT) data, given that the expensive speciali... | 2563superscript2563256^{3}256 start_POSTSUPERSCRIPT 3 end_POSTSUPERSCRIPT images, we distribute the model over 2 GPUs. The methods HalfRes and PatchDDM were trained on one GPU only.
The optimizer we used was AdamW [Loshchilov and Hutter(2017)] with the default parameters. | of 1×1×1\textmm3111\text𝑚superscript𝑚31\times 1\times 1\text{mm}^{3}1 × 1 × 1 italic_m italic_m start_POSTSUPERSCRIPT 3 end_POSTSUPERSCRIPT, resulting in a total scan size of 240×240×155240240155240\times 240\times 155240 × 240 × 155, which we padded to a size of 256×256×256256256256256\times 256\times 256256 × 25... | Training on full resolution (FullRes):
We implemented a distributed version of the proposed architecture that splits the task to two GPUs if necessary. This allows for training directly on full resolution (2563superscript2563256^{3}256 start_POSTSUPERSCRIPT 3 end_POSTSUPERSCRIPT) data, given that the expensive speciali... | For three spatial dimensions (i.e. 3D) this means that reducing the
input size from 2563superscript2563256^{3}256 start_POSTSUPERSCRIPT 3 end_POSTSUPERSCRIPT to 1283superscript1283128^{3}128 start_POSTSUPERSCRIPT 3 end_POSTSUPERSCRIPT results in a reduction | D |
To demonstrate the robustness of our proposed method across diverse levels of data heterogeneity, we vary the Dirichlet parameter σ∈{0.6,1.0,∞}𝜎0.61.0\sigma\!\in\!\{0.6,\\
1.0,\infty\}italic_σ ∈ { 0.6 , 1.0 , ∞ }, where with the descending of σ𝜎\sigmaitalic_σ, the degree of data heterogeneous increases as shown in Fi... | In the existing literature, a significant shortfall in the domain of adaptive FL pertains to the absence of rigorously theoretical analyses for the closed-form expression of the adaptive parameters and quantifying the model divergence. Our contribution contrasts with the prevailing research by effectively bridging this... | According to [38], other adaptive algorithms such as FedAdagrad and FedYogi are proposed to improve the model convergence rate under the situation of heterogeneous data. FedAdam employs adaptive learning rates and momentum by leveraging local updates from client devices to efficiently update the global model. FedAdagra... |
To demonstrate the effectiveness of our proposed algorithm and investigate whether the enhancements introduced by FedAgg remain consistent as the ratio of participating clients increases. Firstly, we partition the four benchmark datasets (i.e., MNIST, EMNIST-L, CIFAR-10, and CIFAR-100) into 100 clients and randomly se... | Nevertheless, in FL systems, the potential of adaptive learning rate-based algorithms in FL remains largely underexplored. Current literature often undervalues the pivotal role of the learning rate, a hyperparameter that requires meticulous tuning to accelerate the convergence speed and FL model performance. In Fig. 2,... | B |
We adopt CLIP (Radford et al., 2021) as the image encoder to extract multi-scale visual features, and leverage a simple bottleneck MLP layer as the learnable projection network. We keep other hyperparameters the same as the language instruction-following LLaMA-Adapter. For ScienceQA (Lu et al., 2022), we concatenate t... | Therein, prompt tuning appends a collection of trainable tokens to pre-trained large models, which are inserted either to the input embeddings (Lester et al., 2021; Liu et al., 2021b) or every intermediate layer (Li & Liang, 2021; Liu et al., 2021a).
LoRA (Hu et al., 2021; Zhang et al., 2023d; Hedegaard et al., 2022) i... | For zero-shot multi-modal evaluation, we select three benchmarks, MME (Fu et al., 2023), MMBench (Liu et al., 2023c), and LVLM-eHub (Xu et al., 2023), covering a wide range of VQA tasks. We compare with two concurrent multi-modal LLMs: LLaVA (Liu et al., 2023b) and MiniGPT-4 (Zhu et al., 2023).
|
Zero-shot Multi-modal Evaluation. To verify the out-of-domain generation ability of our approach, we conduct a two-stage multi-modal training, and then evaluate three benchmarks (MME (Fu et al., 2023), MMBench (Liu et al., 2023c), LVLM-eHub (Xu et al., 2023)) in a zero-shot manner. For the first stage, we utilize the ... | Multi-modal Reasoning.
Besides language instruction, our approach can also incorporate an image encoder via zero-initialized attention to become a multi-modal LLM. Compared to concurrent works (Liu et al., 2023b; Zhu et al., 2023), LLaMA-Adapter showcases higher tuning efficiency with competitive reasoning capacity on ... | B |
Vision language grounding. The goal of visual grounding (VG) is to locate the most relevant object or region in a visual input based on a natural language query (Fang et al., 2015; Rohrbach et al., 2016; Fukui et al., 2016; Ghiasi et al., 2022; Gupta et al., 2020). | Representations learned from large scale noisy datasets such as HowTo100M (Miech et al., 2019), WebVid (Bain et al., 2021), and VideoCC (Nagrani et al., 2022) have demonstrated great potentials in adapting to downstream tasks, including but not limited to text-video retrieval, video question answering, and video captio... | Video-language pre-training typically follows the pipeline: (1) encoding video and text pairs into latent representations, (2) modality fusion, and (3) pre-training on specific objectives.
Existing methods typically optimize these three components in the pre-training pipeline by designing expressive encoders (Bain et a... | Recently, visual grounding has been adapted to pre-training tasks in a self-supervised manner for open-vocabulary image segmentation (Ghiasi et al., 2022; Xu et al., 2022).
For example, OpenSeg (Ghiasi et al., 2022) semantically aligns a caption with extracted image regions via a grounding loss. |
Vision language grounding. The goal of visual grounding (VG) is to locate the most relevant object or region in a visual input based on a natural language query (Fang et al., 2015; Rohrbach et al., 2016; Fukui et al., 2016; Ghiasi et al., 2022; Gupta et al., 2020). | C |
We trained a different encoder for each model, as opposed to the single encoder we trained in all other experiments. This enables ContraSim to be used with representations with different dimensions. Results are summarized in Table 3. We report results with FAISS sampling. Across all pairs, ContraSim achieves superior r... |
Multilingual models, such as Multilingual-BERT (Devlin et al., 2019), learn to represent texts in different languages in the same representation space. Interestingly, these models show cross-lingual zero-shot transferability, where a model is fine-tuned in one language and evaluated in a different language (Pires et a... | They further found that two models trained on different image datasets (CIFAR-10 and CIFAR-100, Krizhevsky et al. 2009) learn representations that are similar in the shallow layers. Similar findings were noted for language models by Wu et al. (2020).
The latter also evaluated the effect of fine-tuning on language model... | In the image–caption benchmark (Figure 5), from the CKA results we might infer that
BERT representations are more similar to computer vision representations than GPT2 representations. That is because with CKA, it is easier to detect the matching image–caption pair with BERT than it is with GPT2. However, ContraSim achi... |
In the multilingual benchmark (Table 2, FAISS results), we found a much greater difference in accuracy between shallow and deep layers in ContraSim compared to previous similarity measures. Using previous similarity measures we might infer that there is no difference in the ability to detect the correct pairs across d... | D |
Figure 13: Error distribution of angles in our method using HRNet-W32 on the test sets of (a) SL-MH, (b) SL-PB, (c) SP360, and (d) HoliCity. Ground-truth and estimated angles are indicated on the horizontal and vertical axes, respectively. The diagonal red lines represent perfect estimation without angle errors. Each ... | To evaluate the error distribution of angles, we compared the estimated and ground-truth camera parameters. Figure 13 shows the error distribution for our method using HRNet-W32. Although a few estimated angles have angle errors, most estimated angles are plotted close to the diagonal lines in Figure 13. (Angles are pl... |
Figure 13: Error distribution of angles in our method using HRNet-W32 on the test sets of (a) SL-MH, (b) SL-PB, (c) SP360, and (d) HoliCity. Ground-truth and estimated angles are indicated on the horizontal and vertical axes, respectively. The diagonal red lines represent perfect estimation without angle errors. Each ... |
Label ambiguity also affects conventional methods in a Manhattan world. For example, it is often the case that three orthogonal directions can be estimated using the Gaussian sphere representation of VPs [74]; however, the representation does not regard the difference between front and back directions. For a fair comp... | In addition, we analyzed the error distribution of camera parameters: angles, focal length, and distortion coefficients. We divided the angle range into 10 equal intervals: [−90∘,−72∘],[−72∘,−54∘],…,[72∘,90∘]superscript90superscript72superscript72superscript54…superscript72superscript90[-90^{\circ},-72^{\circ}],~{}[-72... | A |
A matrix S∈\mathbbCn×n𝑆\mathbbsuperscript𝐶𝑛𝑛S\in{\mathbb C}^{n\times n}italic_S ∈ italic_C start_POSTSUPERSCRIPT italic_n × italic_n end_POSTSUPERSCRIPT is Schur if and only if, for each positive definite Q∈\mathbbCn×n𝑄\mathbbsuperscript𝐶𝑛𝑛Q\in{\mathbb C}^{n\times n}italic_Q ∈ italic_C start_POSTSUPERSCRIPT ... | The implication (i) ⟸⟸\Longleftarrow⟸ (ii) directly follows from the fact that (15) implies σ(Ak)⊆σ(Ae,k)𝜎subscript𝐴𝑘𝜎subscript𝐴𝑒𝑘\sigma(A_{k})\subseteq\sigma(A_{e,k})italic_σ ( italic_A start_POSTSUBSCRIPT italic_k end_POSTSUBSCRIPT ) ⊆ italic_σ ( italic_A start_POSTSUBSCRIPT italic_e , italic_k end_POSTSUBSC... | Moreover, referring to item (vi), in this case the vector p𝑝pitalic_p is not uniquely determined (up to rescaling) since there exist as many linearly independent eigenvectors as the geometric multiplicity of the zero eigenvalue.
In fact, any such selction of p𝑝pitalic_p is a valid one for item (vi) because, with disc... | To show the equivalence of the six statements in Theorem 1, the proof is structured as follows. We first prove the equivalence among statements (i), (ii) and (iii). Then, we prove the following chain of implications:
(iii) ⟹⟹\Longrightarrow⟹ (iv), followed by (iv) ⟹\implies⟹ (v), (v) ⟹\implies⟹ (vi), and finally (vi) ⟹... | Hence, as a consequence of Perron-Frobenius theory, the dominant eigenvalue μ0subscript𝜇0\mu_{0}italic_μ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT of M𝑀Mitalic_M is real and associated with left and right eigenvectors having non-negative elements (Luenberger, 1979, Chapter 6.5, Theorem 1).
In view of Gershgorin’s Circl... | C |
Software engineering failures inform development and maintenance (Petroski et al., 1994; Anandayuvaraj and Davis, 2023; Amusuo et al., 2022).
Previous failure analyses of DL interoperability software focused on the “Development” and “Runtime” components of Figure 1. | We used the HFTorrent dataset from Jiang et al. (Jiang et al., 2023).
At time of experiment, this was the largest available set of real-world DL models, containing 63,182 pre-trained models collected from the HuggingFace model registry.111Future measurements could use the PeaTMOSS dataset (Jiang et al., 2024b) or its s... | Software engineering failures inform development and maintenance (Petroski et al., 1994; Anandayuvaraj and Davis, 2023; Amusuo et al., 2022).
Previous failure analyses of DL interoperability software focused on the “Development” and “Runtime” components of Figure 1. | Deep Learning (DL) achieves state-of-the-art performance in many domains (Grigorescu et al., 2020; Kim et al., 2019).
Software engineers engage in many activities for deep learning, including developing, re-using, fine-tuning, and deploying DL models (Amershi et al., 2019; Han et al., 2021; Jiang et al., 2023, 2024a). | Louloudakis et al. studied behavioral issues resulting from framework-to-framework conversion (Louloudakis et al., 2023a).
They found failures in 10 out of 36 conversions. They created a fault localization and repair pipeline to localize and fix discrepancies (Louloudakis et al., 2023b). | D |
In order to control an unmanned aerial vehicle (UAV) autonomously, there are two complementary parts: the Flight Control Unit (FCU), systems that focus on low-level control of the aircraft, allowing it to fly stably, and the high-level control frameworks that are responsible for providing further autonomy to the vehicl... | To facilitate the implementation of different aerial platforms, Aerostack2 incorporates an AerialPlatform abstract class responsible for managing the capabilities associated with the direct integration of various aerial platforms into the framework. This abstraction facilitates the integration of new platforms into the... |
FCUs can be classified into two blocks: generic or embedded, each presenting distinct advantages and limitations. Generic FCUs offer versatility, accommodating various frames and components for customizable configurations, which is beneficial for developers. However, their integration and calibration require technical... | In 2018 Ebeid et al. presented a survey of open-source hardware and software comparing their main features [7]. In Table I some relevant flight controller projects are listed. These projects may cover both hardware and software development of these controllers. They range from Open Source Hardware (OSH) and Open Source... |
In this case, the objective is to present all the information in a graphical and simple way so that non-developers can use and interact with the aerial system. In this category of components, Aerostack2 also provides a Graphical User Interface (GUI) to use the software framework through a web-based application. This t... | B |
While a higher degree of novelty is unnecessary for claiming protection, it might be crucial for other legal aspects. In particular, LLMs are trained in a supervised fashion on real data, which also include protected works (Bandy and Vincent, 2021). Apart from questions upon the legitimacy of such training (Franceschel... | However, we must remind that current LLMs are not as reliable as humans, e.g., they cannot verify their information and they can propagate biases from training data. In addition, the quality of the output strictly depends on the prompt, which might in turn demand human skills and more time. Writers can be threatened as... |
Whether or not LLM works obtain protection, we believe their societal impact will be tremendous (see also Newton and Dhole (2023)). We have a positive view in terms of the applications of LLMs, but there are intrinsic risks related to their adoption. It is apparent that since LLMs are able to write articles or short s... | In this paper, we have discussed whether or not LLMs can actually be deemed as creative; we started by considering Boden’s three criteria, i.e., value, novelty, and surprise. While LLMs are capable of value and a weak version of novelty and surprise, their inner autoregressive nature seems to prevent them from reaching... | Value refers to utility, performance, and attractiveness (Maher, 2010). It is also related to both the quality of the output, and its acceptance by society. Due to the large impact LLMs are already having (Bommasani et al., 2021) and the quality of outputs of the systems based on them (Stevenson et al., 2022b), it is p... | B |
More recently, to better exploit the 3D spatial information of CT images, many studies focus on using the 3D CNNs, such as [27, 28, 29, 30, 1, 31, 32, 33, 2, 34, 35, 36]. The famous NoduleNet [1] is an end-to-end 3D deep CNN framework, which achieves the nodule detection, false positive reduction, and nodule segmentati... |
Deep learning has achieved remarkable success in various object detection tasks. In the medical field, deep networks are able to reach clinical expert-level performance, e.g. pulmonary nodule detection [1, 2], etc. Nonetheless, these networks are usually domain-specific. In other words, they work well when the trainin... | Source-free unsupervised domain adaptation (SFUDA) denotes the setting of adapting to the target domain given only a well-trained source model and unlabeled target data. One stream of the SFUDA methods is implicitly aligning the feature distribution of the source and target domain using the generative adversarial netwo... |
Nonetheless, these works mainly focus on the shifts between the source and target, and neglect the detection’s characteristics. For instance, the discrimination of the foreground objects and the backgrounds can naturally be an auxiliary supervision for the target data. Besides, the relatively smaller size of the nodul... | Unsupervised domain adaptation (UDA) is a practical setting where the labeled source data are provided for adapting to the unlabeled target data. Most existing methods adopt feature alignment for UDA object detection. In [3], the authors build image-level and instance-level domain classifiers to implement feature align... | D |
Theorem 4.3 shows that the gauge map is differentiable with respect to the output of the neural layers, and hence enables the computation of backpropagation gradients in (13) and the training of the architecture in Fig. 1.
In the next section, we validate the effectiveness of the proposed learning architecture on a mod... | For concreteness, we specifically consider two widely used formulations of the two-stage DCOPF problem, risk-limiting dispatch (RLD) [5] and reserve scheduling [27]. Both are two-stage stochastic linear programs with recourse, and both highlight the structure and difficulty of two-stage problems.
| There are two types of data in our algorithm.
The first type is the load forecasts. They are inputs to the learning algorithm and comprise the datasets on which we train and test the network architecture. In both application contexts, the training dataset consists of 50000500005000050000 load forecasts and testing data... |
In this section, we provide the experimental results of using the proposed algorithm in Table I to solve two-stage DCOPF problems. Particularly, we consider two application contexts, namely, the risk-limiting dispatch and reserve scheduling problems on two systems, the IEEE 118-bus system [52] and a 2000-bus syntheti... | In this paper, we overcome the challenge in policy design and solve two-stage DCOPF problems by presenting a neural network (NN)-based architecture that is computationally efficient and also guarantees the feasibility of learned solutions. In particular, our architecture involves two neural networks, one each for the f... | C |
We showed our approach incorporates unlabelled data into the downstream task prior predictive distribution (Eq. 2). We also argued that, as the generated contrastive data encodes our beliefs about the semantic similarity of different image pairs, incorporating the unlabelled data should improve the functional prior. We... |
Graphical Evaluation. First, we visualise the BNN and self-supervised BNN prior predictive (Fig. 1 and 3). The standard BNN prior predictive reflects a belief that all three image pair groups are similarly likely to have the same label, and thus does not capture semantic information well. In contrast, the self-superv... |
We then further demonstrate that self-supervised BNN prior predictives reflect input-pair semantic similarity better than normal BNN priors (§4). To do so, we develop a methodology to better understand the prior predictive distributions of BNNs. Our approach is to measure the probability of pairs of data points having... |
The basis for our approach is to note that, intuitively, a suitable prior should reflect a belief that the higher the semantic similarity between pairs of inputs, the more likely these inputs are to have the same label. Therefore, rather than inspecting the prior predictive at single points in input space, we examine ... |
To compute our proposed metric, we consider different groups of input pairs. Each group is comprised of input pairs with known semantic similarity. For example, for image data, we could use images of the same class as a group with high semantic similarity, and image pairs from different classes as a group with lower s... | C |
𝔻Tmax:=maxrw(r)maxkVT(r)−1|U(k/T,r)|,assignsubscriptsuperscript𝔻max𝑇subscript𝑟𝑤𝑟subscript𝑘subscript𝑉𝑇superscript𝑟1𝑈𝑘𝑇𝑟\mathbb{D}^{\text{max}}_{T}:=\max_{r}w(r)\max_{k}{V_{T}({r})}^{-1}|U(k/T,r)|,blackboard_D start_POSTSUPERSCRIPT max end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_T end_POSTSUBSCRIP... | the process changes over time. Within this setting, we address fundamental questions and provide the groundwork for meaningful inference on invariants that capture shape of the latent process via point clouds. We explain the general nature of the shape descriptors that fit into our framework, show what
distributional p... | The finite sample performance and the presence of outliers is particularly relevant in our context since genomic data applications are typically in the regime of T<100𝑇100T<100italic_T < 100 and n<10K𝑛10𝐾n<10Kitalic_n < 10 italic_K.
In Section 4.2.1, we elaborate on this and introduce a data-adaptive function that ... | However, the cdf is time-dependent under the alternative and an aggregrate F𝐹Fitalic_F at most reflects the average distribution pattern.
To construct the weight function, we need an empirical version of the most suitable choice for F𝐹Fitalic_F in our case. For this, we use the time-averaged empirical cdf |
Yet the ability to model, analyze and predict the evolution over time of the geometric features of data is of paramount interest in many applications. For example, cell differentiation can be studied by analyzing time series of single-cell mRNA expression data (scRNA); a core problem here is to quantify changes in gen... | B |
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