Miracle-dz/UniFAR-FTUs huggingface dataset:
PlaneMatch : Patch Coplanarity Prediction for Robust RGB-D Registration Supplemental Material

– Section 2 provides an overview of the dataset of our coplanarity benchmark (COP). – Section 3 gives more evaluation results for our coplanarity network, including a comparison of different masking schemes (Section 3.1), evaluation on patch pairs proposed from real cases of scene reconstruction (Section 3.2), and visual qualitative results of coplanarity matching (Section 3.3). – Section 4 provides more evaluations of the reconstruction algorithm. Specifically, we evaluate the robustness of the registration against the initial ratio of incorrect pairs (Section 4.1), and we show more visual results of reconstructions for scenes from various datasets. – Section 5 discusses the limitations of our method. – Finally, Section 6 provides the formulation for a variatnt of our method that only utilizes coplanarity constraints (Section 6.1), the optimization procedure used for that variant (Section 6.2), and the stability analysis used for achieving a robust optimization in that variant (Section 6.3).
Analytic constraints on gamma-ray burst luminosity functions

The brightness distribution of detected gamma-ray bursts enables constraints to be placed on their luminosities; specifically, analyses by previous authors have demonstrated that the range of luminosity from which approximately 90% of the observed bursts are drawn is very likely less than an order of magnitude. It has also been demonstrated that when power-law functional forms with infinite ranges of luminosity (a.) from 0 to Lmax or (b.) from Lmin to ∞ are employed, it is necessary (but perhaps not sufficient) to restrict the power-law index β 2.5, respectively, in order to obtain consistency with the observed brightness distribution. Similarly, these previous works have demonstrated that when 1.8<β<2.5, the range of the burst luminosity function must be restricted and cannot be arbitrarily large. We present here analytic derivations of these results valid for any spatial density function and for both Euclidean and cosmological scenarios. This analysis shows that the limiting values of β are si.
A Static condensation Reduced Basis Element method : approximation and a posteriori error estimation

We propose a new reduced basis element-cum-component mode synthesis approach for parametrized elliptic coercive partial differential equations. In the Offine stage we construct a Library of interoperable parametrized reference components relevant to some family of problems; in the Online stage we instantiate and connect reference components (at ports) to rapidly form and query parametric systems. The method is based on static condensation at the interdomain level, a conforming eigenfunction “port” representation at the interface level, and finally reduced basis (RB) approximation of finite element (FE) bubble functions at the intradomain level. We show under suitable hypotheses that the RB Schur complement is close to the FE Schur complement: we can thus demonstrate the stability of the discrete equations; furthermore, we can develop inexpensive and rigorous (system-level) a posteriori error bounds. We present numerical results for model heat transfer and elasticity problems with particular emphasis on the Online stage; we discuss flexibility, accuracy, computational performance, and also the effectivity of the a posteriori error bounds. 1991 Mathematics Subject Classification. 35J25, 65N30, 65D99. The dates will be set by the publisher.
The linearisation of a simple mechanical control system

A geometric interpretation is given for the linearisation of a mechanical control not considered in this early work was that when the linearisation of the system was actually controllable. In this paper, this special case is considered, and as a consequence, the usual controllability condition for linear systems is given an interpretation involving the geometry inherent in simple mechanical control systems. Other work on controllability of the linearisation of mechanical systems includes (Hughes and Skelton 1980) and (Laub and Arnold 1985). In both of these papers, the emphasis was on the algebraic, rather than the geometric structure of the linearisation.
Experimental Observation of Topologically Protected Helical Edge Modes in Patterned Elastic Plates

Topologically protected waves in classical media provide unique opportunities for one-way wave transport and immunity to defects. Contrary to acoustics and electromagnetics, their observation in elastic solids has so far been elusive because of the presence of multiple modes and their tendency to hybridize at interfaces. Here, we report on the experimental investigation of topologically protected helical edge modes in elastic plates patterned with an array of triangular holes, along with circular holes that produce an accidental degeneracy of two Dirac cones. Such a degeneracy is subsequently lifted by careful breaking of the symmetry along the thicknessdirection,whichemulatesthespinorbitalcouplinginthequantumspinHalleffect.Thejoiningoftwo plates that are mirror-symmetric copies of each other about the plate midthickness introduces a nontrivial interface that supports helical edgewaves. The experimental observation of these topologically protected wave modes in elastic continuous plates opens avenues for the practical realization of structural components with topologically nontrivial waveguiding properties and their application to elastic waveguiding and confinement.
Temporal Graph Functional Dependencies - Technical Report

We propose a class of functional dependencies for temporal graphs, called TGFDs . TGFDs capture both attribute-value dependencies and topological structures of entities over a valid period of time in a temporal graph. It subsumes graph functional dependencies ( GFDs ) and conditional functional dependencies ( CFDs ) as a special case. We study the foundations of TGFDs including sat-isﬁability, implication and validation. We show that the satisﬁability and validation problems are coNP -complete and the implication problem is NP -complete. We also present an axiomatization of TGFDs and provide the proof of the soundness and completeness of the axiomatization.
H ELIX -MO: S AMPLE -E FFICIENT M OLECULAR O PTIMIZATION ON S CENE -S ENSITIVE L ATENT S PACE

Efﬁcient exploration of the chemical space to search the candidate drugs that satisfy various constraints is a fundamental task of drug discovery. Although many excellent deep molecular generative methods have been proposed to produce promising molecules, applying these methods in practice is still challenging since a great number of assessed molecules (samples) are required to provide the optimization direction, which is a considerable expense for drug discovery. To this end, we design a sample-efﬁcient molecular generative method, namely Helix-MO, which can fast adapt to particular optimization scenes with only a small number of assessed samples. Helix-MO explores the chemical space in a scene-sensitive latent space, dynamically ﬁne-tuned by multiple kinds of learning tasks from multiple perspectives. The learning tasks encourage the model to focus on modeling the more promising molecules during the optimization process to promote sample efﬁciency. Extensive experiments demonstrate that Helix-MO can achieve competitive performance with only a few assessed samples on four molecular optimization scenes. Ablation studies verify the impact of the learning tasks in the scene-speciﬁc latent space, efﬁciently identifying the critical characters of the satisfactory molecules. We also deployed Helix-MO on the website PaddleHelix ( https: //paddlehelix.baidu.com/app/drug/drugdesign/forecast ) to provide drug design service and apply it to produce inhibitors of a kinase to demonstrate its practicability.
Learning to Repeat: Fine Grained Action Repetition for Deep Reinforcement Learning

Reinforcement Learning algorithms can learn complex behavioral patterns for sequential decision making tasks wherein an agent interacts with an environment and acquires feedback in the form of rewards sampled from it. Traditionally, such algorithms make decisions, i.e., select actions to execute, at every single time step of the agent-environment interactions. In this paper, we propose a novel framework, Fine Grained Action Repetition (FiGAR), which enables the agent to decide the action as well as the time scale of repeating it. FiGAR can be used for improving any Deep Reinforcement Learning algorithm which maintains an explicit policy estimate by enabling temporal abstractions in the action space. We empirically demonstrate the efficacy of our framework by showing performance improvements on top of three policy search algorithms in different domains: Asynchronous Advantage Actor Critic in the Atari 2600 domain, Trust Region Policy Optimization in Mujoco domain and Deep Deterministic Policy Gradients in the TORCS car racing domain.
Syntactic Vs. Semantic similarity of Artificial and Real Faults in Mutation Testing Studies

Fault seeding is typically used in controlled studies to evaluate and compare test techniques. Central to these techniques lies the hypothesis that artificially seeded faults involve some form of realistic properties and thus provide realistic experimental results. In an attempt to strengthen realism, a recent line of research uses advanced machine learning techniques, such as deep learning and Natural Language Processing (NLP), to seed faults that look like (syntactically) real ones, implying that fault realism is related to syntactic similarity. This raises the question of whether seeding syntactically similar faults indeed results in semantically similar faults and more generally whether syntactically dissimilar faults are far away (semantically) from the real ones. We answer this question by employing 4 fault-seeding techniques (PiTest - a popular mutation testing tool, IBIR - a tool with manually crafted fault patterns, DeepMutation - a learning-based fault seeded framework and CodeBERT - a novel mutation testing tool that use code embeddings) and demonstrate that syntactic similarity does not reflect semantic similarity. We also show that 60%, 47%, 43%, and 7% of the real faults of Defects4J V2 are semantically resembled by CodeBERT, PiTest, IBIR, and DeepMutation faults. We then perform an objective comparison between the techniques and find that CodeBERT and PiTest have similar fault detection capabilities that subsume IBIR and DeepMutation, and that IBIR is the most cost-effective technique. Moreover, the overall fault detection of PiTest, CodeBERT, IBIR, and DeepMutation was, on average, 54%, 53%, 37%, and 7%.
Distributed Stochastic Optimization via Correlated Scheduling

This paper considers a problem where multiple devices make repeated decisions based on their own observed events. The events and decisions at each time-step determine the values of a utility function and a collection of penalty functions. The goal is to make distributed decisions over time to maximize time-average utility subject to time-average constraints on the penalties. An example is a collection of power-constrained sensors that repeatedly report their own observations to a fusion center. Maximum time-average utility is fundamentally reduced because devices do not know the events observed by others. Optimality is characterized for this distributed context. It is shown that optimality is achieved by correlating device decisions through a commonly known pseudo-random sequence. An optimal algorithm is developed that chooses pure strategies at each time-step based on a set of time-varying weights.
Revisiting the Arcade Learning Environment: Evaluation Protocols and Open Problems for General Agents (Extended Abstract)

The Arcade Learning Environment (ALE) is an evaluation platform that poses the challenge of building AI agents with general competency across dozens of Atari 2600 games. It supports a variety of different problem settings and it has been receiving increasing attention from the scientific community. In this paper we take a big picture look at how the ALE is being used by the research community. We focus on how diverse the evaluation methodologies in the ALE have become and we highlight some key concerns when evaluating agents in this platform. We use this discussion to present what we consider to be the best practices for future evaluations in the ALE. To further the progress in the field, we also introduce a new version of the ALE that supports multiple game modes and provides a form of stochasticity we call sticky actions.
Learning Equilibria in Matching Markets with Bandit Feedback

Large-scale, two-sided matching platforms must find market outcomes that align with user preferences while simultaneously learning these preferences from data. Classical notions of stability (Gale and Shapley, 1962; Shapley and Shubik, 1971) are, unfortunately, of limited value in the learning setting, given that preferences are inherently uncertain and destabilizing while they are being learned. To bridge this gap, we develop a framework and algorithms for learning stable market outcomes under uncertainty. Our primary setting is matching with transferable utilities, where the platform both matches agents and sets monetary transfers between them. We design an incentive-aware learning objective that captures the distance of a market outcome from equilibrium. Using this objective, we analyze the complexity of learning as a function of preference structure, casting learning as a stochastic multi-armed bandit problem. Algorithmically, we show that “optimism in the face of uncertainty,” the principle underlying many bandit algorithms, applies to a primal-dual formulation of matching with transfers and leads to near-optimal regret bounds. Our work takes a first step toward elucidating when and how stable matchings arise in large, data-driven marketplaces.
Active Anomaly Detection in Heterogeneous Processes

An active inference problem of detecting an anomalous process among $M$ heterogeneous processes is considered. At each time, a subset of processes can be probed. The objective is to design a sequential probing strategy that dynamically determines which processes to observe at each time and when to terminate the search so that the expected detection time is minimized under a constraint on the probability of misclassifying any process. This problem falls into the general setting of sequential design of experiments pioneered by Chernoff in 1959, in which a randomized strategy, referred to as the Chernoff test, was proposed and shown to be asymptotically optimal as the error probability approaches zero. For the problem considered in this paper, a low-complexity deterministic test is shown to enjoy the same asymptotic optimality while offering significantly better performance in the finite regime and faster convergence to the optimal rate function, especially when the number of processes is large. Furthermore, the proposed test offers considerable reduction in implementation complexity.
Discrimination of Density and Clustering on Four Versions of a Stochastic Display

A number of studies have used stochastically generated visual displays to study detection and discrimination of differences in pattern texture. As in this study, the texture is controlled by a Markov chain paradigm in one or more dimensions. Texture differences are generated either within a given pattern, or between two patterns which are presented simultaneously or sequentially. Other parameters of the display are held constant (e.g., positive and negative images) and therefore not explored. This study investigates the interaction of two texture variables, density and clustering, with the display parameters of positive/negative image and adjancency/separation of texture images. Stimulus display patterns were generated using a two dimensional Markov process to control density and clustering, and were put on 35mm film. Stimuli were presented on a rear projection display, and subjects were required to determine the sameness or difference of the two halves of the display. The major findings of the study are: (1) Performance on the four versions of the display are not equivalent and differ significantly in some respects; (2) Performance on detecting differences in density and in clustering are consistent with earlier studies; and (3) A sharp discontinuity in performance level as a function of the magnitude of standard/variable difference is present for small differences. The findings of this study raise questions as to the generalization of texture data among similar but not identical displays. The presence of the low level discontinuity is also of interest in the interpretation of this data in terms of the theory of signal detectability and the use of the classical ogive. From the application viewpoint, the non-equivalence of the display variants and the presence of the discontinuity may be of significance to problems of target detection on sonar and radar displays.
Social Processes: Self-Supervised Forecasting of Nonverbal Cues in Social Conversations

The default paradigm for the forecasting of human behavior in social conversations is characterized by top-down approaches. These involve identifying predictive relationships between low level nonverbal cues and future semantic events of interest (e.g. turn changes, group leaving). A common hurdle however, is the limited availability of labeled data for supervised learning. In this work, we take the ﬁrst step in the direction of a bottom-up self-supervised approach in the domain. We formulate the task of Social Cue Forecasting to leverage the larger amount of unlabeled low-level behavior cues, and characterize the modeling challenges involved. To address these, we take a meta-learning approach and propose the Social Process (SP) models—socially aware sequence-to-sequence (Seq2Seq) models within the Neural Process (NP) family. SP models learn extractable representations of non-semantic future cues for each participant, while capturing global uncertainty by jointly reasoning about the future for all members of the group. Evaluation on synthesized and real-world behavior data shows that our SP models achieve higher log-likelihood than the NP baselines, and also highlights important considerations for applying such techniques within the domain of social human interactions.
Control Theory: The Double Pendulum Inverted on a Cart

In this thesis the Double Pendulum Inverted on a Cart (DPIC) system is modeled using the Euler-Lagrange equation for the chosen Lagrangian, giving a second-order nonlinear system. This system can be approximated by a linear first-order system in which linear control theory can be used. The important definitions and theorems of linear control theory are stated and proved to allow them to be utilized on a linear version of the DPIC system. Controllability and eigenvalue placement for the linear system are shown using MATLAB. Linear Optimal control theory is likewise explained in this section and its uses are applied to the DPIC system to derive a Linear Quadratic Regulator (LQR). Two different LQR controllers are then applied to the full nonlinear DPIC system, which is concurrently modeled in MATLAB. Also, an in-depth look is taken at the Riccati equation and its solutions. Finally, results from various MATLAB simulations are shown.
Turbulence attenuation in particle-laden flow in smooth and rough channels

Results of point-particle direct numerical simulations of downward gas–solid flow in smooth and rough vertical channels are presented. Two-way coupling and inter-particle collisions are included. The rough walls are shaped as fixed layers of tiny spherical particles with diameter much smaller than the viscous wall unit. The turbulence attenuation induced by the free solid particles in the gas flow is shown to be enhanced with increasing wall roughness. The so-called feedback force, the force exerted by the free particles on the gas, is decomposed into three contributions: the domain average of the mean feedback force, the non-uniform part of the mean feedback force and the fluctuating part of the feedback force. Since the non-uniformity of the mean feedback force increases with wall roughness, the effect of the non-uniform part of the mean feedback force is investigated in detail. For both smooth and rough walls, the non-uniform part of the mean feedback force is shown to contribute significantly to the particle-induced turbulence attenuation.
Definably compact groups definable in real closed fields. I

We study definably compact definably connected groups definable in a sufficiently saturated real closed field $R$. We introduce the notion of group-generic point for $\bigvee$-definable groups and show the existence of group-generic points for definably compact groups definable in a sufficiently saturated o-minimal expansion of a real closed field. We use this notion along with some properties of generic sets to prove that for every definably compact definably connected group $G$ definable in $R$ there are a connected $R$-algebraic group $H$, a definable injective map $\phi$ from a generic definable neighborhood of the identity of $G$ into the group $H\left(R\right)$ of $R$-points of $H$ such that $\phi$ acts as a group homomorphism inside its domain. This result is used in [2] to prove that the o-minimal universal covering group of an abelian connected definably compact group definable in a sufficiently saturated real closed field $R$ is, up to locally definable isomorphisms, an open connected locally definable subgroup of the o-minimal universal covering group of the $R$-points of some $R$-algebraic group.
Comparative study of sampling strategies for sparse photon multispectral lidar imaging: towards mosaic filter arrays

In this paper, we investigate the recovery of range and spectral profiles associated with remote three-dimensional scenes sensed via single-photon multispectral lidar (MSL). We consider two different spatial/spectral sampling strategies and compare their performance for a similar overall number of detected photons. For a regular spatial grid of pixels, the first strategy consists of sampling all the spatial locations of the grid for each of the L wavelengths. The second strategy is consistent with the use of mosaic filter-based arrays and consists of acquiring only one wavelength (out of L) per spatial location. Despite the reduction of spectral content observed in each location, the second strategy has clear potential advantages for fast multispectral imaging using only a single frame read out. We propose a fully automated computational method, adapted for each of the two sampling strategies in order to recover the target range profile, as well as the reflectivity profiles associated with the different wavelengths. These strategies were also assessed with high ambient background. The performance of the two sampling strategies is illustrated using a single-photon MSL system with L = 4 wavelengths (473, 532, 589 and 640 nm). The results presented demonstrate that although the first strategy usually provides more accurate results, the second strategy does not exhibit a significant performance degradation, particularly for sparse photon data (down to 1 photon per pixel on average). These results suggest a way forward for the integration of single-photon detector arrays with mosaic filters for use in a range of emerging photon-starved two-dimensional and three-dimensional imaging applications.