Miracle-dz/UniFAR-FTUs huggingface dataset:
Representing Robot Geometry as Distance Fields: Applications to Whole-body Manipulation

In this work, we propose a novel approach to represent robot geometry as distance fields (RDF) that extends the principle of signed distance fields (SDFs) to articulated kinematic chains. Our method employs a combination of Bernstein polynomials to encode the signed distance for each robot link with high accuracy and efficiency while ensuring the mathematical continuity and differentiability of SDFs. We further leverage the kinematics chain of the robot to produce the SDF representation in joint space, allowing robust distance queries in arbitrary joint configurations. The proposed RDF representation is differentiable and smooth in both task and joint spaces, enabling its direct integration to optimization problems. Additionally, the 0-level set of the robot corresponds to the robot surface, which can be seamlessly integrated into whole-body manipulation tasks. We conduct various experiments in both simulations and with 7-axis Franka Emika robots, comparing against baseline methods, and demonstrating its effectiveness in collision avoidance and whole-body manipulation tasks. Project page: https://sites.google. com/view/lrdf/home
Induced subgraph density. II. Sparse and dense sets in cographs

A well-known theorem of R\"odl says that for every graph $H$, and every $\epsilon>0$, there exists $\delta>0$ such that if $G$ does not contain an induced copy of $H$, then there exists $X\subseteq V(G)$ with $|X|\ge\delta|G|$ such that one of $G[X],\overline{G}[X]$ has edge-density at most $\epsilon$. But how does $\delta$ depend on $\epsilon$? Fox and Sudakov conjectured that the dependence can be taken to be polynomial: for all $H$ there exists $c>0$ such that for all $\epsilon\in(0,1/2)$, R\"odl's theorem holds with $\delta=\epsilon^c$. This conjecture implies the Erd\H{o}s-Hajnal conjecture, and until now it had not been verified for any non-trivial graphs $H$. Our first result shows that it is true when $H=P_4$ (indeed, we can take $\delta=\epsilon$, and insist that one of $G[X],\overline{G}[X]$ has maximum degree at most $\epsilon^2|G|$). ) We will generalize this, and to do so, we need to work with an even stronger property. Let us say $H$ is {\em viral} if there exists $c>0$ such that for all $\epsilon\in(0,1/2)$, if $G$ contains at most $\epsilon^c|G|^{|H|}$ induced copies of $H$, then there exists $X\subseteq V(G)$ with $|X|\ge \epsilon^c|G|$ such that one of $G[X],\overline{G}[X]$ has density at most $\epsilon$. We will show that $P_4$ is viral, using a ``polynomial $P_4$-removal lemma'' of Alon and Fox. We will also show that viral graphs are closed under vertex-substitution, and so all graphs that can be obtained by substitution from copies of $P_4$ are viral. (In a subsequent paper, it will be shown that all graphs currently known to satisfy the Erd\H{o}s-Hajnal conjecture are in fact viral.) Finally, we give a different strengthening of R\"odl's theorem: we show that if $G$ does not contain an induced copy of $P_4$, then its vertices can be partitioned into at most $480\epsilon^{-4}$ subsets $X$ such that one of $G[X],\overline{G}[X]$ has density at most $\epsilon$.
A simpler and parallelizable O(√log n)-approximation algorithm for Sparsest Cut

Currently, the best known tradeoff between approximation ratio and complexity for the Sparsest Cut problem is achieved by the algorithm in [Sherman, FOCS 2009]: it computes $O(\sqrt{(\log n)/\varepsilon})$-approximation using $O(n^\varepsilon\log^{O(1)}n)$ maxflows for any $\varepsilon\in[\Theta(1/\log n),\Theta(1)]$. It works by solving the SDP relaxation of [Arora-Rao-Vazirani, STOC 2004] using the Multiplicative Weights Update algorithm (MW) of [Arora-Kale, JACM 2016]. To implement one MW step, Sherman approximately solves a multicommodity flow problem using another application of MW. Nested MW steps are solved via a certain ``chaining'' algorithm that combines results of multiple calls to the maxflow algorithm. We present an alternative approach that avoids solving the multicommodity flow problem and instead computes ``violating paths''. This simplifies Sherman's algorithm by removing a need for a nested application of MW, and also allows parallelization: we show how to compute $O(\sqrt{(\log n)/\varepsilon})$-approximation via $O(\log^{O(1)}n)$ maxflows using $O(n^\varepsilon)$ processors. We also revisit Sherman's chaining algorithm, and present a simpler version together with a new analysis.
Optimal designs for multivariate logistic mixed models with longitudinal data

ABSTRACT This paper considers the optimal design problem for multivariate mixed-effects logistic models with longitudinal data. A decomposition method of the binary outcome and the penalized quasi-likelihood are used to obtain the information matrix. The D-optimality criterion based on the approximate information matrix is minimized under different cost constraints. The results show that the autocorrelation coefficient plays a significant role in the design. To overcome the dependence of the D-optimal designs on the unknown fixed-effects parameters, the Bayesian D-optimality criterion is proposed. The relative efficiencies of designs reveal that both the cost ratio and autocorrelation coefficient play an important role in the optimal designs.
ClipSitu: Effectively Leveraging CLIP for Conditional Predictions in Situation Recognition

Situation Recognition is the task of generating a structured summary of what is happening in an image using an activity verb and the semantic roles played by actors and objects. In this task, the same activity verb can describe a diverse set of situations as well as the same actor or object category can play a diverse set of semantic roles depending on the situation depicted in the image. Hence a situation recognition model needs to understand the context of the image and the visual-linguistic meaning of semantic roles. Therefore, we leverage the CLIP foundational model that has learned the context of images via language descriptions. We show that deeper-and-wider multi-layer perceptron (MLP) blocks obtain noteworthy results for the situation recognition task by using CLIP image and text embedding features and it even outperforms the state-of-the-art CoFormer, a Transformer-based model, thanks to the external implicit visual-linguistic knowledge encapsulated by CLIP and the expressive power of modern MLP block designs. Motivated by this, we design a cross-attention-based Transformer using CLIP visual tokens that model the relation between textual roles and visual entities. Our cross-attention-based Transformer known as ClipSitu XTF outperforms existing state-of-the-art by a large margin of 14.1\% on semantic role labelling (value) for top-1 accuracy using imSitu dataset. {Similarly, our ClipSitu XTF obtains state-of-the-art situation localization performance. } We will make the code publicly available.
Is Risk-Sensitive Reinforcement Learning Properly Resolved?

Due to the nature of risk management in learning applicable policies, risk-sensitive reinforcement learning (RSRL) has been realized as an important direction. RSRL is usually achieved by learning risk-sensitive objectives characterized by various risk measures, under the framework of distributional reinforcement learning. However, it remains unclear if the distributional Bellman operator properly optimizes the RSRL objective in the sense of risk measures. In this paper, we prove that the existing RSRL methods do not achieve unbiased optimization and can not guarantee optimality or even improvements regarding risk measures over accumulated return distributions. To remedy this issue, we further propose a novel algorithm, namely Trajectory Q-Learning (TQL), for RSRL problems with provable convergence to the optimal policy. Based on our new learning architecture, we are free to introduce a general and practical implementation for different risk measures to learn disparate risk-sensitive policies. In the experiments, we verify the learnability of our algorithm and show how our method effectively achieves better performances toward risk-sensitive objectives.
iMETRE: Incorporating Markers of Entity Types for Relation Extraction

Sentence-level relation extraction (RE) aims to identify the relationship between 2 entities given a contextual sentence. While there have been many attempts to solve this problem, the current solutions have a lot of room to improve. In this paper, we approach the task of relationship extraction in the financial dataset REFinD. Our approach incorporates typed entity markers representations and various models finetuned on the dataset, which has allowed us to achieve an F1 score of 69.65% on the validation set. Through this paper, we discuss various approaches and possible limitations.
Review helps learn better: Temporal Supervised Knowledge Distillation

Reviewing plays an important role when learning knowledge. The knowledge acquisition at a certain time point may be strongly inspired with the help of previous experience. Thus the knowledge growing procedure should show strong relationship along the temporal dimension. In our research, we find that during the network training, the evolution of feature map follows temporal sequence property. A proper temporal supervision may further improve the network training performance. Inspired by this observation, we propose Temporal Supervised Knowledge Distillation (TSKD). Specifically, we extract the spatiotemporal features in the different training phases of student by convolutional Long Short-term memory network (Conv-LSTM). Then, we train the student net through a dynamic target, rather than static teacher network features. This process realizes the refinement of old knowledge in student network, and utilizes it to assist current learning. Extensive experiments verify the effectiveness and advantages of our method over existing knowledge distillation methods, including various network architectures and different tasks (image classification and object detection) .
DECOR: Degree-Corrected Social Graph Refinement for Fake News Detection

Recent efforts in fake news detection have witnessed a surge of interest in using graph neural networks (GNNs) to exploit rich social context. Existing studies generally leverage fixed graph structures, assuming that the graphs accurately represent the related social engagements. However, edge noise remains a critical challenge in real-world graphs, as training on suboptimal structures can severely limit the expressiveness of GNNs. Despite initial efforts in graph structure learning (GSL), prior works often leverage node features to update edge weights, resulting in heavy computational costs that hinder the methods' applicability to large-scale social graphs. In this work, we approach the fake news detection problem with a novel aspect of social graph refinement. We find that the degrees of news article nodes exhibit distinctive patterns, which are indicative of news veracity. Guided by this, we propose DECOR, a novel application of Degree-Corrected Stochastic Blockmodels to the fake news detection problem. Specifically, we encapsulate our empirical observations into a lightweight social graph refinement component that iteratively updates the edge weights via a learnable degree correction mask, which allows for joint optimization with a GNN-based detector. Extensive experiments on two real-world benchmarks validate the effectiveness and efficiency of DECOR1.
Sparse-Input Neural Network using Group Concave Regularization

Simultaneous feature selection and non-linear function estimation are challenging, especially in high-dimensional settings where the number of variables exceeds the available sample size in modeling. In this article, we investigate the problem of feature selection in neural networks. Although the group LASSO has been utilized to select variables for learning with neural networks, it tends to select unimportant variables into the model to compensate for its over-shrinkage. To overcome this limitation, we propose a framework of sparse-input neural networks using group concave regularization for feature selection in both low-dimensional and high-dimensional settings. The main idea is to apply a proper concave penalty to the $l_2$ norm of weights from all outgoing connections of each input node, and thus obtain a neural net that only uses a small subset of the original variables. In addition, we develop an effective algorithm based on backward path-wise optimization to yield stable solution paths, in order to tackle the challenge of complex optimization landscapes. Our extensive simulation studies and real data examples demonstrate satisfactory finite sample performances of the proposed estimator, in feature selection and prediction for modeling continuous, binary, and time-to-event outcomes.
Maximum Overlap Area of Several Convex Polygons Under Translations

Let $k \geq 2$ be a constant. Given any $k$ convex polygons in the plane with a total of $n$ vertices, we present an $O(n\log^{2k-3}n)$ time algorithm that finds a translation of each of the polygons such that the area of intersection of the $k$ polygons is maximized. Given one such placement, we also give an $O(n)$ time algorithm which computes the set of all translations of the polygons which achieve this maximum.
Complex Translation Methods and its Application to Resonances for Quantum Walks

In this paper, some properties of resonances for multi-dimensional quantum walks are studied. Resonances for quantum walks are defined as eigenvalues of complex translated time evolution operators in the pseudo momentum space. For some typical cases, we show some results of existence or nonexistence of resonances. One is a perturbation of an elastic scattering of a quantum walk which is an analogue of classical mechanics. Another one is a shape resonance model which is a perturbation of a quantum walk with a non-penetrable barrier.
Prescribed Performance Controller Design for DC Converter System With Constant Power Loads in DC Microgrid

In this paper, a composite prescribed performance control strategy is developed for stabilizing dc/dc boost converter feeding constant power loads. First, by employing the exact feedback linearization technique, the nonlinear uncertain dc converter system is first transformed into the Brunovsky’s canonical form. Then, a nonlinear disturbance observer is utilized to evaluate the dynamic change of load power and the accuracy of output voltage regulated by feedforward compensation. Next, the prescribed performance controller is elaborately designed to ensure that the tracking error of output voltage is always within the margin of predefined error bounds. Based on the backstepping design approach, the composite nonlinear controller with prescribed performance is determined. Finally, the numerical simulation results are presented to demonstrate the tracking performance of the proposed controller.
Environmental effects on emergent strategy in micro-scale multi-agent reinforcement learning

Multi-Agent Reinforcement Learning (MARL) is a promising candidate for realizing efficient control of microscopic particles, of which micro-robots are a subset. However, the microscopic particles' environment presents unique challenges, such as Brownian motion at sufficiently small length-scales. In this work, we explore the role of temperature in the emergence and efficacy of strategies in MARL systems using particle-based Langevin molecular dynamics simulations as a realistic representation of micro-scale environments. To this end, we perform experiments on two different multi-agent tasks in microscopic environments at different temperatures, detecting the source of a concentration gradient and rotation of a rod. We find that at higher temperatures, the RL agents identify new strategies for achieving these tasks, highlighting the importance of understanding this regime and providing insight into optimal training strategies for bridging the generalization gap between simulation and reality. We also introduce a novel Python package for studying microscopic agents using reinforcement learning (RL) to accompany our results.
Topological transformations of a nematic drop

Morphogenesis of living systems involves topological shape transformations which are highly unusual in the inanimate world. Here, we demonstrate that a droplet of a nematic liquid crystal changes its equilibrium shape from a simply connected tactoid, which is topologically equivalent to a sphere, to a torus, which is not simply connected. The topological shape transformation is caused by the interplay of nematic elastic constants, which facilitates splay and bend of molecular orientations in tactoids but hinders splay in the toroids. The elastic anisotropy mechanism might be helpful in understanding topology transformations in morphogenesis and paves the way to control and transform shapes of droplets of liquid crystals and related soft materials.
A Data-Driven Approach to Geometric Modeling of Systems with Low-Bandwidth Actuator Dynamics

It is challenging to perform system identification on soft robots due to their underactuated, high-dimensional dynamics. In this work, we present a data-driven modeling framework, based on geometric mechanics (also known as gauge theory) that can be applied to systems with low-bandwidth control of the system's internal configuration. This method constructs a series of connected models comprising actuator and locomotor dynamics based on data points from stochastically perturbed, repeated behaviors. By deriving these connected models from general formulations of dissipative Lagrangian systems with symmetry, we offer a method that can be applied broadly to robots with first-order, low-pass actuator dynamics, including swelling-driven actuators used in hydrogel crawlers. These models accurately capture the dynamics of the system shape and body movements of a simplified swimming robot model. We further apply our approach to a stimulus-responsive hydrogel simulator that captures the complexity of chemo-mechanical interactions that drive shape changes in biomedically relevant micromachines. Finally, we propose an approach of numerically optimizing control signals by iteratively refining models, which is applied to optimize the input waveform for the hydrogel crawler. This transfer to realistic environments provides promise for applications in locomotor design and biomedical engineering.
Rydberg atom-based radio frequency sensors: amplitude regime sensing

Rydberg atom-based radio frequency electromagnetic field sensors are drawing wide-spread interest because of their unique properties, such as small size, dielectric construction, and self-calibration. These photonic sensors use lasers to prepare atoms and read out the atomic response to a radio frequency electromagnetic field based on electromagnetically induced transparency, or related phenomena. Much of the theoretical work has focused on the Autler-Townes splitting induced by the radio frequency wave. The amplitude regime, where the change in transmission observed on resonance is measured to determine electric field strength, has received less attention. In this paper, we deliver analytic expressions that are useful for calculating the absorption coefficient and sensitivity in the amplitude regime. We describe the approximations that we applied to obtain the analytic expressions and demonstrate their validity over a large range of the interesting parameter space. The effect of the thermal motion of the atoms is explicitly addressed. Residual Doppler shifts are shown to limit sensitivity. An analytic expression for the amplitude regime of Rydberg atom-based sensing has not, to our knowledge, been obtained previously. The expressions, approximations and descriptions presented in the paper are important for maximizing the sensitivity of Rydberg atom-based sensors and for providing insight into the physics of multi-level interference phenomena.
High Altitude Platform Stations: the New Network Energy Efficiency Enabler in the 6G Era

The rapidly evolving communication landscape, with the advent of 6G technology, brings new challenges to the design and operation of wireless networks. One of the key concerns is the energy efficiency of the Radio Access Network (RAN), as the exponential growth in wireless traffic demands increasingly higher energy consumption. In this paper, we assess the potential of integrating a High Altitude Platform Station (HAPS) to improve the energy efficiency of a RAN, and quantify the potential energy conservation through meticulously designed simulations. We propose a quantitative framework based on real traffic patterns to estimate the energy consumption of the HAPS integrated RAN and compare it with the conventional terrestrial RAN. Our simulation results elucidate that HAPS can significantly reduce energy consumption by up to almost 30\% by exploiting the unique advantages of HAPS, such as its self-sustainability, high altitude, and wide coverage. We further analyze the impact of different system parameters on performance, and provide insights for the design and optimization of future 6G networks. Our work sheds light on the potential of HAPS integrated RAN to mitigate the energy challenges in the 6G era, and contributes to the sustainable development of wireless communications.
Verifications on Dimensional Upper Bounds for a Dmissible Subgroups for the Metapletic Representation

We prove dimensional upper bounds for admissible Lie subgroups H of G = . The notation of admissibility captures natural geometric phenomena of the phase space and it is a sufficient condition for a subgroup to be reproducing . It is expressed in terms of absolutely convergent integrals of Wigner distributions , translated by the affine action of the subgroup . They showed that dim H , where as if H , then dim H , [10] . Both bounds are shown to be optimal.
Greedy Minimum-Energy Scheduling

We consider the problem of energy-efficient scheduling across multiple processors with a power-down mechanism. In this setting a set of $n$ jobs with individual release times, deadlines, and processing volumes must be scheduled across $m$ parallel processors while minimizing the consumed energy. Idle processors can be turned off to save energy, while turning them on requires a fixed amount of energy. For the special case of a single processor, the greedy Left-to-Right algorithm guarantees an approximation factor of $2$. We generalize this simple greedy policy to the case of $m \geq 1$ processors running in parallel and show that the energy costs are still bounded by $2 \text{OPT} + P$, where $\text{OPT}$ is the energy consumed by an optimal solution and $P<\text{OPT}$ is the total processing volume. Our algorithm has a running time of $\mathcal{O}(n f \log d)$, where $d$ is the difference between the latest deadline and the earliest release time, and $f$ is the running time of a maximum flow calculation in a network of $\mathcal{O}(n)$ nodes.
Mixed state branching evolution for cell division models

We prove a scaling limit theorem for two-type Galton-Waston branching processes with interaction. The limit theorem gives rise to a class of mixed state branching processes with interaction using to simulate the evolution for cell division affected by parasites. Such process can also be obtained by the pathwise unique solution to a stochastic equation system. Moreover, we present sufficient conditions for extinction with probability one and the exponential ergodicity in the total variation distance of such process.