We present a unified approach for constraint displacement problems in which a robot finds a feasible path by displacing constraints or obstacles. To this end, we propose a two stage process that returns locally optimal obstacle displacements to enable a feasible path for the robot. In the second stage, these obstacles are displaced to make the computed robot trajectory feasible, that is, collision-free. Several examples are provided that successfully demonstrate our approach on two distinct classes of constraint displacement problems. Introduction As humans, we encounter various situations in our day to day life in which we alter the location of objects - opening closed doors, repositioning chairs or other movable objects, clear objects while picking an object of interest from a cluttered table-top. As opposed to avoiding each object, altering or displacing these objects or constraints allow us to expand the solution space of feasible paths. In such situations, constraints, such as movable obstacles, may be cleared to find feasible paths. Manipulators often need to rearrange or move obstacles aside to accomplish a given set of tasks - a futuristic robot cooking dinner at home, manipulation in industrial settings, shelves replenishment in a grocery store. Service robots may need to reposition chairs or other movable objects to accomplish a task. A robot may need to plan a path through dynamic obstacles as they might clear the path while moving. We define a constraint displacement problem as one that finds a feasible path by displacing constraints while minimizing a problem-specific objective function.

Many machine learning tasks aim to find models that work well not for a single, but for a group of criteria, often opposing ones. One such example is imbalanced data classification, where, on the one hand, we want to achieve the best possible classification quality for data from the minority class without degrading the classification quality of the majority class. One solution is to propose an aggregate learning criterion and reduce the multi-objective learning task to a single-criteria optimization problem. Unfortunately, such an approach is characterized by ambiguity of interpretation since the value of the aggregated criterion does not indicate the value of the component criteria. Hence, there are more and more proposals for algorithms based on multi-objective optimization (MOO), which can simultaneously optimize multiple criteria. However, such an approach results in a set of multiple non-dominated solutions (Pareto front). The selection of a single solution from the Pareto front is a challenge itself, and much attention is paid to the issue of how to select it considering user preferences, as well as how to compare solutions returned by different MOO algorithms among themselves. Thus, a significant gap has been identified in the classifier evaluation methodology, i.e., how to reliably compare methods returning single solutions with algorithms returning solutions in the form of Pareto fronts. To fill the aforementioned gap, this article proposes a new, reliable way of evaluating algorithms based on multi-objective algorithms with methods that return single solutions while pointing out solutions from a Pareto front tailored to the user's preferences. This work focuses only on algorithm comparison, not their learning. The algorithms selected for this study are illustrative to help understand the proposed approach.

This study presents an AI enhanced IoT framework for predictive maintenance and affordability optimization in smart microgrids using a Digital Twin modeling approach. The proposed system integrates real time sensor data, machine learning based fault prediction, and cost aware operational analytics to improve reliability and energy efficiency in distributed microgrid environments. By synchronizing physical microgrid components with a virtual Digital Twin, the framework enables early detection of component degradation, dynamic load management, and optimized maintenance scheduling. Experimental evaluations demonstrate improved predictive accuracy, reduced operational downtime, and measurable cost savings compared to baseline microgrid management methods. The findings highlight the potential of Digital Twin driven IoT architectures as a scalable solution for next generation intelligent and affordable energy systems.

Hash center-based deep hashing methods improve upon pairwise or triplet-based approaches by assigning fixed hash centers to each class as learning targets, thereby avoiding the inefficiency of local similarity optimization. However, random center initialization often disregards inter-class semantic relationships. While existing two-stage methods mitigate this by first refining hash centers with semantics and then training the hash function, they introduce additional complexity, computational overhead, and suboptimal performance due to stage-wise discrepancies. To address these limitations, we propose $\textbf{Center-Reassigned Hashing (CRH)}$, an end-to-end framework that $\textbf{dynamically reassigns hash centers}$ from a preset codebook while jointly optimizing the hash function. Unlike previous methods, CRH adapts hash centers to the data distribution $\textbf{without explicit center optimization phases}$, enabling seamless integration of semantic relationships into the learning process. Furthermore, $\textbf{a multi-head mechanism}$ enhances the representational capacity of hash centers, capturing richer semantic structures. Extensive experiments on three benchmarks demonstrate that CRH learns semantically meaningful hash centers and outperforms state-of-the-art deep hashing methods in retrieval tasks.

Video generation has been advancing rapidly, and diffusion transformer (DiT) based models have demonstrated remark- able capabilities. However, their practical deployment is of- ten hindered by slow inference speeds and high memory con- sumption. In this paper, we propose a novel pipelining frame- work named PipeDiT to accelerate video generation, which is equipped with three main innovations. First, we design a pipelining algorithm (PipeSP) for sequence parallelism (SP) to enable the computation of latent generation and commu- nication among multiple GPUs to be pipelined, thus reduc- ing inference latency. Second, we propose DeDiVAE to de- couple the diffusion module and the variational autoencoder (VAE) module into two GPU groups, whose executions can also be pipelined to reduce memory consumption and infer- ence latency. Third, to better utilize the GPU resources in the VAE group, we propose an attention co-processing (Aco) method to further reduce the overall video generation latency. We integrate our PipeDiT into both OpenSoraPlan and Hun- yuanVideo, two state-of-the-art open-source video generation frameworks, and conduct extensive experiments on two 8- GPU systems. Experimental results show that, under many common resolution and timestep configurations, our PipeDiT achieves 1.06x to 4.02x speedups over OpenSoraPlan and HunyuanVideo.

Low-altitude Unmanned Aerial Vehicle (UAV) networks rely on robust semantic segmentation as a foundational enabler for distributed sensing-communication-control co-design across heterogeneous agents within the network. However, segmentation foundation models deteriorate quickly under weather, lighting, and viewpoint drift. Resource-limited UAVs cannot run gradient-based test-time adaptation, while resource-massive UAVs adapt independently, wasting shared experience. To address these challenges, we propose AdaptFly, a prompt-guided test-time adaptation framework that adjusts segmentation models without weight updates. AdaptFly features two complementary adaptation modes. For resource-limited UAVs, it employs lightweight token-prompt retrieval from a shared global memory. For resource-massive UAVs, it uses gradient-free sparse visual prompt optimization via Covariance Matrix Adaptation Evolution Strategy. An activation-statistic detector triggers adaptation, while cross-UAV knowledge pool consolidates prompt knowledge and enables fleet-wide collaboration with negligible bandwidth overhead. Extensive experiments on UAVid and VDD benchmarks, along with real-world UAV deployments under diverse weather conditions, demonstrate that AdaptFly significantly improves segmentation accuracy and robustness over static models and state-of-the-art TTA baselines. The results highlight a practical path to resilient, communication-efficient perception in the emerging low-altitude economy.

Free-boundary diffeomorphism optimization is a core ingredient in the surface mapping problem but remains notoriously difficult because the boundary is unconstrained and local bijectivity must be preserved under large deformation. Numerical Least-Squares Quasiconformal (LSQC) theory, with its provable existence, uniqueness, similarity-invariance and resolution-independence, offers an elegant mathematical remedy. However, the conventional numerical algorithm requires landmark conditioning, and cannot be applied into gradient-based optimization. We propose a neural surrogate, the Spectral Beltrami Network (SBN), that embeds LSQC energy into a multiscale mesh-spectral architecture. Next, we propose the SBN guided optimization framework SBN-Opt which optimizes free-boundary diffeomorphism for the problem, with local geometric distortion explicitly controllable. Extensive experiments on density-equalizing maps and inconsistent surface registration demonstrate our SBN-Opt's superiority over traditional numerical algorithms.

Learning to optimize (L2O) parametric approximations of AC optimal power flow (AC-OPF) solutions offers the potential for fast, reusable decision-making in real-time power system operations. However, the inherent nonconvexity of AC-OPF results in challenging optimization landscapes, and standard learning approaches often fail to converge to feasible, high-quality solutions. This work introduces a \textit{homotopy-guided self-supervised L2O method} for parametric AC-OPF problems. The key idea is to construct a continuous deformation of the objective and constraints during training, beginning from a relaxed problem with a broad basin of attraction and gradually transforming it toward the original problem. The resulting learning process improves convergence stability and promotes feasibility without requiring labeled optimal solutions or external solvers. We evaluate the proposed method on standard IEEE AC-OPF benchmarks and show that homotopy-guided L2O significantly increases feasibility rates compared to non-homotopy baselines, while achieving objective values comparable to full OPF solvers. These findings demonstrate the promise of homotopy-based heuristics for scalable, constraint-aware L2O in power system optimization.

We present \textsf{ModularSubsetSelection} (MSS), a new algorithm for locally differentially private (LDP) frequency estimation. Given a universe of size $k$ and $n$ users, our $\varepsilon$-LDP mechanism encodes each input via a Residue Number System (RNS) over $\ell$ pairwise-coprime moduli $m_0, \ldots, m_{\ell-1}$, and reports a randomly chosen index $j \in [\ell]$ along with the perturbed residue using the statistically optimal \textsf{SubsetSelection} (SS) (Wang et al. 2016). This design reduces the user communication cost from $Θ\bigl(ω\log_2(k/ω)\bigr)$ bits required by standard SS (with $ω\approx k/(e^\varepsilon+1)$) down to $\lceil \log_2 \ell \rceil + \lceil \log_2 m_j \rceil$ bits, where $m_j < k$. Server-side decoding runs in $Θ(n + r k \ell)$ time, where $r$ is the number of LSMR (Fong and Saunders 2011) iterations. In practice, with well-conditioned moduli (\textit{i.e.}, constant $r$ and $\ell = Θ(\log k)$), this becomes $Θ(n + k \log k)$. We prove that MSS achieves worst-case MSE within a constant factor of state-of-the-art protocols such as SS and \textsf{ProjectiveGeometryResponse} (PGR) (Feldman et al. 2022) while avoiding the algebraic prerequisites and dynamic-programming decoder required by PGR. Empirically, MSS matches the estimation accuracy of SS, PGR, and \textsf{RAPPOR} (Erlingsson, Pihur, and Korolova 2014) across realistic $(k, \varepsilon)$ settings, while offering faster decoding than PGR and shorter user messages than SS. Lastly, by sampling from multiple moduli and reporting only a single perturbed residue, MSS achieves the lowest reconstruction-attack success rate among all evaluated LDP protocols.

Linear Predictive Clustering (LPC) partitions samples based on shared linear relationships between feature and target variables, with numerous applications including marketing, medicine, and education. Greedy optimization methods, commonly used for LPC, alternate between clustering and linear regression but lack global optimality. While effective for separable clusters, they struggle in non-separable settings where clusters overlap in feature space. In an alternative constrained optimization paradigm, Bertsimas and Shioda (2007) formulated LPC as a Mixed-Integer Program (MIP), ensuring global optimality regardless of separability but suffering from poor scalability. This work builds on the constrained optimization paradigm to introduce two novel approaches that improve the efficiency of global optimization for LPC. By leveraging key theoretical properties of separability, we derive near-optimal approximations with provable error bounds, significantly reducing the MIP formulation's complexity and improving scalability. Additionally, we can further approximate LPC as a Quadratic Pseudo-Boolean Optimization (QPBO) problem, achieving substantial computational improvements in some settings. Comparative analyses on synthetic and real-world datasets demonstrate that our methods consistently achieve near-optimal solutions with substantially lower regression errors than greedy optimization while exhibiting superior scalability over existing MIP formulations.