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Generating 3D shapes at part level is pivotal for downstream applications such as mesh retopology, UV mapping, and 3D printing. However, existing part-based generation methods often lack sufficient controllability and suffer from poor semantically meaningful decomposition. To this end, we introduce X-Part, a controllable generative model designed to decompose a holistic 3D object into semantically meaningful and structurally coherent parts with high geometric fidelity. X-Part exploits the bounding box as prompts for the part generation and injects point-wise semantic features for meaningful decomposition. Furthermore, we design an editable pipeline for interactive part generation. Extensive experimental results show that X-Part achieves state-of-the-art performance in part-level shape generation. This work establishes a new paradigm for creating production-ready, editable, and structurally sound 3D assets. Codes will be released for public research.
This is the final paper in the five-part series The Semantic Arrow of Time. Part I identified the FITO category mistake -- treating forward temporal flow as sufficient for establishing meaning. Part II presented the constructive alternative: the OAE link state machine with its mandatory reflecting phase. Part III showed the FITO fallacy operating at industrial scale in RDMA completion semantics. Part IV traced the same pattern through file synchronization, email, human memory, and language model hallucination. This paper closes the series by constructing the Leibniz Bridge: a unified framework that connects the philosophical foundations (Leibniz's Identity of Indiscernibles, as formalized by Spekkens), the protocol engineering (OAE's bilateral transaction structure), and the physical substrate (indefinite causal order in quantum mechanics). The bridge rests on a single principle: mutual information conservation -- the requirement that every causal exchange preserve the total information accessible to both endpoints, with the direction of time emerging not from axiom but from entropy production when a reversible exchange commits. We show that this principle dissolves the apparent im
In the series of papers Motivic GUT Part I: Grand Unified Theory of Topological Order, Motivic GUT Part II: Grand Unified Theory of Symmetry-Protected Topological Order, and Motivic GUT Part III: Grand Unified Theory of Symmetry-Enriched Topological Order, we propose a unified framework for gapped topological phases based on the Grothendieck-Kitaev-Lurie motivic yoga. In the spirit of Grothendieck's rising sea, we argue that the classification problem can only be properly addressed after identifying the correct higher-categorical ambient space in which its full richness appears. In this first part, we propose a unified definition of gapped topological order in spatial dimension $d$ in terms of unitary fusion $(\infty,d)$-categorical data, considered up to Morita equivalence. For $d=2$, this framework recovers unitary modular tensor categories. For $d>2$, it naturally leads to genuinely higher-categorical structures. This suggests a Copernican turn in the theory of topological phases: many existing classification schemes should be reinterpreted as lower-categorical shadow realizations of intrinsically $\infty$-categorical objects.
In the first part of this two-part paper a game-theoretic decentralized real-time control is proposed in the context of Electric Vehicle (EV) Charging Station (CS). This method, relying on a Stackelberg Game-based Alternating Direction of Multipliers (SG-ADMM), intends to steer the EVs' individual objectives towards the CS optimum by means of an incentive design mechanism, while controlling the EV power dispatch in a distributed manner. We integrate SG-ADMM in a hierachical multi-layered Energy Management System (EMS) as the real-time control algorithm, formulating the two-layer approach so that the SG leader (i.e., the CS), holding commitment power, trades off the available power with the incentives to the EVs, and the SG followers (i.e., the EVs) optimizes their charging curve in response to the leader decision. In this second part, we demonstrate the applicability of SG-ADMM as a incentive design mechanism inside an EVCS EMS, testing it in a large-scale EVCS. We benchmark this method with a decentralized (ADMM-based), a centralized and a uncontrolled approach, showing that our method exploits EV-level flexibility in a cost-effective, fair and computationally efficient manner.
Most successes in autonomous robotic assembly have been restricted to single target or category. We propose to investigate general part assembly, the task of creating novel target assemblies with unseen part shapes. As a fundamental step to a general part assembly system, we tackle the task of determining the precise poses of the parts in the target assembly, which we we term ``rearrangement planning''. We present General Part Assembly Transformer (GPAT), a transformer-based model architecture that accurately predicts part poses by inferring how each part shape corresponds to the target shape. Our experiments on both 3D CAD models and real-world scans demonstrate GPAT's generalization abilities to novel and diverse target and part shapes.
Part I of this series (arXiv:2602.09029) develops a sharp Gaussian (LAN/GDP) limit theory for neighboring shuffle experiments when the local randomizer is fixed and has full support bounded away from zero. The present paper characterizes the first universality-breaking frontier: critical sequences of increasingly concentrated local randomizers for which classical Lindeberg conditions fail and the shuffle score exhibits rare macroscopic jumps. For shuffled binary randomized response with local privacy $\varepsilon_0 = \varepsilon_0(n)$, we prove experiment-level convergence (in Le Cam distance) to explicit shift limit experiments: a Poisson-shift limit for the canonical neighboring pair when $\exp(\varepsilon_0(n))/n \to c^2$, and a Skellam-shift limit for proportional compositions $k/n \to π\in (0,1)$ in the same scaling, including an explicit disappearance of the two-sided $δ$-floor away from boundary compositions. For general finite alphabets, we introduce a sparse-error critical regime and prove a multivariate compound-Poisson / independent Poisson vector limit for the centered released histogram, yielding a multivariate Poisson-shift experiment and an explicit limiting $(\varep
In this paper, we study the problem of one-shot skeleton-based action recognition, which poses unique challenges in learning transferable representation from base classes to novel classes, particularly for fine-grained actions. Existing meta-learning frameworks typically rely on the body-level representations in spatial dimension, which limits the generalisation to capture subtle visual differences in the fine-grained label space. To overcome the above limitation, we propose a part-aware prototypical representation for one-shot skeleton-based action recognition. Our method captures skeleton motion patterns at two distinctive spatial levels, one for global contexts among all body joints, referred to as body level, and the other attends to local spatial regions of body parts, referred to as the part level. We also devise a class-agnostic attention mechanism to highlight important parts for each action class. Specifically, we develop a part-aware prototypical graph network consisting of three modules: a cascaded embedding module for our dual-level modelling, an attention-based part fusion module to fuse parts and generate part-aware prototypes, and a matching module to perform classif
In this study, we introduce a refined method for ascertaining error estimations in numerical simulations of dynamical systems via an innovative application of composition techniques. Our approach involves a dual application of a basic one-step numerical method of order p in this part, and for the class of Backward Difference Formulas schemes in the second part [Deeb A., Dutykh D. and AL Zohbi M. Error estimation for numerical approximations of ODEs via composition techniques. Part II: BDF methods, Submitted, 2024]. This dual application uses complex coefficients, resulting outputs in the complex plane. The methods innovation lies in the demonstration that the real parts of these outputs correspond to approximations of the solutions with an enhanced order of p + 1, while the imaginary parts serve as error estimations of the same order, a novel proof presented herein using Taylor expansion and perturbation technique. The linear stability of the resulted scheme is enhanced compared to the basic one. The performance of the composition in computing the approximation is also compared. Results show that the proposed technique provide higher accuracy with less computational time. This dual
Stanisław Leśniewski's mereology was formulated in a specific way, deviating from standard formalizations. Nowadays, Leśniewski's theory is presented in the form of an elementary theory or translated into the language of the theory of relational structures. In this article, firstly, we look at existentially neutral theories, in which we do not postulate the existence of any other collective sets than those obtained from the definition and the basic properties of the relation of being a part. We also examine some existentially involved theories of parts. Among them, there is Grzegorczykian mereology and Leśniewskian mereology. One of the main principles of mereology is the transitivity of the concept of being a part of. This property is often questioned in the literature on the subject. In the final part, we present problems related to the transitivity of this concept.
Target tracking entails the estimation of the evolution of the target state over time, namely the target trajectory. Different from the classical state space model, our series of studies, including this paper, model the collection of the target state as a stochastic process (SP) that is further decomposed into a deterministic part which represents the trend of the trajectory and a residual SP representing the residual fitting error. Subsequently, the tracking problem is formulated as a learning problem regarding the trajectory SP for which a key part is to estimate a trajectory FoT (T-FoT) best fitting the measurements in time series. For this purpose, we consider the polynomial T-FoT and address the regularized polynomial T-FoT optimization employing two distinct regularization strategies seeking trade-off between the accuracy and simplicity. One limits the order of the polynomial and then the best choice is determined by grid searching in a narrow, bounded range while the other adopts $\ell_0$ norm regularization for which the hybrid Newton solver is employed. Simulation results obtained in both single and multiple maneuvering target scenarios demonstrate the effectiveness of our
For a fixed positive integer $k$, let $C(k,n)$ denote the number of two-color partitions of $n$ with odd smallest part and restrictions on even parts, and let $C_k(q)$ be its generating function. We show that $C(1,n)\equiv d(2n-1)\pmod{4}$ and obtain congruences modulo $2$ and $4$ for $C(k,n)$ when $k=2,3$. Using $q$-series methods we derive closed formulas for $C_k(q)$ in terms of eta-quotients and formulate Ramanujan-type congruences for the limiting sequence arising from $\lim_{k\to\infty} C_k(q)$.
Let $A$ be a finite ordered set. Define the ordered set $A^A$ as the set of all maps from $A$ to $A$, ordered pointwise. Let ${}^{A} A$ be the dual of $A^A$. We prove results in the spirit of Parts~I--III, but now using both $A^A$ and ${}^{A}A$. For example, if \[ \Bigl({}^{{}^{ {}^{ {}^{A}A}A}A}A\Bigr)^{A^{A^{A}}} \] is isomorphic to \[ \Bigl({}^{ {}^{ {}^{ {}^{B}B}B}B}B\Bigr)^{B^{B^{B}}} \] for finite ordered sets $A$ and $B$, then $A$ is isomorphic to $B$.
3D object recognition has seen significant advances in recent years, showing impressive performance on real-world 3D scan benchmarks, but lacking in object part reasoning, which is fundamental to higher-level scene understanding such as inter-object similarities or object functionality. Thus, we propose to leverage large-scale synthetic datasets of 3D shapes annotated with part information to learn Neural Part Priors (NPPs), optimizable spaces characterizing geometric part priors. Crucially, we can optimize over the learned part priors in order to fit to real-world scanned 3D scenes at test time, enabling robust part decomposition of the real objects in these scenes that also estimates the complete geometry of the object while fitting accurately to the observed real geometry. Moreover, this enables global optimization over geometrically similar detected objects in a scene, which often share strong geometric commonalities, enabling scene-consistent part decompositions. Experiments on the ScanNet dataset demonstrate that NPPs significantly outperforms state of the art in part decomposition and object completion in real-world scenes.
We show that combining human prior knowledge with end-to-end learning can improve the robustness of deep neural networks by introducing a part-based model for object classification. We believe that the richer form of annotation helps guide neural networks to learn more robust features without requiring more samples or larger models. Our model combines a part segmentation model with a tiny classifier and is trained end-to-end to simultaneously segment objects into parts and then classify the segmented object. Empirically, our part-based models achieve both higher accuracy and higher adversarial robustness than a ResNet-50 baseline on all three datasets. For instance, the clean accuracy of our part models is up to 15 percentage points higher than the baseline's, given the same level of robustness. Our experiments indicate that these models also reduce texture bias and yield better robustness against common corruptions and spurious correlations. The code is publicly available at https://github.com/chawins/adv-part-model.
Uncertainties from deepening penetration of renewable energy resources have posed critical challenges to the secure and reliable operations of future electric grids. Among various approaches for decision making in uncertain environments, this paper focuses on chance-constrained optimization, which provides explicit probabilistic guarantees on the feasibility of optimal solutions. Although quite a few methods have been proposed to solve chance-constrained optimization problems, there is a lack of comprehensive review and comparative analysis of the proposed methods. Part I of this two-part paper reviews three categories of existing methods to chance-constrained optimization: (1) scenario approach; (2) sample average approximation; and (3) robust optimization based methods. Data-driven methods, which are not constrained by any particular distributions of the underlying uncertainties, are of particular interest. Part II of this two-part paper provides a literature review on the applications of chance-constrained optimization in power systems. Part II also provides a critical comparison of existing methods based on numerical simulations, which are conducted on standard power system tes
In Part I an odd meromorphic function f(s) has been constructed from the Riemann zeta-function evaluated at one-half plus s. The conjunction of the Riemann hypothesis and hypotheses advanced by the author in Part I is assumed. In Part IV we derive the two-sided Laplace transform representation of f(s) on the open vertical strip V of all s with real part between zero and four. An additional hypothesis is used to prove that the Laplace density of f(s) on the strip V is positive. Let z(n) be the nth critical zero of the Riemann zeta-function of positive imaginary part in order of magnitude thereof. In Part V an expression is derived for z(1). A relation is obtained of the pair z(n) and the first derivative thereat of the zeta-function to the preceding such pairs.
This is the last part of three episodes to demonstrate a renewal approach for proving the Four Color Theorem without checking by a computer. The first and the second episodes have subtitles: ``RGB-tilings on maximal planar graphs'' and ``R/G/B Kempe chains in an extremum non-4-colorable MPG,'' where R/G/B stand for red, green and blue colors to paint on edges and an MPG stands for a maximal planar graph. We focus on an extremum non-4-colorable MPG $EP$ in the whole paper. In this part we introduce three tools based on RGB-tilings. They are diamond routes, normal and generalized canal lines or rings and $Σ$-adjustments. Using these tools, we show a major result of this paper: no four vertices of degree 5 form a diamond in any extremum $EP$.
We prove concentration inequalities for $f\left( X\right) $ about its median, where $X$ is a random vector in $\mathbb{R}^n$ with independent heavy tailed coordinates of Weibull or power type, and $f:\mathbb{R}^n\rightarrow\mathbb{R}$ is a locally Lipschitz function. This paper is part of a series of four papers, Part I, Part II and two supporting papers. It can be read independently of Part I.
Modular Active Cell Robots (MACROs) is a design approach in which a large number of linear actuators and passive compliant joints are assembled to create an active structure with a repeating unit cell. Such a mesh-like robotic structure can be actuated to achieve large deformation and shape-change. In this two-part paper, we use Finite Element Analysis (FEA) to model the deformation behavior of different MACRO mesh topologies and evaluate their passive and active mechanical characteristics. In part 1, we presented the passive stiffness characteristics of different MACRO meshes. Now, in this part 2 of the paper, we investigate the active strain characteristics of planar MACRO meshes. Using FEA, we quantify and compare the strains generated for the specific choice of MACRO mesh topology and further for the specific choice of actuators actuated in that particular mesh. We simulate a series of actuation modes that are based on the angular orientation of the actuators within the mesh and show that such actuation modes result in deformation that is independent of the size of the mesh. We also show that there exists a subset of such actuation modes that spans the range of deformation beha
This is the second and final part of ``Topological twists of massive SQCD''. Part I is available at arXiv:2206.08943. In this second part, we evaluate the contribution of the Coulomb branch to topological path integrals for $\mathcal{N}=2$ supersymmetric QCD with $N_f\leq 3$ massive hypermultiplets on compact four-manifolds. Our analysis includes the decoupling of hypermultiplets, the massless limit and the merging of mutually non-local singularities at the Argyres-Douglas points. We give explicit mass expansions for the four-manifolds $\mathbb{P}^2$ and $K3$. For $\mathbb{P}^2$, we find that the correlation functions are polynomial as function of the masses, while infinite series and (potential) singularities occur for $K3$. The mass dependence corresponds mathematically to the integration of the equivariant Chern class of the matter bundle over the moduli space of $Q$-fixed equations. We demonstrate that the physical partition functions agree with mathematical results on Segre numbers of instanton moduli spaces.