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Visual SLAM systems combine visual tracking with global loop closure to maintain a consistent map and accurate localization. Loop closure is a computationally expensive process as we need to search across the whole map for matches. This paper presents FastLoop, a GPU-accelerated loop closing module to alleviate this computational complexity. We identify key performance bottlenecks in the loop closing pipeline of visual SLAM and address them through parallel optimizations on the GPU. Specifically, we use task-level and data-level parallelism and integrate a GPU-accelerated pose graph optimization. Our implementation is built on top of ORB-SLAM3 and leverages CUDA for GPU programming. Experimental results show that FastLoop achieves an average speedup of 1.4x and 1.3x on the EuRoC dataset and 3.0x and 2.4x on the TUM-VI dataset for the loop closing module on desktop and embedded platforms, respectively, while maintaining the accuracy of the original system.

Point-gap topology, characterized by spectral winding numbers, is crucial to non-Hermitian topological phases and dramatically alters real-time dynamics. In this paper, we study the evolution of quantum particles in dissipative systems with imaginary gap closing, using the saddle-point approximation method. For trivial point-gap systems, imaginary gap-closing points can also be saddle points. This leads to a single power-law decay of the local Green's function, with the asymptotic scaling behavior determined by the order of these saddle points. In contrast, for nontrivial point-gap systems, imaginary gap-closing points do not coincide with saddle points in general. This results in a dynamical behavior characterized by two different scaling laws for distinct time regimes. In the short-time regime, the local Green's function is governed by the dominant saddle points and exhibits an asymptotic exponential decay. In the long-time regime, however, the dynamics is controlled by imaginary gap-closing points, leading to a power-law decay envelope. Our findings advance the understanding of quantum dynamics in dissipative systems and provide predictions testable in future experiments.

Semantic caching cuts LLM inference costs by serving a cached response to semantically similar queries. Standard practice evaluates these systems using PR-AUC, a metric that only measures how well scores rank and ignores whether they are usable at a fixed threshold. We show this mismatch leads to systematically poor deployment choices, as models with the highest PR-AUC are often the worst in operation. We introduce Precision-Cache Hit Ratio (P-CHR) AUC, a cache-aware metric that measures precision across cache utilization levels, and Calibration Retention Rate (CRR), which captures how much offline ranking quality survives at deployment. We decompose the operational gap between offline and deployed quality into a recoverable calibration component and an irreducible structural component fixed by the dataset's positive rate. Our experiments show that the calibration gap is governed by the training objective rather than data scale, and post-hoc calibration only partially closes it. Ultimately, model selection for semantic caching is a calibration problem, not a ranking one, and measuring it is the first step to closing the gap.

This survey focuses on strong closing lemmas in Hamiltonian dynamics that are proved using spectral invariants (also known as action selectors) in symplectic geometry. We review strong closing lemmas in low-dimensional Hamiltonian dynamics (Reeb flows on contact three-manifolds and area-preserving maps on symplectic surfaces) and outline the key ideas behind their proofs. We also discuss results concerning strong closing lemmas in high-dimensional Hamiltonian dynamics, as well as analogous results for minimal hypersurfaces.

It was shown by Beisegel, Chudnovsky, Gurvich, Milanič, and Servatius in 2022 that every induced $2$-edge path in a vertex-transitive graph closes to an induced cycle. Similar results were obtained for 3-edge paths closing to cycles in edge-transitive graphs, where the cycle can be assumed to be induced if the path is induced. Motivated by these results, we consider the following problem: For a given class of graphs, determine all integers $\ell\geq 0$ such that for every graph in the class, every path of length at most $\ell$ closes to a cycle. We also consider the variant of the problem for induced paths closing to induced cycles. We completely solve these problems for the classes of (finite) vertex-transitive graphs, edge-transitive graphs, and edge-transitive graphs that are not stars. For all but one case of a negative answer, we provide infinite families of connected counterexamples.

In the seminal proposal by Fu and Kane, the superconducting proximity effect is used to realize topological superconductivity in the topological surface state (TSS) of a 3D topological insulator (TI). In a line Josephson junction made on the TI surface, the spin-momentum locking of the TSS guarantees the existence of a pair of spin-non-degenerate, perfectly transmitted Andreev modes. These modes lead to robust gap closing and parity alteration as a function of the superconducting phase difference $\varphi$ across the junction. Here, we report the observation of the predicted gap closing at $\varphi = (2n+1)π$ in a TI Josephson junction ($n$ integer), where the local density of states is probed via tunnel contacts and $\varphi$ is controlled by a flux loop. This phenomenon is robust for a wide range of chemical potentials, supporting its TSS origin. Under an applied perpendicular magnetic field, Josephson vortices form, making $\varphi$ position-dependent. In this case, the gap closing occurs locally at the Josephson vortex cores where $\varphi = (2n+1)π$, which we also observe. Our results confirm the fundamental role of spin-momentum locking in the Andreev physics in the TSS, whic

Motivated by the ergodic closing lemma of Mañé, we investigate the $C^\infty$ closing lemma in higher-dimensional Hamiltonian systems, with a focus on the statistical behavior of periodic orbits generated by $C^\infty$-small perturbations. We demonstrate that, under certain Floer-theoretic conditions, invariant or recurrent Lagrangian submanifolds can give rise to periodic orbits whose statistical properties are controllable. For instance, we show that for Hamiltonian systems preserving the zero section in $T^*\mathbb{T}^n$, $C^\infty$ generically, there exist periodic orbits converging to an invariant measure supported on the zero section.

This letter presents a conflict resolution strategy for an autonomous vehicle mounted with a stereo camera approaching an unsignalized T-intersection. A mathematical model for uncertainty in stereo camera depth measurements is considered and an analysis establishes the proposed adaptive depth sampling logic which guarantees an upper bound on the computed closing speed. Further, a collision avoidance logic is proposed that utilizes the closing speed bound and generates a safe trajectory plan based on the convex hull property of a quadratic Bézier curve-based reference path. Realistic validation studies are presented with neighboring vehicle trajectories generated using Next Generation Simulation (NGSIM) dataset.

We show here that numerous examples abound where changing topology does not necessarily close the bulk insulating charge gap as demanded in the standard non-interacting picture. From extensive determinantal and dynamical cluster quantum Monte Carlo simulations of the half-filled and quarter-filled Kane-Mele-Hubbard model, we show that for sufficiently strong interactions at either half- or quarter-filling, a transition between topological and trivial insulators occurs without the closing of a charge gap. To shed light on this behavior, we illustrate that an exactly solvable model reveals that while the single-particle gap remains, the many-body gap does in fact close. These two gaps are the same in the non-interacting system but depart from each other as the interaction turns on. We purport that for interacting systems, the proper probe of topological phase transitions is the closing of the many-body rather than the single-particle gap.

We consider closed chains of circles $C_1,C_2,\ldots,C_n,C_{n+1}=C_1$ such that two neighbouring circles $C_i,C_{i+1}$ intersect or touch each other with $A_i$ being a common point. We formulate conditions such that a polygon with vertices $X_i$ on $C_i$, and $A_i$ on the (extended) side $X_iX_{i+1}$, is closed for every position of the starting point $X_1$ on $C_1$. Similar results apply to open chains of circles. It turns out that the intersection of the sides $X_iX_{i+1}$ and $X_jX_{j+1}$ of the polygon lies on a circle $C_{ij}$ through $A_i$ and $A_j$ with the property that $C_{ij}, C_{jk}$ and $C_{ki}$ pass through a common point. The six circles theorem of Miquel and Steiner's quadrilateral Theorem appear as special cases of the general results.

Loop closing and relocalization are crucial techniques to establish reliable and robust long-term SLAM by addressing pose estimation drift and degeneration. This article begins by formulating loop closing and relocalization within a unified framework. Then, we propose a novel multi-head network LCR-Net to tackle both tasks effectively. It exploits novel feature extraction and pose-aware attention mechanism to precisely estimate similarities and 6-DoF poses between pairs of LiDAR scans. In the end, we integrate our LCR-Net into a SLAM system and achieve robust and accurate online LiDAR SLAM in outdoor driving environments. We thoroughly evaluate our LCR-Net through three setups derived from loop closing and relocalization, including candidate retrieval, closed-loop point cloud registration, and continuous relocalization using multiple datasets. The results demonstrate that LCR-Net excels in all three tasks, surpassing the state-of-the-art methods and exhibiting a remarkable generalization ability. Notably, our LCR-Net outperforms baseline methods without using a time-consuming robust pose estimator, rendering it suitable for online SLAM applications. To our best knowledge, the integ

In this paper we prove a quantitative closing Lemma for manifolds of negative sectional curvature. As an application we study partner and pseudo-partner orbits for self-crossing closed geodesic.

We prove an effective closing lemma for unipotent flows on quotients of perfect real groups. This is largely motivated by recent developments in effective unipotent dynamics.

The size of the bandgap in a photonic crystal ring is typically intuitively considered to monotonically grow as the modulation amplitude of the grating increases, causing increasingly large frequency splittings between the 'dielectric' and 'air' bands. In contrast, here we report that as the modulation amplitude in a photonic crystal ring increases, the bandgap does not simply increase monotonically. Instead, after the initial increase, the bandgap closes and then reopens again with the dielectric band and the air bands flipped in energy. The air and dielectric band edges are degenerate at the bandgap closing point. We demonstrate this behavior experimentally in silicon nitride photonic crystal microrings, where we show that the bandgap is closed to within the linewidth of the optical cavity mode, whose quality factor remains unperturbed with a value $\approx$ 1$\times$10$^6$ (i.e., linewidth of 2 pm). Moreover, through finite-element simulations, we show that such bandgap closing and band flipping phenomena exist in a variety of photonic crystal rings with varying units cell geometries and cladding layers. At the bandgap closing point, the two standing wave modes with a degenerate

We formulate elementary SFT spectral invariants of a large class of symplectic cobordisms and stable Hamiltonian manifolds, in any dimension. We give criteria for the strong closing property using these invariants, and verify these criteria for Hofer near periodic systems. This extends the class of symplectic dynamical systems in any dimension that satisfy the strong closing property.

We introduce a notion of strong closing property of contact forms, inspired by the $C^\infty$ closing lemma for Reeb flows in dimension three. We then prove a sufficient criterion for strong closing property, which is formulated by considering a monoidal functor from a category of manifolds with contact forms to a category of filtered vector spaces. As a potential application of this criterion, we propose a conjecture which says that a standard contact form on the boundary of any symplectic ellipsoid satisfies strong closing property.

Recent advancements in low-Earth orbit (LEO) satellites represented by large constellations and advanced payloads provide great promises for enabling beyond 5G and 6G telecommunications and high-quality and ubiquitous Internet connectivity to everyone anywhere on Earth. LEO satellite networks are envisioned to bridge the urban-rural connectivity gap for the digital divide. However, the digital divide can hardly be closed by only providing connectivity to rural and remote areas. Various unprecedented challenges brought by the emerging satellite Internet still need to be resolved, such as inconsistent end-to-end performance guarantees and a lack of efficient management and operations in these areas, which are referred to as "performance gap" and "management gap", respectively. This position paper will briefly discuss these gaps, approaches to addressing the gaps, and some research directions based on our recent works.

Recent tunneling conductance measurements of Majorana nanowires show a strong variation in the magnetic field dependence of the superconducting gap among different devices. Here, we theoretically study the magnetic field dependence of the gap closing feature and establish that the degree of convexity (or concavity) of the gap closing as a function of Zeeman field can provide critical constraints on the underlying microscopic parameters of the semiconductor-superconductor hybrid system model. Specifically, we show that the gap closing feature is entirely concave only for strong spin-orbit coupling strength relative to the chemical potential. Additionally, the non-linearity (i.e. concavity or convexity) of the gap closing as a function of magnetic field complicates the simple assignment of a constant effective $ g $-factor to the states in the Majorana nanowire. We develop a procedure to estimate the effective $ g $-factor from recent experimental data that accounts for the non-linear gap closing resulting from the interplay between chemical potential and spin-orbit coupling. Thus, measurements of the magnetic field dependence of the gap closure on the trivial side of the topological

In this paper, we introduce the notion of motif closure and describe higher-order ranking and link prediction methods based on the notion of closing higher-order network motifs. The methods are fast and efficient for real-time ranking and link prediction-based applications such as web search, online advertising, and recommendation. In such applications, real-time performance is critical. The proposed methods do not require any explicit training data, nor do they derive an embedding from the graph data, or perform any explicit learning. Existing methods with the above desired properties are all based on closing triangles (common neighbors, Jaccard similarity, and the ilk). In this work, we investigate higher-order network motifs and develop techniques based on the notion of closing higher-order motifs that move beyond closing simple triangles. All methods described in this work are fast with a runtime that is sublinear in the number of nodes. The experimental results indicate the importance of closing higher-order motifs for ranking and link prediction applications. Finally, the proposed notion of higher-order motif closure can serve as a basis for studying and developing better ran