Search Results (139)

Standard cryptocurrency transaction cost models assume flat geometry and assign execution cost as a proportional fee. This paper proposes GEODEX, a framework that models execution slippage as the geodesic arc length on the Fisher information manifold of a Markov-switching GARCH maximum-entropy model, augmented by a joint curvature–topological fragmentation alarm. The Curvature-Fragmentation Law (Proposition 2) is an analytically derived heuristic. Its empirical validity is confirmed across four crisis episodes. Ablation confirms that each geometric component contributes uniquely: removing the geodesic increases mean squared prediction error by 2.9%, removing topological data analysis by 2.1%, and removing curvature by 1.5%. On five cryptocurrency markets (BTC, ETH, XRP, LTC, and BCH), over 2253 daily observations, the framework achieves competitive prediction error and is the only single-signal model retained in the Model Confidence Set at $\alpha =0.10$ against eight benchmarks. A joint curvature–topological alarm fires a median of two days before price-based circuit breaker thresholds across four crisis episodes, including the Terra collapse (May 2022) and FTX bankruptcy (November 2022). Online inference requires under one second; full offline calibration requires approximately 28 h. The framework requires no additional data beyond the upstream estimation pipeline and supports SDG 10 (Reduced Inequalities) and SDG 16 (Strong Institutions) by enabling accessible geometric liquidity intelligence for regulators and smaller market participants. Full article

We introduce a notion of curvature based on informational holonomy. Let $(M,g)$ be a smooth Riemannian manifold and let $\pi :\mathcal{P}\to M$ be a bundle of state spaces equipped fibrewise with a smooth divergence $D_x$ inducing an information metric $g^{{\mathcal{P}}_x}$. Assuming a connection on $\mathcal{P}$ compatible with this fibrewise information geometry, we measure the deviation of holonomy around small geodesic triangles by transporting a reference state ${\mu }_x$ and comparing it to its image via the induced informational distance $d_x=\sqrt{2D_x}$. Normalizing the resulting distance defect by the geometric area yields a continuous informational holonomy (sectional) curvature$K_{\mathrm{hol}}^{\mathrm{cont}}(x,\mathsf{\Pi })$. We prove that this limit exists for all $(x,\mathsf{\Pi })$ and equals the norm of a vector $W_x(\mathsf{\Pi };{\mu }_x)\in T_{{\mu }_x}{\mathcal{P}}_x$ depending linearly on the curvature of the connection along $\mathsf{\Pi }$. In geometric models induced from the Levi–Civita connection via an isometric representation, $K_{\mathrm{hol}}^{\mathrm{cont}}$ becomes a scalar invariant of $R^g{|}_{\mathsf{\Pi }}$ and, on spaces of constant sectional curvature, reduces to a constant multiple of $|{\sec }_g|$. On the discrete side, we consider quasi-uniform sampling graphs whose edges carry channels approximating parallel transport. Discrete triangle holonomies define a curvature estimator, and under explicit sampling, area-approximation, and channel-consistency assumptions, we establish a discrete-to-continuum convergence theorem with a quantitative error bound controlled by the sampling scale. Full article

Geodesic projection distances on statistical manifolds have been widely applied across various research fields. Nevertheless, the existing closed-form solution is only available for the Gaussian manifold. Multivariate elliptical distributions (MEDs) include the Gaussian, generalized Gaussian, Student’s t distribution, contaminated Gaussian, and other heavy-tailed models. Despite their widespread practical applicability, explicit geodesic projection solutions for MED manifolds remain unexplored. This paper derives the explicit geodesic projection distance from an arbitrary point on the MED manifold equipped with the Fisher metric onto its commonly used submanifold with a fixed mean vector. The core theoretical contribution lies in a novel symmetry-exploitation technique proposed to tackle the highly nonlinear and complex geodesic equations, and this methodological framework is readily extendable to other statistical manifolds. The derived results substantially advance the state-of-the-art by generalizing existing theories from the Gaussian manifold to the broader family of MEDs. Full article

We present a path-based curvature representation of the gravitational bending of light in black-hole (BH) spacetimes. The bending angle is written as a one-dimensional line integral of the optical Gaussian curvature ${\mathcal{K}}_{\mathrm{opt}}$ along the photon trajectory, weighted by a geometric kernel $W(r,b)$. This representation sits within the Gibbons–Werner Gauss–Bonnet (GB) optical-geometry family rather than alongside it: the kernel is fixed by a co-area reduction of the GB surface integral along an undeflected reference path, and the single new computational object is the resulting radial integral together with its cumulative, directly plottable reading of how the deflection builds up along the ray. With the lever-arm choice $W=\sqrt{r^2-b^2}$, the integral reproduces $\hat{\alpha }=4M/b$ for every static, asymptotically flat metric (Theorem 1) and evaluates in closed form for Schwarzschild, Reissner–Nordström (RN), and equatorial Kerr. The representation becomes reliable at a large impact parameter; at the small impact parameters relevant to horizon-scale imaging, it is not numerically competitive with the standard expansions, a limitation we quantify. Beyond leading order the kernel must import information from the bent geodesic, after which the scheme reconstructs the known perturbative series; the second-order mismatch in the lever-arm result therefore measures, rather than hides, the deformation of the photon path away from the straight-line reference. Finite source–observer distances enter through the Ono–Ishihara–Asada (OIA) construction, and a winding-sum continuation outlines the route toward the strong-deflection regime, whose closed-form reduction is left to future work. Full article

Foreign-exchange decisions rest on hierarchically organized evidence whose latent structure is inadequately captured by Euclidean representations. Reinforcement-learning agents trained on flat embeddings inherit stability guarantees that do not transfer to the manifold supporting the latent state. We address both limitations through a hybrid architecture in which a schema-constrained structured chain-of-thought is embedded into a Poincaré ball, transported to a qubit register via angle encoding, and processed by an L-layer hardware-efficient variational ansatz on a state-vector backend. The circuit exposes two read-outs to the policy, namely, a scalar Pauli-Z observable and a projected quantum kernel inducing a fidelity-based similarity over magnet-price attractors, the latter identified via kernel-weighted recurrence density and finite-time Lyapunov statistics. The Lipschitz constraint on the action-value function is lifted from the hyperbolic geodesic distance to a joint metric on ${\mathbb{B}}_{\kappa }^n\times \mathbb{P}\left(\mathcal{H}\right)$. A stability theorem yields an explicit bound depending on the read-out operator norm, on the depth–width product of the ansatz, and on the curvature–Hilbert balance. The pipeline is evaluated on nine major FX crosses over a 2015–2025 out-of-sample window, with rolling-origin walk-forward retraining and broker-published transaction costs. The system attains $2.55\%$ pair-averaged non-compounded monthly P&L and $8.83\%$ maximum drawdown, with Sharpe $1.78$, Calmar $3.43$, and Probabilistic Sharpe Ratio exceeding $0.95$ on every cross. The gain remains significant under a deflated-Sharpe-ratio test with $N_{\mathrm{trials}}=42$ correction. Block-wise ablations exhibit strictly monotone degradation: removing the projected kernel costs $-4.15$ p.p. on annualized P&L, the joint Lipschitz penalty $-6.42$ p.p., the attractor module $-7.64$ p.p., and the hyperbolic embedding $-8.40$ p.p. The quantum block thereby instantiates a structurally non-classical, geometry-aware regularizer identifiable through ablation rather than asymptotically advantageous. Full article

Functional brain networks in schizophrenia (SZ) are often characterized by covariance-based measures, yet covariance matrices live on a curved geometric structure rather than in ordinary Euclidean space, complicating noise-robust inference from scalp EEG. We develop a Riemannian Geometry-based Adaptive Nonlinear Coupling Analysis (RGA-NCA) framework that integrates the affine-invariant Riemannian metric (AIRM), tangent space mapping (TSM), and an anatomically adaptive artifact rejection (AAAR) strategy accounting for regional signal-to-noise heterogeneity. The framework is grounded in the observation that Euclidean summaries of symmetric positive definite matrices are sensitive to noise-driven volume inflation, whereas geodesic distances on the manifold emphasize shape deformation. RGA-NCA was evaluated on four benchmark dynamical systems, a supplementary multichannel EEG-like sample covariance simulation, and a public button-tone SZ/HC EEG dataset associated with the auditory feedback paradigm described by Ford et al. (81 subjects; 49 SZ, 32 healthy controls). Compared with Euclidean and linear baselines, RGA-NCA showed lower sensitivity to noise-driven distance distortion and yielded clearer group-level contrasts in the tested ROI analyses; all four pre-specified frontotemporal and parietal channel pairs remained significant after Benjamini–Hochberg FDR correction. The resulting patterns are consistent with reduced long-range connectivity together with localized hyper-synchronization-like effects in SZ. Quantitatively, the Riemannian structural sensitivity index $(\mathrm{sim}=\exp (-d^2/4))$ remained high across all tested SNR levels (−20 to +10 dB; 50 Monte Carlo trials per level; range 0.936–0.964), with only a 0.026 endpoint change between +10 and −20 dB, whereas the Euclidean metric fell from 0.922 at +10 dB to 0.000 at −20 dB. These findings support Riemannian modeling as a candidate strategy for noisy covariance-based neural data, pending validation in larger independent cohorts. Full article

Background: Statistical shape modeling and generative tooth synthesis require dental point clouds in canonical poses. This study compared canonicalization methods and proposed a hybrid pipeline pairing principal-axis alignment with a neural orientation guide and a trained residual correction. Methods: Seven classical, neural, and hybrid methods were evaluated on 9060 upper tooth point clouds across seven classes from 3DTeethSeg (891 patients, 1805 held out for validation) and 1465 external first molars from FDI16. Alignment was measured by Chamfer Distance to per-sample target poses (CD Target, validation only), Chamfer Distance to class templates (CD Template, both sets), and geodesic rotation error. Results: Neural-guided PCA selection with residual refinement (gPCA-rPointNet) reached the lowest CD Target (0.62 ± 2.43 × 10⁻³) and geodesic rotation error (3.3 ± 14.5 degrees), with 98.2% of predictions below 15 degrees. On the external set, the four PCA-based methods gave a lower CD Template than methods without geometric initialization. Conclusions: A neural orientation guide placed before principal-axis candidate selection resolved the PCA eigenvector sign ambiguity responsible for 180-degree failures on near-symmetric tooth crowns. Residual correction further reduced rotation error. The same pipeline produced consistent canonical poses for first molars on the external dataset, with validation on other tooth classes remaining limited. Full article

This paper introduces a geometric framework for analyzing finite-energy signals observed with additive noise by representing them as points on statistical manifolds equipped with the Fisher–Rao metric. Each signal is associated with a parameter vector θ, which defines a unique probability distribution $p\left(\mathit{x}\right|\mathit{\theta })$ on a statistical manifold. We propose a unified approach based on the normal multivariate model to describe a raw signal mixed with additive stationary noise. In the approach considered, the background noise is typically assumed to be stationary, whereas the unknown signal is regarded as deterministic. Leveraging tools from information geometry, we compute geodesic equations for the statistical manifolds. We re-derive known results regarding the multivariate normal models and extend them to the signal processing domain. We show that in some cases, the geodesic equations can be solved to obtain a closed-form expression of the Fisher–Rao distance. This expression corresponds to a minimum bound when the sub-manifold is not geodesic, revealing a fundamental geometric constraint in signal parameter estimation. We introduce the spectral distance function, which characterizes the influence of each spectral component of the signals on the Fisher–Rao distance. Our findings provide theoretical insights for signal clustering and machine learning applications, where geometric distances can characterize classification and estimation tasks. Full article

This paper develops a deep reinforcement learning framework for cryptocurrency portfolio management in which transaction costs are derived from the Riemannian geometry of the underlying volatility model rather than assumed constant. A Proximal Policy Optimisation agent is trained on a reward function grounded in non-equilibrium thermodynamics: we use the free-energy Bellman equation, in which transaction costs are the geodesic slippage on the Fisher information manifold of a maximum-entropy Markov-switching GARCH model, and regime-transition costs are the Wasserstein-2 distance between the calm and turbulent return distributions. A thermodynamic Carnot bound on portfolio efficiency is established and empirically validated. Five hypotheses are tested across Bitcoin, Ethereum, Ripple, Litecoin, and Bitcoin Cash over January 2017 to March 2026. The geometric-cost agent achieves statistically superior Sharpe ratios relative to flat-fee baselines on four of five assets; portfolio turnover is reduced by 56 to 83 percent relative to signal-following; the thermodynamic friction point at which the agent prefers no-trade is asset-specific and ordered by turbulent half-life; a joint topological and geometric circuit breaker reduces Maximum Drawdown by 28 to 38 percent; and ablation confirms that every component of the observation vector contributes a statistically significant performance gain. The framework requires liquid cryptocurrency markets with validated parametric volatility models; transferability to other asset classes requires upstream recalibration. Full article

For power-grid applications such as transmission corridor inspection, substation asset inspection, and post-disaster emergency repair, reliable UAV self-localization under GNSS-degraded or GNSS-denied conditions is critical to ensuring operational safety and accurate defect geotagging. Due to substantial discrepancies in viewpoint, scale, and geometric structure between oblique UAV images and nadir satellite images, conventional RGB-based cross-view retrieval methods often suffer from unstable alignment and insufficient geometric modeling, particularly in scenarios with repetitive textures and partial overlap. To address these challenges, we propose a cross-view visual geo-localization model that integrates RGBD multimodal inputs with multi-scale attention enhancement. Specifically, MiDaS is used to estimate relative depth from UAV imagery, which is concatenated with RGB to form a four-channel input, while satellite images are padded with an additional zero channel to maintain dimensional consistency. A shared-weight ViTAdapter is adopted to learn joint semantic–geometric representations, and a lightweight Efficient Multi-scale Attention (EMA) module is adopted on spatial feature maps to strengthen multi-scale spatial consistency. In addition, an IoU-weighted InfoNCE loss is employed to accommodate partial matching during training, thereby improving the robustness of feature alignment. Experiments on the GTA-UAV dataset under the cross-area protocol show stable performance across both retrieval and localization metrics. Specifically, Recall@1, Recall@5, and Recall@10 reach 18.12%, 38.83%, and 49.47%, respectively; AP is 28.01 and SDM@3 is 0.53; meanwhile, the top-1 geodesic distance error Dis@1 is 1052.73 m. These results indicate that explicit geometric priors combined with multi-scale spatial enhancement can effectively improve cross-view feature alignment, leading to enhanced robustness and accuracy for localization in challenging power inspection scenarios. Full article

Community detection is a key task in the analysis of complex networks, particularly in social network analysis, where uncovering cohesive and well-separated groups is essential for understanding structural organization and interaction patterns. Many existing centroid-based community detection methods rely primarily on node degree for centroid selection, which often leads to centroid crowding and insufficient spatial separation among communities. To address these limitations, this paper proposes Degree–Distance Centroid–Community Detection with Influential Nodes (DDC-CDIN), a distance-driven and influence-aware community detection framework. In the proposed approach, nodes are first ranked according to an Enhanced Degree Centrality measure that incorporates degree information, neighbourhood structure, and local clustering characteristics to identify structurally influential nodes. Centroids are then selected iteratively from the top-ranked influential nodes by maximizing shortest-path distances, ensuring that the chosen centroids are both representative and well dispersed within the network. Once the centroids are determined, the remaining nodes are assigned to communities based on the minimum geodesic distance, yielding compact, clearly separated clusters. Extensive experiments across multiple real-world networks show that DDC-CDIN achieves competitive performance compared to traditional centroid-based and modularity-driven methods in terms of modularity, community cohesion, and boundary clarity. The results indicate that jointly incorporating influence-aware node ranking with distance-based centroid dispersion effectively mitigates centroid crowding and enhances overall community detection quality. These findings demonstrate the effectiveness and robustness of DDC-CDIN for detecting well-structured and topologically coherent communities in complex networks. Full article

Dynamic Spectrum Access (DSA) has emerged as a viable solution to address spectrum scarcity in shared-spectrum networks. In response, the FCC established the Citizens Broadband Radio Service (CBRS) to manage and facilitate shared use of the federal and non-federal spectrum in a three-tiered access and authorization framework. However, due to the open nature of spectrum access and the usually limited coverage of the monitoring infrastructure, enforcing access rights in a shared-spectrum network becomes a daunting challenge. In this paper, we stipulate the use of crowdsourcing as a viable approach to engaging volunteers in spectrum monitoring in order to enforce spectrum access rights robustly and reliably. The success of this approach, however, hinges strongly on ensuring that spectrum access enforcement is carried out by reliable and trustworthy volunteers within the monitored area. To this end, a hybrid spectrum monitoring framework is proposed, which relies on opportunistically recruiting volunteers to augment the otherwise limited infrastructure of trusted devices. Although a volunteer’s participation has the potential to enhance monitoring significantly, their mobility may become problematic in ensuring reliable coverage of the monitored spectrum area. To ensure continued monitoring, inspite of volunteer mobility, deep learning-based models are used to predict the likelihood that a volunteer will be available within the monitoring area. Three models, namely LSTM, GRU, and Transformer, are explored to assess their feasibility and viability to predict a volunteer’s availability likelihood over an extended time interval, in a given spectrum monitoring area. Recurrent Neural Networks (RNNs) such as GRU and LSTM are effective for tasks involving sequential data, where both spatial and temporal patterns matter, which is the focus of volunteer availability prediction in spectrum monitoring. Transformers, on the other hand, excel at handling long range dependencies and contextual understanding. Furthermore, their parallel processing capabilities allows faster training and inference compared to RNN-based models like GRU and LSTM. A simulation-based study is developed to assess the performance of these models, and carry out a comparative analysis of their ability to predict volunteers’ availability to monitor the spectrum reliably. To this end, a real-world trace dataset of volunteers’ location, collected over five years, is used. The simulation results show that the three models achieve high prediction accuracy of volunteers’ availability, ranging from 0.82 to 0.92. The results also show that a GRU-based model outperforms LSTM and Transformer-based models, in terms of accuracy, Root Mean Square Error (RMSE), geodesic distance, and execution time. Full article

In this article, we introduce analogues of classic Euclidean bounds, including spherical caps, geodesic axis-aligned bounding boxes (AABBs), geodesic oriented bounding boxes (OBBs), and geodesic k-discrete oriented polytopes (k-DOPs). We also formulate k-circle coverage, a union of variable-radius caps solved by a binary integer program over candidates generated from Discrete Global Grid System (DGGS)-based rasterization. As all constructions run directly on the spherical surface, $S^2$, they preserve geodesic distances and avoid projection distortion. We benchmark these methods on seven country boundary polygons consisting of thousands of points, and report construction time, memory, tightness, and query throughput. Results show our analytic geodesic bounds deliver orders of magnitude improvements over exact tests, with trade-offs in tightness: spherical caps are fastest but loosest; geodesic OBBs are a strong balance; geodesic k-DOPs consistently have the tightest bounds. k-circle coverage has spherical cap query speed while also having locally adaptive fits; construction time increases with DGGS resolution. Altogether, these bounds specific to the sphere provide practical, conservative filters for globe-scale Digital Earth queries. Full article

The rapid expansion of telecommunication infrastructure in developing countries has increased the demand for sustainable strategies to deploy field engineers in tower maintenance operations. Traditional approaches often neglect spatial factors, resulting in inefficient workforce allocation, excessive travel, and higher carbon emissions. This study develops an applied geospatial deployment framework that integrates spatial analysis with sustainable supply chain management (SSCM) principles to support operational decision-making in resource-constrained telecommunication maintenance environments. Using publicly available tools, tower and homebase coordinates were mapped and analyzed through Haversine-based geodesic distance calculations, with a comparative assessment against Euclidean approximation, while incorporating operational constraints such as service time per tower, available personnel, and work-hour limitations. The results indicate that the existing two-homebase deployment strategy leads to unbalanced workloads and unnecessary travel distances. By introducing a cluster-based restructuring using k-means to identify four sub-homebases, the proposed approach reduces total round-trip travel distance from 9120 km to 5913 km per maintenance cycle, representing a 35.2% reduction. This distance reduction corresponds to an estimated saving of approximately 593 kg of CO₂ emissions per maintenance cycle, representing an operational-scale reduction in travel-related emissions based on distance-derived fuel consumption modeling and assuming typical fuel efficiency for service vehicles. In addition, the optimized spatial configuration enables a more equitable distribution of engineers and reduces travel-related fatigue. These findings demonstrate the value of integrating geospatial optimization with sustainable supply chain management by aligning operational efficiency with quantifiable environmental and social sustainability outcomes. The proposed framework offers a replicable, low-cost, and data-driven solution for telecommunication infrastructure providers seeking to enhance the sustainability of field service operations in resource-constrained environments. Full article

This article presents a comprehensive and analytically explicit study of optimal discrete quantization on spherical geometries equipped with the geodesic metric. Focusing on highly symmetric configurations on the unit sphere ${\mathbb{S}}^2$, we investigate three explicit models of discrete uniform distributions and derive closed-form expressions for their optimal quantizers and corresponding mean square quantization errors. (I) For N equally spaced points on the equator, we obtain exact error formulas for both divisible and non-divisible cases $n\nmid N$, demonstrating that optimal Voronoi cells form contiguous arcs with midpoint representatives. (II) For two antipodally symmetric small circles at latitudes $\pm {\varphi }_0$, each with M longitudes, we prove a no-cross-circle Voronoi phenomenon, establish symmetry-preserving optimality, and derive finite-sum error formulas together with sharp curvature-dependent bounds and asymptotics. (III) For a single small circle at latitude ${\varphi }_0$, we obtain analogous exact error formulas and show that curvature reduces distortion by a factor of ${cos}^2{\varphi }_0$, while preserving the $n^{-2}$ decay rate. Across all models, we rigorously establish the “block midpoint principle”: optimal Voronoi cells on a circle are contiguous azimuthal blocks, and their optimal representatives are the corresponding azimuthal midpoints. Numerical tables and illustrative figures highlight curvature effects and compare divisible and non-divisible cases. An algorithmic appendix provides pseudocode and a small, commented Python implementation to facilitate reproducibility. Written with didactic clarity while maintaining full mathematical rigor, this work bridges geometric intuition and analytic precision, providing explicit benchmark models that illuminate curvature effects and support further developments in quantization on curved manifolds. Full article