New method optimizes searchers' allocation on perimeters over time.
problem Optimizing searchers' allocation on perimeters to detect intrusions.
method Combinatorial multi-armed bandit (CMAB) with upper confidence bound approach.
result Upper and lower bounds on expected performance of the method.
Minimal partitions with minimal perimeter found in metric spaces.
problem Finding minimal partitions with minimal perimeter in metric spaces.
method Existence proof and regularity analysis of minimal domains.
result Existence and regularity of minimal partitions in various metric spaces.
Hexagonal tilings minimize perimeter with unequal volumes.
problem Finding optimal tessellations with unequal cell volumes.
method Minimizing perimeter functionals for different classes of problems.
result Hexagonal tilings are optimal among partitions with almost equal areas.
Paper finds formulas for minimizing perimeter in special spaces, proving key dimensions and existence.
problem Understanding the structure of perimeter minimizing sets in specific metric spaces.
method Established a monotonicity formula and proved rigidity for perimeter minimizers in RCD(0,N) spaces.
result Sharp Hausdorff dimension estimates for singular strata and existence of blow-down cones.
Foliation of star-shaped polygons with fixed perimeter and area.
problem Characterizing star-shaped polygons with fixed perimeter and area.
method Analyzing families of star-shaped n-polygons in the Euclidean plane.
result Existence and properties of foliations on the space of star-shaped n-polygons.
Infinite hyperbolic manifolds share same perimeter-to-volume ratio.
problem Finding hyperbolic manifolds with a fixed perimeter-to-volume ratio.
method Constructing infinitely many hyperbolic manifolds with nonempty boundaries.
result Existence of incommensurable hyperbolic manifolds with a fixed perimeter-to-volume ratio.
New method tackles anomaly detection in video surveillance using continual learning.
problem Challenges in continual learning for high-dimensional applications like video surveillance.
method Transfer learning and continual learning for online anomaly detection.
result Significantly reduces training complexity and continual learning from recent data.
The paper examines perimeter minimizing sets in curved spaces and finds conditions for their boundary to match a specific structure.
problem Conditions for perimeter minimizing sets in curved spaces to have a boundary matching a product structure.
method Analyzes Riemannian manifolds with non-negative sectional curvature and quadratic volume growth.
result The boundary of a perimeter minimizing set in such manifolds is identified with a slice in the product structure.
Proof shows smooth minimal hypersurfaces for perimeter-minimizing sets in low-dimensional Riemannian manifolds.
problem Finding sets of least perimeter in Riemannian manifolds.
method Short proof using de Giorgi and Miranda's tradition in flat space.
result Reduced boundary of least perimeter sets is a smooth minimal hypersurface in low dimensions.
Study minimizers of quasi-perimeters in RCD spaces with volume constraints.
problem Regularity and topological properties of volume constrained minimizers in RCD spaces.
method New Deformation Lemma and study of interior and exterior points.
result Volume constrained minimizers are open bounded sets with Ahlfors regular boundary.
Perimeter on manifolds leads to new symmetrization methods.
problem Applying symmetrization methods to quasilinear elliptic problems on RN. method Generalization of perimeter to manifolds, using hear kernel regularization.
result New symmetrization method on spheres for quasilinear elliptic problems.
The paper studies properties of RCD(K,N) spaces and their boundaries.
problem Understanding the boundary structure and unit normal on RCD(K,N) spaces. method Proves concentration of boundary measure, discusses localization of unit normal, and develops tools for perimeter minimizers.
result Proves that the boundary measure of sets with finite perimeter is concentrated on the n-regular set Rn. Perimeter minimizers in curved spaces have a singular set no more than 5 dimensions.
problem Understanding the structure of minimizers in spaces with bounded Ricci curvature.
method Analysis of non-collapsed Ricci limit spaces with two-sided curvature bounds.
result The Hausdorff dimension of the singular set is at most \(N-5\).
Improved bio-surveillance through automated document classification.
problem Tracking infectious diseases across global news alerts.
method Recurrent neural networks, TF-IDF, Naive Bayes, logistic regression.
result 97% recall and 93.3% accuracy in bio-surveillance event classification.
The generalized soap bubble problem seeks the least perimeter way to enclose and separate n given volumes in R^m. We study the possible configurations for perimeter minimizing bubble complexes enclosing more than two regions. We prove that perimeter minimizing planar bubble complexes with equal pressure regions and wit…
Classifiers and beamforming algorithms improved audio surveillance detection accuracy.
problem Detecting surveillance sound events with high accuracy and efficiency.
method Evaluated seven classifiers and two beamforming algorithms; used data augmentation and tested with varying SNR levels.
result SVM and Delay-and-Sum (DaS) combination achieved the highest accuracy (86.0%), but had high computational cost.
Study rectifiability of finite perimeter sets in RCD(K,N) spaces.
problem Understanding sets of finite perimeter in RCD(K,N) spaces.
method Developed a Gauss-Green integration by parts formula and proved rectifiability of the reduced boundary.
result Rectifiability of the reduced boundary for sets of finite perimeter over RCD(K,N) spaces.
We show that among sets of finite perimeter balls are the only volume-constrained critical points of the perimeter functional.
We consider sets of locally finite perimeter in Carnot groups. We show that if E is a set of locally finite perimeter in a Carnot group G, then for almost every x in G with respect to the perimeter measure of E, some tangent of E at x is a vertical halfspace. This is a partial extension of a theorem of Franchi-Serapion…
Investigates dual foliations of polygon spaces based on area and perimeter.
problem Understanding dual foliations of polygon spaces guided by area and perimeter.
method Investigated topology of leaves, determined homology groups, and extended isoperimetric duality.
result Homology groups and homotopy types of polygon spaces are determined.
New algorithm rSVDdpd improves robustness and scalability for video surveillance background modeling.
problem Camera tampering and noisy videos make background separation challenging.
method Introduces rSVDdpd, a robust singular value decomposition technique for scalable video surveillance.
result Demonstrates superior performance on benchmark and real-life datasets.
We prove that the least-perimeter partition of the sphere into four regions of equal area is a tetrahedral partition.
Almost perimeter-minimizing boundaries in plentiful groups can be approximated by Lipschitz graphs.
problem Regularity of boundaries in plentiful groups.
method Lipschitz approximation of boundaries.
result Boundary of almost minimizers can be approximated by intrinsic Lipschitz graphs.
We prove a monotonicity result at specific points for the Horizontal Perimeter for a class of surfaces in the Heisenberg group.
This paper explores using a Long short-term memory (LSTM) based sequence autoencoder to learn interesting features for detecting surveillance aircraft using ADS-B flight data. An aircraft periodically broadcasts ADS-B (Automatic Dependent Surveillance - Broadcast) data to ground receivers. The ability of LSTM networks …
Online anomaly detection in surveillance videos with false alarm rate bounds.
problem Lack of theoretical performance analysis and online decision making in anomaly detection.
method Proposes an online anomaly detection method with asymptotic bounds on false alarm rate.
result Demonstrates effectiveness on publicly available data sets, outperforming state-of-the-art algorithms.
We prove the existence of a perimeter-minimizing partition of R^n into regions of unit volume. We conclude with a short tribute to the late Manuel A. Fortes.
DUPLE tackles cross-deployment recognition in fiber-optic perimeter security with meta-learning.
problem Cross-deployment recognition challenges in fiber-optic perimeter security due to label scarcity and distribution shifts.
method DUPLE employs statistically guided meta-learning to enhance recognition robustness across unseen deployments.
result DUPLE consistently outperforms traditional and meta-learning baselines in cross-deployment DFOS benchmarks.
A lens cluster minimizes perimeter in the plane with given area constraints.
problem Minimizing perimeter in the plane with given area constraints.
method Analyzing lens clusters consisting of circular arcs with specific geometric properties.
result Lens clusters are local minimizers of the total perimeter functional.
We prove that a family of entire intrinsic minimal graphs in the Heisenberg group are not perimeter minimizing.
Study finds unique critical points for anisotropic surface energy.
problem Finding unique critical points for anisotropic surface energy.
method Proving finite unions of disjoint open Wulff shapes are volume-constrained critical points.
result Finite unions of disjoint open Wulff shapes are the only critical points.
The paper explores connections between perimeter, area, and visual angle of convex sets.
problem Understanding geometric properties of convex sets through visual angle and related measurements.
method Establishing universal formulas and characterizing convex sets of constant width.
result Crofton's formula is the unique universal formula relating visual angle, length, and area.
Smart city surveillance benefits from sound event recognition.
problem Improving monitoring capabilities in smart cities.
method Exploration of several classifiers on the SESA dataset.
result SGD achieved 72.13% accuracy in sound event recognition.
We prove that, among all convex hyperbolic polygons with given angles, the perimeter is minimized by the unique polygon with an inscribed circle. The proof relies on work of J.-M.\ Schlenker.
Study fractional perimeter asymptotics on Riemannian manifolds as s approaches 0.
problem Asymptotics of fractional perimeter on Riemannian manifolds.
method Analysis of fractional Laplacian and existence of bounded harmonic functions.
result Asymptotics of fractional s-perimeter on all complete manifolds. We develop two types of integral formulas for the perimeter of a convex body K in planar geometries. We derive Cauchy-type formulas for perimeter in planar Hilbert geometries. Specializing to H^2 we get a formula that appears to be new. We show that it implies the standard Cauchy-Santalo formula involving a central ang…
New rectifiability criteria for finite-perimeter sets in Carnot groups.
problem Rectifiability of finite-perimeter sets in Carnot groups.
method Introducing a new notion of rectifiability based on cone properties and studying semigroups generated by horizontal half-spaces.
result Finite-perimeter subsets in Carnot groups can be covered by countably many subsets with cone properties, leading to countable rectifiability with respect to intrinsic Lipschitz graphs.
Online surveillance detects systemic risk in financial markets.
problem Detecting and monitoring systemic risk in financial markets.
method Online monitoring procedures for multiple series, controlling for false rejections.
result Procedures allow timely detection of financial distress.
The study proves properties of optimizers for sets maximizing perimeter under fixed volume constraints.
problem Existence and properties of bounded convex sets in Riemannian manifolds maximizing perimeter under fixed volume constraints.
method Analyzes the properties of optimizers for sets maximizing perimeter under fixed volume constraints in Euclidean, spherical, and hyperbolic spaces.
result Proves that there are no C2-maximisers of perimeter with prescribed volume and that the smallest principal curvature is constant in regions where the set is of class C2. Study proves existence of regions minimizing perimeter in specific geometric structures.
problem Existence of isoperimetric regions in sub-Finsler nilpotent groups.
method Analyzes nilpotent Lie groups with a bracket-generating distribution and asymmetric norms.
result Proves existence of minimizers of perimeter under volume constraint.
The hypercube's perimeter is significantly larger than expected near half volume.
problem Understanding the isoperimetric profile of the hypercube.
method Analytical proof of perimeter bounds and comparison to Gaussian isoperimetric profile.
result The isoperimetric profile of the hypercube does not converge to the Gaussian profile as dimension increases.
Study finds critical points in perimeter functional for fixed volume sets.
problem Finding critical points in perimeter functional for sets of fixed volume.
method Utilizes Mazurwoski--Zhou techniques and new Cacciopoli set connectedness results.
result Constructs smooth almost embedded hypersurfaces with non-zero constant mean curvature.
Supervised learning improves disease outbreak detection accuracy.
problem Early detection of infectious disease outbreaks to protect public health.
method Developed a supervised learning approach based on hidden Markov models for disease outbreak detection.
result Reduces false positive rate by up to 50% while maintaining sensitivity.
Investigates convexity of minimizers under mass constraint using nonlocal perimeter and potential.
problem Convexity of minimizers under mass constraint.
method Nonlocal free energy with nonlocal perimeter and convex potential.
result Quantitative stability theorem for nonlocal free energy assuming symmetry on the potential.
New mathematical surfaces without boundaries found.
problem Existence of nonlocal free boundary minimal surfaces.
method Fractional perimeter critical points with invariant boundary.
result Existence of nonlocal free boundary minimal surfaces without boundaries.
Study optimizes perimeter in convex domains with anisotropic constraints.
problem Optimizing perimeter in convex domains with anisotropic constraints.
method Analytical properties, topological features, and geometric measure theory results.
result Sharp isoperimetric inequalities and existence of minimizers.
We consider isotropic non lower semicontinuous weighted perimeter functionals defined on partitions of domains in Rn. Besides identifying a condition on the structure of the domain which ensures the existence of minimizing configurations, we describe the structure of such minima, as well as their regularity…
Paper describes a video surveillance system for highway traffic events.
problem Detecting specific sequences of situations in highway traffic videos.
method Compares RNN and CNN architectures for analyzing video frames and sequences.
result Best architecture performs well in real conditions.