Researchers analyze sign choices for O-planes in orientifolds, proving stabilisation and deriving topological constraints.
problem Assigning sign choices to O-planes in orientifolds of type II string theory.
method Investigating sequences of invariant p-gerbes and coboundary maps to derive sign choices and topological constraints.
result Sign choice homomorphisms stabilise with the dimension of the orientifold and topological constraints on sign configurations are derived.
In this note we present an explicit isomorphism between Khovanov-Rozansky sl2-homology and ordinary Khovanov homology. This result was originally stated in Khovanov and Rozansky's paper \cite{KRI}, though the details have yet to appear in the literature. The main missing detail is providing a coherent choice of sign…
GANs generate new traffic sign images to improve recognition accuracy.
problem Lack of data limits SqueezeNet's performance in traffic sign recognition.
method Applied pix2pix GANs to translate symbolic sign images to real ones for data augmentation.
result Data augmentation with GANs increased classification accuracy for traffic signs.
Study finds color-coded DMSs improve driver behavior.
problem Improving driver behavior through dynamic message signs.
method Random forest algorithm for route diversion, choice, and compliance analyses.
result Color-coded DMSs are more effective than alphanumeric ones.
New tests for high-dimensional data improve on existing methods.
problem Testing mean vectors in high-dimensional data.
method Generalized multivariate sign transformation, using different norm functions.
result Tests using generalized signs have higher power than existing tests.
By specifying model free preferences towards simple nested classes of lottery pairs, we develop the dual story to stand on equal footing with that of (primal) risk apportionment. The dual story provides an intuitive interpretation, and full characterization, of dual counterparts of such concepts as prudence and tempera…
The Seiberg-Witten equation with multiple spinors generalises the classical Seiberg-Witten equation in dimension three. In contrast to the classical case, the moduli space of solutions M can be non-compact due to the appearance of so-called Fueter sections. In the absence of Fueter sections we define a sign…
Study improves choice model accuracy and heterogeneity representation using mixture models.
problem Improving prediction accuracy and heterogeneity representation in choice models.
method Semi-nonparametric Latent Class Choice Model with mixture models and EM algorithm.
result Mixture models enhance prediction accuracy and heterogeneity representation without sacrificing interpretability.
Paper introduces stable vectorization for multiparameter PH using signed barcodes.
problem Lack of stable vectorization methods for multiparameter persistent homology.
method Signed barcodes as measures for stable vectorization of MPH.
result Stable feature vectors from signed barcodes improve performance in data science.
We present a simple approach to forecasting conditional probability distributions of asset returns. We work with a parsimonious specification of ordered binary choice regression that imposes a connection on sign predictability across different quantiles. The model forecasts the future conditional probability distributi…
New neural architectures invariant to sign flips and basis symmetries for graph representation learning.
problem Learning invariant graph representations from eigenvectors.
method SignNet and BasisNet neural architectures that are invariant to sign flips and basis symmetries.
result Proven to be universal, approximating any continuous function of eigenvectors with desired invariances.
A new method reduces preference distortion in LLM alignment.
problem Vulnerability of traditional LLM alignment methods to human preference heterogeneity.
method Sign Estimator: A simple, provably consistent, and efficient estimator using binary classification loss.
result Substantially reduces preference distortion over a panel of simulated personas.
In electricity markets, it is sensible to use a two-factor model with mean reversion for spot prices. One of the factors is an Ornstein-Uhlenbeck (OU) process driven by a Brownian motion and accounts for the small variations. The other factor is an OU process driven by a pure jump Lévy process and models the characteri…
Introduces a metric on vector-valued one-forms for functional data analysis.
problem Metric on vector-valued one-forms for functional data analysis.
method Diffeomorphism-invariant Riemannian metric calculation and geodesic equations.
result Geodesically and metrically incomplete space with specific curvature properties.
This paper begins with an observation that the isospectral leaves of the signed Toda lattice as well as the Toda flow itself may be constructed from the Tomei manifolds by cutting and pasting along certain chamber walls inside a polytope. It is also observed through examples that although there is some freedom in this …
A new method, Residual-Permuted Sums, improves confidence region construction for linear regression models.
problem Constructing reliable confidence regions for linear regression models with non-symmetric noise.
method Residual-Permuted Sums (RPS) method, which permutes residuals instead of perturbing their signs.
result RPS provides exact finite sample coverage probabilities and is uniformly strongly consistent.
We provide a geometric explanation for the existence of magnification relations for the A, D, E family of caustic singularities, which were established in recent work. In particular, it was shown that for families of general mappings between planes exhibiting any of these caustic singularities, and for any non-caustic …
Study on signed graphs with random signs, focusing on community detection.
problem Community detection in signed stochastic block models.
method Strong concentration inequalities for adjacency and Laplacian matrices, applied to signed Laplacian matrix.
result The sign of the first eigenvector of the Laplacian matrix defines a weakly consistent estimator for balanced community detection.
SELO model predicts link signs better than SDGNN using subgraph encoding and linear optimization.
problem Inferring the sign of links in signed networks with limited sign data.
method Subgraph Encoding via Linear Optimization (SELO) approach to learn edge embeddings.
result SELO model outperforms state-of-the-art methods on multiple real-world signed networks.
We argue that the standard graph Laplacian is preferable for spectral partitioning of signed graphs compared to the signed Laplacian. Simple examples demonstrate that partitioning based on signs of components of the leading eigenvectors of the signed Laplacian may be meaningless, in contrast to partitioning based on th…
Results are obtained on extending flat vector bundles or equivalently general representations from the fundamental group of S, a connected subsurface of the connected boundary of a compact, connected, oriented 3-dimensional manifold, to the whole manifold M. These are applied to representations of fundamental groups of…
Novel GNN for signed and directed networks using magnetic signed Laplacian.
problem Efficiently modeling signed and directed networks for tasks like clustering and link prediction.
method Introduced a magnetic signed Laplacian for directed signed graphs, used it to construct a spectral GNN.
result Demonstrated effective performance on tasks involving signed and directional information.
Same homology via different sign assignments in link Floer theory.
problem Comparing sign assignments in link Floer homology.
method Comparison of sign assignments from two different constructions.
result Small modification of sign convention results in identical chain complexes.
Improved node classification in signed social networks using diffuse interface methods.
problem Classifying nodes in signed social networks (positive and negative interactions).
method Diffuse interface methods based on Ginzburg-Landau functional and extended graph Laplacian.
result Performance improvement in real signed social networks, outperforming state of the art.
Local explanation methods, also known as attribution methods, attribute a deep network's prediction to its input (cf. Baehrens et al. (2010)). We respond to the claim from Adebayo et al. (2018) that local explanation methods lack sensitivity, i.e., DNNs with randomly-initialized weights produce explanations that are bo…
Sign equivariant networks improve model expressiveness for spectral geometric learning.
problem Limited expressiveness of sign invariant models for tasks like graph link prediction.
method Developed sign equivariant neural network architectures based on new analytic sign equivariant polynomials.
result Sign equivariant models achieve theoretical benefits in spectral geometric learning tasks.
We organize the quantum hyperbolic invariants (QHI) of 3-manifolds into sequences of rational functions indexed by the odd integers N≥3 and defined on moduli spaces of geometric structures refining the character varieties. In the case of one-cusped hyperbolic 3-manifolds M we generalize the QHI and get rati…
We define a family of formal Khovanov brackets of a colored link depending on two parameters. The isomorphism classes of these brackets are invariants of framed colored links. The Bar-Natan functors applied to these brackets produce Khovanov and Lee homology theories categorifying the colored Jones polynomial. Further,…
Defines signed quasiregular curves and proves growth theorem.
problem Understanding growth of signed quasiregular curves.
method Proves weak reverse Hölder inequality and uses it to prove growth theorem.
result Proves growth theorem for signed quasiregular curves.
New approach uses graphs for sign language recognition.
problem Challenges in recognizing sign language for deaf individuals.
method Spatial-Temporal Graph Convolutional Network.
result Improved sign language recognition using human skeletal movements.
We investigate how the choice of decision makers can be varied under the presence of risk and uncertainty. Our analysis is based on the approach we have previously applied to individual decision makers, which we now generalize to the case of decision makers that are members of a society. The approach employs the mathem…
PyTorch Geometric Signed Directed fills the gap for GNNs on signed and directed graphs.
problem Lack of unified software packages for GNNs on signed and directed networks.
method Developed a software package with GNN models, synthetic and real-world data, and evaluation metrics.
result Demonstrates the effectiveness of the implemented methods through experiments.
Proposes a privacy-preserving sign selection method for distributed systems.
problem Sign selection in distributed differentially private settings.
method Iterative peeling of stability function combined with exponential mechanism.
result Recovery of support and signs with optimal signal-to-noise ratio.
A new Weyl prior is proposed for Bayesian statistics, offering a more canonical choice for parameter α.
problem Choosing a prior distribution for Bayesian inference.
method Proposed a new Weyl prior based on the Weyl structure on a statistical manifold.
result The Weyl prior is a special case of the α-parallel prior with α = -n, where n is the dimension of the statistical manifold.
New method clusters signed graphs using matrix power means.
problem Clustering signed graphs with positive and negative relations.
method Signed Power Mean Laplacian, defined as matrix power mean of normalized standard and signless Laplacians.
result Signed power mean Laplacian captures ground truth clusters under reasonable settings.
Consider the recovery of an unknown signal x from quantized linear measurements. In the one-bit compressive sensing setting, one typically assumes that x is sparse, and that the measurements are of the form sign(⟨ai,x⟩)∈{±1}. Since such measurements give no informati…
Estimates graph curvature and diameter using Laplacian eigenvalues.
problem Estimating graph curvature and diameter using Laplacian eigenvalues.
method Combination of gradient estimates and strong nodal domain walks.
result Li-Yau type eigenvalue-diameter estimate for signed graphs.
The paper discovers patterns in Maass forms' coefficients related to Fricke signs.
problem Identifying Fricke signs in Maass forms with unknown signs.
method Averaging Fourier coefficients, Linear Discriminant Analysis (LDA), neural networks.
result 96% accuracy in predicting Fricke signs for forms with even parity, 94% for odd parity.
Novel CNN array for sign language recognition using wearable IMUs.
problem Efficiently recognizing sign language from wearable IMU signals.
method Two-dimensional Convolutional Neural Network array architecture for Indian sign language recognition.
result Peak classification accuracies of 94.20% for general sentences and 95.00% for interrogative sentences achieved.
Derives variance kernel for reaction boundary in financial models.
problem Separating components in financial volatility models.
method Operational-time variance kernel, damped Abel response kernel, closed asymptotic form.
result Operational variance has a closed asymptotic form involving various parameters.
In this paper we use theory of embedded graphs on oriented and compact PL-surfaces to construct minimal realizations of signed Gauss paragraphs. We prove that the genus of the ambient surface of these minimal realizations can be seen as a function of the maximum number of Carter's circles. For the case of signed Gaus…
Method predicts which high-dimensional correlation signs will change in the future.
problem Predicting which correlation matrix coefficients will change signs in high-dimensional data.
method Stability of correlation signs depends on three-by-three relationships, inspired by Heider social cohesion theory.
result The method accurately predicts the stability of correlation signs in high-dimensional data.
CSNE embeds signed networks by separating structural and fine-grained information.
problem Improving sign prediction in signed networks using inaccurate or incomplete balance theories.
method Conditional Signed Network Embedding (CSNE) models structural and fine-grained information separately, integrating them rigorously.
result CSNE outperforms state-of-the-art on sign prediction tasks, and MaxEnt priors are competitive in resource-constrained settings.
This paper consists of two parts. First, motivated by classic results, we determine the subsets of a given nilpotent Lie algebra g (respectively, of the Grassmannian of two-planes of g) whose sign of Ricci (respectively, sectional) curvature remains unchanged for an arbitrary choice of a posit…
Derives operational-time variance kernel for reaction boundaries in financial markets.
problem Separating components in volatility models to better understand market dynamics.
method Derives a variance kernel for a latent-order-book reaction boundary, separating structural boundary cumulant, clock projection, and pricing-measure choice.
result Operational variance has a closed asymptotic form for long-memory forcing, with effective signed-forcing intensity and resilience.
Signed seminorms linked to real tropical spaces and matroids.
problem Understanding signed seminorms and their real tropicalizations.
method Introducing signed Goldman-Iwahori space, identifying it as inverse limit of real tropicalizations, and giving matroid-theoretic description.
result Signed seminorms identified as inverse limit of real tropicalizations of projective space.
Unified sign-based compression for federated learning with faster convergence.
problem High communication cost in federated learning with large-scale models.
method Unified noisy perturbation scheme for sign-based compression.
result Achieves faster convergence rate than existing sign-based methods.
The paper finds sign-changing solutions for a specific type of elliptic equation.
problem Existence of sign-changing solutions for a Yamabe type equation.
method Investigates a critical elliptic equation with a Yamabe type operator on a compact manifold with boundary.
result Existence of sign-changing solutions assured under certain geometric conditions.