Study of SO(3)-irreducible geometry in complex 5D and ternary Pauli exclusion principle.
problem Exploring SO(3)-irreducible geometry in complex 5D.
method Defined a ternary skew-symmetric tensor, split the 10D space into irreducible SO(3) subspaces, found invariants and defined geometric structures.
result Defined a SO(3)-irreducible geometric structure on a 5D complex Hermitian manifold.
This paper presents results on the extent to which mean curvature data can be used to determine a surface in space or its shape. The emphasis is on Bonnet's problem: classify and study the surface immersions in R3 whose shape is not uniquely determined by the first fundamental form and the mean curvature function. …
We prove rigidity theorems for shrinking gradient Ricci solitons supporting the Heisenberg-Pauli-Weyl uncertainty principle with the sharp constant in Rn. In addtion, we partially give analogous rigidity results of the Caffarelli-Kohn-Nirenberg inequalities on shrinking Ricci solitons.
The paper proves uncertainty principles on Finsler measure spaces.
problem Uncertainty principles on Finsler measure spaces.
method Analyzes Lp-uncertainty principles on Finsler measure spaces with bounded curvatures. result Sharp Lp-uncertainty principles are proven and characterized. Study sharp lower bounds on negative eigenvalues of magnetic Pauli operator.
problem Counting negative eigenvalues of magnetic Pauli operator.
method Reduction to boundary Dirac operator, Atiyah-Patodi-Singer index theory, Benjamin-Ono equation conservation law.
result New formula on the number of eigenvalues of magnetic Neumann Laplacian in semi-classical limit.
We study the problem of reconstructing an unknown matrix M of rank r and dimension d using O(rd poly log d) Pauli measurements. This has applications in quantum state tomography, and is a non-commutative analogue of a well-known problem in compressed sensing: recovering a sparse vector from a few of its Fourier coeffic…
Proves inequalities on curved spaces with positive curvature.
problem Proving inequalities on manifolds with nonnegative Ricci curvature.
method Analyzes manifolds with nonnegative Ricci curvature and Euclidean volume growth.
result Proves Heisenberg-Pauli-Weyl, Hardy-Sobolev, and Caffarelli-Kohn-Nirenberg inequalities.
New method stabilizes quantum ergodicity for mixed quantization and partial hyperbolicity.
problem Stabilizing quantum ergodicity for complex systems.
method Combines mixed quantization techniques with stable ergodicity results for partially hyperbolic systems.
result Establishes stable quantum ergodicity for spin Hamiltonians.
Extends conformal prediction to contrastive learning for better coverage of positive samples.
problem Lack of principled guarantees on coverage in contrastive learning.
method Introduces minimum-volume covering sets with learnable constraints.
result Improves inclusion-exclusion trade-offs in positive and negative samples.
Alternative proofs for various inequalities on Riemannian manifolds.
problem Various functional inequalities on Riemannian manifolds.
method Generic functional inequality, Riccati pairs, solving Riccati-type ODE.
result Alternative proofs for multiple inequalities, including Hardy-type and Caccioppoli inequalities.
Moebius-Kantor graph connects multiple groups and topological properties.
problem Characterize the Moebius-Kantor graph and its associated groups.
method Topological graph theory, group theory, fixed point theorem, metric space.
result The Moebius-Kantor graph (MK) has a unique algebraic group structure.
Density matrices are positively semi-definite Hermitian matrices with unit trace that describe the states of quantum systems. Many quantum systems of physical interest can be represented as high-dimensional low rank density matrices. A popular problem in {\it quantum state tomography} (QST) is to estimate the unknown l…
Improved MoM estimator enhances classical shadows protocol for quantum measurements.
problem Efficient estimation of expectation values with reduced measurement shots.
method Modified median-of-means estimator with optimal constants and U-statistics.
result Improved performance of modified estimator for Clifford measurements.
Study online learning of quantum processes, showing feasibility for certain types.
problem Learning quantum processes adaptively, especially for bounded gate complexity and Pauli channels.
method Online learning, mistake-bounded model, multiplicative weights update algorithm, Bell sampling.
result Online learning feasible for quantum channels of bounded gate complexity and Pauli channels.
We introduce an irreversible discrete multiplicative process that undergoes Bose-Einstein condensation as a generic model of competition. New players with different abilities successively join the game and compete for limited resources. A player's future gain is proportional to its ability and its current gain. The the…
The paper proves Hardy inequalities on Finsler manifolds using superharmonicity.
problem Establishing Hardy inequalities on Finsler manifolds.
method Using superharmonicity of a weight function and properties of the Finsler-Laplace operator.
result Generalization of Riemannian Hardy inequalities to Finsler manifolds.
This paper compares classical shadows and direct quantum measurement for efficient information extraction.
problem Efficiently extracting classical information from quantum states with limited classical post-processing.
method Quantitative resource analysis comparing classical shadows and direct quantum measurement.
result An efficiency frontier between classical shadows and direct quantum measurement is identified.
Research quantifies financial exclusion risks in UK, focusing on cash infrastructure and socio-economic factors.
problem Localised financial exclusion in the UK as cash infrastructure declines.
method Developed a composite indicator using various input variables.
result Financial exclusion is more prevalent in deprived communities and affluent areas.
Many practical applications such as gene expression analysis, multi-task learning, image recognition, signal processing, and medical data analysis pursue a sparse solution for the feature selection purpose and particularly favor the nonzeros \emph{evenly} distributed in different groups. The exclusive sparsity norm has…
Develops a dynamical method to prove the sharp Berezin-Li-Yau inequality.
problem Proving the sharp Berezin-Li-Yau inequality for convex domains.
method Volume-preserving mean curvature flow and a new monotonicity principle.
result Shows the sharp Berezin-Li-Yau bound for every smooth convex domain.
Introduces joint exclusivity (JE), a new form of negative dependence.
problem Negative dependence structures in probability distributions.
method Defines JE by exclusion of the interior of the non-negative orthant, establishes necessary and sufficient conditions for existence, proposes a canonical construction.
result Sharp necessary and sufficient condition for existence of JE random vectors with prescribed marginals.
We consider the symmetric exclusion process on suitable random grids that approximate a compact Riemannian manifold. We prove that a class of random walks on these random grids converge to Brownian motion on the manifold. We then consider the empirical density field of the symmetric exclusion process and prove that it …
Quantum CNNs can be efficiently simulated classically on simple datasets.
problem Quantum CNNs' success on simple datasets is due to low-bodyness measurements.
method Classical simulation using Pauli shadows on low-bodyness subspace.
result Quantum CNNs' action on low-bodyness subspace can be efficiently simulated classically.
Exclusive Group Lasso improves feature selection in correlated biological data.
problem Correlated features hinder Lasso performance in biological classification problems.
method Proposes and solves the exclusive group Lasso, combining stability selection and random group allocation.
result Exclusive Group Lasso outperforms Lasso in comprehensive selection of informative features.
Exclusive Lasso improves survival prediction in cancer datasets.
problem Enhanced survival prediction in cancer datasets with high-dimensional genomic and clinical data.
method Proposes Exclusive Lasso regularization for feature selection in Cox regression models for grouped variables.
result Demonstrates improved survival prediction performance using Exclusive Lasso compared to standard Cox regression.
The polynomial affine model of gravity is explored in 3D, focusing on cosmological solutions.
problem Exploring deviations from general relativity in a 3D context.
method Developed a polynomial affine model of gravity, applied to homogeneous isotropic cosmological models, and classified solutions.
result Explicit solutions derived from the connection allow the definition of alternative/emergent metrics.
New findings show functional inequalities fail on Finsler manifolds with positive S-curvature.
problem Failure of functional inequalities on Finsler manifolds with positive S-curvature.
method Analysis of Finsler metric measure manifolds with reversibility, flag curvature, and S-curvature.
result Functional inequalities fail on Finsler manifolds with positive S-curvature.
Quantum method detects financial stress regimes from market data.
problem Detecting financial stress regimes from market data.
method Adapted Pauli Correlation Encoding to quantum topological data analysis.
result Quantum method can recover Betti numbers exactly at every scale.
New method selects variables in groups with few nonzeros, improving support recovery.
problem Structured variable selection with sparse patterns across groups.
method Composite norm and proximal algorithm for exclusive group sparsity.
result Asymptotic consistency in signed support recovery under conventional assumptions.
The paper proposes a model to learn disentangled representations using mutual information.
problem Learning disentangled representations from shared and exclusive attributes.
method Mutual information maximization for shared attributes and minimization for disentanglement.
result The proposed model outperforms state-of-the-art models in representation disentanglement.
The prolongation structure of a two-by-two problem is formulated very generally in terms of exterior differential forms on a standard representation of Pauli matrices. The differential system is general without making reference to any specific equation. An integrability condition is provided which gives by construction…
ETM identifies field-specific keywords in text classification.
problem Unsupervised text classification with field-specific keywords.
method Weighted Lasso penalty and pairwise Kullback-Leibler divergence penalty for topic separation.
result ETM improves topic coherence by 22% and 10% compared to LDA.
The paper models SaaS products as insurance, offering new pricing tools.
problem Modeling capped-usage SaaS products with insurance principles.
method Frequency-severity decomposition, premium calculation, Monte Carlo simulations.
result SaaS pricing can be analyzed using insurance actuarial methods.
An exclusion particle model is considered as a highly simplified model of a limit order market. Its price behavior reproduces the well known crossover from over-diffusion (Hurst exponent H>1/2) to diffusion (H=1/2) when the time horizon is increased, provided that orders are allowed to be canceled. For early times a ma…
Negative screening is one method to avoid interactions with inappropriate entities. For example, financial institutions keep investment exclusion lists of inappropriate firms that have environmental, social, and government (ESG) problems. They create their investment exclusion lists by gathering information from variou…
Spaces of polynomials are shown to be Euclidean balls.
problem Understanding the geometry of Lorentzian and real stable polynomials.
method Refined connection between symmetric exclusion process and polynomial geometry.
result Spaces of Lorentzian and real stable polynomials are homeomorphic to closed Euclidean balls.
The biggest problem with the methods of machine learning used today in business analytics is that they do not generalize well and often fail when applied to new data. One of the possible approaches to this problem is to enrich these methods (which are almost exclusively based on statistical algorithms) with some intrin…
The Blaschke rolling disk theorem is extended to non-convex domains.
problem Classical inclusion principle for non-convex domains.
method Geometric conditions based on curvature, algorithm for decomposition.
result Necessary and sufficient conditions for rolling disks in non-convex domains.
New study analyzes security of neural network data reconstruction attacks.
problem Data reconstruction attacks pose a threat to private training data.
method Analyzes security boundary of data reconstruction attacks via neuron exclusivity state.
result Characterizes insecure/secure boundary of data reconstruction attacks.
The paper deals with a formally self-adjoint first order linear differential operator acting on m-columns of complex-valued half-densities over an n-manifold without boundary. We study the distribution of eigenvalues in the elliptic setting and the propagator in the hyperbolic setting, deriving two-term asymptotic form…
Quantum reservoir computing needs coherence influx for effective information processing.
problem Understanding and optimizing quantum reservoir computing.
method Theoretical and numerical analysis of quantum systems, focusing on coherence influx and spectral radius of Pauli transfer matrix.
result Coherence influx is essential for realizing nonstationary echo state property in quantum reservoir computing.
Develops a framework for consistent loss functions with variable transformations.
problem Lack of theoretical understanding of variable transformations in consistent loss functions.
method Formal characterizations of consistency for transformed loss functions in two cases: realization and prediction variables.
result Establishes new identifiable and elicitable functionals for complex predictive tasks.
An ongoing challenge in the analysis of document collections is how to summarize content in terms of a set of inferred themes that can be interpreted substantively in terms of topics. The current practice of parametrizing the themes in terms of most frequent words limits interpretability by ignoring the differential us…
Unsupervised learning is becoming more and more important recently. As one of its key components, the autoencoder (AE) aims to learn a latent feature representation of data which is more robust and discriminative. However, most AE based methods only focus on the reconstruction within the encoder-decoder phase, which ig…
Dagma-DCE improves causal discovery with interpretable measures and open-source code.
problem Arbitrary proxy measures of causal strength in non-parametric causal discovery.
method Uses weighted adjacency matrices based on an interpretable measure of causal strength.
result Achieves state-of-the-art performance in simulated datasets.
This paper introduces modal epistemic tools for risk management.
problem Identifying and certifying risk claims when institutions lack the necessary epistemic stance.
method Develops crisp and fuzzy modal semantics for assurance and working commitment, distinguishing between object-level risk claims and meta-level epistemic diagnostics.
result Risk governance should model evidential incompleteness and failures of escalation, not just hazards and losses.
Various strategies for active learning have been proposed in the machine learning literature. In uncertainty sampling, which is among the most popular approaches, the active learner sequentially queries the label of those instances for which its current prediction is maximally uncertain. The predictions as well as the …
Log-conformal projective pairs restrict to simple geometric structures.
problem Characterizing pairs of projective manifolds with logarithmic conformal tensors.
method Analyzing the nefness and triviality of KX+Δ to deduce geometric properties. result Pairs of projective manifolds with logarithmic conformal tensors are restricted to simple geometric structures.