New proof shows spacetime energy is always positive in higher dimensions.
problem Proving spacetime positive energy in arbitrary dimensions.
method Combines Schoen-Yau, Eichmair, Jang equation, shielding principle.
result Spacetime positive energy theorem proven in arbitrary dimensions.
Extends positive mass theorem to arbitrary dimensions using a new inductive scheme.
problem Overcoming singularities in the Schoen-Yau proof for arbitrary dimensions.
method Inductive scheme combining shielding principle, conformal blow-up, and Cheeger-Naber bound.
result Proof of positive mass theorem in arbitrary dimensions.
We present an elementary argument that one can shield linearised gravitational fields using linearised gravitational fields. This is done by using third-order potentials for the metric, which avoids the need to solve singular equations in shielding or gluing constructions for the linearised metric.
Model analyzes debt recycling strategies under various fiscal regimes and jurisdictions.
problem Understanding debt recycling dynamics and their impact on repayment times and equity growth.
method Developed a calibrated model incorporating mortgage interest rates, borrowing costs, and tax shields.
result Introducing positive interest rates without tax shields contracts success regions and lengthens repayment times, but tax shields partially reverse these effects.
Shielded LMC samples from non-convex spaces with repulsive drift.
problem Sampling from non-convex spaces with convex holes.
method Combining adaptive temperature and repulsive drift.
result Advantages over unconstrained sampling in constrained spaces.
Graph neural networks predict solid-state NMR parameters from atomic structures.
problem Efficiently predicting NMR parameters from atomic structures for complex materials.
method Graph neural networks applied to tensor quantities for anisotropic magnetic shielding and electric field gradient.
result Improved accuracy in predicting NMR properties from diverse and complex materials.
Proves positive mass theorem for spin initial data sets with arbitrary ends and dominant energy shields.
problem Proving the positive mass theorem for spin initial data sets with various ends and energy shields.
method Modification of Witten's approach involving an additional independent timelike direction in the spinor bundle.
result Positive mass theorem for spin initial data sets with arbitrary ends and dominant energy shields.
Generalizes nonnegativity result for Brown-York mass using noncompact fill-ins.
problem Proving nonnegativity of Brown-York mass for noncompact fill-ins.
method Extending positive mass theorem to noncompact and shielded fill-ins.
result Proves nonnegativity of mean curvature for noncompact NNSC fill-ins.
In this appraisal paper, we evaluate the efficacy of SHIELD, a compression-based defense framework for countering adversarial attacks on image classification models, which was published at KDD 2018. Here, we consider alternative threat models not studied in the original work, where we assume that an adaptive adversary …
New method provides scalable safety guarantees for RL agents.
problem Safe reinforcement learning in real-life scenarios.
method State-augmentation and shield design for probabilistic avoidance.
result Strict formal safety guarantees for RL agents, scalable and practical.
Reinforcement learning is a promising approach to synthesizing policies for challenging robotics tasks. A key problem is how to ensure safety of the learned policy---e.g., that a walking robot does not fall over or that an autonomous car does not run into an obstacle. We focus on the setting where the dynamics are know…
Proves positive mass theorem for hyperbolic manifolds with ends.
problem Establishing positive mass theorem for complex initial data sets.
method Used spectral PSC, Jang equation, and quantitative shielding theorem.
result Proved positive mass theorem for asymptotically hyperbolic manifolds.
Recent studies have demonstrated that machine learning approaches like deep neural networks (DNNs) are easily fooled by adversarial attacks. Subtle and imperceptible perturbations of the data are able to change the result of deep neural networks. Leveraging vulnerable machine learning methods raises many concerns espec…
Improves diversity of text-to-image models without sacrificing FID.
problem Lack of diversity and tendency to recreate training set images.
method Adds sparse repellency terms to diffusion SDE to guide trajectories away from a reference set.
result Improves diversity of diffusion models with minimal impact on FID.
Defense strategy improves controller robustness against adversarial attacks.
problem Adversarial attacks on learning-enabled controllers in CPS.
method Two-stage defense strategy treating controller and environment as black-boxes with unknown dynamics.
result Defense strategy effectively improves controller robustness in realistic control domains.
Paper discusses quasilocal mass and fill-ins, proving positivity and exploring definitions.
problem Exploring and defining quasilocal mass and fill-ins in general relativity.
method Analyzes several proposals of quasilocal mass based on Hamiltonian formulation and proves positivity under certain conditions.
result Positivity of Wang-Yau energy under a more general condition.
Proves spacetime positive mass theorem for spin initial data sets with arbitrary ends.
problem Proving the spacetime positive mass theorem for specific spacetime configurations.
method Solving a mixed boundary value problem for the Dirac-Witten operator with a Callias potential.
result Established spacetime positive mass theorem for asymptotically flat spin initial data sets with arbitrary ends.
We perform an optimal localization of asymptotically flat initial data sets and construct data that have positive ADM mass but are exactly trivial outside a cone of arbitrarily small aperture. The gluing scheme that we develop allows to produce a new class of N-body solutions for the Einstein equation, which patently…
We show how to parameterise solutions of the general relativistic vector constraint equation on Einstein manifolds by unconstrained potentials. We provide a similar construction for the trace-free part of tensors satisfying the linearised scalar constraint. Previous work of ours has provided similar different construct…
Flow taxes and stock taxes preserve portfolio neutrality under specific conditions.
problem Analyzing the impact of different types of taxes on portfolio choice.
method Extending the neutrality result to a full system of ownership taxes, showing how each tax modifies the drift of the wealth process.
result The combined system of taxes preserves portfolio neutrality under three conditions, and the drift-shift symmetry generalizes to a drift-shift-and-rescale symmetry.
This work introduces benchmarks for evaluating nanophotonic structures in design simulations.
problem Design and understanding of nanophotonic structures for various applications.
method Development of frameworks and benchmarks for evaluating nanophotonic structures in parametric design problems.
result Strategic use of evaluation fidelity in enhancing structure designs.
Due to globalization, geographic boundaries no longer serve as effective shields for the spread of infectious diseases. In order to aid bio-surveillance analysts in disease tracking, recent research has been devoted to developing information retrieval and analysis methods utilizing the vast corpora of publicly availabl…
Changes in the capital structure before and after the global financial crisis for SMEs are studied, emphasizing their financing problems, distinguishing between internal financing and external financing determinants. The empirical research bears upon 158 small and medium-sized firms listed on Shenzhen and Shanghai Stoc…
The paper establishes distance estimates for manifolds with lower scalar curvature bounds.
problem Distance estimates on manifolds with lower scalar curvature bounds.
method Introduced a definition of relative index via a deformed Dirac operator trick and proved index coincidence with Callias operators.
result Proved short neck inequality and quantitative shielding result with positive scalar curvature.
Study identifies key parameters and input dimensions making LLMs and VLMs brittle.
problem Vulnerability of large language and vision-language models to perturbations.
method Proposed FI measure based on information geometry to quantify sensitivity.
result Small subset of high FI parameters significantly contribute to brittleness.
Pari-mutuel markets are trading platforms through which the common market maker simultaneously clears multiple contingent claims markets. This market has several distinctive properties that began attracting the attention of the financial industry in the 2000s. For example, the platform aggregates liquidity from the ind…
Privacy-preserving crypto exchanges adjust prices based on Gaussian noise.
problem Ensuring fair pricing in privacy-preserving cryptocurrency exchanges.
method Derive Kyle equilibrium with Gaussian noise perturbation, rescaling price-impact and strategy factors.
result Identify a privacy subsidy as a transfer from LP pool to traders, invariant to noise.
GraphShield uses dynamic graph learning to detect and visualize financial risks.
problem Detecting and mitigating risks in financial networks.
method Enhanced Cross-Domain Information Learning, Advanced Risk Recognition, Risk Propagation Visualization.
result GraphShield effectively identifies and visualizes hidden financial risks.
CLEANN detects and mitigates neural network Trojans without labeled data.
problem Trojans in embedded neural networks that bypass detection during inference.
method Dictionary learning and sparse approximation for identifying Trojan triggers, lightweight algorithm/hardware co-design.
result Efficient real-time execution on resource-constrained platforms, competitive attack resiliency.
Deep Learning has established itself to be a common occurrence in the business lexicon. The unprecedented success of deep learning in recent years can be attributed to: abundance of data, availability of gargantuan compute capabilities offered by GPUs, and adoption of open-source philosophy by the researchers and indus…
Develops privacy-preserving methods for longitudinal linear regression.
problem Protecting individual information in longitudinal data with privacy-preserving statistics.
method Proposes a user-level private regression estimator and a privatized covariance estimator for longitudinal linear regression under user-level differential privacy.
result Establishes theoretical guarantees for practical user-level differential privacy estimation and inference in longitudinal linear regression.
Study shows large extra dimensions are hidden from view by black holes.
problem Difficulty in observing large extra dimensions in the universe.
method Analysis of conditions leading to black hole formation in lower dimensional theories.
result Extra dimensions larger than 10−19m are hidden inside black holes. TIP-Search optimizes market prediction accuracy and timeliness under uncertain load.
problem Real-time market prediction requires accurate predictions before a deadline.
method Filters feasible models, dispatches workers, trades accuracy for deadline risk.
result Optimized pool achieves 0.991 timely accuracy and 0.994 raw accuracy.
The flourish of deep learning frameworks and hardware platforms has been demanding an efficient compiler that can shield the diversity in both software and hardware in order to provide application portability. Among the existing deep learning compilers, TVM is well known for its efficiency in code generation and optimi…
Bayesian inference calibrates Hall thruster model uncertainty at varying pressures.
problem Quantifying uncertainty in a multi-component Hall thruster model at different facility pressures.
method Bayesian inference applied to calibrate and quantify prediction uncertainty in a coupled multi-component Hall thruster model.
result Model reduces predictive errors in thrust and discharge current by more than 50% compared to a previous model.
Investigates optimal withdrawal strategies in VA contracts with tax and ratchet mechanisms.
problem Optimizing withdrawal strategies and behavior of policyholders in VA contracts with tax and ratchet mechanisms.
method Solving a backward dynamic programming problem to optimize cash flows from VA contracts, considering hybrid products and taxation effects.
result Tax-shielding effect of the cash fund enhances contract attractiveness, ratchet mechanism discourages early surrender, and cash fund discourages active withdrawals.
We evaluate the applicability of the generic Vickrey-Clarke-Groves (VCG) mechanism as an antimonopoly measure against a profit-maximizing producer with market power operating a portfolio of generating units at the centralized two-settlement energy market. The producer may indicate in its bid not only the altered cost f…
The paper establishes maximum principles and stochastic completeness for pseudo-Hermitian manifolds.
problem Maximum principles and stochastic completeness for pseudo-Hermitian manifolds.
method Established generalized maximum principles and proved stochastic completeness equivalence.
result Stochastic completeness for the heat semigroup is equivalent to generalized maximum principles.
Islamic banks being commercial entities strive to earn profit within shariah ambit. Therefore, they seem to be basing themselves upon two knowledge streams namely i) Islamic jurisprudence principles, and ii) banking principles. Islamic jurisprudence principles primarily aim at bringing shariah compliance while banking …
The starting point of this article is the question "How to retrieve fingerprints of rhythm in written texts?" We address this problem in the case of Brazilian and European Portuguese. These two dialects of Modern Portuguese share the same lexicon and most of the sentences they produce are superficially identical. Yet t…
The h-principle helps solve complex geometric problems.
problem Solving complex geometric problems using the h-principle.
method Developed from the Oka-Grauert principle and Gromov's theory, the h-principle is applied to Oka manifolds and maps.
result Recent developments and applications of the h-principle in complex analysis and geometry.
Extends wealth tax neutrality framework to stochastic volatility and non-homothetic preferences.
problem Ensuring wealth taxes are neutral under various economic conditions.
method Extended Frøseth's neutrality framework to stochastic volatility and non-homothetic preferences, identified four channels of non-neutrality, and applied the framework to global minimum wealth taxes.
result Non-uniform assessment, general equilibrium effects, progressive thresholds, and endogenous labour supply can cause non-neutrality under CRRA preferences.
Bitcoin fails to function as a stable currency or store of value.
problem Bitcoin's failure to serve as a reliable currency or store of value.
method Quantitative finance methods and economic arguments applied to cryptocurrencies.
result Bitcoin does not function as a currency, store of value, or inflation hedge.
The study establishes uncertainty principles on harmonic manifolds of rank one.
problem Developing uncertainty principles for harmonic manifolds of rank one.
method Derivation of various uncertainty principles including Heisenberg, Morgen, Schrödinger, and Hömanders principles.
result Generalization of Hausdorff-Young inequality to harmonic manifolds of rank one.
Enhances cryptocurrency pair trading with DRL, outperforming classical methods.
problem Rigidity and divergence risks in traditional pair trading strategies in crypto markets.
method Hierarchical pair selection, Fixed Risk, Adaptive Mean execution model, PPO with LSTM.
result DRL outperformed heuristic baseline by a statistically significant margin.
Classifier-based AI safety gates fail in self-improvement, even with advanced verification methods.
problem Maintaining reliable oversight of AI systems as they improve over iterations.
method Comprehensive empirical testing on neural controllers and MuJoCo benchmarks, using various classifiers and verification methods.
result Classifier-based safety gates fail in maintaining reliable oversight, even with advanced verification methods.
Shows flexible sheaves as fibrant objects for Gromov's h-principle.
problem Applying the h-principle to partial differential relations.
method Interprets flexible sheaves as fibrant objects in a model structure.
result Flexible sheaves can be understood as fibrant objects.
A new method to break down insurance costs into risk and uncertainty.
problem Understanding and quantifying insurance costs in uncertain environments.
method An axiomatic approach to decompose premium principles into risk and deviation measures.
result Maximal risk and minimal deviation measures can be uniquely identified in decompositions.