A k-space deep learning method corrects EPI ghost artifacts without a reference scan.
problem Nyquist ghost artifacts in EPI MRI due to phase mismatch between even and odd echoes.
method Structured low-rank Hankel matrix approaches combined with data-driven Hankel matrix decomposition and deep convolutional neural networks.
result The proposed k-space deep learning method outperforms existing methods in image quality and computing time.
Paper analyzes learning from ghost imaging without reconstruction bottleneck.
problem High-speed cell classification bottleneck in ghost cytometry.
method Theoretical analysis of learning from ghost imaging without reconstruction.
result Theoretical analysis supports learning from ghost imaging without reconstruction.
Improved pricing of vanilla options using modified Adams method and sinh-acceleration.
problem Calibration of rough Heston model leads to incorrect implied volatility surfaces.
method Modified Adams method and sinh-acceleration for Fourier inversion.
result Corrected implied volatility surface is significantly flatter and fits data poorly.
Ghost points affect stability in finite difference schemes for diffusion equations.
problem Impact of ghost points on stability of finite difference schemes.
method Exploration of explicit Euler finite difference scheme with ghost points on diffusion equation.
result Stability of the scheme is affected by ghost points.
Formula connects length and correlation functions via ghost polygons and Poisson bracket.
problem Understanding functions on moduli spaces of Anosov representations.
method Introduced ghost polygons and ghost algebra to compute Poisson bracket.
result Stability of length and correlation functions under Poisson bracket.
In this paper we define and study the "ghost loop orbifold" of an orbifold X consisting of those loops that remain constant in the coarse moduli space of X. We construct a configuration space model for the ghost loop orbifold using an idea of G. Segal. From this we exhibit the relation between the Hochschild and cy…
The study counts periodic orbits on smooth manifolds, adding ghost orbits for completeness.
problem Counting periodic orbits of vector fields on smooth closed manifolds.
method Enlarging the space of orbits to include ghost orbits, defining weight functions, and showing constancy under deformation.
result The weight function remains constant as the vector field moves and Γ deforms. The (4,5)-torus knot has a unique ghost character with significant implications.
problem Understanding the character variety and fundamental variety of 2-fold branched covers of knots.
method Analyzing the (4,5)-torus knot's ghost character to derive new insights into knot representations and character varieties.
result The (4,5)-torus knot is the simplest example where certain representations cannot be realized by trace-free representations and provides a counterexample to Ng's conjecture.
Ghost mechanism explains abrupt learning in RNNs, revealing constraints on optimization landscapes.
problem Understanding abrupt learning in recurrent neural networks (RNNs) trained on working memory tasks.
method Introducing the ghost mechanism, a process driven by saddle-node bifurcations, to analyze and model abrupt learning.
result A critical learning rate scales as an inverse power law with the timescale of computation, leading to vanishing and oscillatory gradients.
Paper proves generalized Talagrand inequality for Sinkhorn distance.
problem Proving a generalized Talagrand inequality for Sinkhorn distance.
method Using entropy power inequality and infinitesimal displacement convexity of optimal transport map.
result Extends previous results of Gaussian Talagrand inequality for Sinkhorn distance to strongly log-concave case.
A BV algebra is a formal framework within which the BV quantization algorithm is implemented. In addition to the gauge symmetry, encoded in the BV master equation, the master action often exhibits further global symmetries, which may be in turn gauged. We show how to carry this out in a BV algebraic set up. Depending o…
Torus knots (4,5) and (5,6) provide counterexamples to a conjecture about knot contact homology.
problem Ng's conjecture about isomorphism between knot contact homology and character variety fails for certain torus knots.
method Demonstrated through the construction of ghost characters for specific torus knots.
result Counterexamples to Ng's conjecture for (4,5) and (5,6) torus knots. Study predicts configurational energy of high entropy alloys using Bayesian methods.
problem Accurately predict the configurational energy of high entropy alloys with limited data.
method Robust data-driven framework based on Bayesian approaches, including effective pair interaction (EPI) model and ensemble sampling.
result Effective prediction of configurational energy with small data, demonstrating robust performance.
Deep learning boosts rare disease detection from medical claims.
problem Improving diagnosis and treatment of rare diseases.
method Generative adversarial networks (GANs) and recurrent neural networks for sequence modeling.
result Accurate prediction with 0.56 PR-AUC, outperforming benchmarks.
Study reveals hidden null components in overparametrized neural networks.
problem Hidden null components in overparametrized neural networks.
method Structure theorem of null space for neural networks using ridgelet transforms.
result Null components can be uniquely written as linear combinations of ridgelet transforms.
We use conformal, but ghostful, Weyl gravity to study its ghost-free, second derivative, partially massless (PM) spin 2 component in presence of Einstein gravity with positive cosmological constant. Specifically, we consider both gravitational- and self- interactions of PM via the fully non-linear factorization of conf…
Study stability of contingent claim solutions under probabilistic perturbations.
problem Stability of solutions to discrete-time contingent-claim problems under uncertainty.
method Use Rockafellian perturbations to analyze stability of solutions.
result Establishes convergence of dual problems and shadow prices.
We propose a model in which a spliced vector bundle (with an arbitrary number of gauge structures in the splice) possesses a geometry which do not split. The model employs connection 1-forms with values in a space-product of Lie algebras, and therefore interlaces the various gauge structures in a non-trivial manner. Sp…
Combined ML and JVC-SENSE enable high-resolution imaging with fewer shots and less distortion.
problem Severe distortion artifacts and blurring in high-resolution imaging due to shot-to-shot variations in msEPI.
method Employed deep learning to obtain an interim image with minimal artifacts, which was then used in a Joint Virtual Coil Sensitivity Encoding (JVC-SENSE) reconstruction.
result Enabled navigator-free, highly accelerated multishot EPI with fewer shots and improved geometric fidelity.
Gradient method achieves linear convergence for saddle point problems without strong convexity.
problem Solving saddle point problems with non-strongly convex functions.
method Primal-dual gradient method with a novel analysis technique.
result Linear convergence achieved without strong convexity of f. A new model uses 'ghost units' to enable efficient backpropagation in deep neural networks.
problem How to achieve efficient backpropagation in deep neural networks with biological plausibility.
method Introduces 'ghost units' to cancel feedback, enabling efficient error backpropagation.
result Demonstrates that the model can approximate error gradients and achieve good performance on classification tasks.
A new metric GNQ audits LLMs for privacy risks during training.
problem Auditing LLMs for privacy risks during training is computationally hard.
method Gradient Uniqueness (GNQ) metric derived from gradient descent, BS-Ghost GNQ for efficiency.
result GNQ successfully predicts sequence extractability and reveals risk heterogeneity.
New findings on null measurability in symmetrization interface of VC learning.
problem Null measurability issues in symmetrization interface of VC learning.
method Formalized in Lean 4, using Choquet capacitability and patching properties.
result Null-measurable bad event not Borel measurable, separating regularity levels.
A method to assess variable importance in complex predictive models.
problem Assessing the importance of variables in complex predictive models.
method Assigning relevance measures to each variable by comparing predictions with a ghost variable and analyzing joint effects.
result The method provides insights into variable importance and joint effects not available with other methods.
After defining cohomologically higher order BRST and anti-BRST operators for a compact simple algebra {\cal G}, the associated higher order Laplacians are introduced and the corresponding supersymmetry algebra Σ is analysed. These operators act on the states generated by a set of fermionic ghost fields transforming u…
On every split supermanifold equipped with the Rothstein even super-Poisson bracket we construct a deformation quantization by means of a Fedosov-type procedure. In other words, the supercommutative algebra of all smooth sections of the dual Grassmann algebra bundle of an arbitrarily given vector bundle E (equipped wit…
The paper speeds up and improves pricing and calibration for the rough Heston model.
problem Improving the accuracy and speed of pricing vanilla options under the rough Heston model.
method Combining modified Adams method with SINH-acceleration method for Fourier inversion.
result The model implied vol surface is much flatter and fits market data poorly, indicating ghost calibration.
Characterizes quasi-isometric embeddings in coarsely Lipschitz category.
problem Understanding quasi-isometric embeddings in geometric terms.
method Formalizes quasi-isometric embeddings as regular monomorphisms in coarsely Lipschitz category.
result Quasi-isometric embeddings are equivalently characterised as effective, strong, or extremal monomorphisms.
Methodology to measure lag relevance in time series models.
problem Measuring lag relevance in machine learning models for univariate time series.
method Ghost variables, Shapley values, additive importance measures, auto-relevance and partial auto-relevance functions, one-step forecast.
result Calculated relevance measures successfully demonstrate expected lag structure in almost all cases.
New algorithms tackle multi-agent problems with hybrid action spaces.
problem Applying deep reinforcement learning to multi-agent problems with discrete-continuous hybrid action spaces.
method Proposed two novel algorithms: Deep MAPQN and Deep MAHHQN, using centralized training and decentralized execution.
result Empirical results show both algorithms significantly outperform existing methods.
The proper action functional of (4k+3)-dimensional U(1)-Chern-Simons theory including the instanton sectors has a well known description: it is given on the moduli space of fields by the fiber integration of the cup product square of classes in degree-(2k+2) differential cohomology. We first refine this statement from …
Using a supergeometric interpretation of field functionals, we show that for a class of classical field models used for realistic quantum field theoretic models, an infinite-dimensional supermanifold (smf) of classical solutions in Minkowski space can be constructed. That is, we show that the smf of smooth Cauchy data …
Researchers classify and decompose valuations on convex functions.
problem Classifying valuations on convex functions.
method Geometric decomposition of valuations, using properties of special subspaces and Monge-Ampère-type operators.
result Valuations decompose into subspaces defined by vanishing properties.
Four improvements to Batch Normalization improve deep learning performance.
problem Improving Batch Normalization for better deep learning performance.
method Proposed improvements include reasoning about current examples, Ghost Batch Normalization, weight decay regularization, and a new normalization algorithm for small batch sizes.
result Performance gains across all batch sizes with no additional computation during training.
The paper proposes a method to integrate prior information into penalized regression.
problem Improving predictive performance in high-dimensional tasks with prior information.
method Integrating multiple sources of prior information into penalized regression.
result The method improves predictive performance, as shown by simulations and applications.
Using a supergeometric interpretation of field functionals developed in previous papers, we show that for quite a large class of systems of nonlinear field equations with anticommuting fields, infinite-dimensional supermanifolds (smf) of classical solutions can be constructed. Such systems arise in classical field mode…
Study knot contact homology and character varieties to prove a conjecture about knots.
problem Relate knot contact homology to character varieties of branched covers.
method Study trace-free characters of knot groups and their connection to character varieties.
result Prove Ng's conjecture for 2-bridge and 3-bridge knots using ghost characters.
Unified derivation of PAC-Bayes and MI bounds for general VC classes with fast rates.
problem Generalization bounds for machine learning models with VC classes.
method Unified derivation of conditional PAC-Bayesian and mutual information bounds, including MAC-Bayesian bounds.
result Nontrivial bounds for general VC classes and faster rates for specific conditions.
Study on harmonic maps from surfaces with energy bounds and neck domains.
problem Behavior of harmonic maps with bounded energy on complex domains.
method Analysis of a sequence of harmonic maps in generalized neck domains.
result Upper bound of energy density and study of nullity and index limits.
A new method reformulates Optimal Transport Conditional Flow Matching using proximal operators.
problem Optimal Transport Conditional Flow Matching (OT-CFM) for generating models.
method Reformulate OT-CFM using proximal operators and extended Brenier potential.
result OT-CFM dynamics are terminally normally hyperbolic for manifold-supported targets.
Starting from a Lie algebroid A over a space V we lift its action to the canonical transformations on the principle affine bundle R over the cotangent bundle T∗V. Such lifts are classified by the first cohomology H1(A). The resulting object is the Hamiltonian algebroid AH over $…
Quantization of a Lagrangian field system essentially depends on its degeneracy and implies its BRST extension defined by sets of non-trivial Noether and higher-stage Noether identities. However, one meets a problem how to select trivial and non-trivial higher-stage Noether identities. We show that, under certain condi…
Study on RL on volatility surfaces, proving no free lunch for law-seeking methods.
problem Aligning RL agents with no-arbitrage laws in volatile markets.
method Built a law manifold, defined penalties, and used a Goodhart decomposition.
result No free lunch theorem: Law-seeking RL cannot outperform baselines.
We consider a class of abstract nonlinear evolution equations in supermanifolds (smf's) modelled over Z_2-graded locally convex spaces. We show uniqueness, local existence, smoothness, and an abstract version of causal propagation of the solutions. If an a-priori estimate prevents the solutions from blowing-up then an …
This is a simple mathematical introduction into Feynman diagram technique, which is a standard physical tool to write perturbative expansions of path integrals near a critical point of the action. I start from a rigorous treatment of a finite dimensional case (which actually belongs more to multivariable calculus than …
A formulation for a non-trivial composition of two classical gauge structures is given: Two parent gauge structures of a common base space are synthesized so as to obtain a daughter structure which is fundamental by itself. The model is based on a pair of related connections that take their values in the product space …
Motivation: Driver (epi)genomic alterations underlie the positive selection of cancer subpopulations, which promotes drug resistance and relapse. Even though substantial heterogeneity is witnessed in most cancer types, mutation accumulation patterns can be regularly found and can be exploited to reconstruct predictive …
Consider a physical system for which a mathematically rigorous geometric quantization procedure exists. Now subject the system to a finite set of irreducible first class (bosonic) constraints. It is shown that there is a mathematically rigorous BRST quantization of the constrained system whose cohomology at ghost numbe…