Article explores G2-structures with quadratic conditions, finding new ERP and complete solitons.
problem Investigating closed G2-structures satisfying quadratic conditions.
method Analyzing a second-order PDE system involving parameter λ, producing new examples of ERP and complete solitons.
result First examples of ERP G2-structures, including complete inhomogeneous ERP G2-structure.
ERP improves drug discovery by balancing molecule generation quality and efficiency.
problem Generating valid and optimal molecules from large language models.
method Entropy-Reinforced Planning (ERP) for Transformer Decoding.
result ERP outperforms current state-of-the-art algorithms by 1-5 percent on SARS-CoV-2 and human cancer cell targets.
Study hypoelliptic operators on Carnot manifolds, extending index theory results.
problem Index theory of hypoelliptic operators on Carnot manifolds.
method Operator K-theory and geometric K-homology.
result Compute Fredholm index of hypoelliptic operators on Carnot manifolds.
Generative AI agents improve ERP systems by automating complex financial tasks.
problem Static, rule-based workflows limit adaptability and intelligence in ERP systems.
method Introducing Generative Business Process AI Agents (GBPAs) that integrate generative AI with business process modeling and multi-agent orchestration.
result GBPAs achieve up to 40% reduction in processing time and 94% drop in error rate.
This paper improves financial derivative pricing by incorporating multiple hedging instruments.
problem Valuation of financial derivatives with multiple hedging instruments.
method Deep hedging algorithm and reinforcement learning to solve global hedging problems.
result Including options as hedging instruments can significantly decrease equal risk prices and market incompleteness.
New method uses non-translation invariant risk measures for fair financial derivative pricing.
problem Inequalities in financial derivative pricing under traditional risk measures.
method Deep reinforcement learning with modified deep hedging algorithm.
result Effective pricing of financial derivatives without price inflation.
We develop a method that is based on processing gathered Event Related Potentials (ERP) signals and the use of machine learning technique for multivariate analysis (i.e. classification) that we apply in order to analyze the differences between Dyslexic and Skilled readers. No human intervention is needed in the analysi…
Novel Bayesian model improves EEG-based BCI character selection.
problem Accurately identifying target-related responses in EEG-based BCIs.
method Probit-link Split-and-merge Gaussian Process (P-SMGP) prior for feature selection.
result Reduces computational complexity and provides interpretable statistical interpretations.
Objective: Using traditional approaches, a Brain-Computer Interface (BCI) requires the collection of calibration data for new subjects prior to online use. Calibration time can be reduced or eliminated e.g.~by transfer of a pre-trained classifier or unsupervised adaptive classification methods which learn from scratch …
Researchers extend a groupoid approach to calculate Wodzicki residue and Kontsevich-Vishik trace.
problem Calculating Wodzicki residue and Kontsevich-Vishik trace for pseudo-differential operators of any order.
method Groupoid approach to pseudo-differential operators.
result Extension of van Erp and Yuncken's work to operators of any order.
This paper presents a new classification methods for Event Related Potentials (ERP) based on an Information geometry framework. Through a new estimation of covariance matrices, this work extend the use of Riemannian geometry, which was previously limited to SMR-based BCI, to the problem of classification of ERPs. As co…
Scoping review finds EEG key in MCI research, identifying ERP/EEG, QEEG, and machine learning.
problem Identifying MCI early and accurately.
method Scoping review with co-occurrence analysis and PAGER framework.
result Main research themes identified: ERP/EEG, QEEG, and EEG-based machine learning.
Study weightings from singular Lie filtrations.
problem Generalize constructions for singular Lie filtrations.
method Study weightings arising from singular Lie filtrations.
result Generalizes constructions for (regular) Lie filtrations.
This paper discusses e-commerce integration with SAP for Turkish businesses.
problem ERP integration of e-commerce systems for Turkish companies.
method Proposes a solution for integrating ERP with e-commerce systems.
result SAP integration improves company processes and e-commerce efficiency.
A brain computer interface (BCI) is a system which provides direct communication between the mind of a person and the outside world by using only brain activity (EEG). The event-related potential (ERP)-based BCI problem consists of a binary pattern recognition. Linear discriminant analysis (LDA) is widely used to solve…
Equity risk premium is a central component of every risk and return model in finance and a key input to estimate costs of equity and capital in both corporate finance and valuation. An article by Damodaran examines three broad approaches for estimating the equity risk premium. The first is survey based, it consists in …
Study geometric characterization of asymptotic pseudodifferential calculus on spinor bundles.
problem Geometric characterization of asymptotic pseudodifferential calculus on spinor bundles.
method Groupoid approach to pseudodifferential calculus, rescaled bundle.
result Rescaled bundle provides geometric characterization to asymptotic pseudodifferential calculus on spinor bundles.
Let X be a closed connected contact manifold. On X there is a naturally arising class of hypoelliptic (but not elliptic) operators which are Fredholm. In this paper we solve the index problem for this class of operators. The solution is achieved by combining Van Erp's earlier partial result with the Baum-Douglas isomor…
A complete classification of left-invariant closed G2-structures on Lie groups which are extremally Ricci pinched, up to equivalence and scaling, is obtained. There are five of them, they are defined on five different completely solvable Lie groups and the G2-structure is exact in all cases except one, given by the onl…
New index formula for hypoelliptic operators on manifolds.
problem Index computation for hypoelliptic differential operators.
method Generalized index formula for *-maximally hypoelliptic operators.
result Explicit index computations for Hormander's sum of squares operators.
The paper introduces isotropy as a regularizer to enhance portfolio stability.
problem Model uncertainty and estimation errors in diversification strategies.
method Integrates isotropy as a geometric regularizer into mean-variance optimization.
result Isotropy constraint systematically induces negative average-signal exposure, providing a robust crash hedge.
Constructs families of Toeplitz operators for symplectic fibrations.
problem Quantization of symplectic fibrations.
method Smooth families of Szegö projections and Toeplitz operators.
result Deformation quantization of prequantizable symplectic fibrations.
In 1974, Folland and Stein constructed an inhomogeneous pseudo-differential calculus based on analysis on the Heisenberg group. This Heisenberg calculus was generalized by several authors, to any subbundle of the tangent bundle. van Erp and Yuncken, following Debord and Skandalis showed that this calculus can be recove…
Found a new compact G2-structure on a 7-manifold.
problem Identifying compact G2-structures on manifolds.
method Lattice in solvable Lie group, Laplacian coflow analysis.
result Obtained a 4-parameter subfamily of expanding solitons.
Prove non-asymptotic bounds for minimal risk in statistical learning
problem Estimating minimal risk in statistical learning
method Using concentration inequalities
result Non-asymptotic bounds for minimal risk
Researchers construct an index map for contact manifolds using K-theory.
problem Constructing an index for maximally hypoelliptic operators on contact manifolds.
method Using Higson's construction for symbol class in K-theory, they derive a series of maps whose induced map in K-theory is the Heisenberg Atiyah-Singer index map.
result Explicit construction of a series of maps leading to the Heisenberg Atiyah-Singer index map.
The paper explores the index theory of sub-Laplacians on higher nilpotent Carnot manifolds.
problem Characterizing the index theory of sub-Laplacians on higher nilpotent Carnot manifolds.
method Analyzes the structure of hypoelliptic sub-Laplacian type operators and provides examples where the index theory is trivial.
result Provides examples where the index theory of sub-Laplacians is trivial in higher degrees of nilpotency.
Study recovers C*-algebra from fields of Toeplitz algebras on specific groups.
problem Recovering C*-algebra from fields of Toeplitz algebras on specific groups.
method Using continuous fields of Toeplitz algebras and a crossed product.
result Algebra of principal symbols can be recovered from fields of Toeplitz algebras.
We consider topological T-duality of torus bundles equipped with S^{1}-gerbes. We show how a geometry on the gerbe determines a reduction of its band to the subsheaf of S^{1}-valued functions which are constant along the torus fibres. We observe that such a reduction is exactly the additional datum needed for the const…
New extensions for homogeneous distributions on deformations to the normal cone.
problem Extending homogeneous distributions on a specific geometric structure.
method Using the zoom action and Meyer's results on weakly homogeneous distributions.
result All homogeneous extensions of distributions on the DNC are described.
This paper studies the valuation of European contingent claims with short selling bans under the equal risk pricing (ERP) framework proposed in Guo and Zhu (2017) where analytical pricing formulae were derived in the case of monotonic payoffs under risk-neutral measures. We establish a unified framework for this new pr…
Characterizes polyhomogeneous symbols and applies to Heisenberg calculus.
problem Understanding polyhomogeneous symbols and their applications.
method Simple characterisation and generalization of A.~Connes' tangent groupoid.
result Heisenberg calculus on contact manifolds coincides with groupoid calculus.
Based on the cumulated experience over the past 25 years in the field of Brain-Computer Interface (BCI) we can now envision a new generation of BCI. Such BCIs will not require training; instead they will be smartly initialized using remote massive databases and will adapt to the user fast and effectively in the first m…
Multidimensional time series are sequences of real valued vectors. They occur in different areas, for example handwritten characters, GPS tracking, and gestures of modern virtual reality motion controllers. Within these areas, a common task is to search for similar time series. Dynamic Time Warping (DTW) is a common di…
The P300 event-related potential (ERP), evoked in scalp-recorded electroencephalography (EEG) by external stimuli, has proven to be a reliable response for controlling a BCI. The P300 component of an event related potential is thus widely used in brain-computer interfaces to translate the subjects' intent by mere thoug…
Nowadays, organizations collect vast quantities of accounting relevant transactions, referred to as 'journal entries', in 'Enterprise Resource Planning' (ERP) systems. The aggregation of those entries ultimately defines an organization's financial statement. To detect potential misstatements and fraud, international au…
A criterion for training-free time-lagged spectral embeddings of multivariate time series
problem Applicability of fixed-length descriptors for multivariate time series
method Using a stationary Gaussian VAR(1) model and cosine similarity to classify descriptors
result D(τ) separates two classes when signals are approximately stationary and cross-channel temporal coupling is present
BCI system improves word selection efficiency using sequential best-arm identification.
problem Conventional non-adaptive BCI paradigms lead to a lengthy learning process.
method Casted as sequence of best-arm identification tasks in multi-armed bandits, using pre-trained LLMs and STTS algorithm.
result Substantial empirical improvement in word selection efficiency demonstrated.
Tensor models improve joint EEG and fMRI analysis.
problem Jointly analyzing EEG and fMRI for brain function studies.
method Soft and flexible coupling of tensor decompositions for EEG and fMRI.
result Tensorial methods outperform ICA in multi-modal analysis.
Paper tackles P vs NP problem in portfolio optimization with cardinality constraints and Black-Scholes derivatives.
problem Operationalizing the P vs NP problem in cardinality-constrained portfolio selection.
method Mixed-integer quadratic program with genetic algorithms, Monte Carlo sampling, and greedy screening.
result Cardinality constraint reshapes efficient frontier, highlighting trade-offs between stability and computational cost.
Generates samples conditioned on labels using optimal transport.
problem Estimating conditional distributions for specific labels.
method Wasserstein geodesic generator based on optimal transport theory.
result Learned conditional distributions and optimal transport maps.
The paper classifies Finsler surfaces satisfying the T-condition or σT-condition.
problem Characterizing Finsler surfaces based on specific tensor conditions.
method Analyzing Finsler surfaces in dimensions n≥3, proving conditions equivalence, and solving PDEs.
result All Finsler surfaces satisfying the T-condition or σT-condition are classified.
The paper develops a new approach to conditional risk measures using modular convex analysis.
problem Developing a new method for conditional risk measures.
method Random modular approach to conditional certainty equivalents and niveloids in the conditional L∞-space. result Retrieves a conditional variational formula for optimized certainty equivalents and applies it to the conditional entropic risk measure.
Paper constructs solutions to Bogomolny equations with specific boundary and asymptotic conditions.
problem Constructing solutions to Bogomolny equations with given boundary and asymptotic conditions.
method Using generalized Nahm pole boundary condition and real symmetry breaking condition.
result Solutions analogous to instanton solutions, satisfying different asymptotic conditions.
We extend probabilistic programming to handle conditioning on marginal distributions.
problem Conditioning probabilistic programs on marginal distributions of observable variables.
method We define and implement stochastic conditioning, allowing inference in probabilistic programs conditioned on marginal distributions.
result We demonstrate the effectiveness of stochastic conditioning in various real-life scenarios.
New tests for conditional copulas based on decision trees.
problem Testing constancy of conditional dependence structure given conditioning events.
method Data-driven decision trees to maximize differences in conditional Kendall's tau.
result Asymptotic distributions of test statistics under the null hypothesis.
Paper finds necessary condition for logarithmic Minkowski problem in higher dimensions.
problem Logarithmic Minkowski problem in higher dimensions.
method Established a necessary condition through generalization and refinement of previous work.
result Generalizes and refines necessary condition for logarithmic Minkowski problem.
This paper introduces a neural operator for probabilistic conditioning.
problem Probabilistic conditioning of random variables X given Y. method Develops a single operator that maps any joint density to its conditional, approximated by neural operators.
result Neural operators can approximate the conditioning operator to arbitrary accuracy.