Extends SABR model for pricing RFR caplets.
problem Pricing backward RFR caplets in a post-Libor market.
method Closed-form effective SABR parameters for backward RFR caplets.
result Closed-form solution for backward RFR caplets.
Criterion for congruence RFRS towers in hyperbolic lattices.
problem Criteria for hyperbolic lattices to have congruence RFRS towers.
method Criterion based on congruence subgroups.
result Virtually fibered Bianchi groups and new RFRS Kähler groups.
In recent years, the RFRS condition has been used to analyze virtual fibering in 3-manifold topology. Agol's work shows that any 3-manifold with zero Euler characteristic satisfying the RFRS condition on its fundamental group virtually fibers over the circle. In this note we will show that a finitely generated nilpoten…
Simpler proof for Kielak's virtual fibering criterion.
problem Virtual fibering criterion for RFRS groups
method Simpler proof
result Simplified proof of Kielak's criterion
Optimal AFs minimize RFR test error and sensitivity.
problem Finding optimal AFs for RFR to minimize test error and sensitivity.
method Closed-form solution for AFs minimizing test error and sensitivity under different functional parsimony.
result Optimal AFs can be linear, saturated linear, or Hermite polynomial expressions.
Study affine models for alternative risk-free rates and derive caplet pricing formulas.
problem Valuation of caplets/floorlets in models for alternative risk-free rates.
method Affine process for RFRs, explicit valuation formulas for various derivatives.
result Explicit formulas for caplet/floorlet pricing in affine models for RFRs.
In this article we develop the theory of residually finite rationally p (RFRp) groups, where p is a prime. We first prove a series of results about the structure of finitely generated RFRp groups (either for a single prime p, or for infinitely many primes), including torsion-freeness, a Tits alternative, and …
New method optimizes hyperparameters for randomized algorithms like random feature regression.
problem Optimizing hyperparameters in randomized algorithms is challenging due to their stochastic nature.
method Introduced a random objective function and used ensemble Kalman inversion (EKI) for gradient-free optimization.
result Demonstrated successful optimization of hyperparameters in various randomized algorithms.
Derives PDEs for pricing RFR derivatives under a new FMM model.
problem Valuation of interest rate derivatives under a new FMM model.
method Develops PDEs and finite differences methods for numerical solution.
result First use of PDE methods for RFR derivatives valuation.
Profinite rigidity studied for algebraic fibring of groups.
problem Profinite rigidity of groups through algebraic fibring.
method Introducing TAP groups and proving algebraic fibring is a profinite property.
result Algebraic fibring is a profinite property for LERF groups.
Survey on fibring in manifolds and groups, focusing on recent developments and conjectures.
problem Understanding fibring phenomena in manifolds and groups.
method Discussion of state of the art and explanation of recent developments.
result Many conjectures about fibring in higher dimensions, some plausible, some dubious.
In 2007 Agol showed that if N is an aspherical compact 3-manifold with empty or toroidal boundary such that its fundamental group is virtually RFRS, then N is virtually fibered. We give a largely self-contained proof of Agol's theorem using complexities of sutured manifolds.
Paper examines pricing and hedging for cross-currency swaps referencing backward-looking rates.
problem Pricing and hedging cross-currency swaps with backward-looking rates.
method Uses interest rate and currency futures for hedging, analyzes arbitrage-free multi-curve setting.
result Explicit pricing and hedging results for CCBS with backward-looking rates.
SRFRN accelerates image super-resolution using shallow residual units.
problem High computational complexity and time in deep learning image super-resolution.
method SRFRN uses a bicubic interpolated low-resolution image and residual representative units (RFR) for faster and more efficient high-resolution image reconstruction.
result SRFRN achieves superior performance and faster execution time compared to existing methods.
We show that a finitely generated residually finite rationally solvable (or RFRS) group G is virtually fibred, in the sense that it admits a virtual surjection to Z with a finitely generated kernel, if and only if the first L2-Betti number of G vanishes. This generalises (and gives a new proof of) the…
We prove that an irreducible 3-manifold whose fundamental group satisfies a certain group-theoretic property called RFRS is virtually fibered. As a corollary, we show that 3-dimensional reflection orbifolds and arithmetic hyperbolic orbifolds defined by a quadratic form virtually fiber. These include the Seifert Weber …
New method models complex dynamics using a base variable.
problem Modeling complex high-frequency dynamics from time series.
method Constructing a joint model with a base variable and a target variable.
result Successfully models chaotic behavior and reconstructs statistical properties.
Optimizes chip component placement with self-alignment for SMT technology.
problem Achieving precise component placement on PCB during SMT process.
method Proposed machine learning algorithms (SVR and RFR) to predict component positions and developed non-linear optimization model.
result RFR model outperforms in predicting component positions before reflow.
Study develops machine learning model to predict component movement during reflow in SMT.
problem Inaccurate self-alignment of components during reflow process in SMT leads to defects.
method Experimental data analysis followed by advanced machine learning models (SVR, NN, RFR) to predict component shift in x, y, and rotational directions.
result Random forest regression (RFR) model predicts component shift with high accuracy and low error.
New groups found that don't virtually algebraically fiber, related to mapping class group orbits.
problem Existence of finite orbits for higher Prym representations of the mapping class group.
method Study of surface-by-surface and surface-by-free groups.
result Existence of free-by-free and free-by-surface groups that do not algebraically fiber.
Improved model for SOFR, SONIA, and ESTR caplets pricing.
problem Accurate pricing of options on backward-looking rates.
method Extended Turfus and Romero-Bermúdez model to include smile and skew.
result Simple effective variance formulae for caplet pricing.
Non-coherence proven for certain groups with specific mapping tori.
problem Proving non-coherence for groups with specific mapping tori.
method Analyzing the structure of groups as extensions and properties of mapping tori.
result Groups with certain mapping tori are not coherent.
This paper stems from the observation (arising from work of T. Delzant) that "most" Kähler groups virtually algebraically fiber, i.e. admit a finite index subgroup that maps onto Z with finitely generated kernel. For the remaining ones, the Albanese dimension of all finite index subgroups is at most one, i.e. t…
This paper models short rates with jumps using PDEs.
problem Capturing jumps and spikes in interest rates.
method PDE approach for pricing interest rate derivatives.
result Established Feynman-Kač representation and derived solutions.
Study on collateral currency impact in differential swaps valuation.
problem Impact of collateral currency on differential swap valuation and risk management.
method Replication using futures, explicit pricing and hedging strategies.
result Choice of collateral currency can introduce additional risk exposures.
Study uses SAR data to estimate forest vegetation indices, improving monitoring of temperate forests.
problem Limitations of optical satellite data in monitoring forest ecosystems, especially due to atmospheric effects.
method Estimating four vegetation indices (LAI, FAPAR, EVI, NDVI) using multitemporal Sentinel-1 SAR and ancillary data.
result Accurate estimation of forest vegetation indices using SAR data, achieving high R2 and low MAE values.