We compare two different bilateral counterparty valuation adjustment (BVA) formulas. The first formula is an approximation and is based on subtracting the two unilateral Credit Valuation Adjustment (CVA)'s formulas as seen from the two different parties in the transaction. This formula is only a simplified representati…
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48 results for “Simplified Case”
Simplified classification of special measures in CAT(-1) spaces.
problem Classifying horospherical invariant measures in higher rank.
method Expository approach, simplified argument for special case.
result Simplified classification of measures in CAT(-1) spaces.
On nonorientable --manifoldsmath.GT
Study on nonorientable 4-manifolds using simplified fibrations and trisections.
problem Classify and understand nonorientable 4-manifolds.
method Use simplified broken Lefschetz fibrations and trisections, topological modifications of singularities, handlebody decompositions, and mapping classes of surfaces.
result Classify low genus simplified broken Lefschetz fibrations on nonorientable 4-manifolds.
On a Conjecture of Bahri-Xumath.CA
Paper simplifies and proves Bahri-Xu conjecture for various cases.
problem Universal inequality for p points in R^m
method Simplified conjecture, inductive conditions, reduction to basic case m=1
result Proved conjecture for m=1 with arbitrary p, and for p=4,5 and m≥2
Simplified proof of gluing formula for analytic torsion forms.
problem Proving the gluing formula for analytic torsion forms.
method Extending prior work to the family case, presenting a new proof.
result Simplified proof of the gluing formula.
New axioms for singquandles simplify applications and reveal algebraic aspects.
problem Axiomatizing singular knots and links.
method Presented new axioms for singquandles, simplified existing ones, and reformulated for affine singquandles.
result Simplified applications and revealed new algebraic aspects of singquandles.
Survey on metrics with conic singularities on Riemann surfaces.
problem Conformal metrics with conic singularities on Riemann surfaces.
method Study of metrics with constant positive curvature and conic singularities.
result Simplified proofs for interesting cases, including those by C. L. Chai, C. S Lin, and C. L. Wang.
The aim of this note is to extend the results in arXiv:1504.02043 to the case of approximate harmonic maps. More precisely, we will proved that the singular strata of an approximate harmonic map are k-rectifiable, and we will show effect bounds on the quantitative strata. In the process we will simplify many o…
Proves a conjecture about concordance invariant simplifying its relation to Rasmussen's invariant.
problem Concordance invariant and its relation to Rasmussen's invariant.
method Bar-Natan's tangle version of Khovanov homology, distilled into immersed curve theory.
result Simplifies the relation between and Rasmussen's -invariant.
A branched covering surface-knot is a surface-knot in the form of a branched covering over an oriented surface-knot , where we include the case when the covering has no branch points. A branched covering surface-knot is presented by a graph called a chart on a surface diagram of . We can simplify a branched cover…
Simplified proof for dimension reduction of polygonal curves.
problem Preserving the continuous Fréchet distance of polygonal curves.
method Sparse oblivious subspace embeddings for generalized dissimilarity measures.
result Generalized dimension reduction technique works for various distance measures.
Paper studies simplified trisections and their equivalence classes.
problem Understanding right-left equivalence of simplified -trisections.
method Analyzes simplified trisection diagrams and upper-triangular handle-slides.
result At least two simplified -trisections can be right-left equivalent without being related by automorphisms or handle-slides.
Simplified plat diagrams for unlink without stabilization.
problem Equivalence of plats without stabilization for unlink.
method Introducing pocket and flip moves to simplify plats.
result Simplified plat diagrams for unlink using pocket and flip moves.
Taut submanifoldsmath.DG
This is a short, elementary survey article about taut submanifolds. In order to simplify the exposition, we restrict to the case of compact smooth submanifolds of Euclidean or spherical spaces. Some new, partial results concerning taut 4-manifolds are discussed at the end of the text.
Study eigenvector overlaps in large Gaussian matrices, simplifying for GOE.
problem Investigate eigenvector overlaps in large Gaussian matrices.
method Analysis of eigenvector flow under Dyson Brownian motion.
result Explicit computation of limiting rescaled mean squared overlaps.
A simplified, user-friendly repackaging of the curvature estimates implied by the Seiberg-Witten equations is formulated in terms of the convex hull of the set of monopole classes. New results are also obtained concerning boundary cases of the resulting forms of the curvature estimates.
Neural network learns atomic coordinates from Patterson maps in a simplified case.
problem Training a neural network to infer atomic coordinates from Patterson maps.
method Synthetic data training, centering output maps, removing centrosymmetric inversion, and adding empty space.
result The network can generalize to infer atom positions from Patterson maps not in the training set.
Calibration of simplified vine copulas using noise contrastive estimation
problem Modeling complex multivariate dependence structures
method Noise contrastive estimation for calibration
result Improved model accuracy when simplifying assumption is violated
Muon optimizer simplifies matrix optimization with spectral orthogonalization.
problem Matrix optimization challenges, especially with large condition numbers.
method Simplified Muon optimizer using spectral orthogonalization of gradients.
result Simplified Muon converges linearly with independent scalar sequences, outperforming gradient descent and Adam.
New integrators for mechanical systems on Lie groups simplify based on group properties.
problem Designing numerical integrators for mechanical systems on Lie groups.
method Leverage retraction maps and Lie group properties to design structure-preserving integrators.
result Simplified design of integrators for Euler-Poincare and Lie-Poisson equations.
Given a finite simplicial complex L and a collection of pairs of spaces indexed by its vertex set, one can define their polyhedral product. We record a simple formula for its Euler characteristic. In special cases the formula simplifies further to one involving the h-polynomial of L.
Recently we introduced T-duality in the study of topological insulators, and used it to show that T-duality trivialises the bulk-boundary correspondence in 2 dimensions. In this paper, we partially generalise these results to higher dimensions and briefly discuss the 4D quantum Hall effect.
Simplified proof for Cheeger's isoperimetric constant.
problem Cheeger's isoperimetric constant
method Simplified proof of Buser's result
result Simplified proof for Cheeger's isoperimetric constant
A simplified trisection is a trisection map on a 4-manifold such that, in its critical value set, there is no double point and cusps only appear in triples on innermost fold circles. We give a necessary and sufficient condition for a 3-tuple of systems of simple closed curves in a surface to be a diagram of a simplifie…
Classifies 3-manifolds from simplified (2,0)-trisections of 4-manifolds.
problem Classifying 3-manifolds from simplified (2,0)-trisections of 4-manifolds.
method Classifies vertical 3-manifolds as preimages of arcs on the plane for simplified (2,0)-trisection maps.
result Each 6-tuple of vertical 3-manifolds determines the source 4-manifold uniquely up to orientation reversing diffeomorphisms.
Simplified tutorial on doubly robust learning for causal inference.
problem Challenges in applying doubly robust methods due to complexity and software barriers.
method Combines propensity score and outcome modeling for robust causal inference.
result Makes doubly robust learning accessible through simplified methodology and practical examples.
We review the information geometry of linear systems and its application to Bayesian inference, and the simplification available in the Kähler manifold case. We find conditions for the information geometry of linear systems to be Kähler, and the relation of the Kähler potential to information geometric quantities such …
Simplified computation of symmetric gl_1 homology for links.
problem Computing the symmetric gl_1 homology for uncolored links.
method Down-to-earth description, basis construction, and algorithm for computation.
result An algorithm and program for computing the invariant for uncolored links.
NFTs: The Game is Afootq-fin.PM
Simplified NFT games discussed with methods for extracting value.
problem Issues influencing NFT games' structure and stability.
method Three methods for extracting value from NFT games.
result Various design constraints and mutual beneficial games.
Shapes of four dimensional spaces can be studied effectively via maps to standard surfaces. We explain, and illustrate by quintessential examples, how to simplify such generic maps on 4-manifolds topologically, in order to derive simple decompositions into much better understood manifold pieces. Our methods not only al…
Recently we introduced T-duality in the study of topological insulators. In this paper, we study the bulk-boundary correspondence for three phenomena in condensed matter physics, namely, the quantum Hall effect, the Chern insulator, and time reversal invariant topological insulators. In all of these cases, we show that…
Simplified proof of Honda-Huang's contact convexity result.
problem Contact convexity in high dimensions
method Simplified proof of Honda-Huang's main result
result Main result from Honda-Huang's paper simplified and presented
A Simple Factoring Pricing Modelq-fin.PR
In a simplified setting, we show how to price invoice non-recourse factoring taking into account not only the credit worthiness of the debtor but also the assignor's one, together with the default correlation between the two. Indeed, the possible default of the assignor might impact the payoff by means of the bankruptc…
We simplify proof of the theorem that close to any pseudoholomorphic disk there passes a pseudoholomorphic disk of arbitrary close size with any pre-described sufficiently close direction. We apply these results to the Kobayashi and Hanh pseudodistances. It is shown they coincide in dimensions higher than four. The res…
Branched covering surface-knots with degree three have the simplifying numbers less than threemath.GT
A branched covering surface-knot is a surface-knot in the form of a branched covering over a surface-knot. For a branched covering surface-knot, we have a numerical invariant called the simplifying number. We show that branched covering surface-knots with degree three have the simplifying numbers less than three.
This work uncovers the tropical analogue for measured laminations of the convex hull construction of decorated Teichmueller theory, namely, it is a study in coordinates of geometric degeneration to a point of Thurston's boundary for Teichmueller space. This may offer a paradigm for the extension of the basic cell decom…
Proves existence of longest paths in sub-Lorentzian problems.
problem Existence of longest paths in sub-Lorentzian problems.
method Generalizes classical theorem for Lorentzian manifolds to sub-Lorentzian problems.
result Longest paths exist for any left-invariant sub-Lorentzian structures on Carnot groups.
Study simplifies homotopy groups of 6D manifolds.
problem Homotopy groups of 6D manifolds.
method Double suspension homotopy decomposition.
result Easily determines - and -groups.
Simplified proof and new estimate for Kähler-Einstein metrics.
problem Existence of Kähler-Einstein metrics on Calabi-Yau manifolds.
method Alternative a priori estimate for the Monge-Ampère equation.
result Established a new uniform bound for the solution of the Monge-Ampère equation.
In this paper, we propose a Double Thompson Sampling (D-TS) algorithm for dueling bandit problems. As indicated by its name, D-TS selects both the first and the second candidates according to Thompson Sampling. Specifically, D-TS maintains a posterior distribution for the preference matrix, and chooses the pair of arms…
Simplified argument for second order estimate in quaternionic Calabi-Yau problem.
problem Second order estimates for quaternionic Calabi-Yau problem on hyperkähler manifolds.
method Simplified argument to derive the estimate.
result Simplified derivation of second order estimate.
We study the problem of identifying the policy space of a learning agent, having access to a set of demonstrations generated by its optimal policy. We introduce an approach based on statistical testing to identify the set of policy parameters the agent can control, within a larger parametric policy space. After present…
Proposes a new notation for biracks to simplify rack structure analysis.
problem Simplifying birack notation for easier rack structure analysis.
method Introduces a new notation that includes rack structure knowledge from the start.
result Generalizes results from involutive to non-involutive biracks and clarifies rack structure relations.
Trading behavior and excess volatility in toy marketscond-mat.stat-mech
We study the relation between the trading behavior of agents and volatility in toy markets of adaptive inductively rational agents. We show that excess volatility, in such simplified markets, arises as a consequence of {\em i)} the neglect of market impact implicit in price taking behavior and of {\em ii)} excessive re…
Residual Neural Networks (ResNets) achieve state-of-the-art performance in many computer vision problems. Compared to plain networks without residual connections (PlnNets), ResNets train faster, generalize better, and suffer less from the so-called degradation problem. We introduce simplified (but still nonlinear) vers…
Derives adjoint formulas for matrix operations and applies them to specific cases.
problem Computing adjoints for matrix operations and specific matrix types.
method Derives adjoint formulas for matrix operations and applies them to specific cases.
result Closed-form expressions for adjoints in specific matrix types.
We give a detailed explicit computation of weights of Kontsevich graphs which arise from connection and curvature terms within the globalization picture for the special case of symplectic manifolds. We will show how the weights for the curvature graphs can be explicitly expressed in terms of the hypergeometric function…
In this paper we build a method to optimize Multi-Year Prospective Budgets. First we present a systemic model of Local Community Finances. Then, from two acceptable Multi-Year Prospective Budgets the method implements a Genetic Algorithm to generate a collection of admissible Multi-Year Prospective Budgets among which …