arXiv research

This paper addresses credit valuation adjustment with a new closeout convention.

We analyze the practical consequences of the bilateral counterparty risk adjustment. We point out that past literature assumes that, at the moment of the first default, a risk-free closeout amount will be used. We argue that the legal (ISDA) documentation suggests in many points that a substitution closeout should be u…

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…

We present a dialogue on Counterparty Credit Risk touching on Credit Value at Risk (Credit VaR), Potential Future Exposure (PFE), Expected Exposure (EE), Expected Positive Exposure (EPE), Credit Valuation Adjustment (CVA), Debit Valuation Adjustment (DVA), DVA Hedging, Closeout conventions, Netting clauses, Collateral …

We introduce an arbitrage-free framework for robust valuation adjustments. An investor trades a credit default swap portfolio with a risky counterparty, and hedges credit risk by taking a position in defaultable bonds. The investor does not know the return rate of her counterparty's bond, but is confident that it lies …

We present a dialogue on Funding Costs and Counterparty Credit Risk modeling, inclusive of collateral, wrong way risk, gap risk and possible Central Clearing implementation through CCPs. This framework is important following the fact that derivatives valuation and risk analysis has moved from exotic derivatives managed…

Spatial graphs study tangle replacement with equivalence classes.

We introduce new symplectic cut-and-paste operations that generalize the rational blowdown. In particular, we will define $k$-replaceable plumbings to be those that, heuristically, can be symplectically replaced by Euler characteristic $k$ 4-manifolds. We will then classify 2-replaceable linear plumbings, construct 2-r…

We study conditions for existence, uniqueness and invariance of the comprehensive nonlinear valuation equations first introduced in Pallavicini et al (2011). These equations take the form of semilinear PDEs and Forward-Backward Stochastic Differential Equations (FBSDEs). After summarizing the cash flows definitions all…

SGD without replacement decouples into curvature-following and flatness-regularizing steps.

Sampling is a fundamental technique, and sampling without replacement is often desirable when duplicate samples are not beneficial. Within machine learning, sampling is useful for generating diverse outputs from a trained model. We present an elegant procedure for sampling without replacement from a broad class of rand…

Develops algorithms to optimize machine replacement schedules using operational data.

Tangle replacements help in understanding knot properties.

Paper closes convergence gap for SGD without replacement.

New method for simplifying knots with specific properties.

If M and N are equivariantly homotopy equivalent G-manifolds, then the fixed sets M^G and N^G are also homotopy equivalent. The replacement problem asks the converse question: If F is homotopy equivalent to the fixed set M^G, is F = N^G for a G-manifold equivariantly homotopy equivalent to M? We prove that for locally …

Sampling without replacement speeds up optimization in minimax problems.

New research disproves a key conjecture in optimization.

New sketches for weighted $\ell_p$ sampling without replacement improve accuracy and efficiency.

The well-known Gumbel-Max trick for sampling from a categorical distribution can be extended to sample $k$ elements without replacement. We show how to implicitly apply this 'Gumbel-Top-$k$' trick on a factorized distribution over sequences, allowing to draw exact samples without replacement using a Stochastic Beam Sea…

We develop an analog of harmonic replacement in the gauge theory context. The idea behind harmonic replacement dates back to Schwarz and Perron. The technique, as introduced by Jost and further developed by Colding and Minicozzi, involves taking a map $v\colonΣ\to M$ defined on a surface $Σ$ and replacing its values on…

We propose a generative model for adversarial attack. The model generates subtle but predictive patterns from the input. To perform an attack, it replaces the patterns of the input with those generated based on examples from some other class. We demonstrate our model by attacking CNN on MNIST.

Stochastic gradient methods for machine learning and optimization problems are usually analyzed assuming data points are sampled \emph{with} replacement. In practice, however, sampling \emph{without} replacement is very common, easier to implement in many cases, and often performs better. In this paper, we provide comp…

Boring is an operation which converts a knot or two-component link in a 3--manifold into another knot or two-component link. It generalizes rational tangle replacement and can be described as a type of 2--handle attachment. Sutured manifold theory is used to study the existence of essential spheres and planar surfaces …

Improved convergence for VIPs with SEG-RR, a variant of SEG with random reshuffling.

Study bounds the Morse index of a special torus to 1.

Skeleta and other pure subsets of manifold stratified spaces are shown to have neighborhoods which are teardrops of stratified approximate fibrations (under dimension and compactness assumptions). In general, the stratified approximate fibrations cannot be replaced by bundles, and the teardrops cannot be replaced by ma…

A frame independent formulation of analytical mechanics in the Newtonian space-time is presented. The differential geometry of affine values i.e., the differential geometry in which affine bundles replace vector bundles and sections of one dimensional affine bundles replace functions on manifolds, is used. Lagrangian a…

The paper introduces methods to quantify uncertainty in sampling without replacement.

Any autoencoder network can be turned into a generative model by imposing an arbitrary prior distribution on its hidden code vector. Variational Autoencoder (VAE) [2] uses a KL divergence penalty to impose the prior, whereas Adversarial Autoencoder (AAE) [1] uses {\it generative adversarial networks} GAN [3]. GAN trade…

Parrot learns optimal cache replacement policies using imitation learning.

This paper studies the convergence behaviour of dictionary learning via the Iterative Thresholding and K-residual Means (ITKrM) algorithm. On one hand it is proved that ITKrM is a contraction under much more relaxed conditions than previously necessary. On the other hand it is shown that there seem to exist stable fixe…

Let (M,g) be a smooth compact Riemannian manifold without boundary of dimension n>=6. We prove that {align*} \|u\|_{L^{2^*}(M,g)}^2 \le K^2\int_M\{|\nabla_g u|^2+c(n)R_gu^2\}dv_g +A\|u\|_{L^{2n/(n+2)}(M,g)}^2, {align*} for all u\in H^1(M), where 2^*=2n/(n-2), c(n)=(n-2)/[4(n-1)], R_g is the scalar curvature, $K^{-1}=\i…

We present an alternative layer to convolution layers in convolutional neural networks (CNNs). Our approach reduces the complexity of convolutions by replacing it with binary decisions. Those binary decisions are used as indexes to conditional distributions where each weight represents a leaf in a decision tree. This m…

We perform a replacement procedure in order to produce a free boundary minimal surface whose area achieves the min-max value over all disk sweepouts of a manifold whose boundary lie in a submanifold. Our result is based on a proof of the convexity of the energy for free boundary harmonic maps and a generalization of Co…

We introduce a temperature into the exponential function and replace the softmax output layer of neural nets by a high temperature generalization. Similarly, the logarithm in the log loss we use for training is replaced by a low temperature logarithm. By tuning the two temperatures we create loss functions that are non…

Joint replacement is the most common inpatient surgical treatment in the US. We investigate the clinical pathway optimization for knee replacement, which is a sequential decision process from onset to recovery. Based on episodic claims from previous cases, we view the pathway optimization as an intelligence crowdsourci…

Andreas Maurer in the paper "A vector-contraction inequality for Rademacher complexities" extended the contraction inequality for Rademacher averages to Lipschitz functions with vector-valued domains; He did it replacing the Rademacher variables in the bounding expression by arbitrary idd symmetric and sub-gaussian var…

The paper calculates bounds for unknotting rational tangles using knot Floer homology.

Graph neural networks are currently leading the performance charts in learning-based molecule property prediction and classification. Computational chemistry has, therefore, become the a prominent testbed for generic graph neural networks, as well as for specialized message passing methods. In this work, we demonstrate…

Let $(S,\, \ast)$ be a closed oriented surface with a marked point, let $G$ be a fixed group, and let $ρ\colonπ_1(S) \longrightarrow G$ be a representation such that the orbit of $ρ$ under the action of the mapping class group $Mod(S,\, \ast)$ is finite. We prove that the image of $ρ$ is finite. A similar result holds …

Improved proofs for topological and smooth pseudo-isotopies of simply connected 4-manifolds.

Existing applications include a huge amount of knowledge that is out of reach for deep neural networks. This paper presents a novel approach for integrating calls to existing applications into deep learning architectures. Using this approach, we estimate each application's functionality with an estimator, which is impl…

We study stochastic gradient descent {\em without replacement} (\sgdwor) for smooth convex functions. \sgdwor is widely observed to converge faster than true \sgd where each sample is drawn independently {\em with replacement} \cite{bottou2009curiously} and hence, is more popular in practice. But it's convergence prope…

We consider here a generalization of a well known discrete dynamical system produced by the bisection of reflection angles that are constructed recursively between two lines in the Euclidean plane. It is shown that similar properties of such systems are observed when the plane is replaced by a regular surface in ${\mat…

We give two generalizations of the Atiyah-Bott-Berline-Vergne localization theorem for the equivariant cohomology of a torus action: 1) replacing the torus action by a compact connected Lie group action, 2) replacing the manifold having a torus action by an equivariant map. This provides a systematic method for calcula…

See math.CV/0509030 which replaces this paper.

The multimodal web elements such as text and images are associated with inherent memory costs to store and transfer over the Internet. With the limited network connectivity in developing countries, webpage rendering gets delayed in the presence of high-memory demanding elements such as images (relative to text). To ove…