arXiv research

The paper examines properties of self-affine Sierpiński sponges using metric invariants.

The intersection pattern of the translates of the limit set of a quasi-convex subgroup of a hyperbolic group can be coded in a natural incidence graph, which suggests connections with the splittings of the ambient group. A similar incidence graph exists for any subgroup of a group. We show that the disconnectedness of …

We study a regular closure operator in the category of quandles. We show that the regular closure operator and the pullback closure operator corresponding to the reflector from the category of quandles to its full subcategory of trivial quandles coincide, we give a simple description of this closure operator, and analy…

We present two families of knots which have straight number higher than crossing number. In the case of the second family, we have computed the straight number explicitly. We also give a general theorem about alternating knots that states adding an even number of crossings to a twist region will not change whether the …

This paper proposes a novel deep learning-based error correction coding scheme for AWGN channels under the constraint of one-bit quantization in the receivers. Specifically, it is first shown that the optimum error correction code that minimizes the probability of bit error can be obtained by perfectly training a speci…

A new perfectly truthful calibration measure improves prediction reliability.

We prove stability and exponential convergence of the Perfectly Matched Layer (PML) method for acoustic scattering on manifolds with axial analytic quasicylindrical ends. These manifolds model long-range geometric perturbations (e.g. bending or stretching) of tubular waveguides filled with homogeneous or inhomogeneous …

Lazy, perfectly informed investors trade infrequently due to costs.

This paper raises an implicit manifold learning perspective in Generative Adversarial Networks (GANs), by studying how the support of the learned distribution, modelled as a submanifold $\mathcal{M}_θ$, perfectly match with $\mathcal{M}_{r}$, the support of the real data distribution. We show that optimizing Jensen-Sha…

We investigate the dynamics of $2$-generator semigroups of polynomials with bounded planar postcritical set and associated random dynamics on the Riemann sphere. Also, we investigate the space ${\cal B}$ of such semigroups. We show that for a parameter $h$ in the intersection of ${\cal B}$, the hyperbolicity locus ${\c…

We show that several popular few-shot learning benchmarks can be solved with varying degrees of success without using support set Labels at Test-time (LT). To this end, we introduce a new baseline called Centroid Networks, a modification of Prototypical Networks in which the support set labels are hidden from the metho…

This paper is devoted to the classification of the infinite families of Teichmuller curves generated by Prym eigenforms of genus 3 having a single zero. These curves were discovered by McMullen. The main invariants of our classification is the discriminant D of the corresponding quadratic order, and the generators of t…

The study explores homeomorphism groups of self-similar 2-manifolds, including the 2-sphere and Cantor set.

OmniMatch algorithm perfectly matches graphs without edge correlation.

In recent years, machine learning techniques have been increasingly applied in sensitive decision making processes, raising fairness concerns. Past research has shown that machine learning may reproduce and even exacerbate human bias due to biased training data or flawed model assumptions, and thus may lead to discrimi…

Virtually any model we use in machine learning to make predictions does not perfectly represent reality. So, most of the learning happens under model misspecification. In this work, we present a novel analysis of the generalization performance of Bayesian model averaging under model misspecification and i.i.d. data usi…

We present a non-parametric method to estimate the discount curve from market quotes based on the Moore-Penrose pseudoinverse. The discount curve reproduces the market quotes perfectly, has maximal smoothness, and is given in closed-form. The method is easy to implement and requires only basic linear algebra operations…

We correct a mistake in the published version of our paper. Our new conclusion is that the "implied leverage effect" for single stocks is underestimated by option markets for short maturities and overestimated for long maturities, while it is always overestimated for OEX options, except for the shortest maturities wher…

Deep learning models can generalize well even when they fit training data perfectly.

Infinite type surfaces can be perfectly divided into triangles.

We apply a utility-based method to obtain the value of a finite-time investment opportunity when the underlying real asset is not perfectly correlated to a traded financial asset. Using a discrete-time algorithm to calculate the indifference price for this type of real option, we present numerical examples for the corr…

Cubic complexes appear in the theory of finite type invariants so often that one can ascribe them to basic notions of the theory. In this paper we begin the exposition of finite type invariants from the `cubic' point of view. Finite type invariants of knots and homology 3-spheres fit perfectly into this conception. In …

We prove that an open manifold $M$ of dimension at least $5$ which admits a complete CAT(0) polyhedral metric is pseudo-collarable, its fundamental group at infinity is strongly perfectly semistable and has vanishing Chapman-Siebenmann obstruction $τ_{\infty}(M)$. Moreover, this implies that $M$ is topologically collap…

The paper examines how small positive dependence can lead to correlated tail risks.

The paper explains how certain neural network models can still perform well even when they fit training data perfectly.

This research highlights the secrecy potential of nonlinear generative models and their all-or-nothing phase transition.

SGD converges to optimal solution in perfect data fitting problem.

Study finds optimal retirement timing in uncertain wage scenarios.

VAE leverages MMSE channel estimation with data-driven modeling.

Proof confirms perfect representation in deep learning models.

Algorithm optimizes electricity procurement costs by 1.65%.

It seems that what has been said by now about market and competitiveness do not fit perfectly with competences of getting the best of profit. Sometimes, the classical methods of fundamentals of management do not apply to individual companies that face irregular accommodation on the market. It is high time to replace th…

New potentials found for sheaves on Calabi-Yau 4-folds.

Conformal Test Martingales can be 'blind' to significant changes in data distribution.

This paper improves the efficiency of generative models by optimizing the straightness of Rectified Flow.

I unravel the basic long run dynamics of the broker call money market, which is the pile of cash that funds margin loans to retail clients (read: continuous time Kelly gamblers). Call money is assumed to supply itself perfectly inelastically, and to continuously reinvest all principal and interest. I show that the rela…

We consider a simple model of rational agents competing in a single product market described by simple linear demand curve. Contrary to accepted economic theory, the agents' production levels synchronise in the absence of conscious collusion, leading to a downward spiraling of market total production until the monopoly…

The Yamabe Invariant of a smooth compact manifold is by definition the supremum of the scalar curvatures of unit-volume Yamabe metrics on the manifold. For an explicit infinite class of 4-manifolds, we show that this invariant is positive but strictly less than that of the 4-sphere. This is done by using spin^c Dirac o…

Bandlimited random neural networks may not approximate all functions perfectly.

It has been observed \citep{zhang2016understanding} that deep neural networks can memorize: they achieve 100\% accuracy on training data. Recent theoretical results explained such behavior in highly overparametrized regimes, where the number of neurons in each layer is larger than the number of training samples. In thi…

Neural networks can overfit perfectly to noisy data and then grok near-optimal generalization.

Deep networks without non-linearities are equivalent to shallow ones.

Variational Bayes (VB) is a recent approximate method for Bayesian inference. It has the merit of being a fast and scalable alternative to Markov Chain Monte Carlo (MCMC) but its approximation error is often unknown. In this paper, we derive the approximation error of VB in terms of mean, mode, variance, predictive den…

The continuous-time version of Kyle's (1985) model is studied, in which market makers are not fiduciaries. They have some market power which they utilize to set the price to their advantage, resulting in positive expected profits. This has several implications for the equilibrium, the most important being that by setti…

Continuous epimorphisms between certain mapping class groups are induced by homeomorphisms.

In an incomplete financial market, the axiomatic of Time Consistent Pricing Procedure (TCPP), recently introduced, is used to assign to any financial asset a dynamic limit order book, taking into account both the dynamics of basic assets and the limit order books for options. Kreps-Yan fundamental theorem is extended t…

Many modern neural network architectures are trained in an overparameterized regime where the parameters of the model exceed the size of the training dataset. Sufficiently overparameterized neural network architectures in principle have the capacity to fit any set of labels including random noise. However, given the hi…

The Bass model is calibrated to vanilla options using a fixed-point equation.