arXiv research

New method determines arrangement combinatorics from Milnor fiber boundary.

A classical result by Alexander Grigor'yan states that on a stochastically complete manifold the non-negative superharmonic $L^1$-functions are necessarily constant. In this paper we address the question of whether and to what extent the reverse implication holds.

We prove that the Waldhausen Nil-group associated to a virtually cyclic groups that surjects onto the infinite dihedral group vanishes if and only if the corresponding Farrell Nil-group associated to the canonical index two subgroup is trivial. The proof uses the transfer map to establish one direction, and uses contro…

We give an algorithm and source code for a cryptoasset statistical arbitrage alpha based on a mean-reversion effect driven by the leading momentum factor in cryptoasset returns discussed in https://ssrn.com/abstract=3245641. Using empirical data, we identify the cross-section of cryptoassets for which this altcoin-Bitc…

This paper describes Simpson's paradox, and explains its serious implications for randomised control trials. In particular, we show that for any number of variables we can simulate the result of a controlled trial which uniformly points to one conclusion (such as 'drug is effective') for every possible combination of t…

The image of the branch set of a PL branched cover between PL $n$-manifolds is a simplicial $(n-2)$-complex. We demonstrate that the reverse implication also holds: an open and discrete map $f \colon \mathbb{S}^n \to \mathbb{S}^n$ with the image of the branch set contained in a simplicial $(n-2)$-complex is equivalent …

Adversarial domain adaptation reduces sample bias in high energy physics classifier.

In a recent paper, Q. Mérigot proved that representations in SO(2,n) of uniform lattices of SO(1,n) which are Anosov in the sense of Labourie are quasi-Fuchsian, i.e. are faithfull, discrete, and preserve an acausal subset in the boundary of anti-de Sitter space. In the present paper, we prove the reverse implication. …

Let K be a 2-dimensional finite flag complex. We study the CAT(0) dimension of the `Bestvina-Brady group', or `Artin kernel', Gamma_K. We show that Gamma_K has CAT(0) dimension 3 unless K admits a piecewise Euclidean metric of non-positive curvature. We give an example to show that this implication cannot be reversed. …

New loops found in universe's timeline, challenging traditional time direction.

A new perspective on self-attention models using MLPs.

New method identifies whether equity return predictability is due to magnitude shrinkage or directional reversal.

The purpose of this paper is: (i) to construct a space which is semilocally simply connected in the sense of Spanier even though its Spanier group is non-trivial; (ii) to propose a modification of the notion of a Spanier group so that via the modified Spanier group semilocal simple connectivity can be characterized; an…

Venice used 'helicopter money' to subsidize during famine and plague, but it caused instability.

Trend-following strategies outperform in a noisy financial market, mirroring ancient wisdom.

Study shows climate change can cause a 'run on fossil fuels' affecting prices and production.

Study develops sector rotation models using factor and fundamental analysis.

Many deployed learned models are black boxes: given input, returns output. Internal information about the model, such as the architecture, optimisation procedure, or training data, is not disclosed explicitly as it might contain proprietary information or make the system more vulnerable. This work shows that such attri…

The paper explores the geometry of holomorphic flows and orbits.

Classifies reversible and strongly reversible elements in quaternionic groups.

The paper classifies reversible and strongly reversible elements in Hermitian isometry groups.

Graphical models have proven to be powerful tools for representing high-dimensional systems of random variables. One example of such a model is the undirected graph, in which lack of an edge represents conditional independence between two random variables given the rest. Another example is the bidirected graph, in whic…

We analyze four structured products that have caused severe losses to investors in recent years. These products are: return optimization securities, yield magnet notes, reverse exchangeable securities, and principal-protected notes. We describe the basic structure of these products, analyze them probabilistically using…

This paper classifies reversible and strongly reversible elements in affine groups.

Designing models that are robust to small adversarial perturbations of their inputs has proven remarkably difficult. In this work we show that the reverse problem---making models more vulnerable---is surprisingly easy. After presenting some proofs of concept on MNIST, we introduce a generic tilting attack that injects …

In 1996, Huisken-Yau proved that every three-dimensional Riemannian manifold can be uniquely foliated near infinity by stable closed surfaces of constant mean curvature (CMC) if it is asymptotically equal to the (spatial) Schwarzschild solution. Later, their decay assumptions were weakened by Metzger, Huang, Eichmair-M…

New neural net learns time-reversible symplectic dynamics.

A new trading strategy using reinforcement learning for statistical arbitrage.

Algebraic method reveals criterion for quaternionic Möbius group reversibility.

Recent studies have shown that online portfolio selection strategies that exploit the mean reversion property can achieve excess return from equity markets. This paper empirically investigates the performance of state-of-the-art mean reversion strategies on real market data. The aims of the study are twofold. The first…

A Finsler space is said to be geodesically reversible if each oriented geodesic can be reparametrized as a geodesic with the reverse orientation. A reversible Finsler space is geodesically reversible, but the converse need not be true. In this note, building on recent work of LeBrun and Mason, it is shown that a geodes…

Sharp stability results for reverse isoperimetric inequalities in 2D.

Let $G$ be a group. An element $g$ in $G$ is called reversible if it is conjugate to $g^{-1}$ within $G$, and called strongly reversible if it is conjugate to its inverse by an order two element of $G$. Let $\textbf{H}_{\mathbb H}^n$ be the $n$-dimensional quaternionic hyperbolic space. Let $\mathrm{PSp}(n,1)$ be the i…

Boundary rigidity proven for non-reversible Finsler metrics.

On-line portfolio selection has attracted increasing interests in machine learning and AI communities recently. Empirical evidences show that stock's high and low prices are temporary and stock price relatives are likely to follow the mean reversion phenomenon. While the existing mean reversion strategies are shown to …

Conditional diffusion models can approximate target distributions well with Gaussian-mixture reverse kernels.

New knots not rationally concordant to their reverses found.

Study maps research streams in biodiversity finance, identifies key areas.

The paper classifies reversible elements in Seifert-fibered spaces and braid groups.

Reverse annealing boosts quantum matrix factorization performance.

TRS-ODENs learn dynamics with time-reversal symmetry for more efficient learning.

Paper proves rigidity theorems for geodesically reversible Finsler metrics.

Reduces identity testing of reversible Markov chains to simpler symmetric chain tests.

Proof of reverse isoperimetric inequality for black holes.

Paper investigates differentiable fuzzy implications and their suitability for learning.

New algorithm learns bridged diffusion processes without time-reversals.

Consider the problem of pricing options on forwards in energy markets, when spot prices follow a geometric multi-factor model in which several rates of mean reversion appear. In this paper we investigate the role played by slow mean reversion when pricing and hedging options. In particular, we determine both upper and …

Paper improves Oja's algorithm for Markovian data streams.