arXiv research

Study shows how $\operatorname{SL}_2$ Hitchin connection at level four behaves.

Predicts coherence from quantum heat engine noise using machine learning.

By evaluating the Burau representation at t=-1, we obtain a symplectic representation of the braid group. We define the congruence subgroups of the braid group to be the preimages of the principal congruence subgroups of the symplectic group. Our main result is that the level four congruence subgroup of the braid group…

The very definition of an Einstein metric implies that all its geometry is encoded in the Weyl tensor. With this in mind, in this paper we derive higher-order Bochner type formulas for the Weyl tensor on a four dimensional Einstein manifold. In particular, we prove a second Bochner type formula which, formally, extends…

New methods test correlation between network structure and node features.

Hierarchical reinforcement learning (HRL) has recently shown promising advances on speeding up learning, improving the exploration, and discovering intertask transferable skills. Most recent works focus on HRL with two levels, i.e., a master policy manipulates subpolicies, which in turn manipulate primitive actions. Ho…

The Milnor fibre of any isolated hypersurface singularity contains many exact Lagrangian spheres: the vanishing cycles associated to a Morsification of the singularity. Moreover, for simple singularities, it is known that the only possible exact Lagrangians are spheres. We construct exact Lagrangian tori in the Milnor …

We empirically investigate distributions of individual consumption expenditure f or four commodity categories conditional on fixed income levels. The data stems from the Family Expenditure Survey carried out annually in the United Kingdom. W e use graphical techniques to test for normality and lognormality of these dis…

We give a one parameter family of exceptional planar 5-webs. Each web is formed by four pencils of lines and by a foliation defined by the level curves of a function sn_k(x)sn_k(y) where sn_k denotes a Jacobi's elliptic function.

We consider here the problem of classifying orbits of an action of the dif- feomorphism group of 3-space on a tower of fibrations with P2-fibers that generalize the Monster Tower due to Montgomery and Zhitomirskii. As a corollary we give the first steps towards the problem of classifying Goursat 2-flags of small length…

This paper improves level generation using VAEs for coherent, logically following segments.

Proposes BU-SPO method to improve text classification robustness.

This study presents the results of a series of simulation experiments that evaluate and compare four different manifold alignment methods under the influence of noise. The data was created by simulating the dynamics of two slightly different double pendulums in three-dimensional space. The method of semi-supervised fea…

We give a detailed construction of a proper C^2-smooth function on R^4 such that its Hamiltonian flow has no periodic orbits on at least one regular level set. This result can be viewed as a C^2-smooth counterexample to the Hamiltonian Seifert conjecture in dimension four.

We present a new modeling technique for solving the problem of ecological inference, in which individual-level associations are inferred from labeled data available only at the aggregate level. We model aggregate count data as arising from the Poisson binomial, the distribution of the sum of independent but not identic…

We outline the construction of a proper C^2-smooth function on R^4 such that its Hamiltonian flow has no periodic orbits on at least one regular level set. This result can be viewed as a C^2-smooth counterexample to the Hamiltonian Seifert conjecture in dimension four.

Elliptic curves and braid groups linked through configuration spaces.

Energy is a limited resource which has to be managed wisely, taking into account both supply-demand matching and capacity constraints in the distribution grid. One aspect of the smart energy management at the building level is given by the problem of real-time detection of flexible demand available. In this paper we pr…

In this article we complete the proof---for a broad class of four-manifolds---of Witten's conjecture that the Donaldson and Seiberg-Witten series coincide, at least through terms of degree less than or equal to c-2, where c is a linear combination of the Euler characteristic and signature of the four-manifold. This art…

Paper proposes a deep subspace clustering method using multi-level representations.

Adaptive batching improves Gaussian process surrogates for noisy level set estimation.

Most modern neural machine translation (NMT) systems rely on presegmented inputs. Segmentation granularity importantly determines the input and output sequence lengths, hence the modeling depth, and source and target vocabularies, which in turn determine model size, computational costs of softmax normalization, and han…

We study the Hamiltonian vector field $v=(-\partial f/\partial w,\partial f/\partial z)$ on $\mathbb C^2$, where $f=f(z,w)$ is a polynomial in two complex variables, which is non-degenerate with respect to its Newton's polygon. We introduce coordinates in four-dimensional neighbourhoods of the "points at infinity", in …

Researchers infer firm-level supply chain networks from sector-level data to assess systemic risk.

Smooth tori in S^4 are topologically unknotted.

We develop an algorithm that can detect pneumonia from chest X-rays at a level exceeding practicing radiologists. Our algorithm, CheXNet, is a 121-layer convolutional neural network trained on ChestX-ray14, currently the largest publicly available chest X-ray dataset, containing over 100,000 frontal-view X-ray images w…

We introduce a new virtual environment for simulating a card game known as "Big 2". This is a four-player game of imperfect information with a relatively complicated action space (being allowed to play 1,2,3,4 or 5 card combinations from an initial starting hand of 13 cards). As such it poses a challenge for many curre…

Elliptic Chern characters and Atiyah-Witten formula generalized to double loop spaces.

SmartExchange trades memory for computation in neural networks.

Level assessment for foreign language students is necessary for putting them in the right level group, furthermore, interviewing students is a very time-consuming task, so we propose to automate the evaluation of speaker fluency level by implementing machine learning techniques. This work presents an audio processing s…

We prove Witten's formula relating the Donaldson and Seiberg-Witten series modulo powers of degree $c+2$, with $c=-{1/4}(7χ+11σ)$, for four-manifolds obeying some mild conditions, where $χ$ and $σ$ are their Euler characteristic and signature. We use the moduli space of SO(3) monopoles as a cobordism between a link of …

This is the first of two articles in which we give a proof - for a broad class of four-manifolds - of Witten's conjecture that the Donaldson and Seiberg-Witten series coincide, at least through terms of degree less than or equal to c-2, where c is a linear combination of the Euler characteristic and signature of the fo…

Using the empirical data from the Norwegian tax office, we analyse the wealth and income of the richest individuals in Norway during the period 2010--2013. We find that both annual income and wealth level of the richest individuals are describable using the Pareto law. We find that the robust mean Pareto exponent over …

Have you ever wondered how your feature space is impacting the prediction of a specific sample in your dataset? In this paper, we introduce Single Sample Feature Importance (SSFI), which is an interpretable feature importance algorithm that allows for the identification of the most important features that contribute to…

DeepScalper uses RL to capture intraday trading opportunities, balancing risk and profit.

Study rigidifies geometry of electrostatic systems with specific tensor properties.

The inability to see and quantify systemic financial risk comes at an immense social cost. Systemic risk in the financial system arises to a large extent as a consequence of the interconnectedness of its institutions, which are linked through networks of different types of financial contracts, such as credit, derivativ…

We find the optimal investment strategy for an individual who seeks to minimize one of four objectives: (1) the probability that his wealth reaches a specified ruin level {\it before} death, (2) the probability that his wealth reaches that level {\it at} death, (3) the expectation of how low his wealth drops below a sp…

We show that the Nielsen-Thurston classification of mapping classes of the sphere with four marked points is determined by the quantum SU(n)-representations, for any fixed integer $n \geq 2$. In the Pseudo-Anosov case we also show that the stretching factor is a limit of eigenvalues of (non-unitary) SU(2)-TQFT represen…

In this paper we investigate the endogenous information contained in four liquidity variables at a five minutes time scale on equity markets around the world: the traded volume, the bid-ask spread, the volatility and the volume at first limits of the orderbook. In the spirit of Granger causality, we measure the level o…

One out of four children in India are leaving grade eight without basic reading skills. Measuring the reading levels in a vast country like India poses significant hurdles. Recent advances in machine learning opens up the possibility of automating this task. However, the datasets of children's speech are not only rare …

We implement momentum strategies using reward-risk measures as ranking criteria based on classical tempered stable distribution. Performances and risk characteristics for the alternative portfolios are obtained in various asset classes and markets. The reward-risk momentum strategies with lower volatility levels outper…

We prove an analogue of the Kotschick-Morgan conjecture in the context of SO(3) monopoles, obtaining a formula relating the Donaldson and Seiberg-Witten invariants of smooth four-manifolds using the SO(3)-monopole cobordism. The main technical difficulty in the SO(3)-monopole program relating the Seiberg-Witten and Don…

Unified benchmark for GLAD and GLOD methods across 35 datasets.

This study examines non-retail trading on Polymarket, revealing unique behavior patterns and structural limitations.

Paper compares AutoML methods for recommending classification algorithms.

The paper proposes selective forgetting for deep neural networks at a finer level than samples.

Study examines if LLMs' trading styles match real market behavior.