arXiv research

Extends residue theory to flags of holomorphic distributions.

Study on knot $7_4$ surgeries reveals infinite residue characteristics and infinite order points.

The paper studies residues of manifolds and their applications in geometry.

Given a prime $p$, a group is called residually $p$ if the intersection of its $p$-power index normal subgroups is trivial. A group is called virtually residually $p$ if it has a finite index subgroup which is residually $p$. It is well-known that finitely generated linear groups over fields of characteristic zero are …

This work proposes a novel autoencoder for fusing visible and infrared images.

Optimal portfolios are formed by combining momentum, size, and volatility characteristics, enhancing utility for all investors.

Classifies mapping tori of specific groups, generalizing known results.

This is the second of a series of papers dealing with an analog in Arakelov geometry of the holomorphic Lefschetz fixed point formula. We use the main result of the first paper to prove a residue formula "`a la Bott" for arithmetic characteristic classes living on arithmetic varieties acted upon by a diagonalisable tor…

The study proves residual finiteness for certain lattice extensions and negatively curved projective varieties.

Let $M$ be an even-dimensional, oriented closed manifold. We show that the restriction of a singular Riemannian flow on $M$ to a small tubular neighborhood of each connected component of its singular stratum is foliated-diffeomorphic to an isometric flow on the same neighborhood. We then prove a formula that computes c…

The paper studies complex curves with translation structures from differential equations.

Novel LSTM network predicts pulsar timing residuals with few-shot data.

Using the Wodzicki residue, we build Wodzicki-Chern-Simons (WCS) classes in $H^{2k-1}(LM)$ associated to the residue Chern character on the loop space $LM$ of a Riemannian manifold $M^{2k-1}$. These WCS classes are associated to the $L^2$ connection and the Sobolev $s=1$ connections on $LM.$ The WCS classes detect seve…

Motivated by the application of real-time pricing in e-commerce platforms, we consider the problem of revenue-maximization in a setting where the seller can leverage contextual information describing the customer's history and the product's type to predict her valuation of the product. However, her true valuation is un…

In recent years, the RFRS condition has been used to analyze virtual fibering in 3-manifold topology. Agol's work shows that any 3-manifold with zero Euler characteristic satisfying the RFRS condition on its fundamental group virtually fibers over the circle. In this note we will show that a finitely generated nilpoten…

This paper improves fund net value prediction using ARIMA-LSTM hybrid model.

We have previously shown that the truncated Weil algebra of any Lie algebra is a Hopf-cyclic type complex with nontrivial coefficients. In this paper we apply this result to transfer the characteristic classes of transversely orientable foliations into the cyclic cohomology of the groupoid action algebra. Our result in…

In Electricity markets, illiquidity, transaction costs and market price characteristics prevent managers to replicate exactly contracts. A residual risk is always present and the hedging strategy depends on a risk criterion chosen. We present an algorithm to hedge a position for a mean variance criterion taking into ac…

In dealing with high-dimensional data sets, factor models are often useful for dimension reduction. The estimation of factor models has been actively studied in various fields. In the first part of this paper, we present a new approach to estimate high-dimensional factor models, using the empirical spectral density of …

Proves a stack of G-bundles with logarithmic connections is finite type.

Deep neural networks are highly expressive machine learning models with the ability to interpolate arbitrary datasets. Deep nets are typically optimized via first-order methods and the optimization process crucially depends on the characteristics of the network as well as the dataset. This work sheds light on the relat…

A Riemannian metric on a manifold M induces a family of Riemannian metrics on the loop space LM depending on a Sobolev space parameter s. The connection and curvature forms of these metrics take values in pseudodifferential operators. We develop a theory of Wodzicki-Chern-Simons classes using the s=0, 1 connections and…

A new model classifies lightning signals more accurately across different scales.

Mammographic breast density, a parameter used to describe the proportion of breast tissue fibrosis, is widely adopted as an evaluation characteristic of the likelihood of breast cancer incidence. In this study, we present a radiomics approach based on residual learning for the classification of mammographic breast dens…

Paper uses VAEs to control IVS features for financial modeling.

This note announces a general construction of characteristic currents for singular connections on a vector bundle. It develops, in particular, a Chern-Weil-Simons theory for smooth bundle maps $α: E \rightarrow F$ which, for smooth connections on $E$ and $F$, establishes formulas of the type $$ φ\ = \ \text{\rm Res}_φΣ…

We present a systematic study of various statistical characteristics of high-frequency returns from the foreign exchange market. This study is based on six exchange rates forming two triangles: EUR-GBP-USD and GBP-CHF-JPY. It is shown that the exchange rate return fluctuations for all the pairs considered are well desc…

We develop a theory of Cech-Bott-Chern cohomology and in this context we naturally come up with the relative Bott-Chern cohomology. In fact Bott-Chern cohomology has two relatives and they all arise from a single complex. Thus we study these three cohomologies in a unified way and obtain a long exact sequence involving…

Leasing is a popular channel to market new cars. Pricing a leasing contract is complicated because the leasing rate embodies an expectation of the residual value of the car after contract expiration. To aid lessors in their pricing decisions, the paper develops resale price forecasting models. A peculiarity of the leas…

Framework for robust matrix estimation with side information.

A convolutional sequence to sequence non-intrusive load monitoring model is proposed in this paper. Gated linear unit convolutional layers are used to extract information from the sequences of aggregate electricity consumption. Residual blocks are also introduced to refine the output of the neural network. The partiall…

New examples contradict a conjecture about knot surgeries.

Abstract: Non-residually finite hyperbolic groups imply non-residually finite rigid hyperbolic groups.

Residual finiteness is known to be an important property of groups appearing in combinatorial group theory and low dimensional topology. In a recent work [2] residual finiteness of quandles was introduced, and it was proved that free quandles and knot quandles are residually finite. In this paper, we extend these resul…

In this note, residual finiteness of quandles is defined and investigated. It is proved that free quandles and knot quandles of tame knots are residually finite and Hopfian. Residual finiteness of quandles arising from residually finite groups (conjugation, core and Alexander quandles) is established. Further, residual…

Due to the insufficient measurements in the distribution system state estimation (DSSE), full observability and redundant measurements are difficult to achieve without using the pseudo measurements. The matrix completion state estimation (MCSE) combines the matrix completion and power system model to estimate voltage b…

Study of unrestricted virtual braid groups and their properties.

Every non-trivial knot group is fully residually perfect.

Develops a framework for identifying mispriced assets through attention factors for statistical arbitrage.

Due to the rapid growth of machine learning tools and specifically deep networks in various computer vision and image processing areas, application of Convolutional Neural Networks for watermarking have recently emerged. In this paper, we propose a deep end-to-end diffusion watermarking framework (ReDMark) which can be…

Residual flows are shown to approximate MMD well.

Let $p$ be a prime. In this paper, we classify the geometric 3-manifolds whose fundamental groups are virtually residually $p$. Let $M=M^3$ be a virtually fibered 3-manifold. It is well-known that $G=π_1(M)$ is residually solvable and even residually finite solvable. We prove that $G$ is always virtually residually $p$…

Researchers identify critical protein residues using advanced graph theory.

Defines Wodzicki residue using groupoids and fibered distributions.

In this work we prove a Baum-Bott type residue theorem for flags of holomorphic foliations. We prove some relations between the residues of the flag and the residues of their correspondent foliations. We define the Nash residue for flags and we give a partial answer to the Baum-Bott type rationality conjecture in this …

We revisit residual algorithms in both model-free and model-based reinforcement learning settings. We propose the bidirectional target network technique to stabilize residual algorithms, yielding a residual version of DDPG that significantly outperforms vanilla DDPG in the DeepMind Control Suite benchmark. Moreover, we…

Wide residual networks generalize well with uniform convergence to RNTK as width increases.

Unified framework for constructing kernels for transport equations and Koopman eigenfunctions.