arXiv research

DEPTS learns to forecast periodic time series with improved accuracy.

We study periodic monopoles satisfying some mild conditions, called of GCK type. Particularly, we give a classification of periodic monopoles of GCK type in terms of difference modules with parabolic structure, which is a kind of Kobayashi-Hitchin correspondence between differential geometric objects and algebraic obje…

An interesting theme in complex differential geometry is to find a correspondence between algebraic objects and differential geometric objects. One of the most attractive is the non-abelian Hodge theory of Simpson. In this paper, pursuing an analogue of the non-abelian Hodge theory in the context of $q$-difference modu…

Study Swan modules and homotopy types, resolving Wall and Dyer questions.

An FI-module $V$ over a commutative ring $\bf{k}$ encodes a sequence $(V_n)_{n \geq 0}$ of representations of the symmetric groups $(\mathfrak{S}_n)_{n \geq 0}$ over $\bf{k}$. In this paper, we show that for a "finitely generated" FI-module $V$ over a field of characteristic $p$, the cohomology groups $H^t(\mathfrak{S}…

We sketch a geometric proof of the classical theorem of Atiyah, Bott, and Shapiro \cite{ABS} which relates Clifford modules to vector bundles over spheres. Every module of the Clifford algebra $Cl_k$ defines a particular vector bundle over $§^{k+1}$, a generalized Hopf bundle, and the theorem asserts that this correspo…

Enhances financial time series forecasting with a multi-period learning framework.

We explain the correspondences between twisted monopoles with Dirac type singularity and polystable twisted mini-holomorphic bundles with Dirac type singularity on a 3-dimensional torus. We also explain that they are equivalent to polystable parabolic twisted difference modules on elliptic curves.

Study Berry connections for 2d GLSMs, linking to cohomology theories.

Derives an index formula for families of end-periodic Dirac operators.

For a prime number $q\neq 2$ and $r>0$ we study, whether there exists an isometry of order $q^r$ acting on a free $\mathbb{Z}_{p^k}$-module equipped with a scalar product. We investigate, whether there exists such an isometry with no non-zero fixed points. Both questions are completely answered in this paper if $p\neq …

Proposes MLEs for MMJDM with EM-algorithm.

Dynamic portfolio optimization is the process of sequentially allocating wealth to a collection of assets in some consecutive trading periods, based on investors' return-risk profile. Automating this process with machine learning remains a challenging problem. Here, we design a deep reinforcement learning (RL) architec…

Improved trading strategy using deep learning and changepoint detection for market changes.

Generative model captures repetitive industrial processes with varying durations and dynamics.

PSTN improves traffic condition forecasting with deep neural networks.

In this paper we present our scientific discovery that good representation can be learned via continuous attention during the interaction between Unsupervised Learning(UL) and Reinforcement Learning(RL) modules driven by intrinsic motivation. Specifically, we designed intrinsic rewards generated from UL modules for dri…

The deep learning trend has recently impacted a variety of fields, including communication systems, where various approaches have explored the application of neural networks in place of traditional designs. Neural networks flexibly allow for data/simulation-driven optimization, but are often employed as black boxes det…

In the era of big data, practical applications in various domains continually generate large-scale time-series data. Among them, some data show significant or potential periodicity characteristics, such as meteorological and financial data. It is critical to efficiently identify the potential periodic patterns from mas…

ComiRec framework predicts user interests for personalized recommendations.

Study of 2d gauged linear sigma models to derive difference equations and spectral data.

SPADE improves demand forecasting accuracy by 4.5% for post-promotion periods.

We develop a global Poincaré residue formula to study period integrals of families of complex manifolds. For any compact complex manifold $X$ equipped with a linear system $V^*$ of generically smooth CY hypersurfaces, the formula expresses period integrals in terms of a canonical global meromorphic top form on $X$. Two…

This paper studies deep learning methodologies for portfolio optimization in the US equities market. We present a novel residual switching network that can automatically sense changes in market regimes and switch between momentum and reversal predictors accordingly. The residual switching network architecture combines …

The paper explores the geometry of level lines of quasiperiodic functions with many periods.

A knot \widetilde{K} \subset S^3 is q-periodic if there is a \mathbb Z_q-action preserving \widetilde{K} whose fixed set is an unknot U. The quotient of \widetilde{K} under the action is a second knot K. We construct equivariant Heegaard diagrams for q-periodic knots, and show that Murasugi's classical condition on the…

MPPN network improves long-term time series forecasting accuracy.

Floer theory constructs filtrations on quantum cohomology for symplectic manifolds.

SG-NTF completes HDI tensors with spectral mapping and spatio-temporal gating.

We study both the continuous model and the discrete model of the integer quantum Hall effect on the hyperbolic plane in the presence of disorder, extending the results of an earlier paper [CHMM]. Here we model impurities, that is we consider the effect of a random or almost periodic potential as opposed to just periodi…

Paper proposes an efficient method for calibrating spatio-temporal forecasts.

We study the multi-scale temporal correlations and causality connections between the New York Stock Exchange (NYSE) and Bombay Stock Exchange (BSE) monthly average closing price indexes for a period of 300 months, encompassing the time period of the liberalisation of the Indian economy and its gradual global exposure. …

A DRL framework optimizes portfolios using a LFSS module for feature extraction.

In this paper we present the construction of explicit quasi-isomorphisms that compute the cyclic homology and periodic cyclic homology of crossed-product algebras associated with (discrete) group actions. In the first part we deal with algebraic crossed-products associated with group actions on unital algebras over any…

Let K \subset Y be a knot in a three manifold which admits a longitude-framed surgery such that the surgered manifold has first Betti number greater than that of Y. We find a formula which computes the twisted Floer homology of the surgered manifold, in terms of twisted knot Floer homology. Using this, we compute the t…

We introduce conformal Courant algebroids, a mild generalization of Courant algebroids in which only a conformal structure rather than a bilinear form is assumed. We introduce exact conformal Courant algebroids and show they are classified by pairs $(L,H)$ with $L$ a flat line bundle and $H \in H^3(M,L)$ a degree 3 cla…

Study shows invariant curves in tubular origami dynamics, revealing geometric barriers to folding transitions.

The study identifies and analyzes different market regimes in equity markets using advanced signal processing techniques.

FreDN separates trends and periodicities in non-stationary time series forecasts.

The paper proposes a class of financial market models which are based on inhomogeneous telegraph processes and jump diffusions with alternating volatilities. It is assumed that the jumps occur when the tendencies and volatilities are switching. We argue that such a model captures well the stock price dynamics under per…

We make use of wavelet transform to study the multi-scale, self similar behavior and deviations thereof, in the stock prices of large companies, belonging to different economic sectors. The stock market returns exhibit multi-fractal characteristics, with some of the companies showing deviations at small and large scale…

This paper upgrades instanton TQFT to infinity-categories for better simplification.

Study of modular representations in homology of congruence subgroups.

Short-term road traffic prediction (STTP) is one of the most important modules in Intelligent Transportation Systems (ITS). However, network-level STTP still remains challenging due to the difficulties both in modeling the diverse traffic patterns and tacking high-dimensional time series with low latency. Therefore, a …

Classifies modules of surface-knots in terms of their properties.

Mode decomposition is a prototypical pattern recognition problem that can be addressed from the (a priori distinct) perspectives of numerical approximation, statistical inference and deep learning. Could its analysis through these combined perspectives be used as a Rosetta stone for deciphering mechanisms at play in de…

Proves finiteness and holonomicity of skein modules for 3-manifolds.

Defines super projective modules and explores their properties.