arXiv research

The paper tackles the problem of deriving a topological structure among stock prices from high frequency historical values. Similar studies using low frequency data have already provided valuable insights. However, in those cases data need to be collected for a longer period and then they have to be detrended. An effec…

Study uses high-frequency data to predict ruble depreciation during crisis.

Ray marching method visualizes flat surfaces efficiently.

Ray-marching method visualizes 8 Thurston geometries in real-time.

Paper proves March's criterion for transience on symmetric manifolds.

This short note serves as a historical introduction to the Hopf problem: "Does there exist a complex structure on $S^6$?" This unsolved mathematical question was the subject of the Conference "MAM 1 $-$ (Non-)Existence of Complex Structures on $S^6$", which took place at Philipps-Universität Marburg, Germany, between M…

New algorithm recovers 3D molecule structures from noisy data.

Topological anomaly scores predict return curves in S&P 500 stocks

This paper analyzes how banking risks spread through sentiment and policy shocks.

Improved KAN model explains brain dynamics through edge learning and synaptic strength.

Study examines cryptocurrency behavior during and after the pandemic.

In this paper we review the well-known fact that the only spheres admitting an almost complex structure are S^2 and S^6. The proof described here uses characteristic classes and the Bott periodicity theorem in topological K-theory. This paper originates from the talk "Almost Complex Structures on Spheres" given by the …

Lecture notes from the Third International School on Geometry and Physics at the Centre de Recerca Matematica in Barcelona, March 26--30, 2012.

Study examines oil and US stock market interactions during coronavirus crisis.

Machine learning predicts US stock market crashes.

These are lecture notes mainly aimed at graduate students on selected aspects of generalized geometry: in particular generalized complex and Kaehler structures and generalized holomorphic bundles. They are based on lectures given in March 2010 at the Chinese University of Hong Kong.

These are lecture notes on scale calculus and M-polyfolds written for a graduate course at UNICAMP March-June 2018 and an advanced mini-course given during the biannual meeting of Brazilian mathematicians, CBM-32, at IMPA in August 2019.

The study evaluates different probability models for uncertainty visualization using entropy calculations.

Counterexample disproves conjecture about 3-manifold modules.

Study investor sentiment and disagreement on StockTwits during COVID-19.

We review results on and around the almost complex structure on $S^6$, both from a classical and a modern point of view. These notes have been prepared for the Workshop "(Non)-existence of complex structures on $S^6$" (\emph{Erste Marburger Arbeitsgemeinschaft Mathematik -- MAM-1}), held in Marburg in March 2017.

Applying standard techniques from Toeplitz operator theory, we analyze the asymptotics of the Hilbert-Smith norms of the TQFT operators coming from isotopy classes of one dimensional oriented submanifolds on a closed oriented surface. We thereby obtain a Toeplitz operator interpretation and generalization of the asympt…

Suppose $S$ is a closed orientable surface and $\tilde{S}$ is a finite sheeted regular cover of $S$. The following question was posed by Julién Marché in Mathoverflow: Do the lifts of simple curves from $S$ generate $H_{1}(\tilde{S},\mathbb{Z})$? A family of examples is given for which the answer is "no".

Ethereum upgrades increased TPS and lowered fees, with L2s surpassing Solana in 2029.

These lecture notes are based on a mini-course given by the author at the sixth KAWA Winter School on March 23-26, 2015 at the Centro De Giorgi of Scuola Normale Superiore in Pisa. They provide an introduction to the study of the Kahler-Ricci flow on compact Kahler manifolds, and a detailed exposition of some recent de…

Data analysis with log-periodical parametrization of the Brent oil price dynamics has allowed to estimate (very approximately) the date when the dashing collapse of the Brent oil price will achieve the absolute minimum level (corresponding to the so-called singularity point), after which there will occur a rather rapid…

I review several proofs for non-existence of orthogonal complex structures on the six-sphere, most notably by G. Bor and L. Hernandez-Lamoneda, but also by K. Sekigawa and L. Vanhecke that we generalize for metrics close to the round one. Invited talk at MAM-1 workshop, 27-30 March 2017, Marburg.

Two possible definitions of fixed points in the self-similar analysis of time series are considered. One definition is based on the minimal-difference condition and another, on a simple averaging. From studying stock market time series, one may conclude that these two definitions are practically equivalent. A forecast …

Develops discrete geometry for non-constant curvature surfaces.

These are the written discussions of the paper "Bayesian measures of model complexity and fit" by D. Spiegelhalter et al. (2002), following the discussions given at the Annual Meeting of the Royal Statistical Society in Newcastle-upon-Tyne on September 3rd, 2013.

Detects potential depegs in Curve's StableSwap pools to protect LPs.

The predictions of the S&P 500 returns made in 2007 have been tested and the underlying models amended. The period between 2003 and 2008 should be described by the dependence of the S&P 500 stock market index on real GDP because the population pyramid was highly inaccurate. The 2008 trough and 2009 rally are well predi…

Define an arithmetic variety to be the quotient of a bounded symmetric domain by an arithmetic group. An arithmetic variety is algebraic, and the theorem in question states that when one applies an automorphism of the field of complex numbers to the coefficients of an arithmetic variety the resulting variety is again a…

Based on our "finance-prediction-oriented" methodology which involves such elements as log-periodic self-similarity, the universal preferred scaling factor lambda=2, and allows a phenomenon of the "super-bubble" we analyze the 2009 world stock market (here represented by the SP500, Hang Seng and WIG) development. We id…

Topological quantum field theories with gauge group $\textrm{SU}_2$ associate to each surface with marked points $Σ$ and each integer $r>0$ a vector space $V_r (Σ)$ and to each simple closed curve $γ$ in $Σ$ an Hermitian operator $T_r^γ$ acting on that space. We show that the matrix elements of the operators $T_r^γ$ ha…

This article arose from a series of three lectures given at the Banach Center, Warsaw, during period of 24 March to 13 April, 2003. Morse functions are useful tool in revealing the geometric formation of its domain manifolds $M$. They define the handle decompositions of $M$ from which the additive homologies $H_{\ast}(…

Study analyzes market co-movements in critical mineral investments using change point detection and cross-sectional analysis.

HyFAD improves time series imputation by combining time and frequency diffusion.

Investor expectations shifted pessimistically during the 2020 stock market crash and recovery.

SSMs have a built-in bias towards low-frequency components, which can be adjusted.

Geometrically interprets frequency in electric circuits.

Trading affects grid frequency fluctuations, making them more extreme.

Study on frequencies of non-simple curves in surfaces of large genus.

CNNs show sensitivity to low-frequency signals due to image frequency distribution.

The paper examines how parabolic frequency behaves under Ricci flow and Ricci-harmonic flow on manifolds.

New method constrains CNN filter frequencies to improve robustness.

Study uses multi-kernel Hawkes models to analyze high-frequency price dynamics.

Paper extends SI method for detecting CPs in complex systems' frequency domain.