arXiv research

New spectral functionals for Dirac operators with inner fluctuations computed.

Study uses neural networks to predict wall quantities in turbulent flows.

In this paper, we applied the multifractal detrended fluctuation analysis to the daily means of wind speed measured by 119 weather stations distributed over the territory of Switzerland. The analysis was focused on the inner time fluctuations of wind speed, which could be more linked with the local conditions of the hi…

We introduce a novel description of the dynamics of the order book of financial markets as that of an effective colloidal Brownian particle embedded in fluid particles. The analysis of a comprehensive market data enables us to identify all motions of the fluid particles. Correlations between the motions of the Brownian…

Financial markets have been extensively studied as highly complex evolving systems. In this paper, we quantify financial price fluctuations through a coupled dynamical system composed of phase oscillators. We find a Financial Coherence and Incoherence (FCI) coexistence collective behavior emerges as the system evolves …

Study higher rank inner products and their tilings to describe tori degenerations.

Characterizes quandles with abelian inner automorphisms.

Study shows cryptocurrency price fluctuations become more similar to national currencies over time.

A new algorithm tackles bilevel optimization with multiple inner minima.

Bayesian models' singular fluctuation is shown to be akin to specific heat, influencing model complexity and generalization.

This paper constructs quandles with abelian inner automorphism groups from graphs, proving their homogeneity.

Groups with specific properties have vanishing $\ell^2$-Betti numbers.

The author reviews his results on locally compact homogeneous spaces with inner metric, in particular, homogeneous manifolds with inner metric. The latter are isometric to homogeneous (sub-)Finslerian manifolds; under some additional conditions they are isometric to homogeneous (sub)-Riemannian manifolds. The class $Ω$…

Researchers prove inner product recovery is impossible in latent space models.

We classify homotopes of classical symmetric spaces (studied in Part I of this work). Our classification uses the fibered structure of homotopes: they are fibered as symmetric spaces, with flat fibers, over a non-degenerate base; the base spaces correspond to inner ideals in Jordan pairs. Using that inner ideals in cla…

Paper proposes a new method to optimize feature coordinates for better image classification.

The paper challenges the belief that more inner iterations at test time improve performance in implicit deep learning.

We study the nature of fluctuations in variety of price indices involving companies listed on the New York Stock Exchange. The fluctuations at multiple scales are extracted through the use of wavelets belonging to Daubechies basis. The fact that these basis sets satisfy vanishing moments conditions makes them ideal to …

We propose a new approach for properly analyzing stochastic time series by mapping the dynamics of time series fluctuations onto a suitable nonequilibrium surface-growth problem. In this framework, the fluctuation sampling time interval plays the role of time variable, whereas the physical time is treated as the analog…

The average economic agent is often used to model the dynamics of simple markets, based on the assumption that the dynamics of many agents can be averaged over in time and space. A popular idea that is based on this seemingly intuitive notion is to dampen electric power fluctuations from fluctuating sources (as e.g. wi…

Study of Gaussian distributions using entropic Gromov-Wasserstein and inner product Gromov-Wasserstein.

A core capability of intelligent systems is the ability to quickly learn new tasks by drawing on prior experience. Gradient (or optimization) based meta-learning has recently emerged as an effective approach for few-shot learning. In this formulation, meta-parameters are learned in the outer loop, while task-specific m…

This work studies fluctuation in multilayer neural networks using mean field theory.

ANIL adapts only a subset of parameters, reducing computational cost.

Study bounds the index of minimal submanifolds using energy measures and Yang-Mills-Higgs equations.

We propose a quantization based approach for fast approximate Maximum Inner Product Search (MIPS). Each database vector is quantized in multiple subspaces via a set of codebooks, learned directly by minimizing the inner product quantization error. Then, the inner product of a query to a database vector is approximated …

We propose a new approach for analyzing price fluctuations in their strongly correlated regime ranging from minutes to months. This is done by employing a self-similarity assumption for the magnitude of coarse-grained price fluctuation or volatility. The existence of a Cramer function, the characteristic function for s…

Each market has its singular characteristic. Its inner structure is directly responsible for the observed distributions of returns though this fact is widely overlooked. Big orders lead to doubling the tails. The behavior of a market maker with many or few ``friends'' who can reliably loan money or stock to him is quit…

We analyze daily prices of 29 commodities and 2449 stocks, each over a period of $\approx 15$ years. We find that the price fluctuations for commodities have a significantly broader multifractal spectrum than for stocks. We also propose that multifractal properties of both stocks and commodities can be attributed mainl…

Study on singularities of specific polynomial functions.

Trading affects grid frequency fluctuations, making them more extreme.

Graphs with stronger curvature grow faster.

We study one extremal problem on the product of power of generalized inner radii of non-overlapping domains in $\mathbb{C}^{n}$.

We point out that the Homfly polynomial (that is to say, Ocneanu's trace functional) contains two polynomial-valued inner products on the Hecke algebra representation of Artin's braid group. These bear a close connection to the Morton-Franks-Williams inequality. In these structures, the sets of positive, respectively n…

Study on kernel regression risk in high dimensions using Pinsker bound.

A phenomenological investigation of the endogenous and exogenous dynamics in the fluctuations of capital fluxes is investigated on the Chinese stock market using mean-variance analysis, fluctuation analysis and their generalizations to higher orders. Non-universal dynamics have been found not only in $α$ exponents diff…

Study identifies contagion in aggregated defaults despite environmental changes.

In this paper we compare market price fluctuations with the response to fundamental price drops within the Lux-Marchesi model which is able to reproduce the most important stylized facts of real market data. Major differences can be observed between the decay of spontaneous fluctuations and of changes due to external p…

The paper solves the Andreadakis problem for specific groups using inner automorphisms.

We address the question of how stock prices respond to changes in demand. We quantify the relations between price change $G$ over a time interval $Δt$ and two different measures of demand fluctuations: (a) $Φ$, defined as the difference between the number of buyer-initiated and seller-initiated trades, and (b) $Ω$, def…

Conservative SPDEs emerge from fluctuating SGD dynamics in neural networks.

Study on price fluctuations in NFT market, showing heavy-tailed distributions and long-range memory.

Spectral clustering performance depends on eigenvector fluctuations, shown to be Gaussian.

Convex learning for diverse invariances in semi-inner-product space.

We present the first provably sublinear time algorithm for approximate \emph{Maximum Inner Product Search} (MIPS). Our proposal is also the first hashing algorithm for searching with (un-normalized) inner product as the underlying similarity measure. Finding hashing schemes for MIPS was considered hard. We formally sho…

We analyze the fluctuation of the loss from default around its large portfolio limit in a class of reduced-form models of correlated firm-by-firm default timing. We prove a weak convergence result for the fluctuation process and use it for developing a conditionally Gaussian approximation to the loss distribution. Nume…

In this manuscript we present a comprehensive study on the multifractal properties of high-frequency price fluctuations and instantaneous volatility of the equities that compose Dow Jones Industrial Average. The analysis consists about quantification of dependence and non-Gaussianity on the multifractal character of fi…

A new method for efficient nested Monte Carlo simulations in financial modeling.