arXiv research

Employing data on the assessed value of land in 1983 -- 2005 Japan, we investigate the dynamical behavior in the high scale region of non-equilibrium systems. From the detailed quasi-balance and Gibrat's law, we derive a relation between the change of Pareto index and a symmetry in the detailed quasi-balance. The relat…

We test a historical price time series in a financial market (the NASDAQ 100 index) for a statistical property known as detailed balance. The presence of detailed balance would imply that the market can be modeled by a stochastic process based on a Markov chain, thus leading to equilibrium. In economic terms, a positiv…

We develop an efficient sampling method by simulating Langevin dynamics with an artificial force rather than a natural force by using the gradient of the potential energy. The standard technique for sampling following the predetermined distribution such as the Gibbs-Boltzmann one is performed under the detailed balance…

Study on balanced Hermitian threefolds with parallel Bismut torsion.

Schrödinger and Onsager's ideas linked in nonequilibrium thermodynamics.

New sampler tackles complex discrete energy landscapes efficiently.

In this paper, we propose a novel technique to implement stochastic gradient methods, which are beneficial for learning from large datasets, through accelerated stochastic dynamics. A stochastic gradient method is based on mini-batch learning for reducing the computational cost when the amount of data is large. The sto…

We investigate the dynamical behavior in the large scale region of non-equilibrium systems, by employing data on the assessed value of land in 1983 -- 2006 Japan. In the system we find the detailed quasi-balance, which has the symmetry: x_1 -> a {x_2}^θ (x_1 and x_2 are two successive land prices). By using the detaile…

It has been recently shown that a large class of balanced graph cuts allows for an exact relaxation into a nonlinear eigenproblem. We review briefly some of these results and propose a family of algorithms to compute nonlinear eigenvectors which encompasses previous work as special cases. We provide a detailed analysis…

We present a method for performing Hamiltonian Monte Carlo that largely eliminates sample rejection for typical hyperparameters. In situations that would normally lead to rejection, instead a longer trajectory is computed until a new state is reached that can be accepted. This is achieved using Markov chain transitions…

Abstract: Necessary and sufficient conditions for gradient flows of relative entropy in Lindblad equations.

Employing data on the assessed value of land in 1974--2007 Japan, we exhibit a quasistatically varying log-normal distribution in the middle scale region. In the derivation, a Non-Gibrat's law under the detailed quasi-balance is adopted together with two approximations. The resultant distribution is power-law with the …

By using numerical simulation, we confirm that Takayasu--Sato--Takayasu (TST) model which leads Pareto's law satisfies the detailed balance under Gibrat's law. In the simulation, we take an exponential tent-shaped function as the growth rate distribution. We also numerically confirm the reflection law equivalent to the…

Employing profits data of Japanese firms in 2003--2005, we kinematically exhibit the static log-normal distribution in the middle scale region. In the derivation, a Non-Gibrat's law under the detailed balance is adopted together with following two approximations. Firstly, the probability density function of profits gro…

Improved GFlowNets learn more efficiently with trajectory balance.

Study geodesic equation on mixed-volume forms on balanced manifolds, proving existence of solutions.

By employing exhaustive lists of large firms in European countries, we show that the upper-tail of the distribution of firm size can be fitted with a power-law (Pareto-Zipf law), and that in this region the growth rate of each firm is independent of the firm's size (Gibrat's law of proportionate effect). We also find t…

Let $f:S^2\to S^2$ be an orientation-preserving branched covering map of degree $d\geq 2$, and let $Σ$ be an oriented Jordan curve passing through the critical values of $f$. Then $Γ:=f^{-1}(Σ)$ is an oriented graph on the sphere. In a group email discussion in Fall 2010, W. Thurston introduced balanced planar graphs a…

A new XVA strategy rooted in balance sheet perspective improves equity process for bank shareholders.

Recent sparse MRI reconstruction models have used Deep Neural Networks (DNNs) to reconstruct relatively high-quality images from highly undersampled k-space data, enabling much faster MRI scanning. However, these techniques sometimes struggle to reconstruct sharp images that preserve fine detail while maintaining a nat…

We propose a novel method to directly learn a stochastic transition operator whose repeated application provides generated samples. Traditional undirected graphical models approach this problem indirectly by learning a Markov chain model whose stationary distribution obeys detailed balance with respect to a parameteriz…

Study compares empirical systemic risk with balance sheet risk in interbank networks.

Analyzes Indian commercial dynamism using time series data.

Improved GSPGS estimators reduce bias in noisy function measurements.

New metrics found on non-Kähler Calabi-Yau manifolds.

We show that holographic renormalization of relativistic gravity in asymptotically Lifshitz spacetimes naturally reproduces the structure of gravity with anisotropic scaling: The holographic counterterms induced near anisotropic infinity take the form of the action for gravity at a Lifshitz point, with the appropriate …

Employing profits data of Japanese companies in 2002 and 2003, we identify the non-Gibrat's law which holds in the middle profits region. From the law of detailed balance in all regions, Gibrat's law in the high region and the non-Gibrat's law in the middle region, we kinematically derive the profits distribution funct…

In sustained growth with random dynamics stationary distributions can exist without detailed balance. This suggests thermodynamical behavior in fast growing complex systems. In order to model such phenomena we apply both a discrete and a continuous master equation. The derivation of elementary rates from known stationa…

In this paper I give a brief introduction to a family of simple but non-trivial models designed to increase our understanding of collective processes in markets, the so-called Minority Games, and their non-equilibrium statistical mathematical analysis. Since the most commonly studied members of this family define disor…

This article contains the first published example of a real economic balance sheet where the Solvency II ratio substantially depends on the seed selected for the random number generator (RNG) used. The theoretical background and the main quality criteria for RNGs are explained in detail. To serve as a gauge for RNGs, a…

We consider applications of the theory of balanced weight filtrations and iterated logarithms, initiated in arXiv:1706.01073, to PDEs. The main result is a complete description of the asymptotics of the Yang--Mills flow on the space of metrics on a holomorphic bundle over a Riemann surface. A key ingredient in the argu…

Financial and economic history is strewn with bubbles and crashes, booms and busts, crises and upheavals of all sorts. Understanding the origin of these events is arguably one of the most important problems in economic theory. In this paper, we review recent efforts to include heterogeneities and interactions in models…

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…

New gauge fields modify Fokker-Planck dynamics without changing the stationary state.

A growing body of studies on systemic risk in financial markets has emphasized the key importance of taking into consideration the complex interconnections among financial institutions. Much effort has been put in modeling the contagion dynamics of financial shocks, and to assess the resilience of specific financial ma…

Federated Learning is introduced to protect privacy by distributing training data into multiple parties. Each party trains its own model and a meta-model is constructed from the sub models. In this way the details of the data are not disclosed in between each party. In this paper we investigate the model interpretation…

UMAP's true loss function differs from what was previously thought, focusing on nearest neighbor graph similarities.

Paper proposes D3M to improve anti-spoofing detection by balancing loss function and using complementary features.

We report the proof that the expression of extended Gibrat's law is unique and the probability distribution function (pdf) is also uniquely derived from the law of detailed balance and the extended Gibrat's law. In the proof, two approximations are employed that the pdf of growth rate is described as tent-shaped expone…

Employing profits data of Japanese companies in 2002 and 2003, we confirm that Pareto's law and the Pareto index are derived from the law of detailed balance and Gibrat's law. The last two laws are observed beyond the region where Pareto's law holds. By classifying companies into job categories, we find that companies …

Researchers create exact minimal surfaces with helical motifs in biological structures.

We consider instanton solutions of Euclidean Horava-Lifshitz gravity in four dimensions satisfying the detailed balance condition. They are described by geometric flows in three dimensions driven by certain combinations of the Cotton and Ricci tensors as well as the cosmological-constant term. The deformation curvature…

We report the proof that the extension of Gibrat's law in the middle scale region is unique and the probability distribution function (pdf) is also uniquely derived from the extended Gibrat's law and the law of detailed balance. In the proof, two approximations are employed. The pdf of growth rate is described as tent-…

This work presents a general unified theory for coupled nonlinear elastic and inelastic deformations of curved thin shells. The coupling is based on a multiplicative decomposition of the surface deformation gradient. The kinematics of this decomposition is examined in detail. In particular, the dependency of various ki…

This paper uses PCA and FA for feature selection in credit rating.

In this paper we study the automorphism group of smoothly bounded convex domains. We show that such a domain is biholomorphic to a "polynomial ellipsoid" (that is, a domain defined by a weighted homogeneous balanced polynomial) if and only if the limit set of the automorphism group intersects at least two closed comple…

Understanding the power of depth in feed-forward neural networks is an ongoing challenge in the field of deep learning theory. While current works account for the importance of depth for the expressive power of neural-networks, it remains an open question whether these benefits are exploited during a gradient-based opt…

We construct a theoretical model for equilibrium distribution of workers across sectors with different labor productivity, assuming that a sector can accommodate a limited number of workers which depends only on its productivity. A general formula for such distribution of productivity is obtained, using the detail-bala…