arXiv research

Cryptocurrencies show stable prices as a medium of exchange.

Deep learning models outperform traditional methods in stock price prediction.

We analyze structure of the world foreign currency exchange (FX) market viewed as a network of interacting currencies. We analyze daily time series of FX data for a set of 63 currencies, including gold, silver and platinum. We group together all the exchange rates with a common base currency and study each group separa…

A new multivariate stochastic volatility estimation procedure for financial time series is proposed. A Wishart autoregressive process is considered for the volatility precision covariance matrix, for the estimation of which a two step procedure is adopted. The first step is the conditional inference on the autoregressi…

This study proposes a new model for predicting financial distress in SMEs using machine learning.

Money was invented to address the difficulty in the double coincidence of wants between the supply and demand when people exchanged their goods and services. There are two information states in society: one is the initial state that people have goods and services due to division of labor; the other is the final state t…

Despite being described as a medium of exchange, cryptocurrencies do not have the typical attributes of a medium of exchange. Consequently, cryptocurrencies are more appropriately described as crypto assets. A common investment attribute shared by the more than 2,500 crypto assets is that they are highly volatile. An i…

Paper extends Aronson-Bénilan estimates for porous medium equations on manifolds with negative curvature.

Researchers study fractional porous medium equation on hyperbolic space.

Purely real space versions of the differential equations describing the kinematics of a dislocated crystalline medium are considered. The differential geometric structures associated with them are revealed.

Changes in the capital structure before and after the global financial crisis for SMEs are studied, emphasizing their financing problems, distinguishing between internal financing and external financing determinants. The empirical research bears upon 158 small and medium-sized firms listed on Shenzhen and Shanghai Stoc…

Study nonnegative solutions on Riemannian manifolds using fractional porous medium equation.

Emerging economies use countercyclical policies to manage crises and dominant currencies.

In this paper, we study the gradient estimates for the positive solutions of the weighted porous medium equation $Δu^{m}=δ(x)u_{t}+ψu^{m}$ on graphs for $m>1$, which is a nonlinear version of the heat equation. Moreover, as applications, we derive a Harnack inequality and the estimates of the porous medium kernel on …

We study inverse problems consisting on determining medium properties using the responses to probing waves from the machine learning point of view. Based on the understanding of propagation of waves and their nonlinear interactions, we construct a deep convolutional neural network in which the parameters are used to cl…

Study self shrinkers with medium entropy in 4D space.

Researchers solve porous medium equation on noncompact manifolds with Ricci curvature.

In this paper we study gradient estimates for the positive solutions of the porous medium equation: $u_t=Δu^m$ where $m>1$, which is a nonlinear version of the heat equation. We derive local gradient estimates of the Li-Yau type for positive solutions of porous medium equations on Riemannian manifolds with Ricci curv…

In this paper, we prove Perelman type $\mathcal{W}$-entropy formulae and global differential Harnack estimates for positive solutions to porous medium equation on the closed Riemannian manifolds with Ricci curvature bounded below. As applications, we derive Harnack inequalities and Laplacian estimates.

Herein, we applied statistical physics to study incomes of three (low-, medium- and high-income) society classes instead of the two (low- and medium-income)classes studied so far. In the frame of the threshold nonlinear Langevin dynamics and its threshold Fokker-Planck counterpart, we derived a unified formula for desc…

This study compares Bitcoin and Litecoin using cryptocurrency metrics and trading strategies.

In this paper we study the porous medium equation (PME) coupled with the Ricci flow on complete manifolds with bounded nonnegative curvature operator. In particular, we derive Aronson-Bénilan and Li-Yau-Hamilton type differential Harnack estimates for positive solutions to the PME, with a linear forcing term, under the…

Toda flow explained as a porous medium equation.

New digital currency aims for equal wealth distribution.

In modern supervised learning, there are a large number of tasks, but many of them are associated with only a small amount of labeled data. These include data from medical image processing and robotic interaction. Even though each individual task cannot be meaningfully trained in isolation, one seeks to meta-learn acro…

We consider gradient estimates to positive solutions of porous medium equations and fast diffusion equations: $u_t=Δ_φ(u^p)$ associated with the Witten Laplacian on Riemannian manifolds. Under the assumption that the $m$-dimensional Bakry-Emery Ricci curvature is bounded from below, we obtain gradient estimates which…

We study the long-time behaviour of nonnegative solutions of the Porous Medium Equation posed on Cartan-Hadamard manifolds having very large negative curvature, more precisely when the sectional or Ricci curvatures diverge at infinity more than quadratically in terms of the geodesic distance to the pole. We find an une…

We investigate existence and uniqueness of weak solutions of the Cauchy problem for the porous medium equation on negatively curved Riemannian manifolds. We show existence of solutions taking as initial condition a finite Radon measure, not necessarily positive. We then establish uniqueness in the class of nonnegative …

The paper derives gradient estimates for porous medium and fast diffusion equations on metric measure spaces.

In this work we derive local gradient and Laplacian estimates of the Aronson-Bénilan and Li-Yau type for positive solutions of porous medium equations posed on Riemannian manifolds with a lower Ricci curvature bound. We also prove similar results for some fast diffusion equations. Inspired by Perelman's work we discove…

We use machine learning for designing a medium frequency trading strategy for a portfolio of 5 year and 10 year US Treasury note futures. We formulate this as a classification problem where we predict the weekly direction of movement of the portfolio using features extracted from a deep belief network trained on techni…

In this paper, we investigate some new local Aronson-Bénilan type gradient estimates for positive solutions of the porous medium equation $u_{t}=Δu^{m},$ under Ricci flow. As application, the related Harnack inequalities are derived. Our results generalize known results. These results in the paper can be regard as …

We consider the porous medium equation with power-type reaction terms $u^p$ on negatively curved Riemannian manifolds, and solutions corresponding to bounded, nonnegative and compactly supported data. If $p>m$, small data give rise to global-in-time solutions while solutions associated to large data blow up in finite t…

In this paper, by employ the cutoff function and the maximum principle, some Hamilton-Souplet-Zhang type gradient estimates for porous medium type equation are deduced. As a special case, an Hamilton-Souplet-Zhang type gradient estimates of the heat equation is derived which is different from the result of Souplet-Zhan…

Study analyzes order transitions in high, medium, and low market cap stocks using Markov chains.

In this paper we construct the differential equations of the stream lines that characterize plasma regarded as a non-isotropic medium geometrized by a jet rheonomic time-invariant Berwald-Moor metric. Section 1 contains historical notes regarding the Plasma Physics and its geometrical description. Section 2 analyzes th…

In the last decade, social networks became most popular medium for communication and interaction. As an example, micro-blogging service Twitter has more than 200 million registered users who exchange more than 65 million posts per day. Users express their thoughts, ideas, and even their intentions through these tweets.…

The increasing quantity of PV generation connected to distribution networks is creating challenges in maintaining and controlling voltages in those distribution networks. Determining the maximum hosting capacity for new PV installations based on the historical data is an essential task for distribution networks. Analyz…

Study analyzes portfolio performance of crypto and traditional assets.

Study on uniquely determining thermal properties from boundary temperature and heat flux measurements.

The problem of distributed learning and channel access is considered in a cognitive network with multiple secondary users. The availability statistics of the channels are initially unknown to the secondary users and are estimated using sensing decisions. There is no explicit information exchange or prior agreement amon…

Study reconstructs Riemannian metric from Cherenkov radiation in complex media.

Being one of the most important factors of economic growth of the country, innovations became one of the key vectors in Russian economic policy. In this field technology parks are one of the most effective instruments which can provide growth of innovative activity in sectors, regions and economies. In this paper, we m…

Study shows conditions for nonexistence of solutions in Riemannian geometry.

Research develops a DSS for stock selection and asset allocation using fundamental data.

Let $(M, g(t))$, $t\in[0,T)$ be a closed Riemannian $n$-manifold whose Riemannian metric $g(t)$ evolves by the geometric flow $\frac{\partial }{\partial t} g_{ij}=-2S_{ij}$, where $S_{ij}(t)$ is a symmetric two-tensor on $(M,g(t))$. We discuss differential Harnack estimates for positive solution to the porous medium …

Weight Squeezing transfers knowledge from large models to smaller ones, improving performance and speed.

We propose a novel method to train deep convolutional neural networks which learn from multiple data sets of varying input sizes through weight sharing. This is an advantage in chemometrics where individual measurements represent exact chemical compounds and thus signals cannot be translated or resized without disturbi…