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We provide a surprising new application of classical approximation theory to a fundamental asset-pricing model of mathematical finance. Specifically, we calculate an analytic value for the correlation coefficient between exponential…

We consider an intermediate factor situation in two categories: probability measure preserving ergodic theory and compact topological dynamics. In the first we prove a master-key theorem and examine a wide range of applications. In the…

Many visual analytics systems allow users to interact with machine learning models towards the goals of data exploration and insight generation on a given dataset. However, in some situations, insights may be less important than the…

The concern of this paper is a famous combinatorial formula known under the name "exponential formula". It occurs quite naturally in many contexts (physics, mathematics, computer science). Roughly speaking, it expresses that the exponential…

The pointwise mutual information profile, or simply profile, is the distribution of pointwise mutual information for a given pair of random variables. One of its important properties is that its expected value is precisely the mutual…

In this paper, we investigate the economic mobility in some money transfer models which have been applied into the research on wealth distribution. We demonstrate the mobility by recording the time series of agents' ranks and observing…

Detrended fluctuation analysis is used to investigate correlations between the monthly average of the maximum daily temperatures for different locations in the continental US and the different climates these locations have. When we plot the…

In this paper we give an alternative exposition of a recent paper regarding the classification of growth rates of real functions. We take a different point of view, focussing on understanding possible growth rates between polynomial and…

For the pedestrian observer, financial markets look completely random with erratic and uncontrollable behavior. To a large extend, this is correct. At first approximation the difference between real price changes and the random walk model…

The theory of ``Markov-up'' processes is being developed. This is a new class of stochastic processes with ``partial'' markovian features; it could also be called ``one-sided Markov''. Such a behavior may be found in the real world and in…

We examine several recently suggested methods for the detection of long-range correlations in data series based on similar ideas as the well-established Detrended Fluctuation Analysis (DFA). In particular, we present a detailed comparison…

Zero-inflated models are frequently used to deal with data having many zeros. A commonly used model for over-dispersed data containing zeros is known as the zero-inflated Poisson model. However, to account for the heterogeneity of counts…

The standardized mean difference (SMD) is a widely used measure of effect size, particularly common in psychology, clinical trials, and meta-analysis involving continuous outcomes. Traditionally, under the equal variance assumption, the SMD…

Any large organisation, be it public or private, monitors the media for information to keep abreast of developments in their field of interest, and usually also to become aware of positive or negative opinions expressed towards them. At…

Through this paper, an attempt has been made to quantify the underlying relationships between the leading macroeconomic indicators. More clearly, an effort has been made in this paper to assess the cointegrating relationships and examine…

This work models the interconnection of company's investment managers' representations and the market attraction of its shares. The models that reflect the connection of the company's market effectiveness indices and parameters of its…

A new class of models for dynamic networks is proposed, called mutually exciting point process graphs (MEG). MEG is a scalable network-wide statistical model for point processes with dyadic marks, which can be used for anomaly detection…

We define a moment-based estimator that maximizes the empirical saddlepoint (ESP) approximation of the distribution of solutions to empirical moment conditions. We call it the ESP estimator. We prove its existence, consistency and…

The scaling of the optimal AdamW weight decay hyperparameter with model and dataset size is critical as we seek to build larger models, but is poorly understood. We show that weights learned by AdamW can be understood as an exponential…

We consider the design of prediction market mechanisms known as automated market makers. We show that we can design these mechanisms via the mold of \emph{exponential family distributions}, a popular and well-studied probability…