arXiv subjects

Piotr Jaworski

Publications and source records attributed to Piotr Jaworski.

8 recordsLinked to original sources

arXiv2026

Predicting Conflict Impact on Performance in O-RAN

The O-RAN Alliance promotes the integration of intelligent autonomous agents to control the Radio Access Network (RAN). This improves flexibility, performance, and observability in the RAN, but introduces new challenges, such as the detection and management of conflicts among the intelligent autonomous agents. A solution consists of profiling the agents before deployment to gather statistical information about their decision-making behavior, then using the information to estimate the level of conflict among agents with different goals. This approach enables determining the occurrence of conflicts among agents, but does not provide information about the impact on RAN performance, including potential service degradation. The problem becomes more complex when agents generate control actions at different timescales, which makes conflict severity hard to predict. In this paper, we present a novel approach that fills this gap. Our solution leverages the same data used to determine conflict severity but extends its use to predict the impact of such conflicts on RAN performance based on the frequency at which each agent generates actions, giving more weight to faster applications, which exert control more frequently. Via a prototype, we demonstrate that our solution is viable and accurately predicts conflict impact on RAN performance.

cs.NI↗

arXiv2024

On the dependence between a Wiener process and its running maxima and running minima processes

We study a triple of stochastic processes: a Wiener process $W_t$, $t \geq 0$, its running maxima process $M_t=\sup \{W_s: s \in [0,t]\}$ and its running minima process $m_t=\inf \{W_s: s \in [0,t]\}$. We derive the analytical formulas for the joint distribution function and the corresponding copula. As an application we draw out an analytical formula for pricing double barrier options.

math.PR↗

arXiv2024

Gaussian dependence structure pairwise goodness-of-fit testing based on conditional covariance and the 20/60/20 rule

We present a novel data-oriented statistical framework that assesses the presumed Gaussian dependence structure in a pairwise setting. This refers to both multivariate normality and normal copula goodness-of-fit testing. The proposed test clusters the data according to the 20/60/20 rule and confronts conditional covariance (or correlation) estimates on the obtained subsets. The corresponding test statistic has a natural practical interpretation, desirable statistical properties, and asymptotic pivotal distribution under the multivariate normality assumption. We illustrate the usefulness of the introduced framework using extensive power simulation studies and show that our approach outperforms popular benchmark alternatives. Also, we apply the proposed methodology to commodities market data.

stat.ME↗

arXiv2023

Photothermal gas detection using a miniaturized fiber Fabry-Perot cavity

We demonstrate a robust and miniaturized fiber Fabry-Perot cavity-based sensor for photothermal spectroscopic signal retrieval. The proof-of-concept experiment involved the use of a near-infrared pump laser to detect methane molecules on an isolated overtone 2.3 R(4) transition located at 6057.1 cm-1. The photothermal-related modulation of the gas refractive index was induced at the center of the interferometer, which was filled with the sample. Subsequently, the phase change of the resonating probe beam was measured as a shift in the reflected beam intensity, which was proportional to the methane concentration. A normalized noise equivalent absorption coefficient of 7.06 x 10-8 cm-1 W Hz-1/2 was achieved, suggesting significant potential for the design of small and versatile gas detectors with excellent detectivity. We discuss future improvements of the proposed photothermal gas detection approach.

physics.optics↗

arXiv2022

A note on the equivalence between the conditional uncorrelation and the independence of random variables

It is well known that while the independence of random variables implies zero correlation, the opposite is not true. Namely, uncorrelated random variables are not necessarily independent. In this note we show that the implication could be reversed if we consider the localised version of the correlation coefficient. More specifically, we show that if random variables are conditionally (locally) uncorrelated for any quantile conditioning sets, then they are independent. For simplicity, we focus on the absolutely continuous case. Also, we illustrate potential usefulness of the stated result using two simple examples.

math.ST↗

arXiv2017

A note on conditional covariance matrices for elliptical distributions

In this short note we provide an analytical formula for the conditional covariance matrices of the elliptically distributed random vectors, when the conditioning is based on the values of any linear combination of the marginal random variables. We show that one could introduce the univariate invariant depending solely on the conditioning set, which greatly simplifies the calculations. As an application, we show that one could define uniquely defined quantile-based sets on which conditional covariance matrices must be equal to each other if only the vector is multivariate normal. The similar results are obtained for conditional correlation matrices of the general elliptic case.

math.PR↗

arXiv2015

The 20-60-20 Rule

In this paper we discuss an empirical phenomena known as the 20-60-20 rule. It says that if we split the population into three groups, according to some arbitrary benchmark criterion, then this particular ratio implies some sort of balance. From practical point of view, this feature often leads to efficient management or control. We provide a mathematical illustration, justifying the occurrence of this rule in many real world situations. We show that for any population, which could be described using multivariate normal vector, this fixed ratio leads to a global equilibrium state, when dispersion and linear dependance measurement is considered.

math.PR↗

arXiv2006

On Value at Risk for foreign exchange rates - the copula approach

The aim of this paper is to determine the Value at Risk (VaR) of the portfolio consisting of long positions in foreign currencies on an emerging market. Basing on empirical data we restrict ourselves to the case when the tail parts of distributions of logarithmic returns of these assets follow the power laws and the lower tail of associated copula C follows the power law of degree 1. We will illustrate the practical usefulness of this approach by the analysis of the exchange rates of EUR and CHF at the Polish forex market.

physics.soc-ph↗