Non-local diffusion processes have garnered significant attention in various fields due to their ability to capture intricate dynamics beyond the scope of classical diffusion models. In economics, understanding and modeling non-local diffusion phenomena hold promise for explaining complex behaviors in financial markets, particularly in the context of stochastic processes and time series analysis. This abstract delves into the conceptual framework and implications of non-local diffusion in economic processes.

The conventional diffusion models often fail to capture the inherent non-local interactions and long-range dependencies in economic systems, leading to incomplete representations of market dynamics. Non-local diffusion processes offer a more nuanced perspective by accounting for spatial interactions and memory effects, providing a more accurate portrayal of market behavior.

In stochastic processes, non-local diffusion introduces spatially extended interactions that transcend the traditional local diffusion assumption. This enables the incorporation of non-local influences such as global market trends, systemic risk, and investor sentiments into the modeling framework, leading to more robust predictions and risk assessments.

This abstract highlights the potential of non-local diffusion in enhancing our understanding of economic processes and refining stochastic models for financial markets. By embracing the complexities of non-local interactions, economists and analysts can develop more sophisticated tools for risk management, portfolio optimization, and decision-making in an increasingly interconnected and dynamic financial landscape.

Poster Presentation

Session 1

9:15am – 10:30am
Grand Salon

Mathematics

We explore the fascinating world of dual numbers, where a new imaginary unit, ε, satisfies ε² = 0. We compare them with the familiar complex numbers, where the imaginary unit, i, satisfies i² = -1.

We delve into:

Definitions and basic operations of dual and complex numbers.

• Unveiling the surprising properties of ε compared to i.
• Understanding how these number systems go beyond the real numbers.
• Unveiling the power of matrix representations:
• Visualizing complex numbers as 2×2 matrices:
• We represent a complex number a + bi as a 2×2 matrix: [[a, b], [-b, a]]
• Representing dual numbers with matrices for efficient calculations:
• A dual number x + yε corresponds to the matrix: [[x,y], [0, x]] where ε² = 0.
• We discuss the structure and surprises arising when combining these two fields.

Join us on a journey to unlock the secrets of these unique number systems and discover a new way to represent the mathematical world, with the added power of matrix visualization.

Poster Presentation

Session 1

9:15am – 10:30am
Grand Salon

Mathematics

This project is on the subject of twin prime numbers in Number Theory.  These are pairs of primes whose pairwise difference is two, for example 5 and 7 are twin primes.  There are infinitely many prime numbers, many come as a twin pair. We show examples of such pairs when the numbers are quite large. The main question is if there are infinitely many such pairs? We prove several facts concerning prime numbers, including some results related to twin primes.  One of the interesting statements that was proven quite recently says that there is infinitely many pairs of primes with relatively small gaps between them (however, currently   these  gaps are much larger than 2).  At this time it is still no proof or methodology to find infinitely many pairs of twin prime numbers. We. explain the current situation on this topic and give history of the study of pairs with fixed gaps between them.

Poster Presentation

Session 1

9:15am – 10:30am
Grand Salon

Mathematics