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The International Congress of Mathematicians (ICM), inaugurated in 1897, is the greatest effort of the mathematical community to strengthen international communication and connections across all mathematical fields. Meetings of the ICM have historically hosted some of the most prominent mathematicians of their time. Re…
Clustered Regularly Interspaced Short Palindromic Repeats (CRISPR), linked with CRISPR associated (CAS) genes, play a profound role in the interactions between phage and their bacterial hosts. It is now well understood that CRISPR-CAS systems can confer adaptive immunity against bacteriophage infections. However, the p…
We point out that T. Tanaka's recent criticism [quant-ph/0603075] of the results of J. Math. Phys. 43, 3944 (2002) [math-ph/0203005] is based on an assumption which was never made in the latter paper, namely that the diagonalizability of an operator implies that it is normal. Therefore, Tanaka's objections regarding th…
We study cash-flow forecasting for derivatives used in liquidity management and clarify its relation to risk-neutral valuation and replication. While it is well known that expectations under different measures (e.g., $\mathbb{P}$ vs. $\mathbb{Q}$) can yield different undiscounted cash-flows, further inconsistencies ari…
Mathematical models, calibrated to data, have become ubiquitous to make key decision processes in modern quantitative finance. In this work, we propose a novel framework for data-driven model selection by integrating a classical quantitative setup with a generative modelling approach. Leveraging the properties of the s…
Electrospray ion-beam deposition (ES-IBD) is a versatile tool to study structure and reactivity of molecules from small metal clusters to large protein assemblies. It brings molecules gently into the gas phase where they can be accurately manipulated and purified, followed by controlled deposition onto various substrat…
Questions of noise stability play an important role in hardness of approximation in computer science as well as in the theory of voting. In many applications, the goal is to find an optimizer of noise stability among all possible partitions of $\mathbb{R}^n$ for $n \geq 1$ to $k$ parts with given Gaussian measures $μ_…
This essay recounts my personal journey towards a deeper understanding of the mathematical foundations of algorithmic music composition. I do not spend much time on specific mathematical algorithms used by composers; rather, I focus on general issues such as fundamental limits and possibilities, by analogy with metalog…
Tsallis' non-extensive entropy is extended to incorporate the dependence on affinities between the microstates of a system. At the core of our construction of the extended entropy ($\mathcal{H}$) is the concept of the effective number of dissimilar states, termed the effective diversity ($\mathitΔ$). It is a unique in…
Resolving a linear combination of point sources from their band-limited Fourier data is a fundamental problem in imaging and signal processing. With the incomplete Fourier data and the inevitable noise in the measurement, there is a fundamental limit on the separation distance between point sources that can be resolved…