Secure Text Mail Encryption with Generative Adversarial Networks
Author: Alexej Schelle [arxiv.org/abs/2504.07140]
Journal of Information Hiding and Privacy Protection 7, 33-44 (2025)
Abstract: This work presents an encryption model based on Generative Adversarial Networks (GANs). Encryption of RTF-8 data is realized by dynamically generating decimal numbers that lead to the encryption and decryption of alphabetic strings in integer representation by simple addition rules, the modulus of the dimension of the considered alphabet. The binary numbers for the private dynamic keys correspond to the binary numbers of public reference keys, as defined by a specific GAN configuration. For reversible encryption with a bijective mapping between dynamic and reference keys, as defined by the GAN encryptor, secure text encryption can be achieved by transferring a GAN-encrypted public key along with the encrypted text from a sender to a receiver. Using the technique described above, secure text mail transfer can be realized through component-wise encryption and decryption of text mail strings, with total key sizes of up to 10^{8} bits that define random decimal numbers generated by the GAN. From the present model, we assert that encrypted texts can be transmitted more efficiently and securely than from RSA encryption, as long as users of the specific configuration of the GAN encryption model are unaware of the GAN encryptor circuit and configuration, respectively.
Physical aspects of symmetry breaking in non-interacting Bose gases at thermal equilibrium
Author: Alexej Schelle [arxiv.org/abs/2410.10893]
Constructor University Report No. 51 (2025)
Abstract: The theory of non-interacting Bose gases is supplemented by a numerical quantum field description with a two-dimensional non-local order parameter that allows the modeling of wave-like atomic correlations and interference effects in the limit of low atomic densities. From the present model, it is possible to explain certain new fundamental symmetry aspects of ideal and very weakly interacting Bose gases in the limit of fluctuating particle numbers, like the forward propagation of time and the relation to the breaking and preservation of phase gauge symmetry in solids. In the present formalism, the propagation of one-directional time arises from the pre-defined and equivalent convergence of independent quantum fields towards the Boltzmann equilibrium, and it is shown that Glauber coherent states are related to the definition of the quantized field. Coherently coupling condensate and non-condensate parts as a direct consequence of the increasing quantum coherence time between the different quantum field components in the Bose gas from cooling to below the critical temperature, the present model describes symmetry breaking, which is originally known from the definition of a specific gauge field from Elitzur’s theorem for local gauge fields, as a global physical rather than a purely formal mathematical process.
Uncovering Pricing and Behavioural Patterns in Online Apparel: A Data Mining and Machine Learning Approach Using Clickstream Data
Author: Mitali Acharya and Alexej Schelle [Constructor University Report No. 49]
Constructor University Report No. 49 (2025)
Abstract: This project investigates customer behavior and pricing dynamics in the context of online apparel sales, using a real-world clickstream from a European e-commerce platform. Through a structured process of exploratory data analysis and predictive modeling, the study explores how product visuals, attributes, and browsing behavior influence both purchasing patterns and pricing outcomes. Random Forest models were used for both regression and classification tasks to predict product prices and classify items into budget or premium tiers. These model outputs were then combined to detect potential pricing–perception mismatches, where a product appears over- or underpriced relative to how it is perceived based on its features. This approach helps highlight products that may benefit from a review of their pricing or presentation strategy. Key insights from the analysis show that products with frontal model photography tend to perform better in both pricing and sales, while black and blue items generate the highest revenue. These findings lead to clear business recommendations in areas such as pricing, visual merchandising, and product positioning. The project demonstrates how machine learning can be applied not only to forecast outcomes but also to guide practical, data-driven decisions in e-commerce.
Josephson oscillations of two weakly coupled Bose-Einstein condensates
Author: Alexej Schelle [arXiv:2407.06208]
Quanta 2024; 13: 28–37
Abstract: A numerical experiment based on a particle number-conserving quantum field theory is performed for two initially independent Bose-Einstein condensates that are coherently coupled at two temperatures. The present model illustrates ab initio that the initial relative phase of each of the two condensates doesn’t remain random, but is distributed around integer multiple values of 2π from the interference and thermalization of forward and backward propagating matter waves at the Boltzmann equilibrium, that intrinsically measures zero average phases for each of the two independent condensates. Following this approach, focus is put on Anderson’s original Gedanken experiment on whether a Josephson current between two initially separated Bose-Einstein condensates occurs in a deterministic way or not, depending on the initial phase distribution.
Monte-Carlo simulation for the frequency comb spectrum of an atom laser
Author: Alexej Schelle [arXiv:2305.19722]
Quanta 2023; 12: 171–179
Abstract: A theoretical particle-number conserving quantum field theory based on the concept of imaginary time is presented and applied to the scenario of a coherent atomic laser field at ultra-cold temperatures. The proposed theoretical model describes the analytical derivation of the frequency comb spectrum for an atomic laser realized from modeling a coherent atomic beam of condensate and non-condensate quantum field components released from a trapped Bose-Einstein condensate at a given repetition phase and frequency. The condensate part of the atomic vapor is assumed to be subjected to thermal noise induced by the temperature of the surrounding thermal atomic cloud. This new quantum approach uses time periodicity and an orthogonal decomposition of the quantum field in a complex-valued quantum field representation to derive and model the quantum field’s forward- and backward-propagating components as a standing wave field in the same unique time and temperature domain without quantitative singularities at finite temperatures. The complex-valued atom laser field, the resulting frequency comb, and the repetition frequency distribution with the varying shape of envelopes are numerically monitored within a Monte-Carlo sampling method, as a function of temperature and trap frequency of the external confinement.
Lehrbrief zum Kurs Einführung in Data Science
Authors: Alexej Schelle and Max Pumperla [IU Internationale Hochschule]
IU Internationale Hochschule, Einführung in Data Science, Februar 2023.
Abstract: Data Science hat sich als multidisziplinäres Feld entwickelt, das darauf abzielt, aus Daten Werte zu schaffen. Der Kurs “Einführung in Data Science” beginnt mit einem Überblick über Data Science und verwandte Felder und definiert darüber hinaus Datentypen und -Quellen. Der Einsatz datengesteuerter Methoden ist für Unternehmen unerlässlich geworden, und dieser Kurs zeigt auf, wie datengesteuerte Ansätze in einen Unternehmenskontext integriert und operative Entscheidungen mit datengesteuerten Methoden getroffen werden können. Schließlich hebt dieser Kurs die Bedeutungen von Statistik und des Maschinellen Lernens im Bereich der Datenwissenschaften hervor und gibt einen Überblick über relevante Methoden und Ansätze.
Information loss from dimensionality reduction in 5D-Gaussian spectral data
Authors: Alexej Schelle and Hannes Lüling [arXiv:2301.11923]
Whitepaper on arXiv.org (2023)
Abstract: Understanding the loss of information in spectral analytics is a crucial first step towards finding root causes for failures and uncertainties using spectral data in artificial intelligence models built from modern complex data science applications. Here, we show from a very simple entropy model analysis with quantum statistics of spectral data, that the relative loss of information from dimensionality reduction due to projection of an initial multi-dimensional state onto two-dimensional diagrams is less than one percent in the parameter range of small data sets with sample sizes on the order of few hundreds data samples. From our analysis, we also conclude that the structure, density, and expectation value of the entropy probability distribution increase with the sample number and sample size using artificial data models derived from random sampling Monte Carlo simulation methods.
Lehrbrief zum Kurs Angewandte Forschung
Authors: Sabine Beinschab, Alexej Schelle, and Stephan De La Rosa
IU Internationale Hochschule, Einführung in Data Science, 2023.
Abstract: Der Kurs Angewandte Forschung vermittelt Ihnen zentrale Konzepte und Methoden der angewandten empirischen Forschung. Sie erwerben profunde Kenntnisse zur Bewertung der Qualität sowie der Grenzen unterschiedlicher empirischer Forschungsansätze. Zunächst lernen Sie die zentralen theoreEschen Grundlagen empirischer Forschung und die zentralen Prozessschri6e empirischer Forschungsprojekte kennen. Hierbei werden Sie auch für die ethischen und rechtlichen Herausforderungen sensibilisiert. VerEefend behandelt der Kurs die Anwendung zentraler qualitaEver und quanEtaEver Forschungsmethoden, für die jeweils die zentralen Ziele und Entscheidungsfelder, deren Stärken und Schwächen, sowie prakEsche Anwendungsempfehlungen diskuEert werden. Der Kurs versetzt Sie in Ihrem Fachgebiet oder beruflichen Umfeld in die Lage, eine empirische Studie für eine angewandte Problemstellung zu entwickeln und die Qualität empirischer Erkenntnisse sowie deren Aussagekraft kritisch zu evaluieren.
Finite phase coherence time of a bosonic quantum field at the Boltzmann equilibrium
Author: Alexej Schelle [arXiv:2204.01730]
Whitepaper on arXiv.org (2022)
Abstract: A quantitative quantum field approach with non-local order parameters is presented for a very weakly interacting, dilute Bose gas. Within the presented model, which assumes the constraint of particle number conservation at constant average energy in the canonical ensemble, it is shown that both coherent oscillations, as well as decay times of quantum coherence for the forward and backward propagating components of the quantum field created by the atomic cloud of a very weakly interacting Bose-Einstein condensate, are defined by a unique time variable. Within the present numerical theory, a quantitative estimate for the unit time scale for time propagation of a particle in a very weakly interacting Bose gas is derived from the coherence time of the wave field and it is illustrated that this time scale defines a unit time for transitions between different realizations of the Boltzmann equilibrium as defined by the maximum entropy from the vanishing of the chemical potential.
Minimal representations of information for web spiders
Author: Alexej Schelle [https://github.com/alexej-schelle/IdrWebSpiders]
Whitepaper on Github.com (2021)
Abstract: Informal Dataset Representations for web spiders can be standardized as a technique for representing informal data in a compact form, which includes an individual JSON dataset containing the information of interest. It can be implemented equally well for websites, mobile compatible websites and standalone mobile compatible websites and uses public website content, canonical tags, meta viewports or http headers. From the Data Science perspective, a minimal informal dataset representation defines a necessary feed for standard search engines, such as Google, Yahoo or MSN, with a minimum of information to represent a company or personal website at a suitable ranking without the requirement for using further specific and partly very expensive SEO optimization campains.
Spontaneously broken gauge symmetry in a Bose gas with constant particle number
Author: Alexej Schelle [arXiv:1410.7058]
Fluctuations and Noise Letters, Vol. 16, No. 1 (March) 2017
Abstract: The interplay between spontaneously broken gauge symmetries and Bose-Einstein condensation has long been controversially discussed in science, since the equation of motions are invariant under phase transformations. Within the present model it is illustrated that spontaneous symmetry breaking appears as a non-local process in position space, but within disjoint subspaces of the underlying Hilbert space. Numerical simulations show that it is the symmetry of the relative phase distribution between condensate and non-condensate quantum fields which is spontaneously broken when passing the critical temperature for Bose-Einstein condensation. Since the total number of gas particles remains constant over time, the global U(1)-gauge symmetry of the system is preserved.
Transition of a mesoscopic bosonic gas into a Bose-Einstein condensate
Author: Alexej Schelle [arXiv:1110.6646]
Fluctuation and Noise Letters (2012), Vol. 11 No. 4
Abstract: The condensate number distribution during the transition of a dilute, weakly interacting gas of N=200 bosonic atoms into a Bose-Einstein condensate is modeled within number conserving master equation theory of Bose-Einstein condensation. Initial strong quantum fluctuations occuring during the exponential cycle of condensate growth reduce in a subsequent saturation stage, before the Bose gas finally relaxes towards the Gibbs-Boltzmann equilibrium.
Number-conserving master equation theory for a dilute Bose-Einstein condensate
Authors: Alexej Schelle, Thomas Wellens, Dominique Delande, and Andreas Buchleitner [arXiv:1008.0788]
Phys. Rev. A 83, 013615 (2011)
Abstract: We describe the transition of N weakly interacting atoms into a Bose-Einstein condensate within a number-conserving quantum master equation theory. Based on the separation of time scales for condensate formation and non-condensate thermalization, we derive a master equation for the condensate subsystem in the presence of the non-condensate environment under the inclusion of all two body interaction processes. We numerically monitor the condensate particle number distribution during condensate formation, and derive a condition under which the unique equilibrium steady state of a dilute, weakly interacting Bose-Einstein condensate is given by a Gibbs-Boltzmann thermal state of N non-interacting atoms.
Microwave-Driven Atoms: From Anderson Localization to Einstein’s Photoeffect (2009)
Authors: Alexej Schelle, Dominique Delande, and Andreas Buchleitner [arXiv:0809.1082]
Phys. Rev. Lett. 102, 183001 (2009)
Abstract: We study the counterpart of Anderson localization in driven one-electron Rydberg atoms. By changing the initial Rydberg state at fixed microwave frequency and interaction time, we numerically monitor the crossover from Anderson localization to the photo effect in the atomic ionization signal.