Investigations of a compartmental model for leucine kinetics using nonlinear mixed effects models with ordinary and stochastic differential equations

Nonlinear mixed effects models represent a powerful tool to simultaneously analyze data from several individuals. In this study a compartmental model of leucine kinetics is examined and extended with a stochastic differential equation to model non-steady state concentrations of free leucine in the plasma. Data obtained from tracer/tracee experiments for a group of healthy control individuals and a group of individuals suffering from diabetes mellitus type 2 are analyzed. We find that the interindividual variation of the model parameters is much smaller for the nonlinear mixed effects models, compared to traditional estimates obtained from each individual separately. Using the mixed effects approach, the population parameters are estimated well also when only half of the data are used for each individual. For a typical individual the amount of free leucine is predicted to vary with a standard deviation of 8.9% around a mean value during the experiment. Moreover, leucine degradation and protein uptake of leucine is smaller, proteolysis larger, and the amount of free leucine in the body is much larger for the diabetic individuals than the control individuals. In conclusion nonlinear mixed effects models offers improved estimates for model parameters in complex models based on tracer/tracee data and may be a suitable tool to reduce data sampling in clinical studies

Femtosecond wavepacket interferometry using the rotational dynamics of a trapped cold molecular ion

A Ramsey-type interferometer is suggested, employing a cold trapped ion and two time-delayed off-resonant femtosecond laser pulses. The laser light couples to the molecular polarization anisotropy, inducing rotational wavepacket dynamics. An interferogram is obtained from the delay dependent populations of the final field-free rotational states. Current experimental capabilities for cooling and preparation of the initial state are found to yield an interferogram visibility of more than 80\%. The interferograms can be used to determine the polarizability anisotropy with an accuracy of about $\pm 2\%$, respectively $\pm 5\%$, provided the uncertainty in the initial populations and measurement errors are confined to within the same limits

Analyzing Catastrophic Backtracking Behavior in Practical Regular Expression Matching

We develop a formal perspective on how regular expression matching works in Java, a popular representative of the category of regex-directed matching engines. In particular, we define an automata model which captures all the aspects needed to study such matching engines in a formal way. Based on this, we propose two types of static analysis, which take a regular expression and tell whether there exists a family of strings which makes Java-style matching run in exponential time.Comment: In Proceedings AFL 2014, arXiv:1405.527

The effect of additive noise on dynamical hysteresis

We investigate the properties of hysteresis cycles produced by a one-dimensional, periodically forced Langevin equation. We show that depending on amplitude and frequency of the forcing and on noise intensity, there are three qualitatively different types of hysteresis cycles. Below a critical noise intensity, the random area enclosed by hysteresis cycles is concentrated near the deterministic area, which is different for small and large driving amplitude. Above this threshold, the area of typical hysteresis cycles depends, to leading order, only on the noise intensity. In all three regimes, we derive mathematically rigorous estimates for expectation, variance, and the probability of deviations of the hysteresis area from its typical value.Comment: 30 pages, 5 figure

Lemon Factory Extension

Martin works for Urban Future Organization (UFO), an internationally networked architectural practice involved in advanced digital design and fabrication. This new administrative wing is being added to an existing factory outside Messina in Sicily, sitting adjacent to a production building which is actually Italy’s largest producer of lemon juice and lemon extracts / essences. The brief was for a sequence of flexible spaces to house the reception area, staff offices, meeting spaces and canteen, along with a swimming pool and a fitness centre. The interior of the building reacts to the requirement to keep the spaces fluid and able to change their use over time. The project is currently on site and scheduled for completion in Spring 2008. In terms of research questions investigated, the key ones were how to develop new techniques of modulation design and structural design in what is a highly active earthquake zone, and then – given this crucial demand – how to create a new kind of flexible spatial organisation for a rapidly evolving company. In its design processes, the Lemon Factory has to be understood as part of a line of projects being carried out by the UFO practice and by similar entities – such as Ocean or Foreign Office Architects – into free-form, fluid and linear architectural forms, allying to this the pursuit of new forms of digital design and manufacturing in architecture. This project has been exhibited like other UFO project in important events such as the 2004 Venice Biennale, 2006 Beijing Biennale, and also in books like the press through articles such as in Building Design (7 March 2003, pp. 12-15). Urban Future Organization is a collaborative practice in which Martin and Yau are senior design figures, both being equally responsible for designing major projects such as the Lemon Factory near Messina

Memory Effects and Scaling Laws in Slowly Driven Systems

This article deals with dynamical systems depending on a slowly varying parameter. We present several physical examples illustrating memory effects, such as metastability and hysteresis, which frequently appear in these systems. A mathematical theory is outlined, which allows to show existence of hysteresis cycles, and determine related scaling laws.Comment: 28 pages (AMS-LaTeX), 18 PS figure

Formalizing BPE Tokenization

In this paper, we formalize practical byte pair encoding tokenization as it is used in large language models and other NLP systems, in particular we formally define and investigate the semantics of the SentencePiece and HuggingFace tokenizers, in particular how they relate to each other, depending on how the tokenization rules are constructed. Beyond this we consider how tokenization can be performed in an incremental fashion, as well as doing it left-to-right using an amount of memory constant in the length of the string, enabling e.g. using a finite state string-to-string transducer.Comment: In Proceedings NCMA 2023, arXiv:2309.0733

Основи інформатики з елементами програмування та сучасні інформаційні технології навчання. Ч. І. Основи інформатики

У посібнику представлено загальні відомості з основ інформатики: апаратне забезпечення інформаційних систем; операційні системи; прикладне програмне забезпечення; комп’ютерна графіка; текстовий і табличний процесори; бази даних та системи управління базами даних. Посібник складається з двох частин: «Теоретична частина» і «Лабораторні роботи». Посібник містить приклади, рекомендації виконання завдань та примітки у вигляді порад для їхнього раціонального виконання. Навчальний посібник призначений для супроводу курсу «Основи інформатики з елементами програмування та сучасні інформаційні технології навчання», який передбачено навчальним планом для студентів напрямів підготовки: «Початкова освіта», «Дошкільна освіта». Також посібник адресовано педагогічним працівникам і студентам інших напрямів підготовки