Related papers: Analysis Paralysis: when to stop?
A system of particles is studied in which the stochastic processes are one-particle type-change (or one-particle diffusion) and multi-particle annihilation. It is shown that, if the annihilation rate tends to zero but the initial values of…
Scaling arguments provide valuable analysis tools across physics and complex systems yet are often employed as one generic method, without explicit reference to the various mathematical concepts underlying them. A careful understanding of…
Early stopping is a simple and widely used method to prevent over-training neural networks. We develop theoretical results to reveal the relationship between the optimal early stopping time and model dimension as well as sample size of the…
We investigate how a constant time delay influences a parametric autoresonant system. This is a nonlinear system driven by a parametrically chirped force with a negative delay-feedback that maintains adiabatic phase locking with the driving…
In the age of ever increasing demand for big data and data analytics, a question of collecting the data becomes fundamental. What and how to collect the data is essential as it has direct impact on decision making, system operation and…
Two granular gases separated by an adiabatic piston and initially in the same macroscopic state are considered. It is found that a phase transition with an spontaneous symmetry breaking occurs. When the mass of the piston is increased…
Self-regulatory models are common in nature, as described e.g. in (\cite{mur}), (\cite{ha}) and (\cite{Gb}).\\ Let us consider a system made up of a number of glands as a motivation. Each gland secretes a hormone that allows secretion in…
Change-point analysis is a flexible and computationally tractable tool for the analysis of times series data from systems that transition between discrete states and whose observables are corrupted by noise. The change-point algorithm is…
It is widely acknowledged that function symbols are an important feature in answer set programming, as they make modeling easier, increase the expressive power, and allow us to deal with infinite domains. The main issue with their…
If you want to tell people the truth, make them laugh, otherwise they'll kill you. (source unclear) Machine learning and deep learning are the technologies of the day for developing intelligent automatic systems. However, a key hurdle for…
Timed automata (TA) have been widely adopted as a suitable formalism to model time-critical systems. Furthermore, contemporary model-checking tools allow the designer to check whether a TA complies with a system specification. However, the…
Statistics is sometimes described as the science of reasoning under uncertainty. Statistical models provide one view of this uncertainty, but what is frequently neglected is the 'invisible' portion of uncertainty: that assumed not to exist…
The process of diagnosis involves learning about the state of a system from various observations of symptoms or findings about the system. Sophisticated Bayesian (and other) algorithms have been developed to revise and maintain beliefs…
The fundamental elements of evidential reasoning problems are described, followed by a discussion of the structure of various types of problems. Bayesian inference networks and state space formalism are used as the tool for problem…
Reasoning large language models achieve impressive test-time scaling by thinking for longer, but this performance gain comes at significant compute cost. Directly limiting test-time budget hurts overall performance, but not all problems are…
These lectures focus on bifurcation analysis as a tool for studying phase transitions that occur in models of liquid-crystalline systems. We show how this approach bridges the gap between the phenomenological Landau theory and the --- often…
In this paper, we offer a guide for researchers on evaluating reasoning in language models, building the case that reasoning should be assessed through evidence of adaptive, multi-step search rather than final-answer accuracy alone. Under…
The rapid growth and diversity in service offerings and the ensuing complexity of information technology ecosystems present numerous management challenges (both operational and strategic). Instrumentation and measurement technology is, by…
Traditionally, Probability theory was dealing with limit theorems where 'limit" means that time tends to infinity. Questions about finite time dynamics (evolution) were always considered as, although important for practical applications,…
Autocatalysis is a fundamental concept, used in a wide range of domains. From the most general definition of autocatalysis, that is a process in which a chemical compound is able to catalyze its own formation, several different systems can…