Related papers: The Zeta ($\zeta$) Notation for Complex Asymptotes
Test-time adaptation (TTA) adapts the pre-trained models during inference using unlabeled test data and has received a lot of research attention due to its potential practical value. Unfortunately, without any label supervision, existing…
Motivated by questions from program transformations, eight notions of isomorphisms between term rewriting systems are defined, analysed, and classified. The notions include global isomorphisms, where the renaming of variables and function…
The construction of high-quality parallel corpora for translation research has increasingly evolved from simple sentence alignment to complex, multi-layered annotation tasks. This methodological shift presents significant challenges for…
Large Language Models (LLMs) have demonstrated considerable advances, and several claims have been made about their exceeding human performance. However, in real-world tasks, domain knowledge is often required. Low-resource learning methods…
Processing and analyzing time series data\-sets have become a central issue in many domains requiring data management systems to support time series as a native data type. A crucial prerequisite of these systems is time series matching,…
We describe an algorithm for obtaining explicit expressions for lower terms for the conjectured full asymptotics of the moments of the Riemann zeta function, and give two distinct methods for obtaining numerical values of these…
Elementary algebraic constraints on the form of an autocorrelation function C(tw+t,tw)=<A(tw+t)A(tw)> rule out some two-time scalings found in the literature as possible long-time asymptotic forms. The same argument leads to the realization…
Precise formulas are derived for the expected values $<\xi>$, $<\eta>$ and variances $\delta \xi ^2$, $\delta \eta ^2$ of random variables $\xi$, $\eta$ describing the spin asymmetry of some reaction when a background process contribution…
Identifying anomalies in large multi-dimensional time series is a crucial and difficult task across multiple domains. Few methods exist in the literature that address this task when some of the variables are categorical in nature. We…
We present a new language semantics for real-time concurrency. Its operational models are higher-dimensional timed automata (HDTAs), a generalization of both higher-dimensional automata and timed automata. In real-time concurrent systems,…
In a large cyber-physical system, a temporal inconsistency of an output value can arise if there is a non-negligible delay between the instant when a sensor value is acquired from the environment and the instant when a setpoint, based on…
A detailed, internal symmetry exists between individual terms $n^{-s}$, where $n \in P$ is less than a particular value $n_p$, and sums over conjugate regions consisting of adjoining steps $n$ greater than $n_p$. The boundaries of the…
It is usually assumed that the "$t$" parameter in the equations of dynamics can be identified with the indication of the pointer of a clock. Things are not so easy, however. In fact, since the equations of motion can be written in terms of…
Similarities between entities occur frequently in many real-world scenarios. For over a century, researchers in different fields have proposed a range of approaches to measure the similarity between entities. More recently, inspired by…
Time-Basic Petri nets, is a powerful formalism for model- ing real-time systems where time constraints are expressed through time functions of marking's time description associated with transition, representing possible firing times. We…
It is widely believed that special initial conditions must be imposed on any time-symmetric law if its solutions are to exhibit behavior of any kind that defines an `arrow of time'. We show that this is not so. The simplest non-trivial…
A generalization of the Apery-like numbers, which is used to describe the special values $\zeta_Q(2)$ and $\zeta_Q(3)$ of the spectral zeta function for the non-commutative harmonic oscillator, are introduced and studied. In fact, we give a…
The O(N) non-linear sigma model in a $D$-dimensional space of the form ${\bf R}^{D-M} \times {\bf T}^M$, ${\bf R}^{D-M} \times {\bf S}^M$, or ${\bf T}^M \times {\bf S}^P$ is studied, where ${\bf R}^M$, ${\bf T}^M$ and ${\bf S}^M$ correspond…
A brief survey of the zeta function regularization and multiplicative anomaly issues when the associated zeta function of fluctuation operator is the regular at the origin (regular case) as well as when it is singular at the origin…
We show that a well-known asymptotic series for the logarithm of the central binomial coefficient is strictly enveloping in the sense of P\'olya and Szeg\"o, so the error incurred in truncating the series is of the same sign as the next…