Perfect phylogeny consisting of determining the compatibility of a set of characters is known to be NP-complete. We propose in this article a conjecture on the necessary and sufficient conditions of compatibility: Given a set $\mathcal{C}$ of $r$-sta...
We investigate the phenomenology of the "Watcher" measure in the Bousso-Polchinski landscape. We study a small toy landscape analytically. The results are sufficient to allow us to extrapolate "watcher" phenomenology to much larger landscapes. We com...
Compiler error messages serve as an initial resource for programmers dealing with compilation errors. However, previous studies indicate that they often lack sufficient targeted information to resolve code issues. Consequently, programmers typically...
Despite being crucial to health and quality of life, sleep -- especially pediatric sleep -- is not yet well understood. This is exacerbated by lack of access to sufficient pediatric sleep data with clinical annotation. In order to accelerate research...
Motivated by the recent work of Xiao and Zhong [AIMS Math. 9 (2024), 35125--35150: MR4840882], we propose a generalized inverse for a hyper-dual matrix called hyper-dual group generalized inverse (HDGGI). Under certain necessary and sufficient condit...
Originally, the Biswas--Chatterjee--Sen model was shown to exhibit an order/disorder phase transition for a sufficiently large number of negative interactions among actors. In this paper, the model is extended by the existence of nonconformists and i...
We prove that a connected 2-dimensional orbifold with finitely generated and infinite orbifold fundamental group is good. We also describe all the good 2-dimensional orbifolds with finite orbifold fundamental groups...
In this paper, we propose sufficient conditions to guarantee that a linear temporal logic (LTL) formula of the form p Until q, denoted by $p \mathcal{U} q$, is satisfied for a hybrid system. Roughly speaking, the formula $p \mathcal{U} q$ is satisfie...
This manuscript establishes several sufficient conditions for the validity of both the reverse order law and forward order law for NDMPI. Additionally, some characterization of the reverse order law of the NDMPI is obtained. We also explore the appli...
A one-electron Schroedinger equation based on special one-electron potentials for atoms is shown to exist that produces orbitals for an arbitrary molecule that are sufficiently accurate to be used without modification to construct single- and multi-d...
For earlier considered our sequence A166944 in [4] we prove three statements of its connection with twin primes. We also give a sufficient condition for the infinity of twin primes and pose several new conjectures; among them we propose a very simp...
I study a fresh inflationary model with an increasing F-cosmological parameter. The model provides sufficiently e-folds to solve the flatness/horizon problem and the density fluctuations agree with experimental values. The temperature increases dur...
In this paper, we first give a necessary and sufficient condition for a graph to have Laplacian pretty good pair state transfer. As an application of such result, we give a complete characterization of Laplacian pretty good edge state transfer in pat...
For a polynomial $P$ mapping the integers into the integers, define an averaging operator $A_{N} f(x):=\frac{1}{N}\sum_{k=1}^N f(x+P(k))$ acting on functions on the integers. We prove sufficient conditions for the $\ell^{p}$-improving inequality \beg...
We provide a necessary and sufficient condition for a rough control driving a differential equation to be reconstructable, to some order, from observing the resulting controlled evolution. Physical examples and applications in stochastic filtering an...
Take a drinking straw and bend it from its ends. After sufficient bending, the tube buckles forming a kink, where the curvature is localized in a very small area. This instability, known generally as the Brazier effect, is inherent to thin-walled cyl...
Finetuning is a critical step for adapting large language models (LLMs) to domain-specific downstream tasks. To mitigate the substantial computational and memory costs of full-model fine-tuning, Parameter-Efficient Finetuning (PEFT) methods have been...
Software testing is critical to prevent software failures. Therefore, research has been carried out in testing but that is largely limited to the process and technology dimensions and has not sufficiently addressed the human dimension. Even though th...
We discuss the conditions under which pre-big bang models can fit the observed large-scale anisotropy with a primordial spectrum of massive (Kalb--Ramond) axion fluctuations. The primordial spectrum must be sufficiently flat at low frequency and s...
We give a news characterization of variable exponent Sobolev trace spaces. We construct The Perron-Weiner-Brelot operator in nonlinear harmonic space and we give sufficient condition for which this operator is injective....