Floodings of metric graphs

A random walk labeling of a graph G is any labeling of G that could have been obtained by performing a random walk on G. Continuing two recent works, we calculate the number of random walk labelings of perfect trees, combs, and double combs, the torus C 2 × Cn , and the graph obtained by connecting three path graphs at their ends.

Context-free language reachability (CFL-reachability) is a fundamental framework for program analysis. A large variety of static analyses can be formulated as CFL-reachability problems, which determines whether specific source-sink pairs in an edge-labeled graph are connected by a reachable path, i.e., a path whose edge labels form a string accepted by the given CFL. Computing CFL-reachability is expensive. The fastest algorithm exhibits a slightly subcubic time complexity with respect to the input graph size. Improving the scalability of CFL-reachability is of practical interest, but reducing the time complexity is inherently difficult. In this paper, we focus on improving the scalability of CFL-reachability from a more practical perspective---reducing the input graph size. Our idea arises from the existence of trivial edges, i.e., edges that do not affect any reachable path in CFL-reachability. We observe that two nodes joined by trivial edges can be folded---by merging the two nodes with all the edges joining them removed---without affecting the CFL-reachability result. By studying the characteristic of the recursive state machines (RSMs), an alternative form of CFLs, we propose an approach to identify foldable node pairs without the need to verify the underlying reachable paths (which is equivalent to solving the CFL-reachability problem). In particular, given a CFL-reachability problem instance with an input graph G and an RSM, based on the correspondence between paths in G and state transitions in RSM, we propose a graph folding principle, which can determine whether two adjacent nodes are foldable by examining only their incoming and outgoing edges. On top of the graph folding principle, we propose an efficient graph folding algorithm GF. The time complexity of GF is linear with respect to the number of nodes in the input graph. Our evaluations on two clients (alias analysis and value-flow analysis) show that GF significantly accelerates RSM/CFL-reachability by reducing the input graph size. On average, for value-flow analysis, GF reduces 60.96% of nodes and 42.67% of edges of the input graphs, obtaining a speedup of 4.65× and a memory usage reduction of 57.35%. For alias analysis, GF reduces 38.93% of nodes and 35.61% of edges of the input graphs, obtaining a speedup of 3.21× and a memory usage reduction of 65.19%.

We introduce a "qualitative property" for Bott-Chern cohomology of complex non-K\"ahler manifolds, which is motivated in view of the study of the algebraic structure of Bott-Chern cohomology. We prove that such a property characterizes the validity of the $\partial\overline\partial$-Lemma. This follows from a quantitative study of Bott-Chern cohomology. In this context, we also prove a new bound on the dimension of the Bott-Chern cohomology in terms of the Hodge numbers. We also give a generalization of this upper bound, with applications to symplectic cohomologies.

In the framework of a strictly local regular Dirichlet space X we introduce the subspaces PWω, ω > 0, of Paley–Wiener functions of bandwidth ω. It is shown that every function in PWω, ω > 0, is uniquely determined by its average values over a family of balls B(xj, ρ), xj ∈X, which form an admissible cover of X and whose radii are comparable to ω−1∕2. The entire development heavily depends on some Poincare-type inequalities. In the second part of the paper we realize the same idea in the setting of a weighted combinatorial finite or infinite graph G. We have to treat the case of graphs separately since the Poincare inequalities we are using on them are somewhat different from the Poincare inequalities in the first part.

The paramount is ensuring future-proof and robust cybersecurity in the era of quantum computing. According to graph theory, the mathematical concept of Edge Antimagic Labelling (EATL) is leveraged by introducing a theoretical approach for encryption. Based on sum own label, a uniquely labelled edge is each graph edge. This work presents a quantum-resistant and secure encryption framework to exploit the combinational complexity, uniqueness, and inherent non-linearity of EATL. Construct the Quantum safe graphs as a special class of graphs, and the cryptographic key is generated to use the antimagic labelling that derives the dynamic edge weights. Both quantum and classical threats counter to improve the structural masking and key randomness by proposing improved security of EATL. Based on label prediction and graph isomorphism, a numerically hard problem space is provided via graph graph-theoretic foundation. The post-quantum, secure, and lightweight cryptographic models are designed with the powerful tool of EATL, established using graph theory.

The primary aim of this paper is to investigate the practical interest of the incremental norm approach for analysing (realistic) nonlinear dynamical systems. In this framework indeed, incremental stability, a stronger notion than ℒ︁2-gain stability, ensures suitable qualitative and quantitative properties. On the one hand, the qualitative properties essentially correspond to (steady-state) input/output properties, which are not necessarily obtained when ensuring only ℒ︁2-gain stability. On the other hand, it is possible to analyse quantitative robustness performance properties using the notion of (nonlinear) incremental performance, the latter being defined in the continuity of the (linear) H∞ performance (i.e. through the use of a weighting function). As testing incremental properties is a difficult problem, stronger, but computationally more attractive, notions are introduced, namely quadratic incremental stability and performance. Testing these properties reduces indeed to solving convex optimization problems over Linear Matrix Inequalities (LMIs). As an illustration, we consider a classical missile problem, which was already treated using several (linear and nonlinear) approaches. We focus here on the analysis of the nonlinear behavior of this PI controlled missile: using the notions of quadratic incremental stability and performance, the closed loop nonlinear missile is proved to meet desirable control specifications. Copyright © 1999 John Wiley & Sons, Ltd.

The understanding of chaos and strange attractors is one of the most exciting areas of mathematics today. It is the question of how the asymptotic behaviour of deterministic systems can exhibit unpredictability and apparent chaos, due to sensitive dependence upon initial conditions, and yet at the same time preserve a coherent global structure. The field represents a remarkable confluence of several different strands of thought. 1. Firstly came the influence of differential topology, giving global geometric insight and emphasis on qualitative properties. By qualitative properties I mean invariants under differentiable changes of coordinates, as opposed to quantitative properties which are invariant only under linear changes of coordinates. To give an example of this influence, I recall a year-long symposium at Warwick in 1979/80, which involved sustained interaction between pure mathematicians and experimentalists, and one of the most striking consequences of that interaction was a transformation in the way that experimentalists now present their data. It is generally in a much more translucent form: instead of merely plotting a frequency spectrum and calling the incomprehensible part ‘noise’, they began to draw computer pictures of underlying three-dimensional strange attractors.

The Klein-bottle fullerene is a finite trivalent graph embedded on the Klein-bottle such that each face is a hexagon. The paper deals with the problem of labeling the vertices, edges and faces of the Klein-bottle fullerene in such a way that the label of a face and the labels of the vertices and edges surrounding that face add up to a weight of that face and the weights of all 6-sided faces constitute an arithmetic progression of difference d. In this paper we study the existence of such labelings for several differences d.

Dynorphin a-(1–13)-morphine interactions: Quantitative and qualitative eeg properties differ in morphine-naive vs. Morphine-tolerant rats

An one-one correspondence function λ from V(G) ∪ E(G) to the set {1, 2, …, |V(G) | + |E(G) |} is a total labeling of a finite undirected graph G without loops and multiple edges, where |V(G) |and |E(G) | are the cardinality of vertex and edge set of G respectively. A perfectly antimagic total labeling is a totally antimagic total labeling whose vertex and edge-weights that are also pairwise distint. Perfectly antimagic total (PAT) graph is a graph having such labeling. The topic of discovering perfectly antimagic total labeling of some families of graphs is discussed in this paper. We also came up with certain conclusions about dual of a perfectly antimagic total graphs. Finally, we provided that the necessary and sufficient condition for a dual of a regular and irregular PAT graph to be a PAT graph.

Drug checking services (DCS) are harm reduction interventions for people who consume illicit substances. Unregulated drug markets lead to samples with unexpected and variable contents. A retrospective data analysis of Zurich's DCS was performed to determine the nature of these samples. This study aims to investigate the qualitative and quantitative properties of 16,815 customer-provided psychoactive drug samples analyzed chemically through the DCS in Zurich from 1st January 2011 to 31st December 2021. The main analytical method utilized for characterizing these substances was high-performanceliquid chromatography and gas chromatography-mass spectrometry. Data sets are summarized using descriptive statistics. There was a 2.5-fold increase in the number of tested samples over the past decade. An overall proportion of 57.9% (weighted mean) of samples within our database demonstrates unexpected analytical findings and additional low sample contents during the observation period. Substantial differences in quality and quantity between substance groups were detected and an increase of sample quality and content over time was demonstrated. Chemical analysis reveals that over half of substances acquired from unregulated drug markets analyzed through DCS in Zurich are with low qualitative and quantitative properties, which may expose users to risks. Based on longitudinal analyses over a decade, this study contributes to the body of evidence that DCS may potentially manipulate unregulated drug markets towards providing better quality substances, as well as may stabilize these markets over time. The necessity for drug policy changes to make this service accessible in further settings was highlighted, as DCS still often take place in legal grey zones. None to declare.

This study was conducted in order to evaluate the effects of amino chelates on quantitative and qualitative properties of ‘Kabkab’ date fruit in ‘Dashtestan’ city, Boushehr province in the year 2012. The experiment was performed as factorial arrangement in randomized complete block design with three replications. The first factor was amino chelate type including: control, calcium amino chelate, micro-nutrient amino chelate and calcium + micro-nutrient amino chelates and the second factor was two application times including: ‘Khalal’ stage, one week later than the first application. Twenty four ‘Kabkab’ date palms were selected and all horticultural operations were equally done on them. After operating the treatments, was sampled in ‘Tamar’ stage and the characteristics including fruit weight, fruit length, fruit diameter, stone weight, stone length, TSS and pH were measured. Results indicated that amino chelates had significant influence on fruit weight, fruit length, stone weight, TSS. Application time affects some properties such as fruit weight, TSS and pH. Calcium amino chelate significantly increased fruit weight, fruit length and TSS. The highest TSS was observed in calcium amino chelate treatment. The greatest and lowest stone weight obtained in calcium amino chelate and control treatments respectively. Calcium and micro-nutrient amino chelates had the highest fruit weight and the lowest fruit weight was relative to control treatment. Generally, amino chelates had significant and positive influence on most fruit quantitative and qualitative properties.

Polyphenols are plant metabolites with potent physiological activities. Despite their known bitterness and astringency, their specific sensory characteristics remain poorly understood. To clarify the relationship between polyphenol chemical structures and sensory profiles, we developed a sensory evaluation protocol for a young-adult panel. Following four days of intensive monthly training, the panel achieved proficiency in distinguishing bitterness, astringency, and acidity. Four polyphenols with distinct structures-gallic acid, quercetin hydrate, epigallocatechin gallate (EGCG), and a procyanidin-rich fraction (PRF)-were evaluated using flavor profile analysis (FPA) and 3-Alternative Forced Choice (3-AFC) tests for their qualitative properties, and quantitative descriptive analysis (QDA) for their quantitative properties. The results showed that gallic acid was acidic, and EGCG was bitter and astringent, with the intensity being concentration-dependent. In contrast, quercetin hydrate did not show any significant sensory properties. This methodology facilitates the elucidation of the relationship between polyphenol structures, and their organoleptic properties and subsequent findings help to further clarify the role of polyphenol-taste receptor interactions in health benefits.

Measurements involve comparisons of measured values with reference values traceable to measurement standards and are made to support decision-making. While the conventional definition of measurement focuses on quantitative properties (including ordinal properties), we adopt a broader view and entertain the possibility of regarding qualitative properties also as legitimate targets for measurement. A measurement result comprises the following: (i) a value that has been assigned to a property based on information derived from an experiment or computation, possibly also including information derived from other sources, and (ii) a characterization of the margin of doubt that remains about the true value of the property after taking that information into account. Measurement uncertainty is this margin of doubt, and it can be characterized by a probability distribution on the set of possible values of the property of interest. Mathematical or statistical models enable the quantification of measurement uncertainty and underlie the varied collection of methods available for uncertainty evaluation. Some of these methods have been in use for over a century (for example, as introduced by Gauss for the combination of mutually inconsistent observations or for the propagation of "errors"), while others are of fairly recent vintage (for example, Monte Carlo methods including those that involve Markov Chain Monte Carlo sampling). This contribution reviews the concepts, models, methods, and computations that are commonly used for the evaluation of measurement uncertainty, and illustrates their application in realistic examples drawn from multiple areas of science and technology, aiming to serve as a general, widely accessible reference.

We present formulae for computing the Yamada polynomial of spatial graphs obtained by replacing edges of plane graphs, such as cycle-graphs, theta-graphs, and bouquet-graphs, by spatial parts. As a corollary, it is shown that zeros of Yamada polynomials of some series of spatial graphs are dense in a certain region in the complex plane, described by a system of inequalities. Also, the relation between Yamada polynomial of graphs and the chain polynomial of edge-labeled graphs is obtained.