Artificial scent screening systems (known as electronic noses, E‐noses) have been researched extensively. A portable, automatic, and accurate, real‐time E‐nose requires both robust cross‐reactive ...sensing and fingerprint pattern recognition. Few E‐noses have been commercialized because they suffer from either sensing or pattern‐recognition issues. Here, cross‐reactive colorimetric barcode combinatorics and deep convolutional neural networks (DCNNs) are combined to form a system for monitoring meat freshness that concurrently provides scent fingerprint and fingerprint recognition. The barcodes—comprising 20 different types of porous nanocomposites of chitosan, dye, and cellulose acetate—form scent fingerprints that are identifiable by DCNN. A fully supervised DCNN trained using 3475 labeled barcode images predicts meat freshness with an overall accuracy of 98.5%. Incorporating DCNN into a smartphone application forms a simple platform for rapid barcode scanning and identification of food freshness in real time. The system is fast, accurate, and non‐destructive, enabling consumers and all stakeholders in the food supply chain to monitor food freshness.
Monitoring of the freshness of meat is important for food safety and food waste reduction. Few E‐noses have been integrated with food supply chains due to either sensing or pattern recognition issues. Cross‐reactive colorimetric barcode combinatorics and deep convolutional neural networks are combined to form a portable, automatic, and accurate, real‐time platform for monitoring of meat freshness.
Defant, Engen, and Miller defined a refinement of Lassalle's sequence Ak+1 by considering uniquely sorted permutations of length 2k+1 whose first element is ℓ. They showed that each such sequence is ...symmetric in ℓ and conjectured that these sequences are unimodal. We prove that the sequences are unimodal.
This paper provides a comprehensive study of the dimer model on infinite minimal graphs with Fock's elliptic weights Foc15. Specific instances of such models were studied in BdTR17, BdTR18, dT17; we ...now handle the general genus 1 case, thus proving a non-trivial extension of the genus 0 results of Ken02, KO06 on isora-dial critical models. We give an explicit local expression for a two-parameter family of inverses of the Kasteleyn operator with no periodicity assumption on the underlying graph. When the minimal graph satisfies a natural condition, we construct a family of dimer Gibbs measures from these inverses, and describe the phase diagram of the model by deriving asymptotics of correlations in each phase. In the Z 2-periodic case, this gives an alternative description of the full set of ergodic Gibbs measures constructed in KOS06. We also establish a correspondence between elliptic dimer models on periodic minimal graphs and Harnack curves of genus 1. Finally, we show that a bipartite dimer model is invariant under the shrinking/expanding of 2-valent vertices and spider moves if and only if the associated Kasteleyn coefficients are antisymmetric and satisfy Fay's trisecant identity.
A graph $G$ is a cocomparability graph if there exists an acyclic transitive orientation of the edges of its complement graph $\overline{G}$. LBFS$^{+}$ is a variant of the generic Lexicographic ...Breadth First Search (LBFS), which uses a specific tie-breaking mechanism. Starting with some ordering $\sigma_{0}$ of $G$, let $\{\sigma_{i}\}_{i\geq 1}$ be the sequence of orderings such that $\sigma_{i}=$LBFS$^{+}(G, \sigma_{i-1})$. The LexCycle($G$) is defined as the maximum length of a cycle of vertex orderings of $G$ obtained via such a sequence of LBFS$^{+}$ sweeps. Dusart and Habib conjectured in 2017 that LexCycle($G$)=2 if $G$ is a cocomparability graph and proved it holds for interval graphs. In this paper, we show that LexCycle($G$)=2 if $G$ is a $\overline{P_{2}\cup P_{3}}$-free cocomparability graph, where a $\overline{P_{2}\cup P_{3}}$ is the graph whose complement is the disjoint union of $P_{2}$ and $P_{3}$. As corollaries, it's applicable for diamond-free cocomparability graphs, cocomparability graphs with girth at least 4, as well as interval graphs.
In this note, we prove a general identity between a $q$-multisum $B_N(q)$ and a sum of $N^2$ products of quotients of theta functions. The $q$-multisum $B_N(q)$ recently arose in the computation of a ...probability involving modules over finite chain rings.
Extremal problems of double stars Győri, Ervin; Wang, Runze; Woolfson, Spencer
Discrete mathematics and theoretical computer science,
04/2023, Letnik:
24, no 2, Številka:
Graph Theory
Journal Article
Recenzirano
Odprti dostop
In a generalized Tur\'an problem, two graphs $H$ and $F$ are given and the
question is the maximum number of copies of $H$ in an $F$-free graph of order
$n$. In this paper, we study the number of ...double stars $S_{k,l}$ in
triangle-free graphs. We also study an opposite version of this question: what
is the maximum number edges/triangles in graphs with double star type
restrictions, which leads us to study two questions related to the extremal
number of triangles or edges in graphs with degree-sum constraints over
adjacent or non-adjacent vertices.
For a finite, connected simple graph G of order n with degree sequence, s = (di : 1 < i < n,di = deg(vi) and, dj > dj+1, 1 < j < n - 1) the modular sequences, s(mod k), 1 < k < n are introduced. ...Those modular sequences which are graphic constitute the modular graphic family of a graph. Numerous introductory results are presented.
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