bluuebunny/crossref_metadata_2025 huggingface dataset:
Monadic Second-Order Classes of Forests with a Monadic Second-Order 0-1 Law
Authors: Bell Jason P. , Burris Stanley N. , Yeats Karen A.
Published: August 2021

Automata, Logic and Semantics

Let T be a monadic-second order class of finite trees, and let T(x) be its (ordinary) generating function, with radius of convergence rho. If rho >= 1 then T has an explicit specification (without using recursion) in terms of the operations of union, sum, stack, and the multiset operators n and (>= n). Using this, one has an explicit expression for T(x) in terms of the initial functions x and x . (1 - x(n))(-1), the operations of addition and multiplication, and the Polya exponentiation operators E-n, E-(>= n). Let F be a monadic-second order class of finite forests, and let F (x) = Sigma(n) integral(n)x(n) be its (ordinary) generating function. Suppose F is closed under extraction of component trees and sums of forests. Using the above-mentioned structure theory for the class T of trees in F, Compton's theory of 0-1 laws, and a significantly strengthened version of 2003 results of Bell and Burris on generating functions, we show that F has a monadic second-order 0-1 law iff the radius of convergence of F (x) is 1 iff the radius of convergence of T (x) is >= 1.
A linear time algorithm for finding an Euler walk in a strongly connected 3-uniform hypergraph
Authors: Lonc Zbigniew , Naroski Pawel
Published: August 2021

Discrete Algorithms

By an Euler walk in a 3-uniform hypergraph H we mean an alternating sequence v(0), epsilon(1), v(1), epsilon(2), v(2), ... , v(m-1), epsilon(m), v(m) of vertices and edges in H such that each edge of H appears in this sequence exactly once and v(i-1); v(i) is an element of epsilon(i), v(i-1) not equal v(i), for every i = 1, 2, ... , m. This concept is a natural extension of the graph theoretic notion of an Euler walk to the case of 3-uniform hypergraphs. We say that a 3-uniform hypergraph H is strongly connected if it has no isolated vertices and for each two edges e and f in H there is a sequence of edges starting with e and ending with f such that each two consecutive edges in this sequence have two vertices in common. In this paper we give an algorithm that constructs an Euler walk in a strongly connected 3-uniform hypergraph (it is known that such a walk in such a hypergraph always exists). The algorithm runs in time O(m), where m is the number of edges in the input hypergraph.
Vertex-colouring edge-weightings with two edge weights
Authors: Khatirinejad Mahdad , Naserasr Reza , Newman Mike , Seamone Ben , Stevens Brett
Published: August 2021

Graphs and Algorithms

An edge-weighting vertex colouring of a graph is an edge-weight assignment such that the accumulated weights at the vertices yields a proper vertex colouring. If such an assignment from a set S exists, we say the graph is S-weight colourable. It is conjectured that every graph with no isolated edge is \1, 2, 3\-weight colourable. We explore the problem of classifying those graphs which are \1, 2\ -weight colourable. We establish that a number of classes of graphs are S -weight colourable for much more general sets S of size 2. In particular, we show that any graph having only cycles of length 0 mod 4 is S -weight colourable for most sets S of size 2. As a consequence, we classify the minimal graphs which are not \1, 2\-weight colourable with respect to subgraph containment. We also demonstrate techniques for constructing graphs which are not \1, 2\-weight colourable.
On bipartite powers of bigraphs
Authors: Okamoto Yoshio , Otachi Yota , Uehara Ryuhei
Published: August 2021

Graph Theory

The notion of graph powers is a well-studied topic in graph theory and its applications. In this paper, we investigate a bipartite analogue of graph powers, which we call bipartite powers of bigraphs. We show that the classes of bipartite permutation graphs and interval bigraphs are closed under taking bipartite power. We also show that the problem of recognizing bipartite powers is NP-complete in general.
On BMRN*-colouring of planar digraphs
Authors: Bensmail Julien , Fioravantes Foivos
Published: August 2021

In a recent work, Bensmail, Blanc, Cohen, Havet and Rocha, motivated by applications for TDMA scheduling problems, have introduced the notion of BMRN*-colouring of digraphs, which is a type of arc-colouring with particular colouring constraints. In particular, they gave a special focus to planar digraphs. They notably proved that every planar digraph can be 8-BMRN*-coloured, while there exist planar digraphs for which 7 colours are needed in a BMRN*-colouring. They also proved that the problem of deciding whether a planar digraph can be 3-BMRN*-coloured is NP-hard. In this work, we pursue these investigations on planar digraphs, in particular by answering some of the questions left open by the authors in that seminal work. We exhibit planar digraphs needing 8 colours to be BMRN*-coloured, thus showing that the upper bound of Bensmail, Blanc, Cohen, Havet and Rocha cannot be decreased in general. We also generalize their complexity result by showing that the problem of deciding whether a planar digraph can be k-BMRN*-coloured is NP-hard for every k ∈ {3,...,6}. Finally, we investigate the connection between the girth of a planar digraphs and the least number of colours in its BMRN*-colourings.
The analysis of find and versions of it
Authors: Knof Diether , Roesler Uwe
Published: August 2021

Analysis of Algorithms

In the running time analysis of the algorithm Find and versions of it appear as limiting distributions solutions of stochastic fixed points equation of the form X D = Sigma(i) AiXi o Bi + C on the space D of cadlag functions. The distribution of the D-valued process X is invariant by some random linear affine transformation of space and random time change. We show the existence of solutions in some generality via the Weighted Branching Process. Finite exponential moments are connected to stochastic fixed point of supremum type X D = sup(i) (A(i)X(i) + C-i) on the positive reals. Specifically we present a running time analysis of m-median and adapted versions of Find. The finite dimensional distributions converge in L-1 and are continuous in the cylinder coordinates. We present the optimal adapted version in the sense of low asymptotic average number of comparisons. The limit distribution of the optimal adapted version of Find is a point measure on the function [0, 1] there exists t -> 1 + mint, 1 - t.
Quantitative and Algorithmic aspects of Barrier Synchronization in Concurrency
Authors: Bodini OLivier , Dien Matthieu , Genitrini Antoine , Peschanski Frédéric
Published: August 2021

In this paper we address the problem of understanding Concurrency Theory from a combinatorial point of view. We are interested in quantitative results and algorithmic tools to refine our understanding of the classical combinatorial explosion phenomenon arising in concurrency. This paper is essentially focusing on the the notion of synchronization from the point of view of combinatorics. As a first step, we address the quantitative problem of counting the number of executions of simple processes interacting with synchronization barriers. We elaborate a systematic decomposition of processes that produces a symbolic integral formula to solve the problem. Based on this procedure, we develop a generic algorithm to generate process executions uniformly at random. For some interesting sub-classes of processes we propose very efficient counting and random sampling algorithms. All these algorithms have one important characteristic in common: they work on the control graph of processes and thus do not require the explicit construction of the state-space.
Graphs with many vertex-disjoint cycles
Authors: Rautenbach Dieter , Regen Friedrich
Published: August 2021

Graph Theory

We study graphs G in which the maximum number of vertex-disjoint cycles nu(G) is close to the cyclomatic number mu(G), which is a natural upper bound for nu(G). Our main result is the existence of a finite set P(k) of graphs for all k is an element of N-0 such that every 2-connected graph G with mu(G)-nu(G) = k arises by applying a simple extension rule to a graph in P(k). As an algorithmic consequence we describe algorithms calculating minmu(G)-nu(G), k + 1 in linear time for fixed k.
A note on tight cuts in matching-covered graphs
Authors: Zhao Xiao , Chen Sheng
Published: August 2021

Edmonds, Lov\'asz, and Pulleyblank showed that if a matching covered graph
has a nontrivial tight cut, then it also has a nontrivial ELP-cut. Carvalho et
al. gave a stronger conjecture: if a matching covered graph has a nontrivial
tight cut $C$, then it also has a nontrivial ELP-cut that does not cross $C$.
Chen, et al gave a proof of the conjecture. This note is inspired by the paper
of Carvalho et al. We give a simplified proof of the conjecture, and prove the
following result which is slightly stronger than the conjecture: if a
nontrivial tight cut $C$ of a matching covered graph $G$ is not an ELP-cut,
then there is a sequence $G_1=G, G_2,\ldots,G_r, r\geq2$ of matching covered
graphs, such that for $i=1, 2,\ldots, r-1$, $G_i$ has an ELP-cut $C_i$, and
$G_{i+1}$ is a $C_i$-contraction of $G_i$, and $C$ is a $2$-separation cut of
$G_r$.
Clique cycle transversals in graphs with few P₄'s
Authors: Bravo Raquel , Klein Sulamita , Nogueira Loana Tito , Protti Fábio
Published: August 2021

Graph Theory

A graph is extended P4-laden if each of its induced subgraphs with at most six vertices that contains more than two induced P4's is 2K2,C4-free. A cycle transversal (or feedback vertex set) of a graph G is a subset T ⊆ V (G) such that T ∩ V (C) 6= ∅ for every cycle C of G; if, in addition, T is a clique, then T is a clique cycle transversal (cct). Finding a cct in a graph G is equivalent to partitioning V (G) into subsets C and F such that C induces a complete subgraph and F an acyclic subgraph. This work considers the problem of characterizing extended P4-laden graphs admitting a cct. We characterize such graphs by means of a finite family of forbidden induced subgraphs, and present a linear-time algorithm to recognize them.
A new characterization and a recognition algorithm of Lucas cubes
Authors: Taranenko Andrej
Published: August 2021

Graph Theory

Fibonacci and Lucas cubes are induced subgraphs of hypercubes obtained by excluding certain binary strings from the vertex set. They appear as models for interconnection networks, as well as in chemistry. We derive a characterization of Lucas cubes that is based on a peripheral expansion of a unique convex subgraph of an appropriate Fibonacci cube. This serves as the foundation for a recognition algorithm of Lucas cubes that runs in linear time.
Determining Genus From Sandpile Torsor Algorithms
Authors: McDonough Alex
Published: August 2021

We provide a pair of ribbon graphs that have the same rotor routing and
Bernardi sandpile torsors, but different topological genus. This resolves a
question posed by M. Chan [Cha]. We also show that if we are given a graph, but
not its ribbon structure, along with the rotor routing sandpile torsors, we are
able to determine the ribbon graph's genus.
A chip-firing variation and a new proof of Cayley's formula
Authors: Kayll Peter Mark , Perkins Dave
Published: August 2021

Graph Theory

We introduce a variation of chip-firing games on connected graphs. These 'burn-off' games incorporate the loss of energy that may occur in the physical processes that classical chip-firing games have been used to model. For a graph G=(V,E), a configuration of 'chips' on its nodes is a mapping C:V→ℕ. We study the configurations that can arise in the course of iterating a burn-off game. After characterizing the 'relaxed legal' configurations for general graphs, we enumerate the 'legal' ones for complete graphs Kn. The number of relaxed legal configurations on Kn coincides with the number tn+1 of spanning trees of Kn+1. Since our algorithmic, bijective proof of this fact does not invoke Cayley's Formula for tn, our main results yield secondarily a new proof of this formula.
All totally symmetric colored graphs
Authors: Grech Mariusz , Kisielewicz Andrzej
Published: August 2021

Graph Theory

In this paper we describe all edge-colored graphs that are fully symmetric with respect to colors and transitive on every set of edges of the same color. They correspond to fully symmetric homogeneous factorizations of complete graphs. Our description completes the work done in our previous paper, where we have shown, in particular, that there are no such graphs with more than 5 colors. Using some recent results, with a help of computer, we settle all the cases that was left open in the previous paper.
Rhombic alternative tableaux, assemblees of permutations, and the ASEP
Authors: Mandelshtam Olya , Viennot Xavier
Published: August 2021

In this paper, we introduce therhombic alternative tableaux, whose weight generating functions providecombinatorial formulae to compute the steady state probabilities of the two-species ASEP. In the ASEP, there aretwo species of particles, oneheavyand onelight, on a one-dimensional finite lattice with open boundaries, and theparametersα,β, andqdescribe the hopping probabilities. The rhombic alternative tableaux are enumerated by theLah numbers, which also enumerate certainassembl ́ees of permutations. We describe a bijection between the rhombicalternative tableaux and these assembl ́ees. We also provide an insertion algorithm that gives a weight generatingfunction for the assemb ́ees. Combined, these results give a bijective proof for the weight generating function for therhombic alternative tableaux.
Combinatorial description of the cohomology of the affine flag variety
Authors: Lee Seung Jin
Published: August 2021

We construct the affine version of the Fomin-Kirillov algebra, called the affine FK algebra, to investigatethe combinatorics of affine Schubert calculus for typeA. We introduce Murnaghan-Nakayama elements and Dunklelements in the affine FK algebra. We show that they are commutative as Bruhat operators, and the commutativealgebra generated by these operators is isomorphic to the cohomology of the affine flag variety. As a byproduct, weobtain Murnaghan-Nakayama rules both for the affine Schubert polynomials and affine Stanley symmetric functions. This enable us to expressk-Schur functions in terms of power sum symmetric functions. We also provide the defi-nition of the affine Schubert polynomials, polynomial representatives of the Schubert basis in the cohomology of theaffine flag variety.
Parking functions, tree depth and factorizations of the full cycle into transpositions
Authors: Irving John , Rattan Amarpreet
Published: August 2021

Consider the set Fn of factorizations of the full cycle (0 1 2 · · · n) ∈ S{0,1,...,n} into n transpositions. Write any such factorization (a1 b1) · · · (an bn) with all ai < bi to define its lower and upper sequences (a1, . . . , an) and (b1,...,bn), respectively. Remarkably, any factorization can be uniquely recovered from its lower (or upper) sequence. In fact, Biane (2002) showed that the simple map sending a factorization to its lower sequence is a bijection from Fn to the set Pn of parking functions of length n. Reversing this map to recover the factorization (and, hence, upper sequence) corresponding to a given lower sequence is nontrivial.
On (non-) freeness of some tridendriform algebras
Authors: Vong Vincent
Published: August 2021

We present some results on the freeness or non freeness of some tridendriform algebras. In particular, we give a combinatorial proof of the freeness of WQSym, an algebra based on packed words, result already known with an algebraic proof. Then, we prove the non-freeness of an another tridendriform algebra, PQSym, a conjecture remained open. The method of these proofs is generalizable, in particular it has been used to prove the freeness of the dendriform algebra FQSym and the quadrialgebra of 2-permutations.
Symmetric Fundamental Expansions to Schur Positivity
Authors: Roberts Austin
Published: August 2021

We consider families of quasisymmetric functions with the property that if a symmetric function f is a positive sum of functions in one of these families, then f is necessarily a positive sum of Schur functions. Furthermore, in each of the families studied, we give a combinatorial description of the Schur coefficients of f. We organize six such families into a poset, where functions in higher families in the poset are always positive integer sums of functions in each of the lower families.
A noncommutative geometric LR rule
Authors: Richmond Edward , Tewari Vasu , Van Willigenburg Stephanie
Published: August 2021

The geometric Littlewood-Richardson (LR) rule is a combinatorial algorithm for computing LR coefficients derived from degenerating the Richardson variety into a union of Schubert varieties in the Grassmannian. Such rules were first given by Vakil and later generalized by Coskun. In this paper we give a noncommutative version of the geometric LR rule. As a consequence, we establish a geometric explanation for the positivity of noncommutative LR coefficients in certain cases.
Counting connected graphs with large excess
Authors: De Panafieu Élie
Published: August 2021

We enumerate the connected graphs that contain a linear number of edges with respect to the number of vertices. So far, only the first term of the asymptotics was known. Using analytic combinatorics, i.e. generating function manipulations, we derive the complete asymptotic expansion.
Some results on counting roots of polynomials and the Sylvester resultant.
Authors: Monagan Michael , Tuncer Baris
Published: August 2021

We present two results, the first on the distribution of the roots of a polynomial over the ring of integers modulo n and the second on the distribution of the roots of the Sylvester resultant of two multivariate polynomials. The second result has application to polynomial GCD computation and solving polynomial diophantine equations.
Computation with No Memory, and Rearrangeable Multicast Networks
Authors: Gioan Emeric , Burckel Serge , Thomé Emmanuel
Published: August 2021

We investigate the computation of mappings from a set S^n to itself with "in situ programs", that is using no extra variables than the input, and performing modifications of one component at a time, hence using no extra memory. In this paper, we survey this problem introduced in previous papers by the authors, we detail its close relation with rearrangeable multicast networks, and we provide new results for both viewpoints. A bijective mapping can be computed by 2n-1 component modifications, that is by a program of length 2n-1, a result equivalent to the rearrangeability of the concatenation of two reversed butterfly networks. For a general arbitrary mapping, we give two methods to build a program with maximal length 4n-3. Equivalently, this yields rearrangeable multicast routing methods for the network formed by four successive butterflies with alternating reversions. The first method is available for any set S and practically equivalent to a known method in network theory. The second method, a refinment of the first, described when |S| is a power of 2, is new and allows more flexibility than the known method. For a linear mapping, when S is any field, or a quotient of an Euclidean domain (e.g Z/sZ for any integer s), we build a program with maximal length 2n-1. In this case the assignments are also linear, thereby particularly efficient from the algorithmic viewpoint, and giving moreover directly a program for the inverse when it exists. This yields also a new result on matrix decompositions, and a new result on the multicast properties of two successive reversed butterflies. Results of this flavour were known only for the boolean field Z/2Z.
A combinatorial analysis of Severi degrees
Authors: Liu Fu
Published: August 2021

Based on results by Brugallé and Mikhalkin, Fomin and Mikhalkin give formulas for computing classical Severi degrees Nd,δ using long-edge graphs. In 2012, Block, Colley and Kennedy considered the logarithmic versionof a special function associated to long-edge graphs which appeared in Fomin-Mikhalkin’s formula, and conjecturedit to be linear. They have since proved their conjecture. At the same time, motivated by their conjecture, we considera special multivariate function associated to long-edge graphs that generalizes their function. The main result of thispaper is that the multivariate function we define is always linear.The first application of our linearity result is that by applying it to classical Severi degrees, we recover quadraticity of Qd,δ and a bound δ for the threshold of polynomiality ofNd,δ.Next, in joint work with Osserman, we apply thelinearity result to a special family of toric surfaces and obtain universal polynomial results having connections to the Göttsche-Yau-Zaslow formula. As a result, we provide combinatorial formulas for the two unidentified power series B1(q) and B2(q) appearing in the Göttsche-Yau-Zaslow formula.The proof of our linearity result is completely combinatorial. We defineτ-graphs which generalize long-edge graphs,and a closely related family of combinatorial objects we call (τ,n)-words. By introducing height functions and aconcept of irreducibility, we describe ways to decompose certain families of (τ,n)-words into irreducible words,which leads to the desired results.
Affine type A geometric crystal structure on the Grassmannian
Authors: Frieden Gabriel
Published: August 2021

We construct a type A(1) n−1 affine geometric crystal structure on the Grassmannian Gr(k, n). The tropicalization of this structure recovers the combinatorics of crystal operators on semistandard Young tableaux of rectangular shape (with n − k rows), including the affine crystal operator e 0. In particular, the promotion operation on these tableaux essentially corresponds to cyclically shifting the Plu ̈cker coordinates of the Grassmannian.
A bijection for nonorientable general maps
Authors: Bettinelli Jérémie
Published: August 2021

We give a different presentation of a recent bijection due to Chapuy and Dołe ̨ga for nonorientable bipartite quadrangulations and we extend it to the case of nonorientable general maps. This can be seen as a Bouttier–Di Francesco–Guitter-like generalization of the Cori–Vauquelin–Schaeffer bijection in the context of general nonori- entable surfaces. In the particular case of triangulations, the encoding objects take a particularly simple form and we recover a famous asymptotic enumeration formula found by Gao.
Brick polytopes, lattices and Hopf algebras
Authors: Pilaud Vincent
Published: August 2021

Generalizing the connection between the classes of the sylvester congruence and the binary trees, we show that the classes of the congruence of the weak order on Sn defined as the transitive closure of the rewriting rule UacV1b1 ···VkbkW ≡k UcaV1b1 ···VkbkW, for letters a < b1,...,bk < c and words U,V1,...,Vk,W on [n], are in bijection with acyclic k-triangulations of the (n + 2k)-gon, or equivalently with acyclic pipe dreams for the permutation (1,...,k,n + k,...,k + 1,n + k + 1,...,n + 2k). It enables us to transport the known lattice and Hopf algebra structures from the congruence classes of ≡k to these acyclic pipe dreams, and to describe the product and coproduct of this algebra in terms of pipe dreams. Moreover, it shows that the fan obtained by coarsening the Coxeter fan according to the classes of ≡k is the normal fan of the corresponding brick polytope
The generalized Gelfand–Graev characters of GLn(Fq)
Authors: Andrews Scott , Thiem Nathaniel
Published: August 2021

Introduced by Kawanaka in order to find the unipotent representations of finite groups of Lie type, gener- alized Gelfand–Graev characters have remained somewhat mysterious. Even in the case of the finite general linear groups, the combinatorics of their decompositions has not been worked out. This paper re-interprets Kawanaka's def- inition in type A in a way that gives far more flexibility in computations. We use these alternate constructions to show how to obtain generalized Gelfand–Graev representations directly from the maximal unipotent subgroups. We also explicitly decompose the corresponding generalized Gelfand–Graev characters in terms of unipotent representations, thereby recovering the Kostka–Foulkes polynomials as multiplicities.
Dual Immaculate Quasisymmetric Functions Expand Positively into Young Quasisymmetric Schur Functions
Authors: Allen Edward , Hallam Joshua , Mason Sarah
Published: August 2021

We describe a combinatorial formula for the coefficients when the dual immaculate quasisymmetric func- tions are decomposed into Young quasisymmetric Schur functions. We prove this using an analogue of Schensted insertion. We also provide a Remmel-Whitney style rule to generate these coefficients algorithmically.
Rectangular Young tableaux and the Jacobi ensemble
Authors: Marchal Philippe
Published: August 2021

It has been shown by Pittel and Romik that the random surface associated with a large rectangular Youngtableau converges to a deterministic limit. We study the fluctuations from this limit along the edges of the rectangle.We show that in the corner, these fluctuations are gaussian whereas, away from the corner and when the rectangle isa square, the fluctuations are given by the Tracy-Widom distribution. Our method is based on a connection with theJacobi ensemble.
From generalized Tamari intervals to non-separable planar maps
Authors: Fang Wenjie , Préville-Ratelle Louis-François
Published: August 2021

Let v be a grid path made of north and east steps. The lattice TAM(v), based on all grid paths weakly above the grid path v sharing the same endpoints as v, was introduced by Pre ́ville-Ratelle and Viennot (2014) and corresponds to the usual Tamari lattice in the case v = (NE)n. They showed that TAM(v) is isomorphic to the dual of TAM(←−v ), where ←−v is the reverse of v with N and E exchanged. Our main contribution is a bijection from intervals in TAM(v) to non-separable planar maps. It follows that the number of intervals in TAM(v) over all v of length n is 2(3n+3)! (n+2)!(2n+3)! . This formula was first obtained by Tutte(1963) for non-separable planar maps.
Wiener index in graphs with given minimum degree and maximum degree
Authors: Dankelmann Peter , Alochukwu Alex
Published: August 2021

Let $G$ be a connected graph of order $n$.The Wiener index $W(G)$ of $G$ is
the sum of the distances between all unordered pairs of vertices of $G$. In
this paper we show that the well-known upper bound $\big(
\frac{n}{\delta+1}+2\big) {n \choose 2}$ on the Wiener index of a graph of
order $n$ and minimum degree $\delta$ [M. Kouider, P. Winkler, Mean distance
and minimum degree. J. Graph Theory 25 no. 1 (1997)] can be improved
significantly if the graph contains also a vertex of large degree.
Specifically, we give the asymptotically sharp bound $W(G) \leq
{n-\Delta+\delta \choose 2} \frac{n+2\Delta}{\delta+1}+ 2n(n-1)$ on the Wiener
index of a graph $G$ of order $n$, minimum degree $\delta$ and maximum degree
$\Delta$. We prove a similar result for triangle-free graphs, and we determine
a bound on the Wiener index of $C_4$-free graphs of given order, minimum and
maximum degree and show that it is, in some sense, best possible.
The Elser nuclei sum revisited
Authors: Grinberg Darij
Published: August 2021

Fix a finite undirected graph $\Gamma$ and a vertex $v$ of $\Gamma$. Let $E$
be the set of edges of $\Gamma$. We call a subset $F$ of $E$ pandemic if each
edge of $\Gamma$ has at least one endpoint that can be connected to $v$ by an
$F$-path (i.e., a path using edges from $F$ only). In 1984, Elser showed that
the sum of $\left(-1\right)^{\left| F\right|}$ over all pandemic subsets $F$ of
$E$ is $0$ if $E\neq \varnothing$. We give a simple proof of this result via a
sign-reversing involution, and discuss variants, generalizations and
refinements, revealing connections to abstract convexity (the notion of an
antimatroid) and discrete Morse theory.
ASSESSMENT OF THE TECHNOLOGICAL TRANSFORMATION OF THE RUSSIAN MANUFACTURING INDUSTRY CONSIDERING THE DIGITAL FACTOR
Authors:   Northern (Arctic) Federal University named after M.V. Lomonosov, Arkhangelsk, Kalinichenko M.P.
Published: August 2021

The purpose of the study is to assess the technological transformation of the manufacturing industry in Russia, taking into account the digital factor. The analysis of a set of methods that can be used to assess the impact of technologies on the digital transformation of economic systems (country, industry, region, industrial enterprise) is carried out; the results of a SWOT analysis of the Russian manufacturing industry for the medium term are presented (as an initial stage for the subsequent development of functional strategies of industrial enterprises-digital transformation, innovative, competitive, etc.); the results of a survey of experts on a sample of industrial enterprises of the Arkhangelsk region regarding barriers and prospects of digital transformation of manufacturing enterprises are summarized; an economic and mathematical model of the influence of production factors, including the digital factor, on the value added created by the manufacturing industry is developed. Based on the analysis and modeling of the formation of added value in the manufacturing industry, taking into account the contribution of each of the factors of production, a set of solutions is proposed, on the basis of which it is possible to give a new impetus to accelerate the digital transformation of the industry.
SCENARIO STUDY OF INVESTMENT RESOURCE FLOWS FOR THE DEVELOPMENT OF ENTERPRISES AND ENTREPRENEURSHIP
Authors:   Samara State University of Economics, Streltsov A.V. , Yakovlev G.I. ,   Samara State University of Economics
Published: August 2021

The study considers the issues of mobilizing investment resources of enterprises and business structures, highlights the factors that determine the need for an active technical policy in the modern digital economy. The lack and limitation of investment resources for production purposes in the necessary volumes, under favorable conditions for the provision of borrowed funds, is observed throughout the entire post-reform period of the development of the Russian economy. For the purposes of accelerated modernization, it is necessary to increase the scales of generation of all types of investment resources of enterprises, both own and borrowed, in order to ensure expanded reproduction of promising products on a new technical and technological basis. The purpose of the study is to study possible options for the formation of own investment resources of enterprises and business structures, ensuring their relationship with macroeconomic conditions, the need for borrowed funds, with the most important indicators of the efficiency of the enterprise. The methods of logical analysis, meaningful economic interpretation of economic and managerial phenomena in the environment of investment activity of enterprises, analysis of cause-and-effect relationships in the system of organization of technical development of the enterprise were used in the work. As a result, the study proved the hypothesis that depreciation and net profit can serve as a significant source of investments at enterprises, and proper management of the formation and use of the depreciation fund and the accumulation fund, when there are favorable macroeconomic factors, can significantly increase the share of enterprises ' own funds in their investments. It is proposed to carry out regular management of the depreciation fund and the movement of the accumulation fund for the entire period of the useful life of fixed assets. If this work is not carried out in some periods (years), this significantly reduces the possible share of own funds in investments and increases the need for borrowed funds, increases operating costs.
SPATIAL DYNAMICS OF HEALTHCARE DEVELOPMENT OF THE UNITED STATES OF AMERICA
Authors:   Ryazan State Agrotechnological University by P.A. Kostychev, Minat V.N.
Published: August 2021

The features of the spatial dynamics of the development of American healthcare in the long term are revealed. Based on the use of statistical and economic analysis undertaken within the framework of a combination of historical, geospatial and typological approaches, the dynamics of the average annual indicators of the development of US healthcare for 1951-2020 in the context of individual states is studied. Grouping of indicators allowed to identify the relationship between the growth of efficiency, quality, safety, accessibility and effectiveness of US healthcare at the regional level. On the basis of this dependence, a typology of states is carried out, which generally corresponds to the central-peripheral concept of the dynamics of socio-economic development of the United States.
PROGRAM FOR THE DEVELOPMENT OF A FRANCHISE BUSINESS NETWORK ON THE MARKET
Authors:   Samara State University of Economics, Bogatova M.A.
Published: August 2021

The franchise model is currently the most profitable, fast-growing business format that ensures the economic growth of the regional and Russian economy. The subject of the study was the program for the development of a franchise business network in the market. The purpose of this study is to develop effective management measures to expand the use of franchise relations in business networks. The use of the author's approach allowed to build a step-by-step program for scaling a ready-made partner business and increase the level of transparency of franchise relations. The practical significance lies in the development of a set of practical steps within the framework of the implementation of the action program to enhance the use of franchising in the Russian economy, which will increase the number of new participants in franchise systems.
EVOLUTIONARILY STABLE STRATEGIES OF ECONOMIC BEHAVIOR
Authors:   Samara State University of Economics, Nikitina N.V. , Makhmudov F.A. ,   Samara State University of Economics
Published: August 2021

Modern science proceeds from the fact that the basis of economic behavior is volitional «controllability», i.e. awareness of the possible consequences of one's action/inaction by a person, on the basis of which the most effective behavioral models, common in a particular socio-cultural community, are formed from the position of satisfying one's needs. This article analyzes the theoretical and practical properties of understanding evolutionarily stable strategies of economic behavior, which at a subconscious level determine the further development of economic relations.
DEVELOPMENT OF AN EFFECTIVE ALGORITHM OF MAKING A DECISION ABOUT CHOOSING THE TYPE OF STRATEGY OF AN IT SECTOR COMPANY INTERNAL GROWTH
Authors:   .Samara State University of Economics, Troshina E.P.
Published: August 2021

The article discusses the importance of the internal growth strategy for IT sector companies. The corresponding analysis is carried out on the example of the company LLC IC «SIBINTEK». The paper calculates and analyzes the target indicators of the enterprise allocated for a specific company; the current growth strategy is considered; conclusions are drawn about its effectiveness in modern realities.
Actions Large Energy Buyers Can Take to Transform and Decarbonize the Grid: Procurement Practices for Achieving 100% Carbon Free Electricity
Authors: Bird Lori , O'Shaughnessy Eric , Hutchinson Norma
Published: August 2021

Large energy buyers—including corporates, cities, and institutional customers—have played and will continue to play an important role in driving clean energy in the near term, particularly renewables. However, to ensure that the power sector achieves deep decarbonization over the next two to three decades, large energy buyers will need to take additional actions to play a leading role in accelerating the transition to a carbon-free grid. Large energy buyers can implement approaches that help transform the grid such as matching clean energy purchasing with the timing of their energy use, incorporating demand flexibility, purchasing dispatchable clean electricity, adopting enabling technologies (e.g., energy storage), maximizing emissions reductions, and driving an an equitable transition to clean energy.
Canine diffuse idiopathic skeletal hyperostosis – case report
Authors: de Moura Sampaio Lucas , Ribeiro Gomes Caique Augusto , Pires Anacleto Thiago , Akamatsu Angela , Gavião Prado Luan
Published: August 2021

Diffuse idiopathic skeletal hyperostosis is a rare disease characterized by massive and progressive ossification of soft tissues that surround the axial and appendicular skeletons, affecting more frequently the ventral longitudinal ligament. The etiological and therapeutic aspects of the disease have not yet been completely clarified and there is little information available on the occurrence of the disease in the canine species. This work reports the first case of this disease in the national literature and aims to describe the clinical and radiographic aspects of the condition in a seven-year-old bitch presenting gait abnormalities and thoracolumbar postural alterations associated with lower back pain. Diagnosis was made by conventional radiography and initial treatment with a selective COX-2 anti-inflammatory drug has shown good results in pain relief and short-term control of clinical signs.
Electrocardiographic and arterial pressure changes in female dogs subjected to epidural anesthesia with different doses of morphine
Authors: Werneck Fonseca Mariana , Batista de Albuquerque Verônica , T. N. Martins Ferreira Gabriel , de Araújo Marcelo Augusto , Ferreira Wagner Luis , Patto dos Santos Paulo Sergio , Nobre Leal de Souza Oliva Valéria
Published: August 2021

This article investigates the electrocardiographic and blood pressure changes caused by different doses of morphine administered epidurally to bitches undergoing elective ovariohysterectomy. Twenty-four healthy bitches weighing 9.8 ± 4.1 kg were assigned to three experimental groups (in each group, n = 8): (i) group M0.1: 0.1 mg/kg morphine; (ii) group M0.15: 0.15 mg/kg morphine; and (iii) group M0.2: 0.2 mg/kg morphine. In all groups, levobupivacaine was added to achieve a total volume of 0.33 mL/kg. During the procedures, the following parameters were controlled: heart rate and rhythm, systolic blood pressure, rectal temperature and blood lactate. The data were analyzed by means of statistical methods of analysis of variance, such as Kruskal-Wallis, Fisher and Tukey tests. Epidural morphine did not cause significant electrocardiographic or blood pressure changes in the tested doses, which makes the use of this drug a viable alternative for epidural anesthesia.
Drug therapy and nutritional management of metabolic syndrome associated with hyperadrenocorticism in a dog – case report
Authors: De Marco Viviani , Zotelli dos Santos Elidia
Published: August 2021

Hyperadrenocorticism (HAC) is a generic term that refers to clinical and biochemical abnormalities resulting from persistently high concentrations of glucocorticoids in the bloodstream, which may occur spontaneously or iatrogenically. Chronic hypercortisolism may promote abdominal obesity, dyslipidemia, systemic arterial hypertension and insulin resistance, abnormalities associated with the metabolic syndrome (MS). The present study aims to report the presence of MS in a dog with spontaneous HAC, and its satisfactory long-term therapeutic resolution. The animal presented marked alterations in addition to the classic symptoms of HAC: discrete hyperglycemia, insulin resistance, hyperlipidemia, arterial hypertension and obesity. Complete resolution of MS and stable control of HAC were observed after five months of treatment.
QUANTITATIVE DETERMINATION OF TANNIN IN NETTLE BY SPECTROPHOTOMETRIC AND CHROMATOGRAPHIC METHODS
Authors: Apoyan Svetlana H. , Vardapetyan Samvel M. , Hovhannisyan Anahit M. , Mkrtchyan Gohar F.
Published: August 2021

The amount of tannins in the leaves of stinging nettle was determined depending on the phenological phase (budding phase, mass flowering phase and fruiting phase). UV spectrophotometric and high performance liquid chromatographic (HPLC) methods were used to quantify tannins in the plant. It was found that the maximum accumulation of this group of substances in nettle leaves occurs in the fruiting phase. Based on the results of the study, the chromatographic method is optimal for the analysis of tannins in nettle leaves.
Evaluating the impact of faculty development programme initiative: are we really improving skills in MCQ writing?
Authors: Kiran Faiza , Ayub Rukhsana , Rauf Ayesha , Qamar Khadija
Published: August 2021

Objective: This study was done to evaluate the effectiveness of a 3-hour workshop in improving faculty competence in developing high quality test items.
Methodology: The study took place in National University of Medical Sciences and its affiliated institutes in Pakistan, during a period of six months in year 2018. It was a descriptive, cross sectional study. A series of seven workshops on quality assurance in writing MCQs was conducted as part of faculty development program, emphasizing hand-on experience and prompt feedback. Participants’ satisfaction was evaluated with a post-workshop feedback questionnaire (Kirkpatrick 1). A self-made structured questionnaire was given as a pre-test and post-test, to check improvement in cognition, behaviour and item writing skills of faculty (Kirkpatrick 2). Paired t test was applied and difference in mean scores of responses was evaluated.
Results: Total 141 faculty members were trained.  The training session led to high satisfaction in all elements of workshop, significant improvements in boosting confidence in item writing skills(p=0.000), recognizing parts of MCQs (p=0.000), identifying item writing flaws (p=0.000) and levels of Millers pyramid and blooms taxonomy (p=0.000).
Conclusion: Training sessions of short duration are effective in improving the competence of faculty in writing quality test items, provided hands-on experience is built-in and effective feedback is provided.
The Us Recognition of Jerusalem: Aspects and Implications
Authors: Shahzad Hussain
Published: August 2021

The status of Jerusalem lies at the heart of Palestine-Israel conundrum. Its disputed status is pelagus forsit for the resolution of the intractable Palestine conflict. The Palestinians have always regarded Eastern Jerusalem as capital of their future state under Two-nation solution. On the other side, Israel declared in 1998 to further expand Jerusalem by annexing the surrounding areas as well. This paper investigates the Trump administration’s stance on relocating the US embassy from Tel Aviv to Jerusalem, its implications for Palestinian state and broad reactions of the world community.
Constitutional Basis of Ensuring the Right to Privacy in the Age of Informatization
Authors: Madiev Fakhriddin Khoshim o'gli
Published: August 2021

The following article analyzes the theoretical and practical essence and importance of privacy. As well as that the author points out main issues in this sphere. Besides that, laws on privacy in the experience of Uzbekistan is discussed
Ethymological Doublets Between French Verbs And Their Use
Authors: Sobirovich Shakirov Rustam
Published: August 2021

This article examines the origin, use and translation into Uzbek of two French verbs that come from the same word in Latin.
Organizational and Economic Fundamentals of Formation of Investment Funds Improvement
Authors: Munira Baxodirovna Sultonboeva
Published: August 2021

The article examines the organizational and economic basis for the formation of investment funds and the theoretical and methodological basis for improving the mechanism of its implementation. Factors influencing the process of formation of investment funds have been systematically studied. Scientific proposals and practical recommendations for improving the organizational and economic framework for the formation of investment funds have been formed
Seismo-Tectonic Model of Highly Naturally Risked Territories of Uzbekistan
Authors: Yarkulov Z. R. , A Qobilov. , U Berdikulov.
Published: August 2021

Based on a comprehensive analysis of the results of geological-geophysical and seismological studies, neotectionic and seismotectionic models of the central part of Uzbekistan are proposed. These Annotation models are used to predict the probable kinematic type of movements in the focal zones of possible earthquakes.
Presumption of Innocence - A Criminal Procedural Guarantee as A Component of the System
Authors: Bazarova Dildora
Published: August 2021

This article discloses the presumption of innocence - a criminal procedural guarantee as a component of the system. The presumption of innocence is one of the basic constitutional principles that guarantee human rights and freedoms, which means that a person is presumed innocent until proven guilty in accordance with the procedure established by law and a court that has the right to initiate a criminal case.
FACTORS INFLUENCING CLINICAL MANAGEMENT OF CRYPTOCOCCAL MENINGITIS AMONG HEALTH CARE PROVIDERS AT TWO REFERRAL HOSPITALS IN KISUMU COUNTY, KENYA
Authors: Ogendo Robina
Published: August 2021

Purpose: Cryptococcal meningitis is one of the most common and lethal opportunistic infections among human immune virus infected clients/patients before initiation of antiretroviral therapy. It is majorly associated to morbidity and early mortality among human immunodeficiency virus infected patients in resource limited countries. The main objective of this study was to investigate the factors influencing clinical management of cryptococcal meningitis in adults among health care providers at two referral hospitals in Kisumu County, Kenya.

Methodology: A cross-sectional study using quantitative approach was used targeting 119 health care providers. Collection of data was through pretested self- administered questionnaires to examine factors influencing clinical management of cryptococcal meningitis. Data obtained was analyzed using the statistical package for social science version 25. Descriptive analysis was done using frequencies, percentages and means. Inferential analysis was conducted using bivariate logistic regression to determine relationships among the variables, p-values of at or below 0.05 were considered statistically significant.

Results: The major factor associated positively with clinical management of cryptococcal meningitis was the acknowledgement by the health care providers that the world health organization guidelines lead to a better patient outcome (97%, n=113) and inadequate supplies and resources to facilitate management (78%, n=90) was the major factor associated negatively. Health care providers with an experience of five years or less were 40% more likely to agree that the factors were influencing clinical management of cryptococcal meningitis in contrast to those with an experience of six years or more (OR: 0.6; 95%CI: 0.1 – 0.74; p=0.04).

Unique contribution to theory, practice and policy:  The clinical management of cryptococcal meningitis in adults in the study area is majorly negatively influenced by inadequate supplies and resources to facilitate the process of management. The study recommends that the policy makers in the County government of Kisumu and the two hospital management teams need to scale up a timely and constant provision of adequate resources, facilities and supplies, which will promote effective clinical management of cryptococcal meningitis in the study area