Minimal Elements Research Articles

Acoustic Streaming: A Diagnostic Clue to Diagnosing Testicular Teratoma

Teratomatous tissue is commonly seen in a variety of malignant testicular tumors, and while the exact determination of testicular tumor subtypes heavily relies on pathologic diagnosis, ultrasound remains the gold standard in the initial evaluation of such entities. The major groups of testicular tumors may demonstrate characteristic features which can point the radiologist toward a more pruned differential diagnosis. While it is important for the interpreting physician to be aware of such features, it is of equal necessity that they are aware of potential visual phenomena, such as acoustic streaming in the diagnosis of testicular tumors. We present a case of a testicular teratoma with acoustic streaming. This testicular tumor was confirmed to be predominantly a teratoma with a minimal element of seminoma on histopathology.

Multilattices on typical hesitant fuzzy sets

In this paper, we mainly study multilattices on the set of finite nonempty subsets of [0,1] under different orders. Firstly, the relationships among orders ≤ 1, ≤ 2 and ≤ * are discussed. It is shown that the order ≤ * is contained in the orders ≤ 1 and ≤ 2, but the converse is not true, and that there is no inclusion between the orders ≤ 1 and ≤ 2. The lattice and multilattice structures of the set of finite nonempty subsets of [0,1] under ≤ 1 and ≤ * are studied, respectively. It is proved that the set of finite nonempty subsets of [0,1] is neither a lattice nor a multilattice with respect to the order ≤ *, and is not a multilattice with respect to the order ≤ 1. Finally, we extend order ≤ * to the set V([0, 1]) of finite vectors of [0,1] and develop a new order ⪯. It is verified that the quotient set V([0, 1])/ ≡ under the order ⪯ is not a lattice, but is a multilattice. Moreover, we give a method to construct maximal elements and minimal elements for finite vectors of [0,1] with respect to the order ⪯. The results will provide an application of hesitant fuzzy sets in rough sets, information fusion, fuzzy automata, fuzzy transitive systems, etc.

An Adaptive Algorithm for Solving the Axial Three-Index Assignment Problem

In this paper, a probabilistic modification of the minimal element algorithm for solving the axial three-index assignment problem is suggested. Its general idea is to extend the basic greedy-type algorithmic schemes using transition to a probabilistic setup based on variables randomization. The minimization of an objective function is replaced by the minimization of its expectation. The algorithm is implemented in three stages as follows. At the first stage, a motion in the set of random variables is defined. At the second stage, an inequality that expresses the local improvement condition is solved. At the third stage, the probabilities are recalculated, which represents an “adaptation” process. The second stage reveals a feature of the algorithm: the resulting solution depends on the “qualities” of the element itself and also on possible losses of its choice.

Natural partial order and finiteness conditions on semigroups of linear transformations with invariant subspaces

Given a vector space V and a subspace W of V, we consider the semigroup (under composition) S(V, W), consisting of all linear transformations on V which leave the subspace W invariant. In this paper, we characterize the natural partial order on S(V, W). In the partially ordered set, we determine the compatibility of their elements, and find all maximal and minimal elements. Also, we give necessary and sufficient conditions for S(V, W) to be factorizable, unit-regular and directly finite.

Change of fertility indicators of dark-grey forest soil with different systems of basic tillage

The effect of the long-term use of soil tillage systems on the elements of potential fertility and agrochemical properties of dark-grey forest soil was determined. The research was conducted in the Northern Trans-Urals in a stationary experiment in the grain-fallow crop rotation: bare fallow - winter rye - spring wheat - grain legumes - spring barley, developed in time and space. Upon completion of the 5th rotation (2008-2012), the effect of moldboard, non-moldboard, combined, differential, subsoil and surface tillage systems on soil fertility was studied. It was established that various systems of the basic tillage carried out during five rotations of the grain-fallow crop rotation did not have a significant effect on the soil acidity. Non-moldboard and differential soil tillage, as well as plowing had an equal effect on the content of the total absorbed bases. Annual minor tillage, like sub-soil and disk harrowing led to the decrease in the content of the total absorbed bases by 13-29% in the layer of 2040 cm. The use of non-moldboard tillage caused the decrease in the content of gross nitrogen and gross phosphorus; nitrogen - by 0.70 t/ha in the topsoil, and by 1.33 t/ha or by 10-24% in the soil layer of 2040 cm; phosphorus - by 0.30 t/ha and by 0.27 t/ha or 18-23%, respectively, compared to moldboard tillage. Combined tillage with alternating plowing and non-moldboard soil loosening to a depth of 20-22 cm contributed to the increase in the gross nitrogen content by 1.05 t/ha in the 0-20 cm layer, and by 0.41 t/ha or by 8-45% in the soil layer of 20-40 cm, and led to the increase in the content of mobile phosphorus by 0.23 t / ha or by 14% in the topsoil, compared to the moldboard tillage system. All tillage systems had almost equal effect on the content of gross nitrogen in the soil. Tillage systems with the elements of minimization contributed to a slight increase in the total phosphorus content by 6-14% in the soil layer of 0-20 cm. Resource-saving tillage systems did not affect adversely the content of gross potassium forms in the soil layer of 0-40 cm.

Building the Framework for Standardized Clinical Laboratory Reporting of Next-generation Sequencing Data for Resistance-associated Mutations in Mycobacterium tuberculosis Complex.

Tuberculosis is the primary infectious disease killer worldwide, with a growing threat from multidrug-resistant cases. Unfortunately, classic growth-based phenotypic drug susceptibility testing (DST) remains difficult, costly, and time consuming, while current rapid molecular testing options are limited by the diversity of antimicrobial-resistant genotypes that can be detected at once. Next-generation sequencing (NGS) offers the opportunity for rapid, comprehensive DST without the time or cost burden of phenotypic tests and can provide useful information for global surveillance. As access to NGS expands, it will be important to ensure that results are communicated clearly, consistent, comparable between laboratories, and associated with clear guidance on clinical interpretation of results. In this viewpoint article, we summarize 2 expert workshops regarding a standardized report format, focusing on relevant variables, terminology, and required minimal elements for clinical and laboratory reports with a proposed standardized template for clinical reporting NGS results for Mycobacterium tuberculosis.

Species substitution, graph suspension, and graded Hopf algebras of painted tree polytopes

Combinatorial Hopf algebras of trees exemplify the connections between operads and bialgebras. Painted trees were introduced recently as examples of how graded Hopf operads can bequeath Hopf structures upon compositions of coalgebras. We put these trees in context by exhibiting them as the minimal elements of face posets of certain convex polytopes. The full face posets themselves often possess the structure of graded Hopf algebras (with one-sided unit). We can enumerate faces using the fact that they are structure types of substitutions of combinatorial species. Species considered here include ordered and unordered binary trees and ordered lists (labeled corollas). Some of the polytopes that constitute our main results are well known in other contexts. First we see the classical permutohedra, and then certain generalized permutohedra: specifically the graph associahedra of suspensions of certain simple graphs. As an aside we show that the stellohedra also appear as liftings of generalized permutohedra: graph composihedra for complete graphs. Thus our results give examples of Hopf algebras of tubings and marked tubings of graphs. We also show an alternative associative algebra structure on the graph tubings of star graphs.

Tilting modules over Auslander–Gorenstein algebras

For a finite dimensional algebra $\Lambda$ and a non-negative integer $n$, we characterize when the set $\tilt_n\Lambda$ of additive equivalence classes of tilting modules with projective dimension at most $n$ has a minimal (or equivalently, minimum) element. This generalize results of Happel-Unger. Moreover, for an $n$-Gorenstein algebra $\Lambda$ with $n\geq 1$, we construct a minimal element in $\tilt_{n}\Lambda$. As a result, we give equivalent conditions for a $k$-Gorenstein algebra to be Iwanaga-Gorenstein. Moreover, for an $1$-Gorenstein algebra $\Lambda$ and its factor algebra $\Gamma=\Lambda/(e)$, we show that there is a bijection between $\tilt_1\Lambda$ and the set $\sttilt\Gamma$ of isomorphism classes of basic support $\tau$-tilting $\Gamma$-modules, where $e$ is an idempotent such that $e\Lambda $ is the additive generator of projective-injective $\Lambda$-modules.

New MiniPromoter Ple345 (NEFL) Drives Strong and Specific Expression in Retinal Ganglion Cells of Mouse and Primate Retina

Retinal gene therapy is leading the neurological gene therapy field, with 32 ongoing clinical trials of recombinant adeno-associated virus (rAAV)–based therapies. Importantly, over 50% of those trials are using restricted promoters from human genes. Promoters that restrict expression have demonstrated increased efficacy and can limit the therapeutic to the target cells thereby reducing unwanted off-target effects. Retinal ganglion cells are a critical target in ocular gene therapy; they are involved in common diseases such as glaucoma, rare diseases such as Leber's hereditary optic neuropathy, and in revolutionary optogenetic treatments. Here, we used computational biology and mined the human genome for the best genes from which to develop a novel minimal promoter element(s) designed for expression in restricted cell types (MiniPromoter) to improve the safety and efficacy of retinal ganglion cell gene therapy. Gene selection included the use of the first available droplet-based single-cell RNA sequencing (Drop-seq) dataset, and promoter design was bioinformatically driven and informed by a wide range of genomics datasets. We tested seven promoter designs from four genes in rAAV for specificity and quantified expression strength in retinal ganglion cells in mouse, and then the single best in nonhuman primate retina. Thus, we developed a new human-DNA MiniPromoter, Ple345 (NEFL), which in combination with intravitreal delivery in rAAV9 showed specific and robust expression in the retinal ganglion cells of the nonhuman-primate rhesus macaque retina. In mouse, we also developed MiniPromoters expressing in retinal ganglion cells, the hippocampus of the brain, a pan neuronal pattern in the brain, and peripheral nerves. As single-cell transcriptomics such as Drop-seq become available for other cell types, many new opportunities for additional novel restricted MiniPromoters will present.

The Absolute Values and Support Projections for a Class of Operator Matrices Involving Idempotents

Let $\lambda\in \mathbb{R},$ $\mu\in \mathbb{R}$ and $B$ be a linear bounded operator from a Hilbert space $\mathcal{K}$ into another Hilbert space $\mathcal{H}.$ In this paper, we consider the formulas of the absolute value $|Q_{\lambda,\mu}|,$ where $Q_{\lambda,\mu}$ with respect to the decomposition $\mathcal{H}\oplus\mathcal{K}$ have the operator matrix form $Q_{\lambda,\mu}:=\left(\begin{array}{cc}\lambda I&B\\B^*&\mu I\end{array}\right).$ Then the positive part and the support projection of $Q_{\lambda,0}$ are obtained. Also, we characterize the symmetry $J$ such that a projection $E$ is the $J$-projection. In particular, the minimal element of the set of all symmetries $J$ with the property $JE\geqslant0$ is described.

Twenty-Seven Tamoxifen-Inducible iCre-Driver Mouse Strains for Eye and Brain, Including Seventeen Carrying a New Inducible-First Constitutive-Ready Allele.

To understand gene function, the cre/loxP conditional system is the most powerful available for temporal and spatial control of expression in mouse. However, the research community requires more cre recombinase expressing transgenic mouse strains (cre-drivers) that restrict expression to specific cell types. To address these problems, a high-throughput method for large-scale production that produces high-quality results is necessary. Further, endogenous promoters need to be chosen that drive cell type specific expression, or we need to further focus the expression by manipulating the promoter. Here we test the suitability of using knock-ins at the docking site 5′ of Hprt for rapid development of numerous cre-driver strains focused on expression in adulthood, using an improved cre tamoxifen inducible allele (icre/ERT2), and testing a novel inducible-first, constitutive-ready allele (icre/f3/ERT2/f3). In addition, we test two types of promoters either to capture an endogenous expression pattern (MaxiPromoters), or to restrict expression further using minimal promoter element(s) designed for expression in restricted cell types (MiniPromoters). We provide new cre-driver mouse strains with applicability for brain and eye research. In addition, we demonstrate the feasibility and applicability of using the locus 5′ of Hprt for the rapid generation of substantial numbers of cre-driver strains. We also provide a new inducible-first constitutive-ready allele to further speed cre-driver generation. Finally, all these strains are available to the research community through The Jackson Laboratory.

A novel algorithm for the vertex cover problem based on minimal elements of discernibility matrix

Minimal vertex cover problem (MVCP) is a famous important NP-hard problem in graph theory. It has been reported that MVCP is equivalent to finding reducts of information systems in rough sets theory. This relationship motivates our idea to deal with MVCP in terms of approaches to discernibility matrix in rough set. First we point out that only minimal elements in the discernibility matrix are useful for MVCP, and we present a novel algorithm based on minimal elements for MVCP. Then we make experimental comparisons to demonstrate the effectiveness of this new algorithm on big graphs.

Minimal consistent finite element space for the biharmonic equation on quadrilateral grids

Abstract This study presents a finite element space comprising piecewise quadratic polynomials on quadrilateral grids. This space provides a minimal-degree consistent discretisation for the biharmonic equation.

A Bijection for Essentially 4-Connected Toroidal Triangulations

Transversal structures (also known as regular edge labelings) are combinatorial structures defined over 4-connected plane triangulations with quadrangular outer-face. They have been intensively studied and used for many applications (drawing algorithm, random generation, enumeration, ...). In this paper we introduce and study a generalization of these objects for the toroidal case. Contrary to what happens in the plane, the set of toroidal transversal structures of a given toroidal triangulation is partitioned into several distributive lattices. We exhibit a subset of toroidal transversal structures, called balanced, and show that it forms a single distributive lattice. Then, using the minimal element of the lattice, we are able to enumerate bijectively essentially 4-connected toroidal triangulations.

Optimization of the method of constructing reference plans of multimodal transport problem

The classical transport problem is in determination of the optimal plan for the transportation of goods from the points of departure to the points of delivery, taking into account the criterion of the minimum cost of such transportation. Such a problem takes into account only one type of transport, which does not fully correspond to the practical needs of modern logistics enterprises. That is why the object of this research is the classical transport problem, the formulation of which takes into account the presence of several means of cargo delivery, namely: automobile, railway and water. This type of transport problem is defined as multimodal. The implementation of the multimodal transport problem involves the use of various numerical methods and is carried out using software. In fact, the conceptual approach to its solution is a simple selection of possible results. Given the large dimension of the problem, such an approach can be extremely cumbersome, and therefore requires some improvement. During the study, the method for constructing a reference plan for such a problem was optimized based on the criterion of minimizing the number of numerical iterations, and the advantages of the proposed approach compared to those already known were substantiated. The basis of the new approach is the previously known minimal element method, which is to be used to solve the transportation problem, and an analogy with the Steiner problem was drawn. The latter, in turn, made it possible to define a new approach as the Steiner method. The research result is development of a general algorithm for the implementation of the proposed Steiner method. As an approbation of this algorithm, a model example is provided. It demonstrated the identity of the results of solving a multimodal transport problem using all the methods discussed in the article. The development of new methods for the implementation of the multimodal transport problem will make it possible to construct efficient algorithms for solving more complex problems of transport logistics. The criterion for reducing the number of numerical iterations, used at all stages of the implementation of such problems, significantly reduces the time to search for their solutions.

Targeting Protein-Protein Interactions of Tyrosine Phosphatases with Microarrayed Fragment Libraries Displayed on Phosphopeptide Substrate Scaffolds.

Chemical library screening approaches that focus exclusively on catalytic events may overlook unique effects of protein-protein interactions that can be exploited for development of specific inhibitors. Phosphotyrosyl (pTyr) residues embedded in peptide motifs comprise minimal recognition elements that determine the substrate specificity of protein tyrosine phosphatases (PTPases). We incorporated aminooxy-containing amino acid residues into a 7-residue epidermal growth factor receptor (EGFR) derived phosphotyrosine-containing peptide and subjected the peptides to solution-phase oxime diversification by reacting with aldehyde-bearing druglike functionalities. The pTyr residue remained unmodified. The resulting derivatized peptide library was printed in microarrays on nitrocellulose-coated glass surfaces for assessment of PTPase catalytic activity or on gold monolayers for analysis of kinetic interactions by surface plasmon resonance (SPR). Focusing on amino acid positions and chemical features, we first analyzed dephosphorylation of the peptide pTyr residues within the microarrayed library by the human dual-specificity phosphatases (DUSP) DUSP14 and DUSP22, as well as by PTPases from poxviruses (VH1) and Yersinia pestis (YopH). In order to identify the highest affinity oxime motifs, the binding interactions of the most active derivatized phosphopeptides were examined by SPR using noncatalytic PTPase mutants. On the basis of high-affinity oxime fragments identified by the two-step catalytic and SPR-based microarray screens, low-molecular-weight nonphosphate-containing peptides were designed to inhibit PTP catalysis at low micromolar concentrations.

Minimal $W$-Superalgebras and the Modular Representations of Basic Lie Superalgebras

Let $\mathfrak g = \mathfrak g\_\bar 0 + \mathfrak g\_\bar 1$ be a basic Lie superalgebra over $\mathbb{C}$, and $e$ a minimal nilpotent element in $\mathfrak g\_\bar 0$. Set $W\_\chi'$ to be the refined $W$-superalgebra associated with the pair $\mathfrak g,e)$, which is called a minimal $W$-superalgebra. In this paper we present a set of explicit generators of minimal $W$-superalgebras and the commutators between them. In virtue of this, we show that over an algebraically closed field $\mathbb k$ of characteristic $p \gg 0$, the lower bounds of dimensions in the modular representations of basic Lie superalgebras with minimal nilpotent $p$-characters are attainable. Such lower bounds are indicated in \[33] as the super Kac–Weisfeiler property.

On strictly minimal elements w.r.t. preorder relations in set-valued optimization

On strictly minimal elements w.r.t. preorder relations in set-valued optimization

Computing minimal elements of finite families of sets w.r.t. preorder relations in set optimization

Computing minimal elements of finite families of sets w.r.t. preorder relations in set optimization

Minimal Element Selection in the Discernibility Matrix for Attribute Reduction

Discernibility matrix is a beautiful theoretical result to get reducts in the rough set, but the existing algorithms based on discernibility matrix share the same problem of heavy computing load and large store space, since there are numerous redundancy elements in discernibility matrix and these algorithms employ all elements to find reducts. We introduce a new method to compute attribute significance. A novel approach is proposed, called minimal element selection tree, which utilizes many strategies to eliminate redundancy elements in discernibility matrix. This paper presents two methods to find out a minimal reduct for a given decision table based this tree structure. The experimental results with UCI data show that the proposed approaches are effective and efficient than the benchmark methods.