Minimal Degree Research Articles

The Safety and Feasibility of Two-surgeon Technique During Anatomical Laparoscopic Liver Resection

Introduction: Although laparoscopic liver resection(LLR) has the potential advantages such as minimal degree of body wall damage, decreased surgical blood loss, and fewer postoperative complications, it has been associated with a much slower adoption than other laparoscopic procedures. The aim of the study is to assess the impact of

Unified educational space of the EAEU member states

The article deals with the issues of integration of individual national educational systems and the formation of a single Eurasian educational space. The purpose of the article is to assess the degree of readiness of the national higher education systems of the Eurasian Economic Union (EAEU) member states for consistent integration. The assessment was conducted employing the tools of mathematical statistics. At the first stage, the authors formalized the national education system parameters in the form of a scorecard. At the second stage of the study, a comparative analysis of educational systems was carried out based on enlarged groups of quantitative and qualitative indicators. To conduct a comparative analysis of educational systems the authors used comparative logical, descriptive, and cluster analysis methods. According to the analysis results, Armenia and Belarus turned out to be the countries, most close to each other in terms of the totality of qualitative and quantitative indicators of national higher education systems. The conducted analysis allows concluding that Belarus can integrate with other countries most easily. Armenia is ranked the second country capable of such integration. Kazakhstan and Kyrgyzstan are in the third and fourth places, respectively. According to the results of the cluster analysis, Russia has shown a minimal degree of integration of the higher education system with other EAEU countries, as it is the leader in terms of several qualitative and quantitative indicators. The authors have empirically proved that the EAEU member states have similar approaches to the organization of the higher education system and can hypothetically be united into a single educational cluster within a single Eurasian educational space.

The minimal degree standard identity on E ⊗ E

The minimal degree standard identity on E ⊗ E

The rationale for FLEX (cochlear implant) electrode with varying array lengths.

With cochlear implantation (CI) being the standard of care for profoundly deaf cases, more and more patients with low frequency residual hearing are currently being treated with CI. In view of preserving the residual hearing, the ultimate aim of both the surgeons and the CI companies is to achieve zero-degree of electrode insertion trauma. Variations in the size and shape of cochlea, cross-sectional dimensions of ST, electrode insertion techniques with and without metal stylet rod and the experience level of the operating surgeons, all play a role in the electrode array related insertion trauma. An effective electrode design must include flexible array to accommodate the cochlear shape variation, electrode with variety of array lengths to support the concept of cochlear size specific electrode array and finally smaller cross-sectional dimensions of electrode array in matching the cross-sectional dimensions of ST. As per published reports, FLEX electrode array design offers minimal degree of electrode insertion trauma along with the possibility of patient specific electrode array length matching their cochlear size. Looking at the cross-sectional dimensions of FLEX electrode array along with its volume, it appear to be highly safe to the cochlea by not taking too much volume inside the ST. To offer additional support, otological pre-planning software tool like OTOPLAN is now clinically available in measuring the cochlear size in finding the best electrode array match along with the possibilities of anatomy based post-operative speech processor fitting.

Kr-factors in graphs with low independence number

A classical result by Hajnal and Szemerédi from 1970 determines the minimal degree conditions necessary to guarantee for a graph to contain a Kr-factor. Namely, any graph on n vertices, with minimum degree δ(G)≥(1−1r)n and r dividing n has a Kr-factor. This result is tight but the extremal examples are unique in that they all have a large independent set which is the bottleneck. Nenadov and Pehova showed that by requiring a sub-linear independence number the minimum degree condition in the Hajnal-Szemerédi theorem can be improved. We show that, with the same minimum degree and sub-linear independence number, we can find a clique-factor with double the clique size. More formally, we show for every r∈N and constant μ>0 there is a positive constant γ such that every graph G on n vertices with δ(G)≥(1−2r+μ)n and α(G)<γn has a Kr-factor. We also give examples showing the minimum degree condition is asymptotically best possible.

Minimal solutions of the rational interpolation problem

We explore connections between the approach of solving the rational interpolation problem via resolutions of ideals and syzygies, and the standard method provided by the Extended Euclidean Algorithm (EEA). As a consequence, we obtain explicit descriptions for solutions of minimal degrees in terms of the degrees of elements appearing in the EEA. This result allows us to describe the minimal degree in a μ-basis of a polynomial planar parametrization in terms of a critical degree arising in the EEA.

Applicability of infectivity assay for the quantification of infectious human adenovirus genotype 5 in UV-irradiated wastewater

AbstractThe use of infectivity assays in domestic wastewater samples is limited because of the concerns around cytotoxicity to host cells, thus, the UV inactivation efficiency of human adenoviruses (HAdVs) in wastewater remains unclear. In this study, a human adenovirus genotype five (HAdV-5) host cell line (A549 cells) was incubated with wastewater at varied dilutions from 1:1.5 to 1:4 (the ratio of wastewater to a mixture of wastewater and the cell culture medium) and the cytotoxicity was assessed by the cell morphology and viability. No change was observed in either cell viability or morphology in comparison with control samples, even at lowest dilution of 1:1.5, indicating the dilution allowed infectivity assays. The minimal degree of dilution to avoid cytotoxicity may differ with different water matrix. Consequently, the technique was applied to quantify spiked HAdV-5 after the UV disinfection of wastewater. A significant increase in UV disinfection efficiency was noted in wastewater and hydroxyl radicals (OH•) produced by the photosensitization of dissolved organic matter were suggested to be responsible for the enhancement. This study indicated that dilution can be a simple solution to avoid cytotoxicity, and UV inactivation may be enhanced in wastewater due to OH• radicals produced by UV radiation.

On the minimal degree of a transitive permutation group with stabilizer a 2-group

Abstract The minimal degree of a permutation group G is defined as the minimal number of non-fixed points of a non-trivial element of G. In this paper, we show that if G is a transitive permutation group of degree n having no non-trivial normal 2-subgroups such that the stabilizer of a point is a 2-group, then the minimal degree of G is at least 2 3 ⁢ n {\frac{2}{3}n} . The proof depends on the classification of finite simple groups.

FINDING THE LIMIT OF INCOMPLETENESS I

AbstractIn this paper, we examine the limit of applicability of Gödel’s first incompleteness theorem ($\textsf {G1}$ for short). We first define the notion “$\textsf {G1}$ holds for the theory $T$”. This paper is motivated by the following question: can we find a theory with a minimal degree of interpretation for which $\textsf {G1}$ holds. To approach this question, we first examine the following question: is there a theory T such that Robinson’s $\mathbf {R}$ interprets T but T does not interpret $\mathbf {R}$ (i.e., T is weaker than $\mathbf {R}$ w.r.t. interpretation) and $\textsf {G1}$ holds for T? In this paper, we show that there are many such theories based on Jeřábek’s work using some model theory. We prove that for each recursively inseparable pair $\langle A,B\rangle $, we can construct a r.e. theory $U_{\langle A,B\rangle }$ such that $U_{\langle A,B\rangle }$ is weaker than $\mathbf {R}$ w.r.t. interpretation and $\textsf {G1}$ holds for $U_{\langle A,B\rangle }$. As a corollary, we answer a question from Albert Visser. Moreover, we prove that for any Turing degree $\mathbf {0}&lt; \mathbf {d}&lt;\mathbf {0}^{\prime }$, there is a theory T with Turing degree $\mathbf {d}$ such that $\textsf {G1}$ holds for T and T is weaker than $\mathbf {R}$ w.r.t. Turing reducibility. As a corollary, based on Shoenfield’s work using some recursion theory, we show that there is no theory with a minimal degree of Turing reducibility for which $\textsf {G1}$ holds.

In what sense should we talk about the perception of other minds?

By means of spontaneous and unconscious imitation, an observer may be able to directly experience the inner states of another person because the observer and the observed share similar neural pathways. This discovery of a common neural basis reveals the correlative mechanisms through which the intentions of others are perceived. While analysing the implications of this discovery, this paper notes that the correlation does not provide a complete explanation of our understanding of other minds. Instead, the correlation comes into play only to a minimal degree. The paper also explores the epistemological characteristic of the knowledge harboured by other minds. That is, as a kind of private knowledge, the experience of other minds can help us arrive at a relatively consistent understanding of others and engage in communication with them through public expression and the description of mental states. However, it is impossible to truly understand other minds because conscious experience in the strict sense resides only in its owner, and the unique qualia emerging inside the subject cannot be directly observed from a third-person perspective. In this sense, the so-called perception of other minds is not suited to seeking a causal explanation of the ways in which others act, but for reading the meanings expressed by them in a given situation.

Addition–deletion results for the minimal degree of logarithmic derivations of hyperplane arrangements and maximal Tjurina line arrangements

We study the change of the minimal degree of a logarithmic derivation of a hyperplane arrangement under the addition or the deletion of a hyperplane and give a number of applications. First, we prove the existence of Tjurina maximal line arrangements in a lot of new situations. Then, starting with Ziegler’s example of a pair of arrangements of $$d=9$$ lines with $$n_3=6$$ triple points in addition to some double points, having the same combinatorics, but distinct minimal degree of a logarithmic derivation, we construct new examples of such pairs, for any number $$d\ge 9$$ of lines, and any number $$n_3\ge 6$$ of triple points. Moreover, we show that such examples are not possible for line arrangements having only double and triple points, with $$n_3 \le 5$$ .

Body dysmorphic disorder in patients with telangiectasias.

Chronic venous disease (CVD) patients can present with a spectrum of clinical manifestations ranging from severe ulcerations, thrombosis, and varicose vein hemorrhage to milder ones such as telangiectasias. Some CVD patients have a minimal degree of telangiectasias that are almost invisible to the physician. In spite of successful treatment of these telangiectasias, there are patients that might insist on continuing treatment, focusing excessive attention on what they perceive to be persistent telangiectasias that, in their opinion, must be removed. In these cases, one might be facing a possible body dysmorphic disorder (BDD) diagnosis. This is a multicentric study performed in 223 patients with telangiectasias (C1s) seeking treatment; the Body Dysmorphic Disorder Questionnaire (BDDQ) was answered in private by all the patients. Furthermore, each questionnaire was evaluated in accordance with the Diagnostic and Statistical Manual of Mental Disorders (DSM-V) criteria for BDD. From a consecutive sample of 223 patients, 38 patients had criteria for BDD according to the DSM-V; indicating that the prevalence of BDD in patients with telangiectasias is 17%. Telangiectasias can be a stress trigger that changes the way patients perceive their own appearance. BDD patients tend to focus their attention excessively upon these types of veins and demand unnecessary treatment for minimal telangiectasias in order to diminish their discomfort with their physical appearance. Body dysmorphic disorder occurs in patients with limbs with C1s disease in considerable proportion and, upon evaluation, these patients should be referred to a psychiatrist. The initiation of any treatment for telangiectasias prior to the psychiatric assessment should be avoided.

ON UNRAMIFIED SOLVABLE EXTENSIONS OF SMALL NUMBER FIELDS

AbstractWe investigate unramified extensions of number fields with prescribed solvable Galois group G and certain extra conditions. In particular, we are interested in the minimal degree of a number field K, Galois over $\mathbb {Q}$ , such that K possesses an unramified G-extension. We improve the best known bounds for the degree of such number fields K for certain classes of solvable groups, in particular for nilpotent groups.

Bounds for finite semiprimitive permutation groups: order, base size, and minimal degree

AbstractIn this paper, we study finite semiprimitive permutation groups, that is, groups in which each normal subgroup is transitive or semiregular. These groups have recently been investigated in terms of their abstract structure, in a similar way to the O'Nan–Scott Theorem for primitive groups. Our goal here is to explore aspects of such groups which may be useful in place of precise structural information. We give bounds on the order, base size, minimal degree, fixed point ratio, and chief length of an arbitrary finite semiprimitive group in terms of its degree. To establish these bounds, we study the structure of a finite semiprimitive group that induces the alternating or symmetric group on the set of orbits of an intransitive minimal normal subgroup.

Webs of rational curves on real surfaces and a classification of real weak del Pezzo surfaces

We classify webs of minimal degree rational curves on surfaces and give a criterion for webs being hexagonal. In addition, we classify Neron-Severi lattices of real weak del Pezzo surfaces. These two classifications are related to root subsystems of E8.

Phenotype-dependent habitat choice is too weak to cause assortative mating between Drosophila melanogaster strains differing in light sensitivity.

Matching habitat choice is gaining attention as a mechanism for maintaining biodiversity and driving speciation. It revolves around the idea that individuals select the habitat in which they perceive to obtain greater fitness based on a prior evaluation of their local performance across heterogeneous environments. This results in individuals with similar ecologically relevant traits converging to the same patches, and hence it could indirectly cause assortative mating when mating occurs in those patches. White-eyed mutants of Drosophila fruit flies have a series of disadvantages compared to wild type flies, including a poorer performance under bright light. It has been previously reported that, when given a choice, wild type Drosophila simulans preferred a brightly lit habitat while white-eyed mutants occupied a dimly lit one. This spatial segregation allowed the eye color polymorphism to be maintained for several generations, whereas normally it is quickly replaced by the wild type. Here we compare the habitat choice decisions of white-eyed and wild type flies in another species, D. melanogaster. We released groups of flies in a light gradient and recorded their departure and settlement behavior. Departure depended on sex and phenotype, but not on the light conditions of the release point. Settlement depended on sex, and on the interaction between phenotype and light conditions of the point of settlement. Nonetheless, simulations showed that this differential habitat use by the phenotypes would only cause a minimal degree of assortative mating in this species.

Consequence of two protocols and energy doses of low-level laser therapy on the rate of orthodontic canine retraction: A prospective clinical evaluation

Objective: This study aimed to determine whether orthodontically moved maxillary canines exposed to two different protocols and dosage of LLLT exhibited differences in amount and rate of tooth movement. Materials and Methods: Fifteen patients, 12 females and 3males, with mean age of 17.48 ± 2.95 years were included. They had a clinical indication for bilateral extraction of first maxillary premolars. Using a split mouth design, maxillary left and right sides were randomly divided into two groups. In group 1, LLLT delivered at 10 points; 5 from buccal and 5 from palatal aspects with total dose of 8 J/session. In group II, laser applied from buccal side only at 5 points with dose of 4 J per session. In both protocols, gallium aluminum-arsenide diode laser applied in continuous mode with 635 nm, 100 mW, 25 J/cm2, 8 seconds/ point, 0.8 J/point. Amount and rate of maxillary canine retraction and degree of anchorage loss were determined by intraoral and three-dimensional digital models measurements. Results: Clinical and model evaluations demonstrated no significant difference (p˃ 0.05) between both groups. After 24 weeks, total amounts of canine retraction were 6.86±1.60 mm and 6.65±1.59 mm in group I and group II, respectively. Moreover, anchorage loss displayed -0.35 mm ± 0.18 mm in group I and -0.44 mm± 0.24 mm in group II. Conclusion: With the current settings, both protocols and energy doses of LLLT accomplished comparable amount and rate of maxillary canine retraction. Additionally, they displayed an equivalent minimal degree of anchorage loss.

Dermo-Fascial Suspension in Mastopexy for Improvement of Aesthetic Outcomes

Background: Mastopexy is the art of restoring breastvolume and its youthful appearance.Aim: We present a surgical technique for simultaneousmastopexy using auto-augmentation by superiorly baseddermoglandular flap. In addition, we use two dermo-facialflaps to support the breast tissue in high position to restoreand maintain central mound projection and elevate inframammaryfold.Patients and Methods: Auto-augmentation mastopexywas performed for 36 patients using vertical superior pedicledeepithelialized dermoglandular flap that inserted beneaththe breast tissue. Two opposing dermo-facial flaps based onmedial and lateral pillars along the vertical line were used tosupport the deepithelialized dermoglandular tissue that suturedto anterior chest wall and to each other.Results: During follow-up period there was no bottomingout of breast tissues or other major adverse effects except formild asymmetry in early 3 patients and patients showed highrate of satisfaction by the results. The results confirmed thatthis technique corrects ptosis while increasing the projectionand apparent volume of the breast and keep inframammaryfold (IMF) in high position with minimal degree of descendwhich is parallel to that of the nipple.Conclusion: The combined use of dermo-fascial flap tosupport the glandular tissue with auto-augmentation mastopexyimproves the shape; projection and contour of the breast andit also help to have long lasting results. The advantage of thetechnique is that it optimizes the shape and volume of thebreast and creating a narrow breast base with a new highinframammary fold without the use of an implant. With thistechnique recurrent breast ptosis can be minimized aftermastopexy procedures.Evidence Based Medicine: Level IV, case series.

Representing stand-alone automata by characteristic polynomials over a finite field

This paper proposes a method of representing a deterministic stand-alone output automaton by a minimal characteristic polynomial over a finite field. It is shown that defining various automaton transition and output functions allows using the algorithm developed to build the sets of minimal polynomials, different in their powers. Estimates of the relevant sets are given here. We have identified the relation between a characteristic minimal polynomial and an ergodic stochastic matrix defining the sequence developed by a stand-alone automaton. It is shown that the minimal degree of a characteristic polynomial depends linearly on the power of the automaton state set and on the accuracy of representing the elements of a given limiting vector of a stochastic matrix.

New Bounds for the α-Indices of Graphs

Let G be a graph, for any real 0≤α≤1, Nikiforov defines the matrix Aα(G) as Aα(G)=αD(G)+(1−α)A(G), where A(G) and D(G) are the adjacency matrix and diagonal matrix of degrees of the vertices of G. This paper presents some extremal results about the spectral radius ρα(G) of the matrix Aα(G). In particular, we give a lower bound on the spectral radius ρα(G) in terms of order and independence number. In addition, we obtain an upper bound for the spectral radius ρα(G) in terms of order and minimal degree. Furthermore, for n&gt;l&gt;0 and 1≤p≤⌊n−l2⌋, let Gp≅Kl∨(Kp∪Kn−p−l) be the graph obtained from the graphs Kl and Kp∪Kn−p−l and edges connecting each vertex of Kl with every vertex of Kp∪Kn−p−l. We prove that ρα(Gp+1)&lt;ρα(Gp) for 1≤p≤⌊n−l2⌋−1.