2-step Groups Research Articles

Оптимальные оценки количества звеньев базисных горизонтальных ломаных для 2-ступенчатых групп Карно с горизонтальным распределением коранга 1

For a 2-step Carnot group D_n, "dim" D_n=n+1, with horizontal distribution of corank 1, we proved that the minimal number N_(X_(D_n ) ) such that any two points u,v∈D_n can be joined by some basis horizontal k-broken line (i.e. a broken line consisting of k links) L_k^(X_(D_n ) ) (u,v), k≤N_(X_(D_n ) ), does not exeed n+2. The examples of D_n such that N_(X_(D_n ) )=n+i, i=1,2. were found. Here X_(D_n )={X_1,…,X_n} is the set of left invariant basis horizontal vector fields of the Lie algebra of the group D_n, and every link of L_k^(X_(D_n ) ) (u,v) has the form "exp"(asX_i)(w), s∈[0,s_0], a=const.

About coincidence points theorems on 2-step Carnot groups with 1-dimensional centre equipped with Box-quasimetrics

<abstract><p>For some class of 2-step Carnot groups $ D_n $ with 1-dimensional centre we find the exact values of the constants in $ (1, q_2) $-generalized triangle inequality for their $ \text{Box} $-quasimetrics $ \rho_{\text{Box}_{D_n}} $. Using this result we get the best version of the Coincidence Points Theorem of $ \alpha $-covering and $ \beta $-Lipschitz mappings defined on $ (D_n, \rho_{\text{Box}_{D_n}}) $.</p></abstract>

Effects of Different Centrifugation Protocols on the Detection of EGFR Mutations in Plasma Cell-Free DNA.

ObjectivesVarious preanalytical factors, including the collection tube, storage conditions, and centrifugation, affect the detection results of plasma cell-free DNA (cfDNA). We compared the effect of different centrifugation protocols on the detection of EGFR mutations in cfDNA.MethodsWe analyzed 117 plasma specimens from 110 patients with non–small cell lung cancer using the cobas EGFR Mutation Test v2 (Roche Diagnostics). We compared the identified EGFR mutations and semiquantitative index values from the 1- and 2-step centrifugation groups and confirmed the clinical impact of differences in the results after further high-speed centrifugation.ResultsWe detected EGFR mutations in 44 (37.6%) and 47 (40.2%) samples that were centrifuged once and twice, respectively; the 2 groups showed an 89.7% (105/117) concordance and a strong correlation in their semiquantitative index values (r = 0.929). Among the 12 inconsistent result pairs, 9 samples of 2-step centrifugation (75%) were consistent with the results of a recent tissue biopsy.ConclusionsAdditional high-speed centrifugation has been shown to increase the sensitivity of EGFR mutation detection in a commercial in vitro diagnostic real-time polymerase chain reaction device and is an optimal preanalytical factor for detecting low-allele frequency gene mutations using low concentrations of cfDNA.

On finding the exact values of the constant in a $(1,q)$-generalized triangle inequality for Box-quasimetrics on 2-step Carnot groups with 1-dimensional center

On finding the exact values of the constant in a $(1,q)$-generalized triangle inequality for Box-quasimetrics on 2-step Carnot groups with 1-dimensional center

1170 One-step deflation of bakri intrauterine balloon tamponade is not associated with increased blood loss

Postpartum hemorrhage (PPH) is a leading cause of maternal mortality. Bakri intrauterine balloon tamponade (IBT) for refractory hemorrhage decreases morbidity, need for additional surgery, and blood loss; however, the most effective deflation method is unknown. We aimed to determine if 1-step compared to serial deflation of the IBT is associated with less blood loss after removal. Retrospective cohort study of patients with PPH who received IBT from January 2012 to August 2020 at a single institution. Patients were excluded if the IBT remained in place for fewer than 2 hours. The primary exposure was deflation method: 1-step (removed in 1 pass) or serial (in >1 pass). The primary outcome was estimated blood loss (EBL) from the initiation of IBT deflation to discharge. Secondary outcomes included clinically estimable blood loss (≥200 mL) after IBT deflation, need for additional interventions, postpartum fever and endometritis. 279 patients received an IBT which remained in place for ≥2 hours following PPH. The IBT was deflated in a single pass (1-step) in 112 (40%) and serially in 167 (60%). Baseline characteristics and pre-IBT hemorrhage were similar, except the serial group had less pre-existing hypertension, less labor augmentation with oxytocin, more multiple gestations, and higher EBL prior to IBT placement (Table 1). EBL after starting IBT deflation was greater in the 1-step group (42±294 mL 1-step vs 28±48 mL serial, p <0.001). There was no difference in rate of clinically significant EBL (2.7% 1-step vs 2.4% serial, p = 1.0), including after adjusting for pre-IBT EBL and other baseline characteristics. No difference was seen in need for additional interventions. Rates of postpartum fever (29% vs 32%, p=0.57) and endometritis (11% vs 17%, p=0.18) were not different based on 1-step vs serial deflation, respectively (Table 2). Patients with PPH whose IBT was deflated all at once did not have more post-IBT blood loss compared to those deflated serially, nor was there any difference in rate of need for additional interventions.View Large Image Figure ViewerDownload Hi-res image Download (PPT)

Comparison of Pregnancy Prognosis for Gestational Diabetes Diagnosed by the 1-Step and 2-Step Methods

Purpose: To compare pregnancy complications between the 2 groups of patients with gestational diabetes mellitus (GDM): those diagnosed by the 1-step method and those diagnosed by the 2-step method.Methods: In this retrospective cohort study, the data from outpatient and hospitalization medical records of 201 patients diagnosed with GDM between 2013 and 2017 were reviewed. We compared the pregnancy complications of these patients based on whether they were diagnosed by the 1-step or 2-step method. SPSS ver. 20.0 was used to analyze the data from the 2 groups. The odds ratio and 95% confidence interval of the pregnancy outcomes were estimated using binary logistic regression analysis.Results: On comparing pregnancy-related complications between the groups, there was no significant difference in the incidence of preeclampsia or delivery by cesarean section (p&gt;0.99 and p=0.50, respectively). In the 1-step and 2-step groups, the prevalence of premature birth was significantly high at 19.7 % and 40.3% (p=0.01), respectively. There were no significant differences between the 2 groups in terms of macrosomia, large for gestational age (LGA), small for gestational age (SGA), low APGAR score, and neonatal hypoglycemia (p&gt;0.99, p&gt;0.26, p&gt;0.62, p&gt;0.57, and p&gt;0.45, respectively).Conclusion: On comparing the 2 groups, we found that the 1-step and 2-step GDM groups had similar risks of pregnancy complications, namely preeclampsia, delivery by cesarean section, macrosomia, LGA, SGA, low APGAR scores, and neonatal hypoglycemia.

CAD/CAM-fabricated inlay restorations: Can the resin-coating technique improve bond strength and internal adaptation?

This study assessed the effect of the resin-coating technique on the bond strength and internal adaptation of computer-aided design/computer-aided manufacturing (CAD/CAM)-fabricated inlays. Seventy-two mesio-occlusal-distal (MOD) cavities were prepared and distributed into 3 groups according to the resin-coating technique utilized: uncoated group, G-Premio Bond (1-step) group, and Clearfil SE Bond 2+Clearfil Majesty ES Flow (2-step+Flow) group. The MOD inlays were fabricated and cemented with RelyX Ultimate (RXU), G-CEM LinkForce (LinkForce), or Panavia V5 (PV5). After 5,000 thermal cycles, each specimen was sectioned and subjected to microtensile bond strength (MTBS) testing and an internal adaptation evaluation. For the uncoated group, RXU exhibited higher MTBS than LinkForce and PV5 (p<0.05). The MTBS of all 1-step and 2-step+Flow groups was greater than 30 MPa. Resin coating did not influence the MTBS of RXU, whereas resin coating increased the MTBS of LinkForce and PV5. More than 95% gap-free margins were found in all groups.

Sleeve gastrectomy as a rescue of failed gastric banding: comparison of 1- and 2-step approaches.

Series comparing gastric banding (GB) removal and sleeve gastrectomy (SG) when procedures are performed as a 1- or a 2-step approach are contradictory in their outcomes. No series comparing these approaches with midterm weight loss is available. Compare the outcomes and weight loss of SG performed as 1- and 2-step approaches as a revisional procedure for GB failure. University Hospital, France, public practice. Between February 2006 and January 2017, all patients undergoing SG with a previous history of implementation of GB (n = 358) were included in this 2-center, retrospective, observational study. Revisional surgery was proposed in patients with insufficient excess weight loss (excess weight loss ≤50%) or weight regain after GB. A 1-step (1-step group, n = 270) or 2-step (2-step group, n = 88) approach was decided depending on patient's choice and/or surgeon's preference. The primary efficacy endpoint was the comparison of weight loss in the 1- and 2-step groups at the 2-year follow-up. The secondary efficacy endpoints were short-term outcomes (overall mortality and morbidity at postoperative day 30, specific morbidity, reoperation, length of hospital stay, and readmission). In the 1-step group, the mean preoperative body mass index before SG was 40.5 kg/m2 (27.0-69.0), while in the 2-step group, the mean preoperative body mass index was 43.5 kg/m2 (31.5-61.7). Mean operating time was 109 minutes (50-240) in the 1-step group and 78.7 minutes (40-175) in the 2-step group (P = .22). In the 1-step group, 6 conversions to laparotomy occurred, while in the 2-step group, 2 conversions to laparotomy occurred (P = .75). One death (.2%, in the 2-step group) and 39 complications (30 in the 1-step group [11.1%] and 9 in the 2-step group [10.2%]) also occurred. The mean length of hospital stay was 6.2 days in the 1-step group and 4.1 days in the 2-step group. At 2-year follow-up, mean body mass index was 32.4 kg/m2 in the 1-step group and 33.2 kg/m2 in the 2-step group (P = .15), representing excess weight losses of 61.9 and 50.1 (P = .05), respectively. The rates of revisional surgery were .7% and 2.2%, respectively. SG after previous GB is efficient with similar outcomes depending on the 1- or 2-step approach. The 1-step approach seems to have increased weight loss compared with the 2-step approach.

A Role-Play-Based Tutor Training in Preservice Teacher Education for Developing Procedural Pedagogical Content Knowledge by Optimizing Tutor–Student Interactions in the Context of an Outreach Lab

ABSTRACTTo meet the requirements of students’ cooperative learning, our quasi-experimental study addresses how preservice teachers (PSTs), as a component of their procedural pedagogical content knowledge (PCK), might develop more adequate tutor–student interactions during students’ experimentation. Applying the assignment-assistance tutoring model, we combined biology PSTs’ education with our high school students’ outreach program, Genetic Fingerprinting. We developed a role-play-based tutor training in a 2-step (role play and group discussion) and in a 3-step variant (role play, group discussion, and an additional assignment exercise). We audiotaped and transcribed all PST-tutored experimental phases of one control group (without training) and our two training groups. We categorized 2,865 tutor–student interactions content-analytically regarding adequacy in potentially supporting students’ promotive interaction as a core condition of cooperative learning. We examined the PST interaction patterns identified. Our tutor-trained PSTs, especially those who received 3-step training, showed less inadequate tutor–student interactions compared with control group PSTs. Cluster-analytically extracted intervening interaction types were found only in the control group and the rule-complying type dominated the 3-step group. We discuss our training as an effective approach to develop tutor–student interactions as a component of procedural PCK that is part of PSTs’ initial professional development.

An existence and uniqueness result for the Navier–Stokes type equations on the Heisenberg group

The aim of this paper is to give an existence and uniqueness of solutions for the Cauchy problem of the Navier–Stokes type equations associated to the sublaplacian provided by the left invariant vector fields on the Heisenberg group. To avoid the difficulty of the non-commutative which is intrinsic in 2-step stratified Lie groups, we construct the solenoidal space by using the right invariant vector fields on the Heisenberg group.

PS01.174: AN EXAMINATION OF OUTCOMES AFTER ANTE-THORACIC ROUTE WITH RIGHT HEMICOLON RECONSTRUCTION AFTER ESOPHAGECTOMY.

Abstract Background In our institute, we usually use gastric tube for reconstruction organ after esophagectomy. When we can’t use gastric tube, we use right hemi-colon with ante-thoracic route. Previously, we reconstructed by 1-step after esophagectomy, but from 2012, we have done by 2-step for reduce postoperative complications. Methods We enrolled 15 esophageal cancer patients who underwent esophagectomy and right hemicolon reconstruction between April 2004 and December 2016. Results The average age of 15 patients is 67.3. The reasons of using right hemicolon are as follows; post gastrectomy 13, stomach double cancer 2. The reasons of gastrectomy are as follows; gastric cancer 8, duodenum cancer 1, gastric ulcer 4. The average duration from gastrectomy to esophagectomy is 12.5 year. We reconstructed by 1-step for 5 patients, and after 2012, we reconstructed by 2-step for 10 patients. Anastomotic leakages were found in 2 cases (40.0%) in 1-step reconstruction group, and 3 cases (20.0%) in 2-step reconstruction group. In 1-step reconstruction group, 1 case occurred multiple anastomotic leakages and DIC, and another 1 case was found necrosis of reconstructive colon. In 2-step reconstruction group, we found 1 case of major leakage and 1 case of recurrent nerve paralysis and 2 cases of postoperative pneumonia. However, there were no case of tracheotomy. The incidence of pneumonia did not differ between the two groups. And the term of postoperative oral intake tend to shorter in 2-step reconstruction group (P = 0.06). 2 severe postoperative complications (Clavian-Dindo V or IVa) cases were found in 1-step reconstruction group, on the other hand, 2 cases severe complications (CD IIIa) in 2-step reconstruction group. Conclusion In the case of using right hemicolon as a reconstructive organ, 2-step reconstruction approach is useful and superior from the viewpoints of postoperative complications. Disclosure All authors have declared no conflicts of interest.

Treatment efficiency and stability of skeletal Class III malocclusion with a surgery-first approach.

To compare treatment duration in skeletal Class III malocclusion patients managed with a 2-step treatment (surgery-first approach, SFA) and conventional 3-step treatment, and to compare stability of surgical outcomes between segmentation and non-segmentation in the 2-step treatment group. The sample population consisted of 37 patients who completed orthognathic surgery (OGS) and orthodontic correction at the Charm Aesthetic Surgery Clinic (Taipei, Taiwan) between 2012 and 2015. Of these, 26 received 2-step treatment and 11 received 3-step treatment. To compare treatment efficiency and stability, three time points were analysed: T0 , before treatment (before OGS in the 2-step group and before orthodontic treatment in the 3-step group); T1 , after OGS but before orthodontic correction (cone beam computed tomography (CBCT) was obtained within 2weeks of OGS); and T2 , after orthodontic correction (CBCT was obtained on the day of bracket removal). The post-OGS (T1 ) CBCT items were individually superimposed on the pre-treatment (T0 ) CBCT items to determine the distance of B point migration. A significant difference was found in treatment times between 2-step treatment and conventional 3-step treatment. In addition, no significant difference was found when comparing B-X (mm) and B-Y (mm) at T2 -T1 for the segmentation and non-segmentation groups. Using SFA for skeletal Class III malocclusions saves approximately 6months of treatment time over 3-step treatment; the stability of the segmentation group was comparable to that of the non-segmentation group, a result that is possibly associated with the fixation of 2 miniplates.

A retrospective study comparing outcomes in a midwestern US population after introduction of IADPSG guidelines for gestational diabetes

Objective: More evidence is required to endorse the 1-step approach for gestational diabetes mellitus (GDM) for clinical practice. Since 2010, our department has pragmatically allowed faculty to self-select the guidelines they use to screen and diagnose GDM. We sought to compare the maternal and neonatal outcomes from these two simultaneous cohorts. Study design: We performed a retrospective cohort study of all singleton pregnancies delivered between October 2011 and –November 2013 at our hospital. Patients were excluded if they had preexisting diabetes, were not screened or screened inappropriately, or their fetus had congenital anomalies. Patients were grouped by their screening strategy, and maternal and neonatal outcomes were analyzed. Results: The 1-step group had a higher incidence of GDM (21.6% versus 5.0%). Initial results suggested higher rates of neonatal hypoglycemia, phototherapy for hyperbilirubinemia, and a lower rate of gestational HTN. After adjustment, these differences disappeared, but a lower rate of large for gestational age (LGA) infants was discovered (adjusted odds ratios (aOR) 0.78). Conclusion: The picture remains unclear as to whether the 1-step approach is associated with significantly improved outcomes compared with the 2-step approach. We did find a lower risk for a LGA infant in our 1-step cohort, but it is unlikely that the 1-step approach would be cost-effective due to the absence of other improved outcomes.

Rigidity of 2-Step Carnot Groups

In the present paper, we study the rigidity of 2-step Carnot groups, or equivalently, of graded 2-step nilpotent Lie algebras. We prove the alternative that depending on bi-dimensions of the algebra, the Lie algebra structure makes it either always of infinite type or generically rigid, and we specify the bi-dimensions for each of the choices. Explicit criteria for rigidity of pseudo H- and J-type algebras are given. In particular, we establish the relation of the so-called $$J^2$$ -condition to rigidity, and we explore these conditions in relation to pseudo H-type algebras.

Vanishing of cohomology and parameter rigidity of actions of solvable Lie groups

We give a sufficient condition for parameter rigidity of actions of solvable Lie groups, by vanishing of (uncountably many) first cohomologies of the orbit foliations. In some cases, we can prove that vanishing of finitely many cohomologies is sufficient. For this purpose we use a rigidity property of quasiisometry. As an application we prove some actions of 2-step solvable Lie groups on mapping tori are parameter rigid. Special cases of these actions are considered in a paper of Matsumoto and Mitsumatsu. We also remark on the relation between transitive locally free actions of solvable Lie groups and lattices in solvable Lie groups, and apply results in rigidity theory of lattices in solvable Lie groups to construct transitive locally free actions with some properties.

A randomized controlled trial of the effect of 2-step orthosis treatment for a mallet finger of tendinous origin

Study DesignA randomized clinical trial, with patients treated either by new 2-step orthosis or by the figure–eight-type orthosis with the distal interphalangeal (DIP) joint extended. Purpose of the StudyTo report on our new orthosis and to evaluate the treatment efficacy of using a 2-step orthosis for the treatment of a mallet finger of tendinous origin compared with a conventional orthosis. MethodsForty-four patients were randomized into the 2-step or conventional orthosis groups. Primary outcomes were active DIP joint flexion and extensor lag, pain, and the Abouna–Brown criteria. ResultsThe 2-step orthosis was associated with a smaller active DIP extensor lag, compared with the conventional orthosis (−7.5 ± 4.5° vs −16.4 ± 6.9°, P = .001), combined with a significantly higher Abouna–Brown criteria (χ2 = 14.57, P = .01). No other between-group differences were identified. ConclusionThe therapeutic effectiveness of the 2-step orthosis, over a conventional orthosis, was supported by a large effect size of the treatment in improving residual active extensor lag at the DIP and overall Abouna–Brown criteria. Our study thus suggested that the initial immobilization involved in new 2-step orthosis and is thus a good immobilization technique. Level of EvidenceIb.

Rigidity of quasiconformal maps on Carnot groups

AbstractWe show that quasiconformal maps on many Carnot groups must be biLipschitz. In particular, this is the case for 2-step Carnot groups with reducible first layer. These results have implications for the rigidity of quasiisometries between negatively curved solvable Lie groups.

Spectral multipliers on 2-step groups: topological versus homogeneous dimension

Let $G$ be a $2$-step stratified group of topological dimension $d$ and homogeneous dimension $Q$. Let $L$ be a homogeneous sub-Laplacian on $G$. By a theorem due to Christ and to Mauceri and Meda, an operator of the form $F(L)$ is of weak type $(1,1)$ and bounded on $L^p(G)$ for all $p \in (1,\infty)$ whenever the multiplier $F$ satisfies a scale-invariant smoothness condition of order $s > Q/2$. It is known that, for several $2$-step groups and sub-Laplacians, the threshold $Q/2$ in the smoothness condition is not sharp and in many cases it is possible to push it down to $d/2$. Here we show that, for all $2$-step groups and sub-Laplacians, the sharp threshold is strictly less than $Q/2$, but not less than $d/2$.

One or two steps for laparoscopic conversion of failed adjustable gastric banding to sleeve gastrectomy: a nationwide French study on 3357 morbidly obese patients

BackgroundAdjustable gastric banding (AGB) has been a very common bariatric procedure, but long-term AGB related complications have led to an increased number of second procedures. Sleeve gastrectomy (SG) is one option and can be done as a 1- or 2-step procedure. ObjectivesTo compare the 1-step and 2-step approachs of conversion of AGB to SG with respect to postoperative mortality and morbidity. SettingNationwide study, France. MethodsAll morbidly obese patients who underwent AGB followed by SG in France between 2007 and 2012 were included. Multivariate analyses were conducted using the French National Health Service Database data to ascertain predictive factors for 90-day postoperative mortality and morbidity. ResultsThere were 2061 and 1296 patients in the 1-step and 2-step conversion groups, respectively. The readmission rate was 22.8% and 16.5% in the 1- and 2-step groups, respectively (P<.001). More patients required an intensive care unit stay in the 1-step group (11.7 % versus 6.7%; P<.001). The 90-day mortality was .1%, with no difference between the 2 groups (1% versus .08%). The complication rate was 14.7% (1-step 15.9% versus 2-step 12.7%; P = .009). The timing of AGB removal (P = .02), patient age 50–60 years (P = .004), hypertension (P = .01), surgical approach (P = .002), and hospital status (P = .015) were significantly associated with the complication rate. ConclusionThis study indicates that the 2-step conversion of failed AGB to SG results in a significantly reduced rate of postoperative staple line leaks, gastric tube stricture, respiratory complication, and need for intensive care unit stay.

A 24-Week, Randomized, Controlled Study to Evaluate the Tolerability, Safety and Efficacy of 2 Different Titration Schemes of the Rivastigmine Patch in Japanese Patients with Mild to Moderate Alzheimer's Disease

Aim: To investigate whether 1-step titration of the rivastigmine patch (initiated at 5 cm² and titrated to 10 cm² after 4 weeks) is well tolerated in Japanese patients with Alzheimer's disease (AD) as compared to 3-step titration (initiated at 2.5 cm² and titrated by 2.5 cm² every 4 weeks to 10 cm²). Methods: A 24-week, multicenter, randomized, double-blind study was conducted in Japan between July 2012 and May 2014. Patients with mild to moderate AD aged 50-85 years were randomized 1:1 to 1-step or 3-step titration of the rivastigmine once-daily patch. The primary endpoint was the proportion of patients with adverse events leading to discontinuation. Results: Of 216 patients randomized, 215 (1-step, n = 107; 3-step, n = 108) were included in the safety analysis. The primary endpoint outcome was 15.0% in the 1-step group and 18.5% in the 3-step group. The observed treatment difference was −3.6% (95% confidence interval: −17.0, 9.6), falling within the prespecified acceptance range. Conclusion: The tolerability of two different titration schemes was similar in Japanese patients with AD.