Periodic Points Research Articles

Comparison of rostral facet joint violations in robotic- and navigation-assisted pedicle screw placement for adult lumbar spine instrumentation

BACKGROUND CONTEXTFacet joint violation by pedicle screws may lead to adjacent-segment disease and postoperative pain. Previous studies have reported the incidence of rostral facet joint violation using various pedicle screw insertion techniques. However, the incidence of facet joint violations with robotic guidance has not been determined. PURPOSETo investigate and compare the incidence of rostral facet joint violation by pedicle screws under robotic guidance and computerized tomography (CT) navigation guidance. STUDY DESIGN/SETTINGRetrospective matched cohort. PATIENT SAMPLEAll patients who underwent robotic-assisted lumbar fusion at a major spine center up until 2023 were retrospectively identified and matched 1:3 to patients undergoing CT navigation guidance based by on age, sex, rostral vertebral level, and length of construct. Inclusion criteria consisted of age greater than 18 years, bilateral pedicle screw fixation, and presence of a postoperative CT scan of the lumbar spine or abdomen/pelvis at any point in the post-operative period. OUTCOME MEASURESRostral facet joint violations. METHODSDescriptive statistics were used to compare cohorts: frequencies, chi-squared analysis for categorical variables, and t-test for continuous variables. RESULTSA total of 408 rostral pedicle screws were implanted in 204 patients (Robot: 102; Navigation: 306). Overall, 13 (12.3%) rostral facet joint violations were observed in the robot cohort and 75 (24.5%) in the navigation cohort (p=.01). Specifically, fewer robotic violations were observed at the L2 (3.5% vs. 32.1%, p=.003) and L3 levels (3.9% vs. 18.1%, p=.08) compared to navigation. No difference was observed at L4 and L5. Bilateral violations are significantly reduced with robotic approaches (5.3% vs. 14.4%, p=.03). Lastly, more facet joint violations were observed during open approaches (robot: 18.8%, navigation: 27.3%) than percutaneous approaches (robot: 11.6%, navigation: 7.1%) in both groups (p<.001). The rate of L4 facet violations was 18.8% in the robotic cohort and 27.3% in the navigation cohort. The rate of L5 facet violations was 31.3% in the robotic cohort and 29.2% in the navigation cohort. CONCLUSIONSUse of robotic assistance in lumbar pedicle screws significantly reduced the rate of rostral facet joint violations compared to navigation guidance at L2 and L3 levels, but not at L4 and L5, with facet violations approaching nearly one-third of the patients at L5 screws. Rostral facet violations can play a significant role in adjacent segment degeneration and disease. Technical factors and trajectory issues likely play a role and addressing these components should minimize unintended facet violation and proximal adding on.

The research of mean equicontinuity, mean sensitivity, and shadowing property

We study the dynamical properties of mean equicontinuity, mean sensitivity, tracking property, and periodic points set in the hyperspace of uniform space. Let (Y,ξ) be uniform space, T:Y→Y be uniformly continuous and (C(Y),Cξ) be hyperspace of (Y,ξ).Then, we can get some conclusions: (a) T is mean equicontinous if and only if the induced map CT is mean equicontinous; (b) if the induced map CT is mean sensitive, then T is mean sensitive; (c) the induced map CT has tracking property implying that T has tracking property; (d) P(T) is dense in Y implying that P(CT) is dense in C(Y). In addition, we also study dynamical property of (G,h)− tracking property in metric G− space, and prove that if the map T has (G,h)− tracking property, then, for any k>1, the map Tk has (G,h)− tracking property.

Periodic points and arithmetic degrees of certain rational self-maps

Consider a cohomologically hyperbolic birational self-map defined over the algebraic numbers, for example, a birational self-map in dimension two with the first dynamical degree greater than one, or in dimension three with the first and the second dynamical degrees distinct. We give a boundedness result about heights of its periodic points. This is motivated by a conjecture of Silverman for polynomial automorphisms of affine spaces. We also study the Kawaguchi–Silverman conjecture concerning dynamical and arithmetic degrees for certain rational self-maps in dimension two. In particular, we reduce the problem to the dynamical Mordell–Lang conjecture and verify the Kawaguchi–Silverman conjecture for some new cases. As a byproduct of the argument, we show the existence of Zariski dense orbits in these cases.

Common fixed-point theorem for commuting maps on a metric space

Several novel uses of theorems for fixed points in commuting mapping in a fully metric domain are presented. Several conclusions from full metric fixed point theory are improved and extended by our work. Our proofs are inspired by the study of commuting mappings [B. Fisher and S. Sessa, on a fixed point theorem of Gregus, 1986] and [P. Sumati Kumari, Fixed and periodic point theory in certain spaces, 2013].

Electronic Health Record–Based Nudge Intervention and Axillary Surgery in Older Women With Breast Cancer

Choosing Wisely recommendations advocate against routine use of axillary staging in older women with early-stage, clinically node-negative (cN0), hormone receptor-positive (HR+), and HER2-negative breast cancer. However, rates of sentinel lymph node biopsy (SLNB) in this population remain persistently high. To evaluate whether an electronic health record (EHR)-based nudge intervention targeting surgeons in their first outpatient visit with patients meeting Choosing Wisely criteria decreases rates of SLNB. This nonrandomized controlled trial was a hybrid type 1 effectiveness-implementation study with subsequent postintervention semistructured interviews and lasted from October 2021 to October 2023. Data came from EHRs at 8 outpatient clinics within an integrated health care system; participants included 7 breast surgical oncologists. Data were collected for female patients meeting Choosing Wisely criteria for omission of SLNB (aged ≥70 years with cT1 and cT2, cN0, HR+/HER2- breast cancer). The study included a 12-month preintervention control period; baseline surveys assessing perceived acceptability, appropriateness, and feasibility of the designed intervention; and a 12-month intervention period. A column nudge was embedded into the surgeon's schedule in the EHR identifying patients meeting Choosing Wisely criteria for potential SLNB omission. The primary outcome was rate of SLNB following nudge deployment into the EHR. Similar baseline demographic and tumor characteristics were observed before (control period, n = 194) and after (intervention period, n = 193) nudge deployment. Patients in both the control and intervention period had a median (IQR) age of 75 (72-79) years. Compared with the control period, unadjusted rates of SLNB decreased by 23.1 percentage points (46.9% SLNB rate prenudge to 23.8% after; 95% CI, -32.9 to -13.8) in the intervention period. An interrupted time series model showed a reduction in the rate of SLNB following nudge deployment (adjusted odds ratio, 0.26; 95% CI, 0.07 to 0.90; P = .03). The participating surgeons scored the intervention highly on acceptability, appropriateness, and feasibility. Dominant themes from semistructured interviews indicated that the intervention helped remind the surgeons of potential Choosing Wisely applicability without the need for additional clicks or actions on the day of the patient visit, which facilitated use. This study showed that a nudge intervention in the EHR significantly decreased low-value axillary surgery in older women with early-stage, cN0, HR+/HER2- breast cancer. This user-friendly and easily implementable EHR-based intervention could be a beneficial approach for decreasing low-value care in other practice settings or patient populations. ClinicalTrials.gov Identifier: NCT06006910.

Stable/unstable holonomies, density of periodic points, and transitivity for continuum-wise hyperbolic homeomorphisms

We discuss different regularities on stable/unstable holonomies of cw-hyperbolic homeomorphisms and prove that if a cw-hyperbolic homeomorphism has continuous joint stable/unstable holonomies, then it has a dense set of periodic points in its non-wandering set. For that, we prove that the hyperbolic cw-metric (introduced in Artigue et al (2024 J. Differ. Equ. 378 512–38)) can be adapted to be self-similar (as in Artigue (2018 Ergodic Theory Dyn. Syst. 38 2422–46)) and, in this case, continuous joint stable/unstable holonomies are pseudo-isometric. We also prove transitivity of cw-hyperbolic homeomorphisms assuming that the stable/unstable holonomies are isometric. In the case the ambient space is a surface, we prove that a cw F -hyperbolic homeomorphism has continuous joint stable/unstable holonomies when every bi-asymptotic sector is regular.

Lunar distress communications: Interoperability, frequencies, and harmful interference, which normative model for the artemis accords?

A new space era begins with the Artemis Accords. These will allow the return of humans to the Moon. The starting point of this historic period was marked by the signing of this international agreement on October 13, 2020. Eight States are at the origin of these accords: the United States of America, Australia, Canada, Italy, Japan, Luxembourg, the United Arab Emirates, and the United Kingdom. Since then, thirteen other governments – including France – have joined this international space program led by NASA. Artemis will require the implementation of a new communication architecture called “LunaNet”, encompassing the search and rescue service known as “LunaSAR”. Therefore, like on Earth, on the Moon, search and rescue of people in distress will require the interoperability of international communications. From a legal point of view, the Artemis Accords are based on existing space law, particularly the 1967 Outer Space Treaty. According to this, Lunar missions shall be conducted for peaceful purposes. Transparency in the implementation of international partnerships is another key principle of this space program. From this, at the operational level, interoperability of the systems based on existing or future standards naturally follows. Beyond the technical or commercial aspects, what takes precedence over all other considerations is the safety of the astronauts working for the completion of the Artemis program. Thus, generally, the possible assistance brought to the astronauts in distress is foreseen in the United Nations treaties and principles on outer space. Regarding the implementation of the Artemis program, personnel will operate on board a spacecraft, a space station, or from the surface of the Moon. This is why NASA plans to implement the Astronaut's Lunar Lifeline, known as Lunar Search and Rescue or LunaSAR. Integrated with the LunaNet system, this system will assist workers in distress. In this study, therefore, we will focus on standards for communications interoperability, in the context of search and rescue of persons in distress. To do so, we will examine the Artemis program through the lens of satellite-assisted Earth search and rescue principles and techniques. In particular, we will focus on the COSPAS-SARSAT alerting service and the International Aeronautical and Maritime Search and Rescue (IAMSAR) Manual. In this context, issues such as, for example, the implementation of the Treaty on Principles Governing the Activities of States in the Exploration and Use of Outer Space, including the Moon and Other Celestial Bodies of 1967, the Agreement on the Rescue of Astronauts, the Return of Astronauts and the Return of Objects Launched into Outer Space of 1968 and the Agreement Governing the Activities of States on the Moon and Other Celestial Bodies of 1979 as well as the protection of SAR frequencies and potential harmful interference will be addressed.

Chaotic dynamics of a continuous and discrete generalized Ziegler pendulum

We present analytical and numerical results on integrability and transition to chaotic motion for a generalized Ziegler pendulum, a double pendulum subject to an angular elastic potential and a follower force. Several variants of the original dynamical system, including the presence of gravity and friction, are considered, in order to analyze whether the integrable cases are preserved or not in presence of further external forces, both potential and non-potential. Particular attention is devoted to the presence of dissipative forces, that are analyzed in two different formulations. Furthermore, a study of the discrete version is performed. The analysis of periodic points, that is presented up to period 3, suggests that the discrete map associated to the dynamical system has not dense sets of periodic points, so that the map would not be chaotic in the sense of Devaney for a choice of the parameters that corresponds to a general case of chaotic motion for the original system.

RBF Neural Network for Chaotic Motion Control of Collision Vibration System

Aiming at the control problem of chaotic motion of a kind of collision vibration system with gap, a chaotic motion control of collision vibration system based on RBF neural network is proposed. Firstly, the system mechanical model and chaotic motion are introduced, and then a chaotic controller based on RBFNN is designed to control and simulate the chaotic attractor. The model information of the system is not used in the control method. In this paper, the model of the system is used only to generate the input / output data of the system, and it is not used for the design of the controller. The parameters of AHGSA algorithm are set as follows: the population size is 30, the maximum number of iterations is 100,G0, a = 18, and the proportional coefficient P = 0.96. Small disturbances are applied to the controllable parameter ωof the system to suppress the chaotic motion of the system and make the system tend to stable periodic motion. In order to more clearly show the control effect of chaotic motion, the chaotic motion is controlled when the system iterates 400 times. The results show that the chaotic motion can be quickly controlled to periodic 1-1 motion, the phase diagram is a closed curve, and there is a peak in the spectrum diagram. Chaotic motion can be quickly controlled as periodic 2-2 motion, the phase diagram is two closed curves, and two obvious peaks appear in the spectrum diagram. The proposed method can effectively control the chaotic motion of the system, and the expected target can be not only the fixed point of period 1, but also other periodic orbits.

RECURRENCE SETS FOR PARTIAL INVERSE

Two types of recurrence sets are introduced for inverse semigroup partial actions in topological spaces. Some applications to the basic dynamical properties of the action are indicated, covering topics as topological transitivity, limit points and periodic points. We then explore the connections of these recurrence sets with similar notions for related types of imperfect symmetries (prefix inverse semigroup expansions, partial group and groupoid actions).

On Morse–Smale diffeomorphisms on simply connected manifolds

We study relations between a structure of non-wandering set of a Morse–Smale diffeomorphism f and its carrying closed manifold Mn. We prove that if f has no any saddle periodic points with one-dimensional unstable manifolds, and for any periodic point σ of Morse index (n−1) its unstable manifolds do not intersect stable invariant manifolds of saddle periodic points different from σ, then Mn is simply connected. This fact does not follow from Morse inequalities that give only restrictions on homology groups of Mn.

Moduli Spaces of Quadratic Maps: Arithmetic and Geometry

Abstract We establish an implication between two long-standing open problems in complex dynamics. The roots of the $n$th Gleason polynomial $G_{n}\in{\mathbb{Q}}[c]$ comprise the $0$-dimensional moduli space of quadratic polynomials with an $n$-periodic critical point. $\operatorname{Per}_{n}(0)$ is the $1$-dimensional moduli space of quadratic rational maps on ${\mathbb{P}}^{1}$ with an $n$-periodic critical point. We show that if $G_{n}$ is irreducible over ${\mathbb{Q}}$, then $\operatorname{Per}_{n}(0)$ is irreducible over ${\mathbb{C}}$. To do this, we exhibit a ${\mathbb{Q}}$-rational smooth point on a projective completion of $\operatorname{Per}_{n}(0)$, using the admissible covers completion of a Hurwitz space. In contrast, the Uniform Boundedness Conjecture in arithmetic dynamics would imply that for sufficiently large $n$, $\operatorname{Per}_{n}(0)$ itself has no ${\mathbb{Q}}$-rational points.

Structural Characteristics of Fibrillar Crystals in Uniaxially Stretched Isotactic Polypropylene Dominated by Temperature and Strain

AbstractThe spherulitic morphology of isotactic polypropylene can be transformed into the oriented fibrillar morphology through hot stretching processes with varying temperature (Ts) or altering strain (εt). The effects of Ts and εt on the structural characteristics of fibrillar crystals are comprehensively investigated with respect to crystal orientation, long periodic spacing, lamellar thickness (Lc), crystallinity (Xc), melting point, and chain relaxation behavior. Small‐angle X‐ray scattering patterns illustrate that the fibrillar crystals consist of alternated stacks of crystalline lamellae and amorphous layers. High Ts leads to a low orientation degree of lamellae, whereas large εt facilitates a high orientation level. The Xc and mean Lc are improved continuously with the increasing of Ts or εt, indicating a stretching‐enhanced crystallization behavior driven by the two factors. The endothermic profiles reveal that new chain‐folded lamellae with relatively thinner thickness form during the hot stretching process. The formation of thinner lamellae is dominated by the melting–recrystallization mechanism. This work would provide guidance for optimizing process conditions to manipulate the microstructure of hot‐stretched semicrystalline polymers.

Misiurewicz polynomials and dynamical units, part II

Fix an integer d≥2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d\\ge 2$$\\end{document}. The parameters c0∈Q¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$c_0\\in \\overline{\\mathbb {Q}}$$\\end{document} for which the unicritical polynomial fd,c(z)=zd+c∈C[z]\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f_{d,c}(z)=z^d+c\\in \\mathbb {C}[z]$$\\end{document} has finite postcritical orbit, also known as Misiurewicz parameters, play a significant role in complex dynamics. Recent work of Buff, Epstein, and Koch proved the first known cases of a long-standing dynamical conjecture of Milnor using their arithmetic properties, about which relatively little is otherwise known. Continuing our work from a companion paper, we address further arithmetic properties of Misiurewicz parameters, especially the nature of the algebraic integers obtained by evaluating the polynomial defining one such parameter at a different Misiurewicz parameter. In the most challenging such combinations, we describe a connection between such algebraic integers and the multipliers of associated periodic points. As part of our considerations, we also introduce a new class of polynomials we call p-special, which may be of independent number theoretic interest.

Presence of molecular residual disease after pathologic complete response among patients with inflammatory breast cancer.

3044 Background: Inflammatory breast cancer (IBC) is known to recur more frequently than non-IBC after pathologic complete response (pCR). The presence of circulating tumor cells (CTCs), a marker of molecular residual disease (MRD), has been associated with higher likelihood of metastasis. We sought to characterize CTCs and its relationship with pCR in IBC patients. Methods: Patients diagnosed with IBC were enrolled in a prospective registry from 2005-2022. Serial blood draws were performed before, during, and after neoadjuvant systemic therapy (NST), and 6-months and 1-year post-surgery. CTCs were enumerated using CellSearch™. Patients with ≥ 1 CTC at any timepoint in the post-operative period were included in the positive CTC cohort. T-tests, one-way ANOVA, and chi-squared tests were used to compare differences between groups. Kaplan-Meier analysis was used for survival outcomes. Results: A total of 112 patients were included. The median age of diagnosis was 50.5 years (IQR 17) and BMI was 29.3 kg/m2 (IQR 11.3). Patients were predominantly White (85, 75.9%) with clinical stage IIIB-C (94, 84.9%), node-positive (107, 95.5%), and HER2-negative (66, 59.0%) disease. Almost all patients (109, 97.3%) received trimodality therapy – NST, modified radical mastectomy, and adjuvant radiation. At a median follow-up period of 7.1 years (95% CI: 4.7-9.4), the overall survival (OS) rate was 72.3%. Baseline CTC positivity rate was 61.8% (42/68). More than half of the patients (61, 54.5%) had a positive CTC at some point in the post-operative surveillance period. Among the 39 patients who achieved pCR (34.8%), 15 (38.5%) had positive CTCs during follow-up. There were no differences in age, BMI, menopause status, clinical stage, nodal status, grade, presence of LVI, and number of lymph nodes (LNs) removed by CTC status. However, patients with positive CTCs had a significantly higher number of positive LNs at resection (p = 0.01), were more likely to be HER2-negative (p = 0.001), and were less likely to achieve pCR (p = 0.01). Triple negative disease (p &lt; 0.0001), lack of pCR (p = 0.006), and positive CTCs (0.007) were associated with poor prognosis. When pCR was combined with CTC status, patients with positive CTCs demonstrated significantly worse survival, despite having achieved pCR, compared to those with pCR and negative CTC status (5-year OS: 35.0% vs. 83.1%, respectively, p = 0.016). Conclusions: A high proportion of IBC patients who achieved pCR had MRD, as demonstrated by persistent CTCs. CTCs portended worse prognosis in patients with IBC, even after pCR. Future incorporation of longitudinal CTC monitoring may be helpful in identifying patients at risk for relapse despite having achieved a pCR. [Table: see text]

Periodic points of solenoidal automorphisms in terms of adeles

Periodic points of solenoidal automorphisms in terms of adeles

#1212 Trends in real-world lipid lowering therapy use among adult patients with chronic kidney disease: 5-year single center experience in the Philippines

Abstract Background and Aims Patients with chronic kidney disease (CKD) carry an extremely high burden for atherosclerotic cardiovascular disease (ASCVD), which worsens as CKD progresses. Several international guidelines, including the 2013 Kidney Disease: Improving Global Outcomes (KDIGO) guidelines, have recommended the use of lipid-lowering therapy (LLT) in this high-risk population. To evaluate the implementation of these recommendations in real-world practice, we assessed patterns of dyslipidemia management among patients with CKD. Specific objectives include describing the prevalence and intensity of LLT prescription [stratified by estimated glomerular filtration rate (GFR) and whether requiring renal replacement therapy or not] as well as adherence to guideline recommendations on LLT use. Method We conducted a single-center, cross-sectional study covering the period of January 2019 to December 2023. A review of inpatient and outpatient medical records of the Department of Medicine, University of the Philippine—Philippine General Hospital was done. Eligible patients were at least 18 years of age, and diagnosed with CKD. Exclusion criteria included having a concomitant diagnosis of Acute Kidney Injury, and being pregnant or breastfeeding at any point in the study period. Sociodemographic, clinical, and laboratory data were based off the latest entry in each patient's medical record. No clinical data were collected beyond those that were available on the records. Classification of statin intensity was based on the 2019 American Heart Association/American College of Cardiology Guidelines on the Management of Blood Cholesterol as well as the 2020 Philippine Clinical Practice Guidelines on the Management of Dyslipidemia. All analyses were descriptive and done using STATA 18. Categorical variables were summarized as frequencies and percentages. Continuous variables were reported as measures of central tendency [i.e. mean (SD) or median (IQR), as appropriate]. Results Of the 3845 patients included in the study, 2922 (76%) were prescribed LLT. The most common LLT were statins (92%), followed by statin/ezetimibe combinations (6%), then statin/fibrate combinations (2%). None were prescribed PCKS9 inhibitors, niacin, omega-3 fatty acids, or bile acid sequestrants. Among non-dialytic patients, the distribution of LLT use was as follows: a) eGFR ≥ 60 ml/min/1.73 m2: 40% (173/431) b) eGFR 30-60 ml/min/1.73 m2: 76% (1198/1576) c) eGFR &amp;lt;30 ml/min/1.73 m2: 84% (1551/1838). Among dialytic patients, 68% (601/884) were already on LLT prior to initiation of dialysis while 35% (283/884) were started on LLT after dialysis initiation. Notably, 89% (786/884) of these dialytic patients were still on moderate-to-high-intensity statin doses. Based on recommendations from the 2013 KDIGO guidelines, only 78% (2610/3334) of eligible patients were prescribed on LLT, while 61% (312/511) of ineligible patients were prescribed on LLT. Similar rates of adherence were seen to other international guideline recommendations on the management of dyslipidemia in CKD (e.g. 2018 American Heart Association/American College of Cardiology Guideline on the Management of Blood Cholesterol, 2019 European Society of Cardiology/European Atherosclerosis Society guidelines for the management of dyslipidaemias, 2020 Clinical Practice Guidelines for the management of dyslipidemia in the Philippines). Conclusion Real-world LLT use among CKD patients remains high, even at lower eGFRs. More importantly, a large proportion of patients remain under- and over-treated, highlighting significant gaps between guideline recommendations and real-world clinical practice. Further investigation regarding the underlying reasons for these practice variations is necessary to improve quality of care, and safely reduce the burden of dyslipidemia and ASCVD among CKD patients.

Migration of Hem-o-Lok clips into the bladder after radical prostatectomy – own experience

Non-absorbable polymer Hem-o-Lok clips are widely used during nerve-sparing radical prostatectomy for clipping of the neurovascular bundle, as well as for rapid knotless fixation of sutures during the formation of urethrovesical anastomosis. At the same time, cases of migration of Hem-o-Lok clips into the bladder at various times after RP have been described. Our retrospective analysis of 1321 patients, who underwent laparoscopic radical prostatectomy at A.M. Granov Russian Scientific Center of Radiology and Surgical Technologies from 2014 to 2023, revealed 3 cases of Hem-o-Lok clip intravesical migration. Also, to search for similar cases of this rare complication a literature review was conducted. The frequency of postoperative intra-bladder clip migration in our study was 0.23 % (3/1321). One case of spontaneous clip passage was observed 3 months later the radical prostatectomy. In two other cases, long-term symptoms of dysuria (in 7 months and 4 years, respectively) revealed clip incrustation, which led to the removal of the clips through endoscopic intervention and laser cystolithotripsy. Despite the low incidence of this complication, the use of Hem-o-Lok clips during laparoscopic radical prostatectomy, should be minimized reasonably, particularly during the urethro-vesical anastomosis formation. If lower urinary tract symptoms and/or hematuria occur at any point in the postoperative period, it’s advisable to conduct an instrumental examination of the bladder to rule out potential clip migration and possible incrustation.

Some interesting birational morphisms of smooth affine quadric 3-folds *

We study a family of birational maps of smooth affine quadric 3-folds, over the complex numbers, of the form x1x4−x2x3= constant, which seems to have some (among many others) interesting/unexpected characters: (a) they are cohomologically hyperbolic, (b) their second dynamical degree is an algebraic number but not an algebraic integer, and (c) the logarithmic growth of their periodic points is strictly smaller than their algebraic entropy. These maps are restrictions of a polynomial map on C4 preserving each of the quadrics. The study in this paper is a mixture of rigorous and experimental ones, where for the experimental study we rely on Bertini which is a reliable and fast software for expensive numerical calculations in complex algebraic geometry.

Estimation for Markov Chains with Periodically Missing Observations

When we observe a stationary time series with observations missing at periodic time points, we can still estimate its marginal distribution well, but the dependence structure of the time series may not be recoverable at all, or the usual estimators may have much larger variance than in the fully observed case. We show how non‐parametric estimators can often be improved by adding unbiased estimators. We focus on a simple setting, first‐order Markov chains on a finite state space, and an observation pattern in which a fixed number of consecutive observations is followed by an observation gap of fixed length, say workdays and weekends. The new estimators perform astonishingly well in some cases, as illustrated with simulations. The approach extends to continuous state space and to higher‐order Markov chains.