Primary Operator Research Articles

MP-453092-1 FEASIBILITY OF REMOTE MAPPING AND CLINICAL SUPPORT USING NOVEL SOFTWARE

Covid redefined how the world functions. The electrophysiology (EP) community identified multiple needs that arose due to this paradigm and redefined workflows. The geographic paucity of experienced clinical mapping support was a crucial issue that limited the worldwide adoption of complex ablation procedures. To ascertain the feasibility and safety of utilizing a novel software for remote mapping and remote clinical support for all spectrums of cardiac ablation procedures and to compare the adoption of ablation technology in that geography. Ablation procedures performed at Metromed International Cardiac Centre (MICC), India were included in this early feasibility analysis (EFA). All procedures were performed by a single EP operator. Remote Clinical support was provided by an EP physician (primary operator's sibling) in the USA. All mapping was performed by an experienced mapper from a remote location 400 miles away from the primary EP operator in India. The mapping system utilized was Ensite Precision with SJM Connect software. 300 contiguous ablation procedures from 2020 to 2022 were included in this EFA. The proprietory SJM Connect software allows remote access to the Ensite console via a secured connection. The software requires the operator to be granted access to the Ensite console via a permission request that must be acknowledged on the Ensite Console. The software will then allow the remote operator to levels of access to the system, view-only access, or complete control of the console to provide full remote support. Communication occurs between the remote user and the console via a chat function and over a voice call. This remote connection can be terminated at any time from either the console or the remote operator. There is no PHI displayed. Results detailing case demographics and acute procedural success and safety will be presented. Results comparing the adoption of ablation technology with the previous 3 years in this geography will be presented. This EFA demonstrates the safety and efficacy of using remote clinical support and remote mapping for ablation procedures. This opens a world of possibilities including the expansion of ablation technology to all corridors of the world with experienced clinical and mapping support connecting the EP community on a worldwide platform. Additional studies and strategies are needed to further understand the implication of remote support algorithms in bridging the healthcare gaps in the field of cardiac EP.

A retrospective cohort study of the characteristics of unsuccessful operative vaginal deliveries

IntroductionUnsuccessful operative vaginal delivery (OVD) is associated with high rates of materno-fetal morbidity. We aimed to examine institutional rates of unsuccessful OVDs (uOVD) and compare them with successful OVD (sOVD) in order to identify factors to aid patient selection and education. MethodsA 6-month retrospective cohort study was performed on all unsuccessful and successful OVDs in a tertiary level maternity hospital in the Republic of Ireland. Maternal demographics and obstetric factors were assessed to evaluate potential underlying risk factors for unsuccessful operative vaginal delivery versus successful vaginal delivery. ResultsThere were 4,191 births during the study period with an OVD rate of 14.2% (n = 595) with 28 (4.7% of OVDs) being unsuccessful. Unsuccessful OVD were predominately nulliparous (25; 89.2%) with a mean maternal age of 30.1 years (range 20–42), with more than half (n = 15, 53.5%) being induced. The most common indication for induction was prolonged rupture of membranes (PROM) (n = 7, 25%) which was significantly different from the successful OVD group. A senior obstetrician was significantly more likely to be the primary operator in uOVD when compared to sOVD. (82.1 % V 54.1% p < 0.01). The majority of unsuccessful OVD were vacuum deliveries (n = 17; 60.7%), with a significantly higher mean birthweight when compared to successful OVD (3.695 kg V 3.483 kg; p < 0.01). Following an unsuccessful OVD, women were more likely to have a postpartum haemorrhage (64.2 % V 31.5% p < 0.01) and their infant was more likely to require admission to the neonatal intensive care unit (NICU) (32.1 % V 5.8% p < 0.01) when compared with successful OVD. ConclusionRisk factors for unsuccessful OVD were higher birth weight and induction of labour. There was a higher incidence of postpartum haemorrhage and NICU admission when compared with successful OVD.

Missing corner in the sky: massless three-point celestial amplitudes

We present the first computation of three-point celestial amplitudes in Minkowski space of massless scalars, photons, gluons, and gravitons. Such amplitudes were previously considered to be zero in the literature because the corresponding scattering amplitudes in the plane wave basis vanish for generic momenta due to momentum conservation. However, the delta function for the momentum conservation has support in the soft and colinear regions, and contributes to the Mellin and shadow integrals that give non-zero celestial amplitudes. We further show that when expanding in the (shadow) conformal basis for the incoming (outgoing) particle wave functions, the amplitudes take the standard form of correlators in two-dimensional conformal field theory. In particular, the three-point celestial gluon amplitudes take the form of a three-point function of a spin-one current with two spin-one primary operators, which strongly supports the relation between soft spinning particles and conserved currents. Moreover, the three-point celestial amplitudes of one graviton and two massless scalars take the form of a correlation function involving a primary operator of conformal weight one and spin two, whose level-one descendent is the supertranslation current.

Use of video laryngoscopy versus direct laryngoscopy as a teaching tool for neonatal intubation: A systematic review.

Endotracheal intubation and positive pressure ventilation following delivery are required in 32.9% of neonates <31 weeks gestational age and in 5.9% of older newborn babies [1]. Competency in intubation is important, yet opportunities for learners to develop this skill in the clinical environment are limited. Direct laryngoscopy (DL) provides a direct view of the airway during intubation. Unfortunately, visualization of the airway is only available to the primary operator, preventing supervising instructors from simultaneously viewing the airway and allowing them to provide real-time feedback to learners. Video laryngoscopy (VL) is a specialized clinical instrument that utilizes an indirect view of the airway that is digitally projected onto a screen via camera, which allows multiple simultaneous viewers to view the airway during intubation attempts and permits instructors to provide real-time feedback to learners accordingly. This systematic review explores whether VL-supported learning is superior to DL for the development of skill in neonatal intubation. Systematic searches of MEDLINE, EMBASE, CINAHL and the Cochrane Library were conducted without language restrictions. Studies published between January 2011 and November 2021 were examined. Randomized controlled trials (RCTs) comparing the effectiveness of VL versus DL for supporting neonatal intubation learning were included. Rate of successful intubation was the primary outcome measure. Both authors independently extracted study data and conducted risk of bias assessment. Four RCTs met the inclusion criteria, with two incorporating crossover designs. Each examined the effectiveness of VL versus DL, with concurrent supervisor support, as a tool for learning neonatal intubation in medical residents. All studies reported significantly higher intubation success rates with VL. VL and real-time supervisor feedback is a more effective tool for supporting the development of neonatal intubation skill, compared with DL. Future investigations should include learners from other professions whose scope of practice includes neonatal intubation (eg, respiratory therapists).

Assessment of the self-confidence of obstetrics & gynecology fellows to perform a postpartum hemostasis hysterectomy.

Hemostasis Hysterectomy (HH) is a last resort surgical procedure performed in situations of uncontrolled post-partum hemorrhage in maternity wards. The chances of being confronted with this situation are scarce during residency, and the situation is not well suited for teaching. Nevertheless, every obstetrician-gynecologist can be confronted with this stressful situation, and should therefore possess the surgical competence required, regardless of his routine practice. The aim of the present study is to evaluate clinical exposure and self-awareness concerning HH amongst obstetrics and gynecology residents and fellows. We performed a survey amongst French obstetrics and gynecology fellows. An anonymous survey was sent by email between December 1, 2020 to July 1, 2021. Half of the interrogated fellows had practiced (as operator) an HH during residency with a senior and only 22,6% in post-residency. During the last year of residency 70% of them had performed less than 10 scheduled hysterectomies as primary operator. The laparoscopic approach was the most frequently practiced. Very few hysterectomies were performed as primary operator. Fellows with a surgical or mixed activity (both gynecological surgery and obstetrical activity in current practice) felt significantly more capable of performing HH compared to those with exclusive obstetrical or reproductive medicine activity; respectively 60% vs 36%, p=0.008; Odds Ratio: 2.629 (95% CI 1.2214; 5.8094). The number of scheduled hysterectomies or HH performed as primary operator is very low during residency or fellowship. It remains largely inferior to the number deemed necessary in previous publications about the learning curve for scheduled hysterectomy, which varies from 18 to 80 interventions. Nowadays, the increasing number of residents, added to the decrease of hemostasis hysterectomies through better management of post-partum hemorrhage, pushes towards the development of specific training, such as "damage control simulation".

Editor's Choice – Estimated Radiation Dose to the Operator During Endovascular Aneurysm Repair

To estimate operator organ doses from fluoroscopically guided infrarenal endovascular aneurysm repair (EVAR) procedures, using the detailed exposure information contained in radiation dose structured reports. Conversion factors relating kerma area product (PKA) to primary operator organ doses were calculated using Monte Carlo methods for 91 beam angles and seven x-ray spectra typical of clinical practice. A computer program was written, which selects the appropriate conversion factor for each exposure listed in a structured report and multiplies it by the respective PKA. This system was used to estimate operator doses for 81 EVAR procedures for which structured reports were available. The impact of different shielding scenarios and variations in operator position was also investigated. Without any shielding, the median estimated effective dose was 113 μSv (interquartile range [IQR] 71, 252 μSv). The highest median organ doses were for the colon (154 μSv, IQR 81, 343) and stomach (133 μSv, IQR 76, 307). These dose estimates represent all exposures, including fluoroscopy and non-fluoroscopic digital acquisitions. With minimal shielding provided by 0.25 mm of Pb covering the torso and upper legs, the effective dose was reduced by a factor of around 6. With additional shielding from ceiling and table shields, a 25 to 50 fold reduction in dose is achievable. Estimated doses were highest where the primary beam was pointed directly away from the operator. The models suggest that with optimal use of shielding, operator doses can be reduced to levels equivalent to one to two days of natural background exposure and well below statutory dose limits.

Strategies and techniques for percutaneous Veno-Arterial ECMO cannulation and decannulation in children.

To describe the techniques used for percutaneous veno-arterial extracorporeal membrane oxygenation (VA-ECMO) cannulation and decannulation in children with the pediatric interventional cardiologist (PIC) as the primary operator, and present outcomes of this initial clinical experience. Percutaneous VA-ECMO during cardiopulmonary resuscitation (CPR) has been successfully performed in adults, but currently, not much data exists on children. This is a single-center study including VA-ECMO cannulations performed by the PIC between 2019 and 2021. Efficacy was defined as the successful initiation of VA-ECMO without surgical cutdown. Safety was defined as the absence of additional procedures related to cannulation. Twenty-threepercutaneous VA-ECMO cannulations were performed by PIC on 20 children with 100% success. Fourteen (61%) were performed during ongoing CPR, and nine for cardiogenic shock. The Median age was 15 (0.15-18) years, and the median weight was 65 (3.3-180) kg. All arterial cannulations were via the femoral artery except in one, 8-week-old infant who was cannulated in the carotid artery. A distal perfusion cannula was placed in the ipsilateral limb in 17 (78%). The median time from initiating cannulation to ECMO flow was 35 (13-112) minutes. Two patients required arterial graft placement at the time of decannulation and one needed below-knee amputation. ECMO support was maintained for a median of 4 (0.3-38) days. Thirty-day survival was 74%. Percutaneous VA-ECMO cannulations can be effectively performed, even during CPR with the Pediatric Interventional Cardiologist being the primary operator. This is an initial clinical experience. Future outcome studies compared with standard surgical cannulations are necessary to advocate routine percutaneous VA-ECMO in children.

Classification of Unitary RCFTs with Two Primaries and Central Charge Less Than 25

We classify all two-dimensional, unitary, rational conformal field theories with two primaries, central charge $c<25$, and arbitrary Wronskian index. In mathematical parlance, we classify all strongly regular vertex operator algebras (VOAs) with central charge $c<25$ and exactly two simple modules. We find that any such theory is either one of the Mathur-Mukhi-Sen (MMS) theories $\mathsf{A}_{1,1}$, $\mathsf{G}_{2,1}$, $\mathsf{F}_{4,1}$, or $\mathsf{E}_{7,1}$, or it is a coset of a chiral algebra with one primary operator (also known as a holomorphic VOA) by such an MMS theory. By leveraging existing results on the classification of holomorphic VOAs, we are able to explicitly enumerate all of the aforementioned cosets and compute their characters. This leads to 123 theories, most of which are new. We emphasize that our work is a bona fide classification of RCFTs, not just of characters. Our techniques are general, and we argue that they offer a promising strategy for classifying chiral algebras with low central charge beyond two primaries.

The ANZ hernia repair practices study: low consensus on inguinal and small ventral hernia management and infrequent long-term follow-up.

The ANZ hernia repair practices study: low consensus on inguinal and small ventral hernia management and infrequent long-term follow-up.

A comparison of ICG-NIR with blue dye and technetium for the detection of sentinel lymph nodes in vulvar cancer.

The sentinel lymph node (SLN) procedure for vulva cancer is a safe alternative to a radical inguino-femoral lymphadenectomy (IFLN) for small unifocal tumours. SLN evaluation through biopsy and ultra-staging has helped gynaecological oncology surgeons improve operative morbidity with no cost to oncologic safety. Established techniques for groin SLN detection and excision in vulvar cancer use 99mTc-nanocolloid radiotracer and blue dye (BD) for identification of the SLN. Indocyanine green (ICG)-near infrared (ICG-NIR) techniques for SLN mapping have proven utility in other gynaecological cancer sites and is gaining interest as a technique for SLN mapping in vulvar cancer METHODS: Fifty consecutive patients with unifocal vulvar squamous cell cancers of <40mm lateral diameter and with depth of invasion > 1mm underwent SLN mapping and excision using a combination of 99mTc-nanocolloid, BD and ICG. SLN detection results were recorded on a per-patient and per-groin basis. The success rates SLN for detection by individual tracer substance or combinations of tracer were determined by presence of one or more tracer, detectable in the SLN specimen. 92% of patients had a successful SLN procedure. The per-groin detection rate was 84%. All successfully mapped SLN were identified with the combination of ICG-NIR and 99mTc-nanocolloid compared to 69% with BD 99mTc-nanocolloid. Success rates for the SLN procedure were not dependent on prior excision of the primary lesion or operator experience. Incorporation of ICG-NIR into standard SLN mapping protocols may allow for the abandonment of routine use of BD and its poor side effect profile.

The impact of COVID-19 on international tourism flows to Italy: Evidence from mobile phone data.

This paper analyses the response to the COVID-19 pandemic of inbound tourism to Italy looking at variation across countries and provinces. To this end, it uses weekly data on the number of foreign visitors in Italy from January 2019 until February 2021, as provided by a primary mobile telephony operator. We document a very robust negative relation at the province level between the local epidemic situation and the inflow of foreign travellers. Moreover, provinces with a historically higher share in art-tourism, and those that used to be 'hotel intensive' were hit the most during the pandemic, while provinces with a more prevalent orientation to business tourism proved to be more resilient. Entry restrictions with varying degrees of strictness played a key role in explaining cross-country patterns. After controlling for these restrictions, we observed that the number of travellers that could arrive by private means of transportation decreased proportionally less. Overall, this evidence emphasises that contagion risk considerations played a significant role in shaping international tourism patterns during the pandemic.

Mentoring the Ross Procedure in Adults Does Not Compromise Perioperative or Long-term Outcomes

BackgroundRecent reports that the Ross procedure restores normal life expectancy in young adults with aortic valve disease have renewed interest in this complex procedure. Because only a few centers perform a high volume of Ross procedures, there are limited data on the safety of learning and teaching the Ross procedure. MethodsA total of 234 consecutive adult patients at a single center underwent the Ross procedure performed by an experienced surgeon acting as the primary operator (n = 186; 1994-2021) or mentoring surgeon (n = 48; 2001-2021). Cumulative sum analysis of cardiopulmonary bypass times was performed to evaluate learning curves as primary surgeon and mentored surgeon. Kaplan-Meier analysis was used to estimate long-term survival and freedom from Ross-related reintervention. ResultsPatients’ mean age was 42 ± 11 years; 169 (72%) were male. Baseline demographic characteristics were similar between cohorts. Operative death occurred in 5 (2%) patients: 3 (2%) as primary surgeon and 2 (4%) as mentor (P = .28). In-hospital reoperation was required in 8 (3%) patients: 6 (3%) as primary surgeon and 2 (4%) as mentor (P = .75). Up to 10 years, there was no difference in survival between primary operator cases and mentored cases (94.4% [91.2%-97.9%]) vs 95.8% [90.3%-100%]; log-rank, P = .85). ConclusionsAlthough the Ross procedure is technically complex, it can be taught to experienced aortic root surgeons without compromising short- or long-term outcomes.

Preoperative priming results in improved operative performance with surgical trainees

BackgroundPreoperative warm-up regimens are increasingly utilised in the surgical field, however no consensus on benefits of priming across surgical experience has been realised. The aim of this study was to evaluate the impact of simulation preoperative priming on operative performance across levels of resident experience. MethodsA single-blinded randomised control trial was carried out in a regional surgical training centre. Volunteers were randomised to undergo simulated surgical warm-up procedure prior to their first case as primary operator or proceed directly to surgery. ResultsPerformances of 147 operative procedures were collected over an 18 month period, experience ranging from PGY2-PGY 7. Senior participants consistently outperformed junior residents in unprimed operative cases (p = 0.005). In primed operative performances no significant difference in aggregate performance scores was found (p = 0.07). ConclusionPriming confers a greater advantage to junior residents with particular regard to generic surgical skills. Senior residents demonstrate improved self-efficacy scores measured following priming.

OPE coefficients and the mass-gap from the integrable scattering description of 2D CFT’s

Many two-dimensional conformal field theories have an alternative integrable scattering description, which reproduces their spectrum of conformal weights. Taking as an example the case of the Lee-Yang nonunitary CFT and the 3-state Potts minimal model, we derive formulas, in terms of their integrable description, for the OPE coefficients of a certain specific primary operator and two identical but otherwise essentially arbitrary operators. As a side result we also obtain a novel formula for the mass-gap relation for the integrable massive deformation of the CFT. These results are obtained through expressing the first nontrivial coefficient in the UV expansion of the energy in terms of the integrable CFT data, i.e. the kink and anti-kink TBA solutions.

Abstract 12738: Tracking Fluoroscopic Time Amongst Cardiology Trainees

Introduction: ACC and ESC guidelines for cardiologists in training recommend 200-300 coronary angiographies as primary operator before completion of training. There are different ways to measure an operator's proficiency of performing a coronary angiogram including contrast volume, fluoroscopy time, and total time of procedure. Data from previous studies has shown that fluoroscopy time is the best measure of trainee progression. Fluoroscopy time is significantly longer in trainees who have performed less than 100 interventions. Objectives: Utilize fluoroscopy time during cardiac catheterization to help direct safety in cardiology trainees. Methods: Cardiac catheterization operator data from UCD cardiology fellows between 2014 - 2017. Data was categorized into 3 categories: left heart catheterizations (LHC) , right heart catheterization (RHC), and left and right catheterization combination (LHC + RHC). Data was excluded if the operator performed any other procedure in addition to catheterization. Data was analyzed using a One-way ANOVA analysis. Results: A total of 853 cardiac catheterizations performed by trainees. LHC fluoroscopic time declined from year 1 (9.64 mins) to year 2 (7.62 mins, p: 0.009) (figure 1). LHC + RHC fluoroscopic time declined from year 1 (12.89 mins) to year 2 (10.77 mins, p: 0.007). There was no statically significant change in fluoroscopic time in operators over their three years of training who performed RHC. Operators in their third year of training did not have any statistically significant improvement in their fluoroscopic time when compared to their second year of training. Conclusions: Fluoroscopic time decreases after first year of training in LHC and LHC + RHC cases. There is no significant change in fluoroscopic time amongst fellows who perform RHC regardless of years of experience. Safety efforts to minimize fluoroscopic time should be focused on fellows in their first year of training

Surgical Priming Improves Operative Performance in Surgical Trainees: A Crossover Randomized Control Trial

The aim of this study was to evaluate the impact of a surgical warm-up using a virtual reality simulator on operative performance. This was a single-blinded cross-over randomized control trial in a single tertiary Orthopedic training center. Orthopedic trainees were recruited, and each morning participants rostered to theatre were randomized to either undergo a simulated surgical procedure on a virtual reality simulation system prior to their first case as primary operator (priming arm), or to perform their usual preparatory routine for surgery (control arm). Consultant orthopedic trainers were recruited within the orthopedic unit to carry out subjective surgical performance assessments using a validated global rating scale tool on the first case the participant performed on the list as primary operator. Over 3 study periods a total of 151 data points were collected, with 49 matched data points across priming status and procedural level of difficulty. Subjective assessment tools consistently demonstrated improved operative performance by participants following surgical priming (p = 0.001). This study highlights that introduction of preoperative priming to improve operative preparation, and optimizes operative performance. This has not only implications for improved resident training, but also signals towards beneficial downstream effects on patient outcomes, and theatre list planning.

Celestial holography on Kerr-Schild backgrounds

We explore the celestial holography proposal for non-trivial asymptotically flat backgrounds including the Coulomb field of a static and spinning point charge, their gravitational counterparts described by the Schwarzschild and Kerr metrics, as well as the Aichelburg-Sexl shockwave and spinning shockwave geometries and their electromagnetic cousins. We compute celestial two-point amplitudes on these Kerr-Schild type backgrounds which have the desirable feature, due to the presence of an external source, that they are non-vanishing for general operator positions and are not constrained by the kinematic delta functions of flat space celestial CFT correlators. Of particular interest is the case of shockwave backgrounds where the two-point scattering amplitude of massless scalars can be interpreted as a standard CFT three-point correlator between two massless asymptotic states and a conformal primary shockwave operator. We furthermore show that the boundary on-shell action for general backgrounds becomes the generating functional for tree-level correlation functions in celestial CFT. Finally, we derive (conformal) Faddeev-Kulish dressings for particle-like backgrounds which remove all infrared divergent terms in the two-point functions to all orders in perturbation theory.

Default distal radial approach for all coronary procedures – a prospective study

Abstract Background Radial artery approach for coronary interventions has substantially improved the outcome especially in acute coronary syndrome patients. However, radial artery occlusion is the achilles' heel of such an approach. Purpose To obviate such problems, distal radial artery (DRA) approach is evolving but technical challenge is the small size of the artery. We looked at the feasibility, safety and advantages of it. Methods Patient population included any patient requiring a diagnostic or percutaneous coronary interventions (PCI) in our catheterization laoratory from March 2020 to March 2022. A primary operator performed all procedures as default, if the patient had a palpable DRA. After local anaesthesia infiltration, using seldinger technique and micropuncture kit, 5 to 7F hydrophilic sheaths were introduced and a cocktail of verapamil and heparin was given routinely. Sheaths were removed immediately after procedure but dedicated side specific compression devices were used but removed 45 min after diagnostic and 2 hours after PCI. Clinical patency of radial artery was assessed at discharge and follow up. Results A total of 682 procedures were performed (50% were diagnostic). Out of all PCIs 59% were for ACS). Elective PCIs included very complex cases including PCI for bifurcation, left main and rota assisted complex PCIs. 651 patients had right distal radial approach and 28 had left. Mean age of patients were 66.8±12.9 years (26 to 97). Females constituted 218 (32%). Mean time from 1st needle puncure to successful vascular access took 1.2±0.8 min (20 sec to 6 min). Average attempts to obtain successful vascular access was 1.3±0.7 (1 to7 attempts). There were 15 failures (2%) to obtain DRA access requiring change over to 6 ipsilateral radial, 2 ulnar, 4 contralateral distal radial, 2 femoral and 1 brachial access. Interestingly, in 5 different occaisions previous procedure related occluded radial arteries were recanalized through this access. Most importantly, no case of radial artery occlusion was encountered at discharge or at follow up by clinical examinations. No other vascular complications were encountered except mild transient bruising in 6 cases and early small hematoma in 3 cases. Patient's comfort, nursing staffs' satisfaction and trend towards early discharges were also noticed. There was a distinct improvement in obtaining faster access with lower failure rates by the operator after initial 90, especially after 150 procedures. Conclusions A default approach through distal radial artery in anatomical snuff box for all coronary interventions is feasible, safe and possibly superior to conventional radial access with better patient comfort and caring staff's satisfaction. Though learning curve is longer and more challenging, success rates were much higher and vascular access was faster after initial phase. Clinically radial artry occlusion was not seen but needs further study and more objective evidence. Funding Acknowledgement Type of funding sources: None.

A stochastic regularized second-order iterative scheme for optimal control and inverse problems in stochastic partial differential equations.

Numerous applied models used in the study of optimal control problems, inverse problems, shape optimization, machine learning, fractional programming, neural networks, image registration and so on lead to stochastic optimization problems in Hilbert spaces. Under a suitable convexity assumption on the objective function, a necessary and sufficient optimality condition for stochastic optimization problems is a stochastic variational inequality. This article presents a new stochastic regularized second-order iterative scheme for solving a variational inequality in a stochastic environment where the primary operator is accessed by employing sampling techniques. The proposed iterative scheme, which fits within the general framework of the stochastic approximation approach, has its almost-sure convergence analysis given in a Hilbert space. We test the feasibility and the efficacy of the proposed stochastic approximation approach for a stochastic optimal control problem and a stochastic inverse problem, both associated with a second-order stochastic partial differential equation. This article is part of the theme issue 'Non-smooth variational problems and applications'.

On the real-time evolution of pseudo-entropy in 2d CFTs

In this work, we study the real-time evolution of pseudo-(Rényi) entropy, a generalization of entanglement entropy, in two-dimensional conformal field theories (CFTs). We focus on states obtained by acting primary operators located at different space points or their linear combinations on the vacuum. We show the similarities and differences between the pseudo-(Rényi) entropy and entanglement entropy. For excitation by a single primary operator, we analyze the behaviors of the 2nd pseudo-Rényi entropy in various limits and find some symmetries associated with the subsystem and the positions of the inserted operators. For excitation by linear combinations, the late time limit of the nth pseudo-Rényi entropy shows a simple form related to the coefficients of the combinations and Rényi entropy of the operators, which can be derived by using the Schmidt decomposition. Further, we find two kinds of particular spatial configurations of insertion operators in one of which the pseudo-(Rényi) entropy remains real throughout the time evolution.