Advancing mathematics by guiding human intuition with AI.

The practice of mathematics involves discovering patterns and using these to formulate and prove conjectures, resulting in theorems. Since the 1960s, mathematicians have used computers to assist in the discovery of patterns and formulation of conjectures1, most famously in the Birch and Swinnerton-Dyer conjecture2, a Millennium Prize Problem3. Here we provide examples of new fundamental results in pure mathematics that have been discovered with the assistance of machine learning-demonstrating a method by which machine learning can aid mathematicians in discovering new conjectures and theorems. We propose a process of using machine learning to discover potential patterns and relations between mathematical objects, understanding them with attribution techniques and using these observations to guide intuition and propose conjectures. We outline this machine-learning-guided framework and demonstrate its successful application to current research questions in distinct areas of pure mathematics, in each case showing how it led to meaningful mathematical contributions on important open problems: a new connection between the algebraic and geometric structure of knots, and a candidate algorithm predicted by the combinatorial invariance conjecture for symmetric groups4. Our work may serve as a model for collaboration between the fields of mathematics and artificial intelligence (AI) that can achieve surprising results by leveraging the respective strengths of mathematicians and machine learning.

Catalytic Olefin Transpositions Facilitated by Ruthenium N,N,N-Pincer Complexes.

In this report, we demonstrate olefin transposition/isomerization reactions catalyzed by a series of N,N,N-pincer (1,3-bis(2-pyridylimino)isoindoline) Ru-hydride complexes. The protocol proceeds at room temperature for most substrates, achieving excellent yields, regioselectivity, and diastereoselectivity in short reaction times. The air-stable Ru-chloride derivatives of these complexes exhibit comparable reactivity enabling benchtop setup and synthetic versatility. Furthermore, we demonstrate the potential for one-pot cascade sequences of the products derived from the transposition reactions.

Reactions of N2O and CO on neutral Rh10On clusters: a density functional study.

Density functional theory calculations were performed to identify product, reactant and intermediate dissociative/associative structures for the oxygen abstraction and addition reactions: Rh10On + CO → Rh10On-1 + CO2, n = 1-5 and Rh10On + N2O → Rh10On+1 + N2, n = 0-4 reactions. In the case of the oxygen abstraction reactions, the energetics of the reaction path were very similar in energy regardless of the number of oxygen atoms on the Rh10On cluster, whereas for the addition of oxygen to the Rh10On cluster, the reaction was found to become significantly less exothermic with each successive addition of oxygen.

Current Surgical Practice for Children Born with a Cleft lip and/or Palate in the United Kingdom.

OBJECTIVE: This study describes primary surgical reconstructions performed for children born with a cleft lip and/or palate (CL ± P) in the United Kingdom (UK). DESIGN: Data forms completed at the time of surgery included details on timing, technique, and adjuncts used during the operative period. Demographic data on participants were validated via parental questionnaires. SETTING: Data were obtained from the Cleft Collective, a national longitudinal cohort study. PATIENTS: Between 2015 and 2021, 1782 Cleft Collective surgical forms were included, relating to the primary reconstructions of 1514 individual children. RESULTS: The median age at primary cheiloplasty was 4.3 months. Unilateral cleft lips (UCL) were reconstructed with an anatomical subunit approximation technique in 53%, whereas bilateral cleft lips (BCL) were reconstructed with a broader range of eponymous techniques. Clefts of the soft palate were reconstructed at a median age of 10.3 months with an intravelar veloplasty in 94% cases. Clefts of the hard palate were reconstructed with a vomer flap in 84% cases in a bimodal age distribution, relating to reconstruction carried out simultaneously with either lip or soft palate reconstruction. Antibiotics were used in 96% of cases, with an at-induction-only regimen used more commonly for cheiloplasties (P < .001) and a 5 to 7-day postoperative regime used more commonly for soft palatoplasties (P < .001). Perioperative steroids were used more commonly in palatoplasties than cheiloplasties (P < .001) but tranexamic acid use was equivalent (P = .73). CONCLUSIONS: This study contributes to our understanding of current cleft surgical pathways in the UK and will provide a baseline for analysis of the effectiveness of utilized protocols.

Direct Aroylation of Olefins through a Cobalt/Photoredox-Catalyzed Decarboxylative and Dehydrogenative Coupling with α-Oxo Acids.

Invited for the cover of this issue is the group of Jon Tunge at the University of Kansas. The image depicts the direct cross-coupling of α-oxo acids and styrenes through the release of CO2 and H2 gas in a metallaphotoredox process. Read the full text of the article at 10.1002/chem.202202781.

Direct Aroylation of Olefins through a Cobalt/Photoredox-Catalyzed Decarboxylative and Dehydrogenative Coupling with α-Oxo Acids.

A photoredox/cobalt dual catalytic procedure has been developed that allows benzoylation of olefins. Here the photoredox catalyst effects the decarboxylation of α-ketoacids to form benzoyl radicals. After addition of this radical to styrenes, the cobalt catalyst abstracts a H-atom. Hydrogen evolution from the putative cobalt hydride intermediate allows a Heck-like aroylation without the need for a stoichiometric oxidant. Mechanistic studies reveal that electronically different styrenes lead to a curved Hammett plot, thus suggesting a change in product-determining step in the catalytic mechanism.

Exploring the Relationship Between Palatal Cleft Type and Width With the Use of Relieving Incisions in Primary Repair.

OBJECTIVE: The mainstay of palatal repair in the United Kingdom is the intravelar veloplasty (IVVP). It is not always possible to align the oral mucosa in the midline to achieve tension-free repair. The addition of lateral relieving incisions may aid transposition of the oral mucosa to allow closure. The aim of this study was to explore cleft features that may predispose to a requirement for relieving incisions in order to allow palate closure. DESIGN: We performed a national multiinstitutional retrospective study using data from the UK Cleft Collective cohort study. PATIENTS: The study sample consisted of 474 patients who had undergone IVVP at the time of palatal closure across all 16 of the UK cleft units. RESULTS: We found strong evidence for the requirement for relieving incisions in patients with an increased degree of clefting per the Veau classification (P < .001), increasing palatal soft-edge width (P < .001) and moderate evidence of an associated use in patients with Pierre Robin sequence (P = .015). Insufficient data were available to explore the relationship between intertuberosity distance and the presence of fistula formation with the use of relieving incisions. CONCLUSIONS: The results of this study identify cleft features that increase the likelihood for requiring lateral relieving incisions to allow palatal closure. The degree to which the addition of relieving incisions to IVVP affects maxillary growth and speech outcomes is unknown. Further study is required to answer this important question.

A History of the Frenchay Hospital Plastic Surgery Unit, Bristol, United Kingdom.

Frenchay Hospital has long since been established as the center for plastic surgery in Bristol, providing care to the city and its surrounding catchment area. From humble origins in the Second World War when the site took on the role of a large military hospital providing reconstructive surgery for the victims of war to a busy modern-day National Health Service establishment, the plastic surgery unit at Frenchay Hospital has grown and developed through in parallel with the genesis and development of the specialty. Recent centralization of care in Bristol has seen a massive reorganization of services, and with it the closure of Frenchay Hospital. Because the plastic surgery unit establishes a new home at Southmead Hospital, this review documents the foundations of reconstructive surgery in Bristol and the South West United Kingdom.

A Model of Drosophila Larva Chemotaxis.

Detailed observations of larval Drosophila chemotaxis have characterised the relationship between the odour gradient and the runs, head casts and turns made by the animal. We use a computational model to test whether hypothesised sensorimotor control mechanisms are sufficient to account for larval behaviour. The model combines three mechanisms based on simple transformations of the recent history of odour intensity at the head location. The first is an increased probability of terminating runs in response to gradually decreasing concentration, the second an increased probability of terminating head casts in response to rapidly increasing concentration, and the third a biasing of run directions up concentration gradients through modulation of small head casts. We show that this model can be tuned to produce behavioural statistics comparable to those reported for the larva, and that this tuning results in similar chemotaxis performance to the larva. We demonstrate that each mechanism can enable odour approach but the combination of mechanisms is most effective, and investigate how these low-level control mechanisms relate to behavioural measures such as the preference indices used to investigate larval learning behaviour in group assays.

Association of Perioperative Antibiotics with the Prevention of Postoperative Fistula after Cleft Palate Repair.

Background: There is debate amongst surgeons regarding the use of antibiotics to prevent fistulae after palatoplasty. Prescribing should be evidence based, as antibiotic stewardship is integral to reducing antibiotic resistance. Our aim was to determine whether differing perioperative regimens affect the prevalence of postoperative fistulae. Methods: The sample comprised participants from the Cleft Collective who had undergone palatoplasty. Participants were recruited across all 16 UK cleft centers between 2013 and 2021. The exposure was perioperative antibiotic regimen prescribed at the time of palatoplasty. The primary outcome was the presence of palatal fistula. Results: Fistula data were available for 167 participants when exploring antibiotic regimen and for 159 when exploring antibiotic agent. There was no evidence to suggest a difference in fistula rate between those receiving antibiotics on induction only versus as an inpatient or up to 7 days postoperatively (χ2 = 4.57; P = 0.10). There was no evidence to suggest a difference in fistula rate between those who received co-amoxiclav and those who had an alternative antibiotic (χ2 = 0.16; P = 0.69). Postoperative fistulae increased with the extent of the cleft (χ2 = 20.39; P < 0.001). When adjusting for cleft type, no evidence of an association between antibiotic regimen and fistulae was found (inpatient antibiotics: OR 1.36; 95% confidence interval, 0.53-3.51; antibiotics up to 7 days postoperatively: OR 0.68; 95% confidence interval, 0.26-1.80). Conclusions: The choice of antibiotic and dosing regimen does not influence the formation of postoperative fistulae. These results should be supported by interventional trials.

Azathioprine-Induced Hypersensitivity Vasculitis.

Vasculitic skin rash is a rare but known manifestation of azathioprine hypersensitivity reactions, with several published case reports. In this report, we describe the case of a 63-year-old man on azathioprine for autoimmune hepatitis, who developed a delayed systemic hypersensitivity reaction with biopsy-proven vasculitis, approximately 10 months into his treatment. This resolved after azathioprine discontinuation and has not recurred to date after subsequent administration of 6-mercaptopurine. This case highlights the need for continued monitoring for delayed hypersensitivity reactions to azathioprine after initiation of therapy.

Single-Step Synthesis of γ-Ketoacids through a Photoredox-Catalyzed Dual Decarboxylative Coupling of α-Oxo Acids and Maleic Anhydrides.

A photocatalytic methodology for the single step synthesis of γ-ketoacids from α-ketoacids has been developed. This method employs maleic anhydrides as traceless synthetic equivalents of acrylic acids, achieving a selective cross-coupling via a dual decarboxylative strategy, where molecular CO2 is released as the only waste byproduct. The method has also been expanded to incorporate a highly regioselective, 3-component coupling with various alcohols to access functionalized γ-ketoesters.

Syndromes associated with Robin sequence: a national prospective cohort study.

OBJECTIVES: To determine the prevalence of syndromic Robin sequence (RS) in the UK and if this group of patients had an increased need for airway and feeding management compared with a non-syndromic RS cohort. DESIGN: A prospective national multicentre study of cases submitted to the Cleft Collective cohort studies. SETTING: Specialist cleft services in the UK. PATIENTS: 259 participants who fulfilled the diagnosis of RS. This group was compared with 548 participants with cleft palate only (CPO). MAIN OUTCOME MEASURES: The primary outcome measure was the presence of a syndrome in patients with RS and CPO. Secondary outcome measures included the use of airway and feeding adjuncts. RESULTS: An associated syndrome was seen in 28% of patients with RS and 14% of patients with CPO. The most common syndrome for the RS group was Stickler syndrome (27%). Syndromic status was significantly higher among patients with RS compared with those with CPO (OR 2.36, 95% CI 1.65 to 3.39; p<0.001). Patients with syndromic RS have an increased reliance on airway adjuncts compared with the patients without syndromic RS (OR 2.02, 95% CI 1.13 to 3.64; p=0.018). There was no evidence of a difference in the use of feeding adjuncts between syndromic and non-syndromic RS groups (OR 2.43, 95% CI 0.78 to 7.58; p=0.126). CONCLUSION: The presence of a syndrome has implications for management of patients with RS. Early identification of a syndrome may help prevent the consequences of a missed syndromic diagnosis. Routine ophthalmological and genetic screening for Stickler syndrome should be mandatory for all patients with RS.

An Economical and Versatile High-Throughput Protein Purification System Using a Multi-Column Plate Adapter.

Protein purification is imperative to the study of protein structure and function and is usually used in combination with biophysical techniques. It is also a key component in the development of new therapeutics. The evolving era of functional proteomics is fueling the demand for high-throughput protein purification and improved techniques to facilitate this. It was hypothesized that a multi column plate adaptor (MCPA) can interface multiple chromatography columns of different resins with multi-well plates for parallel purification. This method offers an economical and versatile method of protein purification that can be used under gravity or vacuum, rivaling the speed of an automated system. The MCPA can be used to recover milligram yields of protein by an affordable and time efficient method for subsequent characterization and analysis. The MCPA has been used for high-throughput affinity purification of SH3 domains. Ion exchange has also been demonstrated via the MCPA to purify protein post Ni-NTA affinity chromatography, indicating how this system can be adapted to other purification types. Due to its setup with multiple columns, individual customization of parameters can be made in the same purification, unachievable by the current plate-based methods.

Analysis of stereotactic accuracy of the cosman-robert-wells frame and nexframe frameless systems in deep brain stimulation surgery.

INTRODUCTION: The primary goal of stereotactic systems in deep brain stimulation (DBS) surgery is accurate delivery of a DBS lead to a target identified on imaging. Thus, it is critical to understand the accuracy of the stereotactic systems and the factors which may be associated with a decrease in accuracy. METHODS: Ninety patients underwent microelectrode recording-guided placement of 139 DBS leads by a single surgeon using the Cosman-Roberts-Wells (CRW) frame (n = 70) or a frameless skull-mounted trajectory guide (Nexframe; n = 69). The final DBS location was identified on a postoperative CT fused to the preoperative CT and MRI scans. The difference between this final location and the expected location was calculated. RESULTS: The vector error was 2.65 mm (standard error, 0.22) for the frame and 2.78 mm (standard error, 0.25) for the frameless methods (p = 0.69). There was a gradual decline in error for both systems over time, as the vector error of the last 20 implants was 1.99 for the CRW frame and 2.04 for the Nexframe (p = 0.86). CONCLUSIONS: This study shows that the CRW frame and Nexframe frameless systems have equivalent accuracy. Furthermore, the accuracy of both techniques improved over time, from 3 mm initially to 2 mm with current techniques.

Edge of the Present: A Virtual Reality Tool to Cultivate Future Thinking, Positive Mood and Wellbeing.

Depression and suicidality are characterized by negative imagery as well as impoverished positive imagery. Although some evidence exists supporting the link between positive imagery and enhanced mood, much work needs to be done. This study explored the impact of an immersive virtual reality experience (Edge of the Present-EOTP) on an individual's mood, state of well-being, and future thinking. Using a 10-min mixed reality experience, 79 individuals explored virtual landscapes within a purposefully built, physical room. A pre and post survey containing mental health measures were administered to each participant. An optional interview following the virtual work was also conducted. The results indicated that positive mood and well-being increased significantly post-intervention. Hopelessness scores and negative mood decreased, whilst sense of presence was very high. This pilot study is among the first to assess the feasibility of a mixed reality experience as a potential platform for depression and suicide prevention by increasing well-being and mood as well as decreasing hopelessness symptoms.

Linear Integration of ERK Activity Predominates over Persistence Detection in Fra-1 Regulation.

ERK signaling regulates the expression of target genes, but it is unclear how ERK activity dynamics are interpreted. Here, we investigate this question using simultaneous, live, single-cell imaging of two ERK activity reporters and expression of Fra-1, a target gene controlling epithelial cell identity. We find that Fra-1 is expressed in proportion to the amplitude and duration of ERK activity. In contrast to previous "persistence detector" and "selective filter" models in which Fra-1 expression only occurs when ERK activity persists beyond a threshold duration, our observations demonstrate that the network regulating Fra-1 expression integrates total ERK activity and responds to it linearly. However, exploration of a generalized mathematical model of the Fra-1 coherent feedforward loop demonstrates that it can perform either linear integration or persistence detection, depending on the basal mRNA production rate and protein production delays. Our data indicate that significant basal expression and short delays cause Fra-1 to respond linearly to integrated ERK activity.

Automatic detection of MLC relative position errors for VMAT using the EPID-based picket fence test.

Multi-leaf collimators (MLCs) ensure the accurate delivery of treatments requiring complex beam fluences like intensity modulated radiotherapy and volumetric modulated arc therapy. The purpose of this work is to automate the detection of MLC relative position errors ⩾0.5 mm using electronic portal imaging device-based picket fence tests and compare the results to the qualitative assessment currently in use. Picket fence tests with and without intentional MLC errors were measured weekly on three Varian linacs. The picket fence images analysed covered a time period ranging between 14-20 months depending on the linac. An algorithm was developed that calculated the MLC error for each leaf-pair present in the picket fence images. The baseline error distributions of each linac were characterised for an initial period of 6 months and compared with the intentional MLC errors using statistical metrics. The distributions of median and one-sample Kolmogorov-Smirnov test p-value exhibited no overlap between baseline and intentional errors and were used retrospectively to automatically detect MLC errors in routine clinical practice. Agreement was found between the MLC errors detected by the automatic method and the fault reports during clinical use, as well as interventions for MLC repair and calibration. In conclusion the method presented provides for full automation of MLC quality assurance, based on individual linac performance characteristics. The use of the automatic method has been shown to provide early warning for MLC errors that resulted in clinical downtime.