A neural network solves, explains, and generates university math problems by program synthesis and few-shot learning at human level.

We demonstrate that a neural network pretrained on text and fine-tuned on code solves mathematics course problems, explains solutions, and generates questions at a human level. We automatically synthesize programs using few-shot learning and OpenAI's Codex transformer and execute them to solve course problems at 81% automatic accuracy. We curate a dataset of questions from Massachusetts Institute of Technology (MIT)'s largest mathematics courses (Single Variable and Multivariable Calculus, Differential Equations, Introduction to Probability and Statistics, Linear Algebra, and Mathematics for Computer Science) and Columbia University's Computational Linear Algebra. We solve questions from a MATH dataset (on Prealgebra, Algebra, Counting and Probability, Intermediate Algebra, Number Theory, and Precalculus), the latest benchmark of advanced mathematics problems designed to assess mathematical reasoning. We randomly sample questions and generate solutions with multiple modalities, including numbers, equations, and plots. The latest GPT-3 language model pretrained on text automatically solves only 18.8% of these university questions using zero-shot learning and 30.8% using few-shot learning and the most recent chain of thought prompting. In contrast, program synthesis with few-shot learning using Codex fine-tuned on code generates programs that automatically solve 81% of these questions. Our approach improves the previous state-of-the-art automatic solution accuracy on the benchmark topics from 8.8 to 81.1%. We perform a survey to evaluate the quality and difficulty of generated questions. This work automatically solves university-level mathematics course questions at a human level and explains and generates university-level mathematics course questions at scale, a milestone for higher education.

Global Consensus Recommendations on Improving the Safety of Chronic Total Occlusion Interventions.

Safety is of critical importance to chronic total occlusion (CTO) percutaneous coronary intervention (PCI). This global consensus statement provides guidance on how to optimise the safety of CTO) PCI, addressing the following 12 areas: 1. Set-up for safe CTO PCI; 2. Guide catheter--associated vessel injuries; 3. Hydraulic dissection, extraplaque haematoma expansion, and aortic dissections; 4. Haemodynamic collapse during CTO PCI; 5. Side branch occlusion; 6. Perforations; 7. Equipment entrapment; 8. Vascular access considerations; 9. Contrast-induced acute kidney injury; 10. Radiation injury; 11 When to stop; and, 12. Proctorship. This statement complements the global CTO crossing algorithm; by advising how to prevent and deal with complications, this statement aims to facilitate clinical practice, research, and education relating to CTO PCI.

Advances in CrossBoss/Stingray use in antegrade dissection reentry from the Asia Pacific Chronic Total Occlusion Club.

Antegrade dissection reentry with Stingray device (Boston Scientific, Marlborough, MA) accounts for 20-34% of the chronic total occlusion (CTO) cases in the various hybrid operators' CTO registries and is an important component of CTO crossing algorithms. The Stingray device can facilitate antegrade dissection and reentry, however its use is low outside North America and Europe. The Asia Pacific CTO Club along with three experience Stingray operators from the US, Europe and India, created an algorithm guiding use of the CrossBoss and Stingray catheter. This APCTO Stingray algorithm defines when to use the CrossBoss and Stingray device recommending a reduction in CrossBoss use except for in-stent restenosis lesions and immediate transition from knuckle wiring to the Stingray device. When antegrade wiring fails, choice of Stingray-facilitated reentry versus parallel wiring depends on operator experience, device availability, cost concerns, and anatomical factors. When the antegrade wire enters the subintimal space, we recommend using a rotational microcatheter to produce a channel and deliver the Stingray balloon-so called the "bougie technique." We recommend early switch to Stingray rather than persisting with single wire redirection or parallel wire. We recommend choosing a suitable reentry zone based on preprocedural computer tomography or angiogram, routine use of stick and swap, routine use of Subintimal TRAnscatheter Withdrawal (STRAW) through the Stingray balloon, and the multi stick and swap technique. We believe these techniques and algorithm can facilitate incorporation of the Stingray balloon into the practice of CTO interventionists globally.

Retrograde Versus Antegrade Approach for Coronary Chronic Total Occlusion in an Algorithm-Driven Contemporary Asia-Pacific Multicentre Registry: Comparison of Outcomes.

BACKGROUND: The use of a retrograde approach and algorithm-driven CTO (chronic total occlusion) percutaneous coronary intervention (PCI) has become widespread, and many registries have reported good results. This study established a new algorithm and applied it to current CTO practice and collected a CTO registry to document the results. It compared the outcomes of a retrograde versus antegrade approach in a contemporary multicentre CTO registry. METHODS: Between 1 January 2016 and 31 December 2016, consecutive patients who underwent CTO PCI performed by eight high-volume CTO operators were included in a registry. RESULTS: During this period, 485 patients with 497 CTOs were treated with technical and procedural success rates of 93.8% and 89.9%, respectively. Antegrade and retrograde technical success was 95.9% and 91.2% (p = 0.03), respectively. Procedural success for antegrade and retrograde was 94.4% and 84.6%, respectively (p < 0.001). The pure retrograde success rate was 80% and pure antegrade success rate was 75%. Technical success in different Japanese Chronic Total Occlusion (JCTO) score groups was 100% (JCTO 0), 96.2% (JCTO 1), 95.3% (JCTO 2), and 92.5% (JCTO ≥ 3), with no statistical difference in success rates between different JCTO scores. In-hospital major adverse cardiac event (MACE) was 3.8% and more common in the retrograde group (6.6% vs 1.5%). CONCLUSIONS: The retrograde approach, when used by experienced operators who have been well trained in retrograde approach, can produce higher retrograde success in complex CTO lesions. The use of an algorithm approach can improve procedural efficiency, reduce contrast and radiation dosage, and reduce the time spent in failure mode. These tools remain vital to the development of future CTO PCI.

Procedure failure of chronic total occlusion percutaneous coronary intervention in an algorithm driven contemporary Asia-Pacific Chronic Total Occlusion Club (APCTO Club) multicenter registry.

OBJECTIVE: With the evolution of chronic total occlusion (CTO) percutaneous coronary intervention (PCI) technique and equipment, the success rate of CTO PCI has improved over the years. We examined the failed cases in this expert registry and looked at the mode of failure. METHODS: In 2016, consecutive CTO PCI performed by eight high volume CTO with an agreed CTO algorithm were examined in a registry. RESULTS: There was a total of 485 patients with 497 CTOs were treated with technical and procedural success rates of 93.8% and 89.9%, respectively. The mean J-CTO score was 2.9 ± 1.2. The main mode of failure in cases with only antegrade attempt was inability to wire to true lumen despite advanced antegrade wiring technique for example, parallel wiring or IVUS guided wiring (10 out of 11 cases). The mode of failure in retrograde attempt was: 30% was due to inability to wire the collateral channel; 30% was due to failed reverse controlled antegrade and retrograde subintimal tracking (CART); 30% was due to inability to cross CTO by retrograde microcatheter. Four cases were terminated prematurely due to procedure complications. CONCLUSION: Similar to previous reported studies, primary failure mode of only antegrade attempt was inability to wire to true lumen. However, contrary to other registries where failure to cross the retrograde channel with wire was the predominant failure mode, the retrograde failure mode was equally divided between failure to cross the channel with wire, failure to do reverse CART, and failure to cross the CTO with the microcatheter.

A Molecular Dynamics Investigation of the Thermostability of Cold-Sensitive I707L KlenTaq1 DNA Polymerase and Its Wild-Type Counterpart.

DNA polymerase I from Thermus aquaticus ( Taq DNA polymerase) is useful for polymerase chain reactions because of its exceptional thermostability; however, its activity at low temperatures can cause amplification of unintended products. Mutation of isoleucine 707 to leucine (I707L) slows Taq DNA polymerase at low temperatures, which decreases unwanted amplification due to mispriming. In this work, unrestrained molecular dynamics (MD) simulations were performed on I707L and wild-type (WT) Taq DNA polymerase at 341 and 298 K to determine how the mutation affects the dynamic nature of the protein. The results suggest that I707L Taq DNA polymerase remains relatively immobile at room temperature and becomes more flexible at the higher temperature, while the WT Taq DNA polymerase demonstrates less substantial differences in dynamics at high and low temperatures. These results are in agreement with previous experimental results on the I707L mutant Taq DNA polymerase that show dynamic differences at high and low temperatures. The decreased mobility of the mutant at low temperature suggests that the mutant remains longer in the blocked conformation, and this may lead to reduced activity relative to the WT at 298 K. Principal component analysis revealed that the mutation results in decoupled movements of the Q helix and fingers domain. This decoupled nature of the mutant gives way to an increasingly flexible N-terminal end of the Q helix at 341 K, a characteristic not seen for WT Taq DNA polymerase.

Chronic Total Occlusion Wiring: A State-of-the-Art Guide From The Asia Pacific Chronic Total Occlusion Club.

OBJECTIVE: Despite the advances in wire technology and development of algorithm-driven methodology for chronic total occlusion (CTO) intervention, there is a void in the literature about the technical aspects of CTO wiring. The Asia Pacific CTO Club, a group of 10 experienced operators in the Asia Pacific region, has tried to fill this void with this state-of-the-art review on CTO wiring. METHODS: This review explains, for proximal cap puncture: choices of wires, shaping of the wire, use of dual lumen catheter, and method of step-down of wire penetration force for successful wiring. In wiring the CTO body, the techniques of loose tissue tracking, intentional intimal plaque tracking, and intentional subintimal wiring are described in detail. For distal lumen wiring, a blunt distal cap, presence of a distal cap side branch, calcium, and sharp tapered distal stump predict cap toughness, and wire penetration force should be stepped-up in these cases. The importance of choosing between redirection, parallel wiring, and Stingray (Boston Scientific, Marlborough, MA, USA) for angiographic guidance is discussed along with which will be more successful. On the retrograde side, the problems encountered with distal cap puncture and methods to overcome these problems are explained. The method of wiring the CTO body through a retrograde approach depending on the morphology of the CTO is described. Different reverse controlled antegrade and retrograde tracking (CART) wiring methods - including end balloon wiring, side balloon entry, and conventional reverse CART - are explained in detail. CONCLUSION: This is a systematic CTO wiring review, which is believed to be beneficial for CTO operators worldwide.

The inherent catastrophic traps in retrograde CTO PCI.

When we learn to drive, our driving instructor tells us how to check the side mirror and turn your head to check the blind spot before changing lanes. He tells us how to stop at stop signs, how to drive in slippery conditions, the safe stopping distances, and these all make our driving safe. Similarly, when we learn PCI, our mentors teach us to seat the guiding catheter co-axially, to wire the vessel safely, to deliver balloon and stents over the wire, to watch the pressure of the guiding, in order that we perform PCI safely and evade complications. In retrograde CTO PCI, there is no such published teaching. Also many individual mentors have not had the wide experience to see all the possible complications of retrograde CTO PCI and, therefore, may not be able to warn their apprentice. As the number of retrograde procedures increase worldwide, there is a corresponding increase in catastrophic complications, many of which, we as experts, can see are easily avoidable. To breach this gap in knowledge, this article describes 12 commonly met inherent traps in retrograde CTO PCI. They are inherent because by arranging our equipment in the manner to perform retrograde CTO PCI, these complications are either induced directly or happen easily. We hope this work will enhance safety of retrograde CTO PCI and avoid many catastrophic complications for our readers and operators. © 2017 Wiley Periodicals, Inc.

Angiographic study of the clinical liaison of drug-eluting stent and paclitaxel-eluting balloon in unifocal side branch ostium stenosis (ASCLEPIUS).

A reliable stenting strategy for treating isolated side branch (SB) ostium stenosis is not well established. The purpose of this study was to examine the 6-month angiographic outcome of a novel technique, called the shoulder technique, on this lesion subtype. Symptomatic patients with isolated SB ostium stenosis, defined as ≥75% diameter stenosis at SB ostium and <50% diameter stenosis in main vessel (MV), were treated with paclitaxel-eluting balloon in MV and drug-eluting stent in SB using the shoulder technique. Angiographic restudy was performed at 5-9 months and clinical follow-up was scheduled regularly every 3 months. There were 46 patients of age 66 ± 12 years with male predominance (76%) recruited. Diagonal ostium (67%) was the most frequent target lesion site. The size and length of paclitaxel-eluting balloon and drug-eluting stent used in MV and SB were 3.01 ± 0.25 and 20 ± 4 mm, and 2.39 ± 0.25 and 17 ± 6 mm, respectively. Angiographic restudy was performed on 43 (93.5%) patients at 6.5 ± 1.6 months. The late loss in MV and SB were 0.04 ± 0.19 and 0.19 ± 0.32 mm, respectively. Angiographic restensosis was seen in 2 (4.7%) patients at SB, whereas no stenosis was induced in MV. Improvement of symptom was reported in 36 (78%) patients. At 1-year follow-up, no death, myocardial infarction, and stent thrombosis was observed; target vessel revascularization was performed on 3 (6.5%) patients. Treatment of isolated SB ostium stenosis using the shoulder technique is associated with a favorable short-term angiographic outcome.

A conservative isoleucine to leucine mutation causes major rearrangements and cold sensitivity in KlenTaq1 DNA polymerase.

Assembly of polymerase chain reactions at room temperature can sometimes lead to low yields or unintentional products due to mispriming. Mutation of isoleucine 707 to leucine in DNA polymerase I from Thermus aquaticus substantially decreases its activity at room temperature without compromising its ability to amplify DNA. To understand why a conservative change to the enzyme over 20 Å from the active site can have a large impact on its activity at low temperature, we solved the X-ray crystal structure of the large (5'-to-3' exonuclease-deleted) fragment of Taq DNA polymerase containing the cold-sensitive mutation in the ternary (E-DNA-ddNTP) and binary (E-DNA) complexes. The I707L KlenTaq1 ternary complex was identical to the wild-type in the closed conformation except for the mutation and a rotamer change in nearby phenylalanine 749, suggesting that the enzyme should remain active. However, soaking out of the nucleotide substrate at low temperature results in an altered binary complex made possible by the rotamer change at F749 near the tip of the polymerase O-helix. Surprisingly, two adenosines in the 5'-template overhang fill the vacated active site by stacking with the primer strand, thereby blocking the active site at low temperature. Replacement of the two overhanging adenosines with pyrimidines substantially increased activity at room temperature by keeping the template overhang out of the active site, confirming the importance of base stacking. These results explain the cold-sensitive phenotype of the I707L mutation in KlenTaq1 and serve as an example of a large conformational change affected by a conservative mutation.

Role of arginine in mediating protein-carbon nanotube interactions.

Arginine-rich proteins (e.g., lysozyme) or poly-L-arginine peptides have been suggested as solvating and dispersing agents for single-wall carbon nanotubes (CNTs) in water. In addition, protein structure-function in porous and hydrophobic materials is of broad interest. The amino acid residue, arginine (Arg(+)), has been implicated as an important mediator of protein/peptide-CNT interactions. To understand the structural and thermodynamic aspects of this interaction at the molecular level, we employ molecular dynamics (MD) simulations of the protein lysozyme in the interior of a CNT, as well as of free solutions of Arg(+) in the presence of a CNT. To dissect the Arg(+)-CNT interaction further, we also perform simulations of aqueous solutions of the guanidinium ion (Gdm(+)) and the norvaline (Nva) residue in the presence of a CNT. We show that the interactions of lysozyme with the CNT are mediated by the surface Arg(+) residues. The strong interaction of Arg(+) residue with the CNT is primarily driven by the favorable interactions of the Gdm(+) group with the CNT wall. The Gdm(+) group is not as well-hydrated on its flat sides, which binds to the CNT wall. This is consistent with a similar binding of Gdm(+) ions to a hydrophobic polymer. In contrast, the Nva residue, which lacks the Gdm(+) group, binds to the CNT weakly. We present details of the free energy of binding, molecular structure, and dynamics of these solutes on the CNT surface. Our results highlight the important role of Arg(+) residues in protein-CNT or protein-carbon-based material interactions. Such interactions could be manipulated precisely through protein engineering, thereby offering control over protein orientation and structure on CNTs, graphene, or other hydrophobic interfaces.

Molecular dynamics study of the opening mechanism for DNA polymerase I.

During DNA replication, DNA polymerases follow an induced fit mechanism in order to rapidly distinguish between correct and incorrect dNTP substrates. The dynamics of this process are crucial to the overall effectiveness of catalysis. Although X-ray crystal structures of DNA polymerase I with substrate dNTPs have revealed key structural states along the catalytic pathway, solution fluorescence studies indicate that those key states are populated in the absence of substrate. Herein, we report the first atomistic simulations showing the conformational changes between the closed, open, and ajar conformations of DNA polymerase I in the binary (enzyme:DNA) state to better understand its dynamics. We have applied long time-scale, unbiased molecular dynamics to investigate the opening process of the fingers domain in the absence of substrate for B. stearothermophilis DNA polymerase in silico. These simulations are biologically and/or physiologically relevant as they shed light on the transitions between states in this important enzyme. All closed and ajar simulations successfully transitioned into the fully open conformation, which is known to be the dominant binary enzyme-DNA conformation from solution and crystallographic studies. Furthermore, we have detailed the key stages in the opening process starting from the open and ajar crystal structures, including the observation of a previously unknown key intermediate structure. Four backbone dihedrals were identified as important during the opening process, and their movements provide insight into the recognition of dNTP substrate molecules by the polymerase binary state. In addition to revealing the opening mechanism, this study also demonstrates our ability to study biological events of DNA polymerase using current computational methods without biasing the dynamics.

Angiographic result of T-stenting with small protrusion using drug-eluting stents in the management of ischemic side branch: the ARTEMIS study.

The aim of this study was to examine the mid-term angiographic result of T-stenting with small protrusion (TAP) as the bailout strategy for treating coronary bifurcation lesions. From 2009 to 2012, symptomatic patients who had severe coronary bifurcation stenoses were treated with one-stent strategy using drug-eluting stents, with kissing balloon inflation performed whenever side branch (SB) impingement occurred. TAP was performed if residual diameter stenosis of SB was ≥75%, presence of ≥type B dissection or flow impairment was observed in the SB. Seventy-one patients (83% male, mean age of 61 ± 12 years) were recruited into the study. MEDINA classification 1,1,1 lesions were observed in over 60% of patients. The mean stent size and length in the main vessel (MV) and SB were 2.86 ± 0.43 and 30 ± 12, and 2.45 ± 0.26 and 16 ± 6 mm, respectively. Restudy angiography was performed on 64 (90 %) patients at 9.2 ± 3.9 months. Angiographic restenosis was observed in 8 (12.5%) patients with late lumen loss in the MV and SB being 0.22 ± 0.19 and 0.34 ± 0.37 mm, respectively. The use of TAP as the bailout technique for treating coronary bifurcation lesions is associated with good angiographic outcomes, in terms of late lumen loss and restenosis, at 9 months.

Extraplaque blood withdrawal stenting: A miraculous cure for subintimal hematoma.

We report the Extraplaque Blood Withdrawal stenting technique to treat chronic total occlusion percutaneous coronary intervention (CTO PCI)-induced extraplaque hematoma.

Ten tips and tricks for successful distal true lumen wiring from three-dimensional wiring experts.

Antegrade wiring is the dominant method used in chronic total occlusion percutaneous coronary intervention (CTO PCI). However, distal cap puncture for distal true lumen wiring remains a significant barrier toward success. Three-dimensional (3D) fluoroscopic wiring can improve the speed, safety, and success of distal cap wiring. In this article, we provide 10 tips for every CTO interventionist to use when performing 3D wiring in distal true lumen wiring.

Acellular Piscine Dermis for Pediatric Hand Burn Reconstruction.

Pediatric hand burns are difficult to treat, with thin tissue with critical structures close to the skin and the small scale of the anatomy of children's hands. Additionally, pediatric burns can be challenging due to the concern for donor-site morbidity and the paucity of donor sites when reconstructing these wounds. In this report, we discuss the successful application of a piscine-derived acellular dermal matrix in a 13-month-old child with deep partial thickness and full-thickness burns to the right upper extremity. She had excellent long term cosmetic results and function by 3 years postoperatively, including full extension and flexion of all digits in her right hand.

Structural factors that determine selectivity of a high fidelity DNA polymerase for deoxy-, dideoxy-, and ribonucleotides.

In addition to discriminating against base pair mismatches, DNA polymerases exhibit a high degree of selectivity for deoxyribonucleotides over ribo- or dideoxynucleotides. It has been proposed that a single active site residue (steric gate) blocks productive binding of nucleotides containing 2'-hydroxyls. Although this steric gate plays a role in sugar moiety discrimination, its interactions do not account fully for the observed behavior of mutants. Here we present 10 high resolution crystal structures and enzyme kinetic analyses of Bacillus DNA polymerase I large fragment variants complexed with deoxy-, ribo-, and dideoxynucleotides and a DNA substrate. Taken together, these data present a more nuanced and general mechanism for nucleotide discrimination in which ensembles of intermediate conformations in the active site trap non-cognate substrates. It is known that the active site O-helix transitions from an open state in the absence of nucleotide substrates to a ternary complex closed state in which the reactive groups are aligned for catalysis. Substrate misalignment in the closed state plays a fundamental part in preventing non-cognate nucleotide misincorpation. The structures presented here show that additional O-helix conformations intermediate between the open and closed state extremes create an ensemble of binding sites that trap and misalign non-cognate nucleotides. Water-mediated interactions, absent in the fully closed state, play an important role in formation of these binding sites and can be remodeled to accommodate different non-cognate substrates. This mechanism may extend also to base pair discrimination.

Dual-Lumen Catheter and Floating-Wire Technique to Access Protruding Aorto-Ostial Stent.

PCI in the setting of previous aorto-ostial stenting can be difficult, especially if there is excessive stent protrusion. Various techniques have been described, including double-wire technique, double-guide snare technique, side-strut sequential ballooning technique, and guide extension facilitated sidestrut stenting. These techniques can sometimes be complicated, and intervention through a side-strut may lead to excessive stent deformation or avulsion of the protruding segment. Our novel technique uses a dual-lumen catheter and floating wire to back the JR4 guide away from the protruding stent while maintaining stability for another guidewire to enter the central lumen.

Synergistic Coronary Artery Calcium Modification With Combined Atherectomy and Intravascular Lithotripsy.

BACKGROUND: Severe coronary artery calcification (CAC) remains challenging during percutaneous coronary intervention (PCI) and often requires 1 or more advanced calcium modification tools. OBJECTIVES: We describe the combination use of rotational (RA) or orbital atherectomy (OA), with intravascular lithotripsy (IVL), termed rotatripsy and orbital-tripsy, respectively, for modifying CAC prior to stent implantation during PCI. METHODS: We performed a retrospective analysis of patients treated with rotatripsy or orbital-tripsy at our center between July 2019 and March 2022. The primary efficacy endpoint was procedural success (successful stent implantation, <30% residual stenosis visually, Thrombolysis in Myocardial Infarction 3 flow; absence of types C to F dissection/perforation or loss of side branch ≥2.0mm visually) without in-hospital major adverse cardiovascular event (MACE, defined as cardiovascular death, myocardial infarction [MI], target-vessel revascularization). RESULTS: A total of 25 patients (14 rotatripsy and 11 orbital-tripsy) were included in our study. The mean age was 72.2 ± 7.6 years and 76% were men. PCI was guided by intravascular imaging in 24 patients (96%). All cases were treated with either RA or OA before utilization of IVL. Procedural success was achieved in 22 cases (88%) with 1 sidebranch loss without periprocedural MI (4%) and 2 in-patient deaths (8%) unrelated to the procedure (1 intracerebral hemorrhage and 1 cardiac arrest). CONCLUSION: We describe efficacious use of both rotatripsy and orbital-tripsy to modify severe CAC during PCI in a real-world setting. Intravascular imaging can guide appropriate use of these devices to complement each other to modify severe CAC to achieve optimal outcomes.