Stochastic Lipschitz dynamic programming Ahmed, Shabbir; Cabral, Filipe Goulart; Freitas Paulo da Costa, Bernardo
Mathematical programming,
02/2022, Letnik:
191, Številka:
2
Journal Article
Recenzirano
Odprti dostop
We propose a new algorithm for solving multistage stochastic mixed integer linear programming (MILP) problems with complete continuous recourse. In a similar way to cutting plane methods, we ...construct nonlinear Lipschitz cuts to build lower approximations for the non-convex cost-to-go functions. An example of such a class of cuts are those derived using Augmented Lagrangian Duality for MILPs. The family of Lipschitz cuts we use is MILP representable, so that the introduction of these cuts does not change the class of the original stochastic optimization problem. We illustrate the application of this algorithm on two case studies, comparing our approach with the convex relaxation of the problems, for which we can apply SDDP, and for a discretized approximation, applying SDDiP.
Practical quantum computing will require error rates well below those achievable with physical qubits. Quantum error correction
offers a path to algorithmically relevant error rates by encoding ...logical qubits within many physical qubits, for which increasing the number of physical qubits enhances protection against physical errors. However, introducing more qubits also increases the number of error sources, so the density of errors must be sufficiently low for logical performance to improve with increasing code size. Here we report the measurement of logical qubit performance scaling across several code sizes, and demonstrate that our system of superconducting qubits has sufficient performance to overcome the additional errors from increasing qubit number. We find that our distance-5 surface code logical qubit modestly outperforms an ensemble of distance-3 logical qubits on average, in terms of both logical error probability over 25 cycles and logical error per cycle ((2.914 ± 0.016)% compared to (3.028 ± 0.023)%). To investigate damaging, low-probability error sources, we run a distance-25 repetition code and observe a 1.7 × 10
logical error per cycle floor set by a single high-energy event (1.6 × 10
excluding this event). We accurately model our experiment, extracting error budgets that highlight the biggest challenges for future systems. These results mark an experimental demonstration in which quantum error correction begins to improve performance with increasing qubit number, illuminating the path to reaching the logical error rates required for computation.
Risk-averse multistage stochastic programs appear in multiple areas and are challenging to solve. Stochastic Dual Dynamic Programming (SDDP) is a well-known tool to address such problems under ...time-independence assumptions. We show how to derive a dual formulation for these problems and apply an SDDP algorithm, leading to converging and deterministic upper bounds for risk-averse problems.
A series of strontium titanates-vanadates (STVN) with nominal cation composition Sr1-xTi1-y-zVyNizO3-δ (x = 0–0.04, y = 0.20–0.40 and z = 0.02–0.12) were prepared by a solid-state reaction route in ...10% H2–N2 atmosphere and characterized under reducing conditions as potential fuel electrode materials for solid oxide fuel cells. Detailed phase evolution studies using XRD and SEM/EDS demonstrated that firing at temperatures as high as 1200 °C is required to eliminate undesirable secondary phases. Under such conditions, nickel tends to segregate as a metallic phase and is unlikely to incorporate into the perovskite lattice. Ceramic samples sintered at 1500 °C exhibited temperature-activated electrical conductivity that showed a weak p(O2) dependence and increased with vanadium content, reaching a maximum of ~17 S/cm at 1000 °C. STVN ceramics showed moderate thermal expansion coefficients (12.5–14.3 ppm/K at 25–1100 °C) compatible with that of yttria-stabilized zirconia (8YSZ). Porous STVN electrodes on 8YSZ solid electrolytes were fabricated at 1100 °C and studied using electrochemical impedance spectroscopy at 700–900 °C in an atmosphere of diluted humidified H2 under zero DC conditions. As-prepared STVN electrodes demonstrated comparatively poor electrochemical performance, which was attributed to insufficient intrinsic electrocatalytic activity and agglomeration of metallic nickel during the high-temperature synthetic procedure. Incorporation of an oxygen-ion-conducting Ce0.9Gd0.1O2-δ phase (20–30 wt.%) and nano-sized Ni as electrocatalyst (≥1 wt.%) into the porous electrode structure via infiltration resulted in a substantial improvement in electrochemical activity and reduction of electrode polarization resistance by 6–8 times at 900 °C and ≥ one order of magnitude at 800 °C.
Purpose
Lifestyle is linked to the risk of developing metabolic syndrome (MetS); however, its relationship with dietary patterns remains unclear. This systematic review and meta-analysis aims to ...analyse the association of a posteriori dietary patterns with the metabolic syndrome.
Methods
The PubMed, CINAHL and Scopus databases were searched for epidemiological studies of dietary patterns and MetS. The association between dietary patterns and MetS was estimated using a random-effects meta-analysis with 95 % confidence intervals (CIs).
Results
A total of 28 cross-sectional studies and three cohort studies were included in the meta-analysis. In a comparison of the highest to the lowest category of prudent/healthy dietary patterns, the pooled odds ratio (OR) for MetS was 0.83 (95 % CI 0.76, 0.90;
P
for heterogeneity =0.0; and
I
2
= 72.1 %) in cross-sectional studies, and the pooled relative risk (RR) for MetS in cohort studies was 0.91 (95 % CI 0.68, 1.21;
P
for heterogeneity =0.005;
I
2
= 81.1 %). The pooled OR for MetS in a comparison of the highest to the lowest category of Western dietary patterns was 1.28 (95 % CI 1.17, 1.40;
P
for heterogeneity =0.0; and
I
2
= 72.0 %) in cross-sectional studies, and the RR was 0.96 (95 % CI 0.53, 1.73;
P
for heterogeneity =0.102;
I
2
= 62.6 %) in cohort studies.
Conclusions
The results from cross-sectional studies showed that a prudent/healthy pattern is associated with a lower prevalence of MetS, whereas a Western/unhealthy is associated with an increased risk for MetS. Additional prospective studies are needed to confirm the association between dietary patterns and MetS.
Systematic reviews (SR) have always been used as the best evidence to compare three radical prostatectomy (RP) techniques: retropubic radical prostatectomy (RRP), laparoscopic radical prostatectomy ...(LRP), and robotic radical prostatectomy (RARP). Despite the superiority of minimally invasive surgery in relation to perioperative outcomes, the literature still cannot establish which technique is superior in relation to oncological outcomes. A new methodology called Reverse Systematic Review (RSR) was created to gather the best evidence in the literature based on a heterogeneous sample, allowing the comparison of oncological outcomes from a population point of view.
To apply the RSR to compare RP techniques in relation to oncological outcomes: positive surgical margin (PSM) and biochemical recurrence rate (BCR).
A search was carried out in eight databases between 2000 and 2020 through SR studies referring RRP, LRP, or RARP (80 SR). All references used in these SR were captured referring to 1724 reports. Preoperative and oncological outcomes were compared and correlated among RRP, LRP, and RARP.
Five hundred fifty-nine (32.4%) reports for RRP, 413 (23.9%) for LRP, and 752 (43.7%) for RARP, and a total of 1,353,485 patients were found. Regarding PSM, 284 reports were collected for RRP, 324 for LRP, and 499 for RARP, with rates of 23.6%, 20.7%, and 19.2%, respectively, and only the RRP with statistical difference (
< 0.001). Using a nonlinear regression model, the BCR was correlated with follow-up time at 1, 2, 3, 5, 7, and 10 years: 10%, 15%, 18%, 20%, 23%, and 38% for RRP; 6%, 9%, 13%, 20%, 23%, and 10% for LRP; and 8%, 12%, 16%, 23%, 27%, and 19% for RARP. The absence of long-term work for RARP prevented more accurate projections of BCR.
RSR proved to be effective in generating a population and heterogeneous sample capable of demonstrating better oncological results for minimally invasive surgery (LRP and RARP) compared to RRP. It demonstrated the maturity of temporal follow-up data for RRP and LRP and the impact of absence of late follow-up from RARP studies on the long-term rate of BCR.
After 20 years of coexistence of the three main radical prostatectomy techniques, the RSR was able to detect better results from minimally invasive surgery in relation to PSMs and long-term BCRs.
We establish the existence of solutions to a class of nonlinear stochastic differential equations of reaction–diffusion type in an infinite-dimensional space, with diffusion corresponding to a given ...transition kernel. The solution obtained is the scaling limit of a sequence of interacting particle systems and satisfies the martingale problem corresponding to the target differential equation.
ContextThe advantages of minimally invasive surgery for radical prostatectomy (RP) have been demonstrated in a number of systematic reviews (SRs). However, the rigorous study selection process for SR ...means that a lot of information can be excluded, leading to a very specific clinical scenario that is often unrepresentative of real life. Our new reverse SR methodology generates a heterogeneous population database that covers a wide range of clinical scenarios. ObjectiveTo compare perioperative surgical results and complications for open retropubic RP (RRP), laparoscopic RP (LRP), and robot-assisted RP (RARP) in a reverse SR. Evidence acquisitionEight databases were searched for SRs on RRP, LRP, or RARP between 2000 and 2020 (80 SRs). All references used in these SRs were captured for analysis (1724 articles). Perioperative outcomes and complications were compared among the RRP, LRP, and RARP approaches. Evidence synthesisWe identified 559 (32.4%) reports on RRP, 413 (23.9%) on LRP, and 752 (43.7%) on RARP, involving 1 353 485 patients overall. RARP showed a significantly higher annual volume of surgery per surgeon (AVSS) in comparison to RRP and LRP (mean 64.29, 43.26, and 41.47, respectively), a higher percentage of low-risk patients (prostate-specific antigen <10 ng/ml, Gleason <7, stage <cT2), and a lower rate of lymphadenectomy, culminating in a lower complication rate (12.3% for RARP, 16.3% for LRP, 20.2% for RRP). Among all outcomes, only AVSS was significantly correlated with complication rates. An AVSS of 30, 95 and 95 surgeries/yr was required for RARP, LRP, and RRP, respectively, to obtain a complication rate of 12.3% (average for RARP). RARP showed better performance for all perioperative variables studied except for operative time (operative time: 199.8 vs 214.9 vs 169.5 min; estimated blood loss: 228.2 vs 408.0 vs 852.1 ml; blood transfusion rate: 2.8% vs 6.5% vs 19.8%; length of stay: 2.9 vs 5.7 vs 6.1 d; catheter time: 7.8 vs 8.5 vs 11.0 d for RARP vs LRP vs RRP). ConclusionsOur reverse SR involved a wide real-life representative sample and reference values established in the literature and revealed that minimally invasive surgery had the best perioperative and complication results, especially RARP, which was associated with less complex cases, higher annual surgeon volume, and greater performance. Patient summaryWe used a wide sample representative of real-life surgical practice and reference values established in the literature for three techniques for removal of the prostate to guide patients and physicians in deciding the best surgical treatment for prostate cancer according to availability.
A numerical model of a 5 km long curved floating bridge, planned for the Bjørnafjord, in Norway, is subjected to strong wind events with stationary mean properties that vary along the bridge axis. A ...Weather Research and Forecasting model (WRF) is used to estimate the mean wind speeds and directions in the fjord, with a 500 m resolution, during a 20-year period. The wind turbulence intensities are estimated as functions of the position along the bridge and the wind direction, using an artificial neural network trained on nearby sonic anemometer data and formulations given in the national annex of the Eurocode. A skew wind buffeting formulation is used to estimate the linear static response and the linear quasi-steady buffeting response in the frequency domain. The response under inhomogeneous winds is compared with the response under equivalent homogeneous winds. The inhomogeneous wind response is, on average, 1.5% to 47% larger, depending on the type of analysis and response component, but a high variability is observed, with much larger differences for some wind cases. These findings motivate case-specific investigations of inhomogeneous wind effects to improve fatigue and extreme response predictions of long wind-sensitive structures.
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