A Random Matrix Model of Adiabatic Quantum Computing

We present an analysis of the quantum adiabatic algorithm for solving hard instances of 3-SAT (an NP-complete problem) in terms of Random Matrix Theory (RMT). We determine the global regularity of the spectral fluctuations of the instantaneous Hamiltonians encountered during the interpolation between the starting Hamiltonians and the ones whose ground states encode the solutions to the computational problems of interest. At each interpolation point, we quantify the degree of regularity of the average spectral distribution via its Brody parameter, a measure that distinguishes regular (i.e., Poissonian) from chaotic (i.e., Wigner-type) distributions of normalized nearest-neighbor spacings. We find that for hard problem instances, i.e., those having a critical ratio of clauses to variables, the spectral fluctuations typically become irregular across a contiguous region of the interpolation parameter, while the spectrum is regular for easy instances. Within the hard region, RMT may be applied to obtain a mathematical model of the probability of avoided level crossings and concomitant failure rate of the adiabatic algorithm due to non-adiabatic Landau-Zener type transitions. Our model predicts that if the interpolation is performed at a uniform rate, the average failure rate of the quantum adiabatic algorithm, when averaged over hard problem instances, scales exponentially with increasing problem size.Comment: 9 pages, 7 figure

Comparison of PBO solvers in a dependency solving domain

Linux package managers have to deal with dependencies and conflicts of packages required to be installed by the user. As an NP-complete problem, this is a hard task to solve. In this context, several approaches have been pursued. Apt-pbo is a package manager based on the apt project that encodes the dependency solving problem as a pseudo-Boolean optimization (PBO) problem. This paper compares different PBO solvers and their effectiveness on solving the dependency solving problem.Comment: In Proceedings LoCoCo 2010, arXiv:1007.083

Sacituzumab govitecan in metastatic triple-negative breast cancer

BACKGROUND: Patients with metastatic triple-negative breast cancer have a poor prognosis. Sacituzumab govitecan is an antibody-drug conjugate composed of an antibody targeting the human trophoblast cell-surface antigen 2 (Trop-2), which is expressed in the majority of breast cancers, coupled to SN-38 (topoisomerase I inhibitor) through a proprietary hydrolyzable linker. METHODS In this randomized, phase 3 trial, we evaluated sacituzumab govitecan as compared with single-agent chemotherapy of the physician's choice (eribulin, vinorelbine, capecitabine, or gemcitabine) in patients with relapsed or refractory metastatic triple-negative breast cancer. The primary end point was progression-free survival (as determined by blinded independent central review) among patients without brain metastases. RESULTS A total of 468 patients without brain metastases were randomly assigned to receive sacituzumab govitecan (235 patients) or chemotherapy (233 patients). The median age was 54 years; all the patients had previous use of taxanes. The median progression-free survival was 5.6 months (95% confidence interval [CI], 4.3 to 6.3; 166 events) with sacituzumab govitecan and 1.7 months (95% CI, 1.5 to 2.6; 150 events) with chemotherapy (hazard ratio for disease progression or death, 0.41; 95% CI, 0.32 to 0.52; P<0.001). The median overall survival was 12.1 months (95% CI, 10.7 to 14.0) with sacituzumab govitecan and 6.7 months (95% CI, 5.8 to 7.7) with chemotherapy (hazard ratio for death, 0.48; 95% CI, 0.38 to 0.59; P<0.001). The percentage of patients with an objective response was 35% with sacituzumab govitecan and 5% with chemotherapy. The incidences of key treatment-related adverse events of grade 3 or higher were neutropenia (51% with sacituzumab govitecan and 33% with chemotherapy), leukopenia (10% and 5%), diarrhea (10% and <1%), anemia (8% and 5%), and febrile neutropenia (6% and 2%). There were three deaths owing to adverse events in each group; no deaths were considered to be related to sacituzumab govitecan treatment. CONCLUSIONS Progression-free and overall survival were significantly longer with sacituzumab govitecan than with single-agent chemotherapy among patients with metastatic triple-negative breast cancer. Myelosuppression and diarrhea were more frequent with sacituzumab govitecan

Composing Symmetry Propagation and Effective Symmetry Breaking for SAT Solving

International audienc

Failed literal detection for QBF

Abstract. Failed literal detection (FL) in SAT is a powerful approach for preprocessing. The basic idea is to assign a variable as assumption. If boolean constraint propagation (BCP) yields an empty clause then the negated assumption is necessary for satisfiability. Whereas FL is common in SAT, it cannot easily be applied to QBF due to universal quantification. We present two approaches for FL to preprocess prenex CNFs. The first one is based on abstraction where certain universal variables are treated as existentially quantified. Second we combine QBF-specific BCP (QBCP) in FL with Q-resolution to validate assignments learnt by FL. Finally we compare these two approaches to a third common approach based on SAT. It turns out that the three approaches are incomparable. Experimental evaluation demonstrates that FL for QBF can improve the performance of search- and elimination-based QBF solvers.