For Fixed Control Parameters the Quantum Approximate Optimization Algorithm's Objective Function Value Concentrates for Typical Instances

The Quantum Approximate Optimization Algorithm, QAOA, uses a shallow depth quantum circuit to produce a parameter dependent state. For a given combinatorial optimization problem instance, the quantum expectation of the associated cost function is the parameter dependent objective function of the QAOA. We demonstrate that if the parameters are fixed and the instance comes from a reasonable distribution then the objective function value is concentrated in the sense that typical instances have (nearly) the same value of the objective function. This applies not just for optimal parameters as the whole landscape is instance independent. We can prove this is true for low depth quantum circuits for instances of MaxCut on large 3-regular graphs. Our results generalize beyond this example. We support the arguments with numerical examples that show remarkable concentration. For higher depth circuits the numerics also show concentration and we argue for this using the Law of Large Numbers. We also observe by simulation that if we find parameters which result in good performance at say 10 bits these same parameters result in good performance at say 24 bits. These findings suggest ways to run the QAOA that reduce or eliminate the use of the outer loop optimization and may allow us to find good solutions with fewer calls to the quantum computer.Comment: 16 pages, 1 figur

Robotic partial nephrectomy for posterior tumors through a retroperitoneal approach offers decreased length of stay compared with the transperitoneal approach: A propensity-matched analysis

INTRODUCTION: We sought to compare surgical outcomes between transperitoneal and retroperitoneal robotic partial nephrectomy (RPN) for posterior tumors. PATIENTS AND METHODS: Using our multi-institutional RPN database, we reviewed 610 consecutive cases for posterior renal masses treated between 2007 and 2015. Primary outcomes were complications, operative time, length of stay (LOS), surgical margin status, and estimated glomerular filtration rate (eGFR) preservation. Secondary outcomes were estimated blood loss, warm ischemia time (WIT), disease recurrence, and disease-specific mortality. Due to significant differences in treatment year and tumor size between approaches, retroperitoneal cases were matched 1:4 to transperitoneal cases based on propensity scores using the greedy algorithm. Outcomes were compared between approaches using the chi-square and Mann-Whitney U tests. RESULTS: After matching, 296 transperitoneal and 74 retroperitoneal cases were available for analysis, and matched groups were well balanced in terms of treatment year, age, gender, race, American Society of Anesthesiologists physical status classification (ASA) score, body mass index, tumor laterality, tumor size, R.E.N.A.L. (radius, exophytic/endophytic properties, nearness of tumor to the collecting system or sinus, anterior/posterior, location relative to polar lines) score, and hilar location. Compared with transperitoneal, the retroperitoneal approach was associated with significantly shorter mean LOS (2.2 vs 2.6 days, p = 0.01), but longer mean WIT (21 vs 19 minutes, p = 0.01). Intraoperative (p = 0.35) and postoperative complications (p = 0.65), operative time (p = 0.93), positive margins (p = 1.0), and latest eGFR preservation (p = 0.25) were not significantly different between approaches. No differences were detected in the other outcomes. CONCLUSIONS: Among high-volume surgeons, transperitoneal and retroperitoneal RPN achieved similar outcomes for posterior renal masses, although with slight differences in LOS and WIT. Retroperitoneal RPN may be an effective option for the treatment of certain small posterior renal masses

Stimulus Variability Affects the Amplitude of the Auditory Steady-State Response

In this study we investigate whether stimulus variability affects the auditory steady-state response (ASSR). We present cosinusoidal AM pulses as stimuli where we are able to manipulate waveform shape independently of the fixed repetition rate of 4 Hz. We either present sounds in which the waveform shape, the pulse-width, is fixed throughout the presentation or where it varies pseudo-randomly. Importantly, the average spectra of all the fixed-width AM stimuli are equal to the spectra of the mixed-width AM. Our null hypothesis is that the average ASSR to the fixed-width AM will not be significantly different from the ASSR to the mixed-width AM. In a region of interest beamformer analysis of MEG data, we compare the 4 Hz component of the ASSR to the mixed-width AM with the 4 Hz component of the ASSR to the pooled fixed-width AM. We find that at the group level, there is a significantly greater response to the variable mixed-width AM at the medial boundary of the Middle and Superior Temporal Gyri. Hence, we find that adding variability into AM stimuli increases the amplitude of the ASSR. This observation is important, as it provides evidence that analysis of the modulation waveform shape is an integral part of AM processing. Therefore, standard steady-state studies in audition, using sinusoidal AM, may not be sensitive to a key feature of acoustic processing

Effect of trainee level on surgical time and postoperative complications of anterior cruciate ligament reconstruction

PURPOSE: The objective of this study was to investigate the association between trainee level and surgical time and postoperative complications of anterior cruciate ligament reconstruction (ACLR). METHODS: A retrospective chart review of patients who underwent ACLR at an academic orthopaedic ambulatory surgery center collected demographic and clinical information, including the number of trainees present and trainee level. Unadjusted and adjusted regression analyses assessed the association between trainee number and level with surgical time (time from skin incision to closure) and postoperative complications. RESULTS: Of 799 patients in this study operated on by one of five academic sports surgeons, 87% had at least one trainee involved. The average surgical time overall was 93 ± 21 minutes and by trainee level was 99.7 (junior resident), 88.5 (senior residents), 96.6 (fellows), and 95.6 (no trainees). Trainee level was significantly associated with surgical time (P = 0.0008), with increased surgical time in cases involving fellows (0.0011). Fifteen complications (1.9%) were observed within 90 days of surgery. No notable risk factors of postoperative complications were identified. CONCLUSION: Resident trainee level does not have a notable effect on surgical time or postoperative complications for ACLR at an ambulatory surgery center, although cases involving fellows had longer surgical times. Trainee level was not associated with risk of postoperative complications

Self-interest And Public Interest: The Motivations Of Political Actors

Self-Interest and Public Interest in Western Politics showed that the public, politicians, and bureaucrats are often public spirited. But this does not invalidate public-choice theory. Public-choice theory is an ideal type, not a claim that self-interest explains all political behavior. Instead, public-choice theory is useful in creating rules and institutions that guard against the worst case, which would be universal self-interestedness in politics. In contrast, the public-interest hypothesis is neither a comprehensive explanation of political behavior nor a sound basis for institutional design