Classical simulation of commuting quantum computations implies collapse of the polynomial hierarchy

We consider quantum computations comprising only commuting gates, known as IQP computations, and provide compelling evidence that the task of sampling their output probability distributions is unlikely to be achievable by any efficient classical means. More specifically we introduce the class post-IQP of languages decided with bounded error by uniform families of IQP circuits with post-selection, and prove first that post-IQP equals the classical class PP. Using this result we show that if the output distributions of uniform IQP circuit families could be classically efficiently sampled, even up to 41% multiplicative error in the probabilities, then the infinite tower of classical complexity classes known as the polynomial hierarchy, would collapse to its third level. We mention some further results on the classical simulation properties of IQP circuit families, in particular showing that if the output distribution results from measurements on only O(log n) lines then it may in fact be classically efficiently sampled.Comment: 13 page

A stochastic model for the evolution of the web allowing link deletion

Recently several authors have proposed stochastic evolutionary models for the growth of the web graph and other networks that give rise to power-law distributions. These models are based on the notion of preferential attachment leading to the ``rich get richer'' phenomenon. We present a generalisation of the basic model by allowing deletion of individual links and show that it also gives rise to a power-law distribution. We derive the mean-field equations for this stochastic model and show that by examining a snapshot of the distribution at the steady state of the model, we are able to tell whether any link deletion has taken place and estimate the link deletion probability. Our model enables us to gain some insight into the distribution of inlinks in the web graph, in particular it suggests a power-law exponent of approximately 2.15 rather than the widely published exponent of 2.1

The use of graft materials in vaginal pelvic floor surgery

ObjectiveTo review recent literature on graft materials used in vaginal pelvic floor surgery.MethodsA Pubmed‐search (“anterior vaginal wall” or “cystocele”), (“posterior vaginal wall” or “rectocele”) and (“vaginal vault” or “pelvic prolapse”) and (“mesh” or “erosion” or “graft” or “synthetic”) from 1995 to 2005 was performed; recent reviews [Birch C. The use of prosthetics in pelvic reconstructive surgery. Best Pract Res Clin Obstet Gynaecol 2005;19:979–91 [1]; Maher C, Baessler K. Surgical management of anterior vaginal wall prolapse: an evidence‐based literature review. Int Urogynecol J Pelvic Floor Dysfunct 2005 (May 25) [Electronic Publication] [2]; Maher C, Baessler K. Surgical management of posterior vaginal wall prolapse: an evidence‐based literature review. Int Urogynecol J Pelvic Floor Dysfunct 2006;17:84–8 [3]; Altman D, Mellgren A, Zetterstrom J. Rectocele repair using biomaterial augmentation: current documentation and clinical experience. Obstet Gynecol Surv 2005;60:753–60 [4]] were added.ResultThere are few prospective randomized trials that prove the benefit of implanting grafts in vaginal pelvic floor surgery. Many articles are retrospective case series with small sample sizes or incomplete outcome variables. Serious complications such as erosions are often not mentioned. Inconsistent or unclear criteria for anatomic cure make it difficult to compare outcomes. Quality of life issues such as dyspareunia, urinary or bowel symptoms are often ignored.ConclusionDue to a lack of well‐designed prospective randomized trials, recommendations for using graft materials in vaginal reconstructive surgery cannot be made. At this time, grafts should have limited use in a carefully selected patient population.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/135429/1/ijgo279.pd

Characterization of Alkali Metal Dispensers and Non-Evaporable Getter Pumps in Ultra-High Vacuum Systems for Cold Atomic Sensors

A glass ultrahigh vacuum chamber with rubidium alkali metal dispensers and non-evaporable getter pumps has been developed and used to create a cold atomic sample in a chamber that operates with only passive vacuum pumps. The ion-mass spectrum of evaporated gases from the alkali metal dispenser has been recorded as a function of dispenser current. The efficacy of the non-evaporable getter pumps in promoting and maintaining vacuum has been characterized by observation of the Rb vapor optical absorption on the D2 transition at 780 nm and vacuum chamber pressure rate of rise tests. We have demonstrated a sample of laser-cooled Rb atoms in this chamber when isolated and operating without active vacuum pumps

Supporting Education, Research, and Training in the 21st Century

The expanding array of digital devices accessing the Internet around the globe provides new opportunities to collaborate in educating Adventist teachers and educational leaders to continue the teaching ministry of Jesus Christ in the 21st century. Partnerships among the Curriculum and Instruction Resource Center Linking Educators (CIRCLE), the Adventist Learning Community (ALC), and the Institute of Church Ministry (ICM) now connect more Adventists to education and training resources electronically than ever before