Streaming Verification for Graph Problems: Optimal Tradeoffs and Nonlinear Sketches

We study graph computations in an enhanced data streaming setting, where a space-bounded client reading the edge stream of a massive graph may delegate some of its work to a cloud service. We seek algorithms that allow the client to verify a purported proof sent by the cloud service that the work done in the cloud is correct. A line of work starting with Chakrabarti et al. (ICALP 2009) has provided such algorithms, which we call schemes, for several statistical and graph-theoretic problems, many of which exhibit a tradeoff between the length of the proof and the space used by the streaming verifier. This work designs new schemes for a number of basic graph problems---including triangle counting, maximum matching, topological sorting, and single-source shortest paths---where past work had either failed to obtain smooth tradeoffs between these two key complexity measures or only obtained suboptimal tradeoffs. Our key innovation is having the verifier compute certain nonlinear sketches of the input stream, leading to either new or improved tradeoffs. In many cases, our schemes in fact provide optimal tradeoffs up to logarithmic factors. Specifically, for most graph problems that we study, it is known that the product of the verifier's space cost $v$ and the proof length $h$ must be at least $\Omega(n^2)$ for $n$-vertex graphs. However, matching upper bounds are only known for a handful of settings of $h$ and $v$ on the curve $h \cdot v=\tilde{\Theta}(n^2)$. For example, for counting triangles and maximum matching, schemes with costs lying on this curve are only known for $(h=\tilde{O}(n^2), v=\tilde{O}(1))$, $(h=\tilde{O}(n), v=\tilde{O}(n))$, and the trivial $(h=\tilde{O}(1), v=\tilde{O}(n^2))$. A major message of this work is that by exploiting nonlinear sketches, a significant ``portion'' of costs on the tradeoff curve $h \cdot v = n^2$ can be achieved

A Powerful New Quantitative Genetics Platform, Combining Caenorhabditis elegans High-Throughput Fitness Assays with a Large Collection of Recombinant Strains.

The genetic variants underlying complex traits are often elusive even in powerful model organisms such as Caenorhabditis elegans with controlled genetic backgrounds and environmental conditions. Two major contributing factors are: (1) the lack of statistical power from measuring the phenotypes of small numbers of individuals, and (2) the use of phenotyping platforms that do not scale to hundreds of individuals and are prone to noisy measurements. Here, we generated a new resource of 359 recombinant inbred strains that augments the existing C. elegans N2xCB4856 recombinant inbred advanced intercross line population. This new strain collection removes variation in the neuropeptide receptor gene npr-1, known to have large physiological and behavioral effects on C. elegans and mitigates the hybrid strain incompatibility caused by zeel-1 and peel-1, allowing for identification of quantitative trait loci that otherwise would have been masked by those effects. Additionally, we optimized highly scalable and accurate high-throughput assays of fecundity and body size using the COPAS BIOSORT large particle nematode sorter. Using these assays, we identified quantitative trait loci involved in fecundity and growth under normal growth conditions and after exposure to the herbicide paraquat, including independent genetic loci that regulate different stages of larval growth. Our results offer a powerful platform for the discovery of the genetic variants that control differences in responses to drugs, other aqueous compounds, bacterial foods, and pathogenic stresses

Subcutaneous furosemide in advanced heart failure: service improvement project

Objectives: In severe heart disease, parenteral administration of loop diuretic is often needed. We present clinical outcomes from episodes of care using subcutaneous continuous infusion of furosemide (CSCI-furosemide).Methods: Retrospective review of service improvement data. The heart failure nurse specialist, supported by the heart failure-palliative care multi-disciplinary team, works with the community or hospice staff who administer the CSCI-furosemide. Data collected for consecutive patients receiving CSCI-furosemide included: age, sex, New York Heart Association (NYHA) class, preferred place of care, goal of treatment, infusion-site reactions, and signs and symptoms of fluid retention (including weight and self-reported breathlessness).Results: 116 people (men 86 [66%]; mean age 79 years, 49 to 97; NYHA class 3 [36/116, 31%] or 4 heart failure [80/116, 69%]) received 130 episodes of CSCI-furosemide (average duration 10 days, 1 to 49), over half in the patient’s own home/care home (80/129,; 61%) aiming to prevent hospital admission. 40/129 (31%) were managed in the hospice, and 9 (7.0%) in a community hospital. Average daily furosemide dose was 125 mg (40 to 300mg). The goal of treatment was achieved in (119/130, 91.5%) episodes.The median reduction in weight was 4kg (interquartiles -7 kg to -2 kgs, -22 to +9 kgs). Self-reported breathlessness reduced from 8.2 (+/-1.9) to 5.2 (+/-1.8). Adverse events occurred in 31/130 (24%) episodes; all but 4/130 (3%, localised skin infection) were mild.Conclusions: These preliminary data indicate that CSCI-furosemide is safe and effective for people with severe heart failure. An adequately powered randomised controlled trial is indicated

Transphyseal anterior cruciate ligament reconstruction using living parental donor hamstring graft: Excellent clinical results at 2 years in a cohort of 100 patients

Methods: One hundred consecutive juveniles undergoing ACL reconstruction with a living parental hamstring allograft were recruited prospectively and reviewed 2 years after ACL reconstruction with IKDC Knee Ligament Evaluation, and KT1000 instrumented laxity testing. Skeletally immature participants obtained annual radiographs until skeletal maturity, and long leg alignment radiographs at 2 years. Radiographic Posterior tibial slope was recorded. Results: Of 100 juveniles, the median age was 14 years (range 8-16) and 68% male. At surgery, 30 juveniles were graded Tanner 1 or 2, 21 were Tanner 3 and 49 were Tanner 4 or 5. There were no cases of iatrogenic physeal injury or leg length discrepancy on long leg radiographs at 2 years, despite a median increase in height of 8 cm. Twelve patients had an ACL graft rupture and 9 had a contralateral ACL injury. Of those without further ACL injury, 82% returned to competitive sports, IKDC ligament evaluation was normal in 52% and nearly normal in 48%. The median side to side difference on manual maximum testing with the KT1000 was 2 mm (range - 1 to 5). A radiographic PTS of 12° or more was observed in 49%. Conclusions: ACL reconstruction in the juvenile with living parental hamstring tendon allograft is a viable procedure associated with excellent clinical stability, patient-reported outcomes and return to sport over 2 years. Further ACL injury to the reconstructed and the contralateral knee remains a significant risk, with identical prevalence observed between the reconstructed and contralateral ACL between 12 and 24 months after surgery

A predictive model for fluid-saturated, brittle granular materials during high-velocity impact events

Granular materials -- aggregates of many discrete, disconnected solid particles -- are ubiquitous in natural and industrial settings. Predictive models for their behavior have wide ranging applications, e.g. in defense, mining, construction, pharmaceuticals, and the exploration of planetary surfaces. In many of these applications, granular materials mix and interact with liquids and gases, changing their effective behavior in non-intuitive ways. Although such materials have been studied for more than a century, a unified description of their behaviors remains elusive. In this work, we develop a model for granular materials and mixtures that is usable under particularly challenging conditions: high-velocity impact events. This model combines descriptions for the many deformation mechanisms that are activated during impact -- particle fracture and breakage; pore collapse and dilation; shock loading; and pore fluid coupling -- within a thermo-mechanical framework based on poromechanics and mixture theory. This approach allows for simultaneous modeling of the granular material and the pore fluid, and includes both their independent motions and their complex interactions. A general form of the model is presented alongside its specific application to two types of sands that have been studied in the literature. The model predictions are shown to closely match experimental observation of these materials through several GPa stresses, and simulations are shown to capture the different dynamic responses of dry and fully-saturated sand to projectile impacts at 1.3 km/s