Continuous Monitoring of A/B Tests without Pain: Optional Stopping in Bayesian Testing

A/B testing is one of the most successful applications of statistical theory in modern Internet age. One problem of Null Hypothesis Statistical Testing (NHST), the backbone of A/B testing methodology, is that experimenters are not allowed to continuously monitor the result and make decision in real time. Many people see this restriction as a setback against the trend in the technology toward real time data analytics. Recently, Bayesian Hypothesis Testing, which intuitively is more suitable for real time decision making, attracted growing interest as an alternative to NHST. While corrections of NHST for the continuous monitoring setting are well established in the existing literature and known in A/B testing community, the debate over the issue of whether continuous monitoring is a proper practice in Bayesian testing exists among both academic researchers and general practitioners. In this paper, we formally prove the validity of Bayesian testing with continuous monitoring when proper stopping rules are used, and illustrate the theoretical results with concrete simulation illustrations. We point out common bad practices where stopping rules are not proper and also compare our methodology to NHST corrections. General guidelines for researchers and practitioners are also provided

Extending Context Window of Large Language Models via Positional Interpolation

We present Position Interpolation (PI) that extends the context window sizes of RoPE-based pretrained LLMs such as LLaMA models to up to 32768 with minimal fine-tuning (within 1000 steps), while demonstrating strong empirical results on various tasks that require long context, including passkey retrieval, language modeling, and long document summarization from LLaMA 7B to 65B. Meanwhile, the extended model by Position Interpolation preserve quality relatively well on tasks within its original context window. To achieve this goal, Position Interpolation linearly down-scales the input position indices to match the original context window size, rather than extrapolating beyond the trained context length which may lead to catastrophically high attention scores that completely ruin the self-attention mechanism. Our theoretical study shows that the upper bound of interpolation is at least $\sim 600 \times$ smaller than that of extrapolation, further demonstrating its stability. Models extended via Position Interpolation retain its original architecture and can reuse most pre-existing optimization and infrastructure.Comment: Fix template issue

Acceleration of electrons in a self-modulated laser wakefield

Acceleration of electrons in a self-modulated laser-wakefield is investigated. The generated electron beam is oberved to have a multi-component beam profile and its energy distribution undergoes discrete transitions as the conditions are varied. These features can be explained by simple simulations of electron propagation in a 3-D plasma wave. © 1999 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87719/2/333_1.pd

Electron acceleration by self-modulated laser wakefield in a relativistically self-guided channel

The relativistic self-focusing of an intense laser pulse (I ∼ 4×1018 W/cm2,I∼4×1018W/cm2, λ = 1 μm,λ=1μm, τ = 400 fsτ=400fs) in a gas jet 750 μm in length was observed using sidescattering imaging. A self-modulated laser wakefield was generated to accelerate self-trapped electrons. The energy distribution and transverse emittance of the electron beam changed due to the onset of the relativistic self-guiding. © 1997 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87563/2/408_1.pd

Criss-crossing Laser Beams Zoom Electrons Along

Crossing two high-intensity laser beams in a plasma (a collection of charged particles) can have some interesting effects. In a recent experiment performed by researchers at the University of Michigan and the Institute of Physics in China, energy from a higher-power laser pulse was transferred to a lower-power laser pulse. The lower-power pulse had been accelerating electrons with its wakefield (like a wave accelerating a surfer). The extra energy to this lower-power pulse enhanced the electron acceleration and decreased the divergence of the electron beam. These features are desirable for proposed laser particle accelerators that would be powered by relatively inexpensive and convenient laser light, which is much more powerful than conventional radio-frequency waves

Nonlinear optics in relativistic plasmas

We discuss various nonlinear optical processes that occur as an intense laser propagates through a relativistic plasma. These include the experimental observations of electron acceleration driven by laser-wakefield generation, relativistic self-focusing, waveguide formation and laser self-channeling. © 1998 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87450/2/103_1.pd

An optical trap for relativistic plasma

The first optical trap capable of confining relativistic electrons, with kinetic energy ⩽350 keV was created by the interference of spatially and temporally overlapping terawatt power, 400 fs duration laser pulses ( ⩽ 2.4×1018 W/cm2)(⩽2.4×1018W/cm2) in plasma. Analysis and computer simulation predicted that the plasma density was greatly modulated, reaching a peak density up to 10 times the background density (ne/n0 ∼ 10)(ne/n0∼10) at the interference minima. Associated with this charge displacement, a direct-current electrostatic field of strength of ∼ 2×1011 eV/m∼2×1011eV/m was excited. These predictions were confirmed experimentally by Thomson and Raman scattering diagnostics. Also confirmed were predictions that the electron density grating acted as a multi-layer mirror to transfer energy between the crossed laser beams, resulting in the power of the weaker laser beam being nearly 50% increased. Furthermore, it was predicted that the optical trap acted to heat electrons, increasing their temperature by two orders of magnitude. The experimental results showed that the number of high energy electrons accelerated along the direction of one of the laser beams was enhanced by a factor of 3 and electron temperature was increased ∼100 keV as compared with single-beam illumination. © 2003 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70416/2/PHPAEN-10-5-2093-1.pd

Evidence of Ionization Blue Shift Seeding of Forward Raman Scattering

We report on the results of spectroscopic experiments that were conducted by focusing an intense ultra‐short laser pulse onto a helium gas target. The scattered light from the interaction region was measured spectrally and spatially from various directions as a function of laser intensity and plasma density. The experimental data showed that forward Stimulated Raman Scattering (SRS) was sensitive to the focus position of laser relative to the nozzle. Together with the plasma channel that was imaged by a CCD camera, the measurements indicate that SRS is seeded by the ionization blue‐shifted light. The cross‐phase modulation between the SRS and laser beam was also observed in the experiment. © 2004 American Institute of PhysicsPeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87541/2/585_1.pd

Risk of COVID-19 Transmission Aboard Aircraft: An Epidemiological Analysis Based on the National Health Information Platform.

OBJECTIVES This study aims to investigate the risk of COVID-19 transmission on aircraft. METHODS We obtained data on all international flights to Lanzhou, China, from June 1 to August 1, 2020, through the Gansu Province National Health Information Platform and the official website of the Gansu Provincial Center for Disease Control and Prevention. Statistical analysis was then performed. RESULTS Three international flights arrived in Lanzhou. The flights had a total of 700 passengers, of whom 405 (57.9%) were male and 80 (11.4%) were children below age fourteen. Twenty-seven (3.9%) passengers were confirmed to have COVID-19. Confirmed patients were primarily male (17, 65.4%) with a median age of 27.0 years. The majority of confirmed cases were seated in the middle rows of the economy class, or near public facility areas such as restrooms and galleys. The prevalence of COVID-19 did not differ between passengers sitting on window, aisle or middle seats. Compared with passengers sitting on the same row up to two rows behind a confirmed case, passengers seated in the two rows ahead a confirmed case were at a slightly higher risk of being infected. CONCLUSIONS COVID-19 may be transmitted during a passenger flight, although there is still no direct evidence