Higher-order Quasi-Monte Carlo Training of Deep Neural Networks

We present a novel algorithmic approach and an error analysis leveraging Quasi-Monte Carlo points for training deep neural network (DNN) surrogates of Data-to-Observable (DtO) maps in engineering design. Our analysis reveals higher-order consistent, deterministic choices of training points in the input data space for deep and shallow Neural Networks with holomorphic activation functions such as tanh. These novel training points are proved to facilitate higher-order decay (in terms of the number of training samples) of the underlying generalization error, with consistency error bounds that are free from the curse of dimensionality in the input data space, provided that DNN weights in hidden layers satisfy certain summability conditions. We present numerical experiments for DtO maps from elliptic and parabolic PDEs with uncertain inputs that confirm the theoretical analysis

Efficient injection from large telescopes into single-mode fibres: Enabling the era of ultra-precision astronomy

Photonic technologies offer numerous advantages for astronomical instruments such as spectrographs and interferometers owing to their small footprints and diverse range of functionalities. Operating at the diffraction-limit, it is notoriously difficult to efficiently couple such devices directly with large telescopes. We demonstrate that with careful control of both the non-ideal pupil geometry of a telescope and residual wavefront errors, efficient coupling with single-mode devices can indeed be realised. A fibre injection was built within the Subaru Coronagraphic Extreme Adaptive Optics (SCExAO) instrument. Light was coupled into a single-mode fibre operating in the near-IR (J-H bands) which was downstream of the extreme adaptive optics system and the pupil apodising optics. A coupling efficiency of 86% of the theoretical maximum limit was achieved at 1550 nm for a diffraction-limited beam in the laboratory, and was linearly correlated with Strehl ratio. The coupling efficiency was constant to within <30% in the range 1250-1600 nm. Preliminary on-sky data with a Strehl ratio of 60% in the H-band produced a coupling efficiency into a single-mode fibre of ~50%, consistent with expectations. The coupling was >40% for 84% of the time and >50% for 41% of the time. The laboratory results allow us to forecast that extreme adaptive optics levels of correction (Strehl ratio >90% in H-band) would allow coupling of >67% (of the order of coupling to multimode fibres currently). For Strehl ratios <20%, few-port photonic lanterns become a superior choice but the signal-to-noise must be considered. These results illustrate a clear path to efficient on-sky coupling into a single-mode fibre, which could be used to realise modal-noise-free radial velocity machines, very-long-baseline optical/near-IR interferometers and/or simply exploit photonic technologies in future instrument design.Comment: 15 pages, 16 figures, 1 table, published in A&

MTSS1 is a critical epigenetically regulated tumor suppressor in CML

Chronic myeloid leukemia (CML) is driven by malignant stem cells that can persist despite therapy. We have identified Metastasis suppressor 1 (Mtss1/MIM) to be downregulated in hematopoietic stem and progenitor cells from leukemic transgenic SCLtTA/Bcr-Abl mice and in patients with CML at diagnosis, and Mtss1 was restored when patients achieved complete remission. Forced expression of Mtss1 decreased clonogenic capacity and motility of murine myeloid progenitor cells and reduced tumor growth. Viral transduction of Mtss1 into lineage depleted SCLtTA/Bcr-Abl bone marrow cells decreased leukemic cell burden in recipients, and leukemogenesis was reduced upon injection of Mtss1 overexpressing murine myeloid 32D cells. Tyrosine kinase inhibitor (TKI) therapy and reversion of Bcr-Abl expression increased Mtss1 expression but failed to restore it to control levels. CML patient samples revealed higher DNA methylation of specific Mtss1 promoter CpG sites that contain binding sites for Kaiso and Rest transcription factors. In summary, we identified a novel tumor suppressor in CML stem cells that is downregulated by both Bcr-Abl kinase-dependent and -independent mechanisms. Restored Mtss1 expression markedly inhibits primitive leukemic cell biology in vivo, providing a therapeutic rationale for the Bcr-Abl-Mtss1 axis to target TKI resistant CML stem cells in patients

Statistical mechanics of transcription-factor binding site discovery using Hidden Markov Models

Hidden Markov Models (HMMs) are a commonly used tool for inference of transcription factor (TF) binding sites from DNA sequence data. We exploit the mathematical equivalence between HMMs for TF binding and the "inverse" statistical mechanics of hard rods in a one-dimensional disordered potential to investigate learning in HMMs. We derive analytic expressions for the Fisher information, a commonly employed measure of confidence in learned parameters, in the biologically relevant limit where the density of binding sites is low. We then use techniques from statistical mechanics to derive a scaling principle relating the specificity (binding energy) of a TF to the minimum amount of training data necessary to learn it.Comment: 25 pages, 2 figures, 1 table V2 - typos fixed and new references adde

Systematic study of carrier correlations in the electron-hole recombination dynamics of quantum dots

The ground state carrier dynamics in self-assembled (In,Ga)As/GaAs quantum dots has been studied using time-resolved photoluminescence and transmission. By varying the dot design with respect to confinement and doping, the dynamics is shown to follow in general a non-exponential decay. Only for specific conditions in regard to optical excitation and carrier population, for example, the decay can be well described by a mono-exponential form. For resonant excitation of the ground state transition a strong shortening of the luminescence decay time is observed as compared to the non-resonant case. The results are consistent with a microscopic theory that accounts for deviations from a simple two-level picture.Comment: 8 pages, 7 figure

Ignition delays, heats of combustion, and reaction rates of aluminum alkyl derivatives used as ignition and combustion enhancers for supersonic combustion

The subject of this paper is the design of supersonic combustors which will be required in order to achieve the needed reaction rates in a reasonable sized combustor. A fuel additive approach, which is the focus of this research, is the use of pyrophorics to shorten the ignition delay time and to increase the energy density of the fuel. Pyrophoric organometallic compounds may also provide an ignition source and flame stabilization mechanism within the combustor, thus permitting use of hydrocarbon fuels in supersonic combustion systems. Triethylaluminum (TEA) and trimethylaluminum (TMA) were suggested for this application due to their high energy density and reactivity. The objective here is to provide comparative data for the ignition quality, the energy content, and the reaction rates of several different adducts of both TEA and TMA. The results of the experiments indicate the aluminum alkyls and their more stable derivatives reduce the ignition delay and total reaction time to JP-10 jet fuel. Furthermore, the temperature dependence of ignition delay and total reaction time of the blends of the adducts are significantly lower than in neat JP-10

Analytic regularity for a singularly perturbed system of reaction-diffusion equations with multiple scales: proofs

We consider a coupled system of two singularly perturbed reaction-diffusion equations, with two small parameters $0< \epsilon \le \mu \le 1$, each multiplying the highest derivative in the equations. The presence of these parameters causes the solution(s) to have \emph{boundary layers} which overlap and interact, based on the relative size of $\epsilon$ and $$. We construct full asymptotic expansions together with error bounds that cover the complete range $0 < \epsilon \leq \mu \leq 1$. For the present case of analytic input data, we derive derivative growth estimates for the terms of the asymptotic expansion that are explicit in the perturbation parameters and the expansion order