65 research outputs found
Subset Sampling and Its Extensions
This paper studies the \emph{subset sampling} problem. The input is a set
of records together with a function that assigns
each record a probability . A query returns a
random subset of , where each record is
sampled into independently with probability . The goal is to
store in a data structure to answer queries efficiently. If
fits in memory, the problem is interesting when is
dynamic. We develop a dynamic data structure with
expected \emph{query} time,
space and amortized expected \emph{update}, \emph{insert} and
\emph{delete} time, where
. The query time and
space are optimal. If does not fit in memory, the problem is
difficult even if is static. Under this scenario, we present an
I/O-efficient algorithm that answers a \emph{query} in
amortized expected I/Os using space, where is the memory
size, is the block size and is the number of iterative
operations we need to perform on before going below . In
addition, when each record is associated with a real-valued key, we extend the
\emph{subset sampling} problem to the \emph{range subset sampling} problem, in
which we require that the keys of the sampled records fall within a specified
input range . For this extension, we provide a solution under the
dynamic setting, with expected
\emph{query} time, space and amortized
expected \emph{update}, \emph{insert} and \emph{delete} time.Comment: 17 page
2-Selenouridine Triphosphate Synthesis and Se-RNA Transcription
2-Selenouridine (SeU) is one of the naturally occurring modifications of Se-tRNAs (SeU-RNA) at the wobble position of the anticodon loop. Its role in the RNA-RNA interaction, especially during the mRNA decoding, is elusive. To assist the research exploration, herein we report the enzymatic synthesis of the SeU-RNA via 2-selenouridine triphosphate (SeUTP) synthesis and RNA transcription. Moreover, we have demonstrated that the synthesized SeUTP is stable and recognizable by T7 RNA polymerase. Under the optimized conditions, the transcription yield of SeU-RNA can reach up to 85% of the corresponding native RNA. Furthermore, the transcribed SeU-hammerhead ribozyme has the similar activity as the corresponding native, which suggests usefulness of SeU-RNAs in function and structure studies of noncoding RNAs, including the Se-tRNAs
From Supercurrents to Soft Terms
In this paper,hidden sectors of Ferrara-Zumino multiplets with contributions
to soft terms coming from quantum supergravity are investigated in framework of
gravity mediation. The two-point correlator of Ferrara-Zumino multiplets can be
parameterized, which implies the wave function renormalizations of components
fields in gravity supermultiplet can be evaluated in relatively simple form.
Soft terms are calculated via supercurrent approach. We find gaugino masses are
independent of sfermion masses on general grounds. The unification of gaugino
masses is not universal. In comparison with general gauge mediation, there are
no sum rules for sfermion masses of each generation.Comment: v3, 9 p
Variant Supercurrents and Linearized Supergravity
In this paper the variant supercurrents based on consistency and completion
in off-shell N=1 supergravity are studied. We formulate the embedding relations
for supersymmetric current and energy tensor into supercurrent multiplet.
Corresponding linearized supergravity is obtained with appropriate choice of
Wess-Zumino gauge in each gravity supermultiplet.Comment: v1: 9 pp; v2: minor changes; v3: 10 pp, published versio
Size and Location Diagnosis of Rolling Bearing Faults: An Approach of Kernel Principal Component Analysis and Deep Belief Network
Diagnosing incipient faults of rotating machines is very important for reducing economic losses and avoiding accidents caused by faults. However, diagnoses of locations and sizes of incipient faults are very difficult in a noisy background. In this paper, we propose a fault diagnosis method that combines kernel principal component analysis (KPCA) and deep belief network (DBN) to detect sizes and locations of incipient faults on rolling bearings. Effective information of raw vibration signals processed by KPCA method is used as input signals of the DBN of which weights of the first RBM are initialized by contribution rates of principal components. A DBN with complex structures can be cut into a briefer network by KPCA-DBN model. That model reduces network structure and increases convergence rate. As a result, an average test accuracy by KPCA-DBN can reach 99.1% for identification of 12 labels including incipient faults and the training time is 28s which is half of that by DBN model. The average accuracy of rolling bearing location detection nearly gets to 100% and the average accuracy of fault size detection is above 99%. Compared with SVM, BP, CNN, Deep EMD-PCA (Empirical Mode Decomposition-Principal Component Analysis), CNN-SVM and DBN, it is found that training time can be shortened and detection accuracy can be improved by KPCA-DBN model. The proposed method is beneficial to realize sizes and locations detection of incipient faults online
Sound trapping in an open resonator
The ability of sound energy confinement with high-quality factor resonance is of vital importance for acoustic devices requiring high intensity and hypersensitivity in biological ultrasonics, enhanced collimated sound emission (i.e. sound laser) and high-resolution sensing. However, structures reported so far have been experimentally demonstrated with a limited quality factor of acoustic resonances, up to several tens in an open resonator. The emergence of bound states in the continuum makes it possible to realize high quality factor acoustic modes. Here, we report the theoretical design and experimental demonstration of acoustic bound states in the continuum supported by a single open resonator. We predicted that such an open acoustic resonator could simultaneously support three types of bound states in the continuum, including symmetry protected bound states in the continuum, Friedrich-Wintgen bound states in the continuum induced by mode interference, as well as a new type-mirror symmetry induced bound states in the continuum. We also experimentally demonstrated their existence with quality factor up to one order of magnitude greater than the highest quality factor reported in an open resonator
Topological Supercavity Resonances in the Finite System
Acoustic resonant cavities play a vital role in modern acoustical systems. The ultrahigh quality-factor resonances are highly desired for some applications such as high-resolution acoustic sensors and acoustic lasers. Here, a class of supercavity resonances is theoretically proposed and experimentally demonstrated in a coupled acoustic resonator system, arising from the merged bound states in the continuum (BICs) in geometry space. Their topological origin is demonstrated by explicitly calculating their topological charges before and after BIC merging, accompanied by charges annihilation. Compared with other types of BICs, they are robust to the perturbation brought by fabrication imperfection. Moreover, it is found that such supercavity modes can be linked with the Friedrich-Wintgen BICs supported by an entire rectangular (cuboid) resonator sandwiched between two rectangular (or circular) waveguides and thus more supercavity modes are constructed. Then, these coupled resonators are fabricated and such a unique phenomenon-moving, merging, and vanishing of BICs-is experimentally confirmed by measuring their reflection spectra, which show good agreement with the numerical simulation and theoretical prediction of mode evolution. The results may find exciting applications in acoustic and photonics, such as enhanced acoustic emission, filtering, and sensing
A General Framework of Bound States in the Continuum in an Open Acoustic Resonator
Bound states in the continuum (BICs) provide a viable way of achieving high-Q
resonances in both photonics and acoustics. In this work, we proposed a general
method of constructing Friedrich-Wintgen (FW) BICs and accidental BICs in a
coupled acoustic waveguide-resonator system. We demonstrated that FW BICs can
be achieved with arbitrary two degenerate resonances in a closed resonator
regardless of whether they have the same or opposite parity. Moreover, their
eigenmode profiles can be arbitrarily engineered by adjusting the position of
attached waveguide. That suggests an effective way of continuous switching the
nature of BIC from FW BIC to symmetry-protected BIC or accidental BICs. Also,
such BICs are sustained in the coupled waveguide-resonator system with shapes
such as rectangle, ellipse, and rhomboid. These interesting phenomena are well
explained by the two-level effective non Hermitian Hamiltonian, where two
strongly coupled degenerate modes play a major role in forming such FW BICs.
Besides, we found that such an open system also supports accidental BICs in
geometry space instead of momentum space via tuning the position of attached
waveguide, which are attributed to the quenched coupling between the waveguide
and eigenmodes of the closed cavity. Finally, we fabricated a series of 3D
coupled-resonator-waveguide and experimentally verified the existence of FW
BICs and accidental BICs by measuring the transmission spectra. Our results
complement the current BIC library in acoustics and provide new routes for
designing novel acoustic devices, such as in acoustic absorbers, filters and
sensors.Comment: 20 pages, 6 figure
Robust estimation of bacterial cell count from optical density
Optical density (OD) is widely used to estimate the density of cells in liquid culture, but cannot be compared between instruments without a standardized calibration protocol and is challenging to relate to actual cell count. We address this with an interlaboratory study comparing three simple, low-cost, and highly accessible OD calibration protocols across 244 laboratories, applied to eight strains of constitutive GFP-expressing E. coli. Based on our results, we recommend calibrating OD to estimated cell count using serial dilution of silica microspheres, which produces highly precise calibration (95.5% of residuals <1.2-fold), is easily assessed for quality control, also assesses instrument effective linear range, and can be combined with fluorescence calibration to obtain units of Molecules of Equivalent Fluorescein (MEFL) per cell, allowing direct comparison and data fusion with flow cytometry measurements: in our study, fluorescence per cell measurements showed only a 1.07-fold mean difference between plate reader and flow cytometry data
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