Achieving the Fundamental Quantum Limit of Linear Waveform Estimation.

Sensing a classical signal using a linear quantum device is a pervasive application of quantum-enhanced measurement. The fundamental precision limits of linear waveform estimation, however, are not fully understood. In certain cases, there is an unexplained gap between the known waveform-estimation quantum Cramér-Rao bound and the optimal sensitivity from quadrature measurement of the outgoing mode from the device. We resolve this gap by establishing the fundamental precision limit, the waveform-estimation Holevo Cramér-Rao bound, and how to achieve it using a nonstationary measurement. We apply our results to detuned gravitational-wave interferometry to accelerate the search for postmerger remnants from binary neutron-star mergers. If we have an unequal weighting between estimating the signal's power and phase, then we propose how to further improve the signal-to-noise ratio by a factor of sqrt[2] using this nonstationary measurement.

The Significance of the Redox Gene in the Prognosis and Therapeutic Response of Glioma.

OBJECTIVES: Glioblastoma (GBM) is a fatal adult central nervous system tumor. Due to its high heterogeneity, the survival rate and prognosis of patients are poor. Thousands of people die of this disease every year all over the world. At present, the treatment of GBM is mainly through surgical resection and the combination of later drugs, radiotherapy, and chemotherapy. An abnormal redox system is involved in the malignant progression and treatment tolerance of glioma, which is the main reason for poor survival and prognosis. The construction of a GBM redox-related prognostic model may be helpful in improving the redox immunotherapy and prognosis of GBM. METHODS: Based on glioma transcriptome data and clinical data from The Cancer Genome Atlas, databases, a risk model of redox genes was constructed by univariate and multivariate Cox analysis. The good prediction performance of the model was verified by the internal validation set of The Cancer Genome Atlas, and the external data of Chinese Glioma Genome Atlas. RESULTS: The results confirmed that the higher the risk score, the worse the survival of patients. Age and isocitrate dehydrogenase status were significantly correlated with risk scores. The analysis of immune infiltration and immunotherapy found that there were significant differences in the immune score, matrix score, and ESTIMATE score between high and low-risk groups. reverse transcription polymerase chain reaction and immunohistochemical staining of glioma samples confirmed the expression of the hub gene. CONCLUSION: Our study suggests that the 5 oxidative-related genes nitricoxidesynthase3 , NCF2 , VASN , FKBP1B , and TXNDC2 are hub genes, which may provide a reliable prognostic tool for glioma clinical treatment.

Warm Acupuncture Reduces Pain and Inflammation in Rats with Lumbar Disc Herniation Induced by Autologous Nucleus Pulposus Transplantation via Regulating p38MAPK/NF-κB Pathway.

Background: : Warm acupuncture (WA) has analgesic and anti-inflammatory effects. However, the underlying mechanism of these effects remain unclear. Objectives: : To explore the analgesic and anti-inflammatory effects of WA and the potential underlying mechanism in male Sprague-Dawley rats with non-compressive lumbar disk herniation (LDH) caused by autologous nucleus pulposus (NP) transplantation. Methods: : We used low-frequency (2 Hz) electrical stimulation and WA (40℃) to treat GB30 and BL54 acupoints in rats for 30 mins per day. We monitored the paw withdrawal threshold of rats during the experiment and measured serum cytokine levels using commercial kits. Dorsal root ganglion (DRG) tissue pathology was analyzed via H&E staining. We used qRT-PCR to measure the mRNA expression levels of IL-1ß, IL-6, and TNF-α genes in DRG. Western blot was used to analyze the expression levels of IL-1ß, IL-6, TNFα, P-p38MAPK, p38MAPK, P-IκBα, IκB α, and NF-κB p65 proteins. Results: : WA treatment significantly increased the pain threshold of rats, reduced serum IL-6, PEG2, NO, SP, NP-Y, and MMP-3 levels, and effected histopathological improvements in the DRG in rats. Moreover, WA treatment significantly downregulated the expression levels of inflammation-associated genes (Il-1ß, Il-6, and Tnf-α) and proteins (IL-1ß, IL-6, TNF-α, P-p38MAPK, P-IκBα, and NF-κB p65) in the DRG of non-compressive LDH rats. Conclusion: : WA can alleviate pain and inhibit inflammatory response in rats with non-compressive LDH caused by autologous NP transplantation, and these effects are likely associated with the inhibition of the p38MAPK/NF-κB pathway.

Quantum Precision Limits of Displacement Noise-Free Interferometers.

Current laser-interferometric gravitational wave detectors suffer from a fundamental limit to their precision due to the displacement noise of optical elements contributed by various sources. Several schemes for displacement noise-free interferometers (DFI) have been proposed to mitigate their effects. The idea behind these schemes is similar to decoherence-free subspaces in quantum sensing; i.e., certain modes contain information about the gravitational waves but are insensitive to the mirror motion (displacement noise). We derive quantum precision limits for general DFI schemes, including optimal measurement basis and optimal squeezing schemes. We introduce a triangular cavity DFI scheme and apply our general bounds to it. Precision analysis of this scheme with different noise models shows that the DFI property leads to interesting sensitivity profiles and improved precision due to noise mitigation and larger gain from squeezing.

Black Hole Spectroscopy by Mode Cleaning.

We formulate a Bayesian framework to analyze ringdown gravitational waves from colliding binary black holes and test the no-hair theorem. The idea hinges on mode cleaning-revealing subdominant oscillation modes by removing dominant ones using newly proposed "rational filters." By incorporating the filter into Bayesian inference, we construct a likelihood function that depends only on the mass and spin of the remnant black hole (no dependence on mode amplitudes and phases) and implement an efficient pipeline to constrain the remnant mass and spin without Markov chain Monte Carlo. We test ringdown models by cleaning combinations of different modes and evaluating the consistency between the residual data and pure noise. The model evidence and Bayes factor are used to demonstrate the presence of a particular mode and to infer the mode starting time. In addition, we design a hybrid approach to estimate the remnant black hole properties exclusively from a single mode using Markov chain Monte Carlo after mode cleaning. We apply the framework to GW150914 and demonstrate more definitive evidence of the first overtone by cleaning the fundamental mode. This new framework provides a powerful tool for black hole spectroscopy in future gravitational-wave events.

Nonlinearities in Black Hole Ringdowns.

The gravitational wave strain emitted by a perturbed black hole (BH) ringing down is typically modeled analytically using first-order BH perturbation theory. In this Letter, we show that second-order effects are necessary for modeling ringdowns from BH merger simulations. Focusing on the strain's (ℓ,m)=(4,4) angular harmonic, we show the presence of a quadratic effect across a range of binary BH mass ratios that agrees with theoretical expectations. We find that the quadratic (4,4) mode's amplitude exhibits quadratic scaling with the fundamental (2,2) mode-its parent mode. The nonlinear mode's amplitude is comparable to or even larger than that of the linear (4,4) mode. Therefore, correctly modeling the ringdown of higher harmonics-improving mode mismatches by up to 2 orders of magnitude-requires the inclusion of nonlinear effects.

Semi-Supervised and Unsupervised Deep Visual Learning: A Survey.

State-of-the-art deep learning models are often trained with a large amount of costly labeled training data. However, requiring exhaustive manual annotations may degrade the model's generalizability in the limited-label regime.Semi-supervised learning and unsupervised learning offer promising paradigms to learn from an abundance of unlabeled visual data. Recent progress in these paradigms has indicated the strong benefits of leveraging unlabeled data to improve model generalization and provide better model initialization. In this survey, we review the recent advanced deep learning algorithms on semi-supervised learning (SSL) and unsupervised learning (UL) for visual recognition from a unified perspective. To offer a holistic understanding of the state-of-the-art in these areas, we propose a unified taxonomy. We categorize existing representative SSL and UL with comprehensive and insightful analysis to highlight their design rationales in different learning scenarios and applications in different computer vision tasks. Lastly, we discuss the emerging trends and open challenges in SSL and UL to shed light on future critical research directions.

Erratum: Constraints on Low-Energy Effective Theories from Weak Cosmic Censorship [Phys. Rev. Lett. 126, 031102 (2021)].

This corrects the article DOI: 10.1103/PhysRevLett.126.031102.

Constraints on Low-Energy Effective Theories from Weak Cosmic Censorship.

We examine the weak cosmic censorship conjecture (WCCC) for the extremal charged black hole in possible generalizations of Einstein-Maxwell theory due to the high-order corrections, up to fourth-derivative terms. Our derivation is based on Wald's gedanken experiment to destroy an extremal black hole. We find that the WCCC no longer holds for all possible generalizations. Thus, the WCCC can serve as a new constraint to the high-order effective field theories. However, our constraint is independent of photon's self-interactions so that precision measurement of quantum electrodynamics cannot constrain the WCCC. For higher-dimension operators induced by the one-loop correction for the minimally coupled spinor and scalar to gravity, our constraint is satisfied.

Direct Determination of Supermassive Black Hole Properties with Gravitational-Wave Radiation from Surrounding Stellar-Mass Black Hole Binaries.

A significant number of stellar-mass black-hole (BH) binaries may merge in galactic nuclei or in the surrounding gas disks. With purposed space-borne gravitational-wave observatories, we may use such a binary as a signal carrier to probe modulations induced by a central supermassive BH (SMBH), which further allows us to place constraints on the SMBH's properties. We show in particular the de Sitter precession of the inner stellar-mass binary's orbital angular momentum (AM) around the AM of the outer orbit will be detectable if the precession period is comparable to the duration of observation, typically a few years. Once detected, the precession can be combined with the Doppler shift arising from the outer orbital motion to determine the mass of the SMBH and the outer orbital separation individually and each with percent-level accuracy. If we further assume a joint detection by space-borne and ground-based detectors, the detectability threshold could be extended to a precession period of ∼100 yr.

Quantum expander for gravitational-wave observatories.

The quantum uncertainty of laser light limits the sensitivity of gravitational-wave observatories. Over the past 30 years, techniques for squeezing the quantum uncertainty, as well as for enhancing gravitational-wave signals with optical resonators have been invented. Resonators, however, have finite linewidths, and the high signal frequencies that are produced during the highly scientifically interesting ring-down of astrophysical compact-binary mergers still cannot be resolved. Here, we propose a purely optical approach for expanding the detection bandwidth. It uses quantum uncertainty squeezing inside one of the optical resonators, compensating for the finite resonators' linewidths while keeping the low-frequency sensitivity unchanged. This quantum expander is intended to enhance the sensitivity of future gravitational-wave detectors, and we suggest the use of this new tool in other cavity-enhanced metrological experiments.

Satellite testing of a gravitationally induced quantum decoherence model.

Quantum mechanics and the general theory of relativity are two pillars of modern physics. However, a coherent unified framework of the two theories remains an open problem. Attempts to quantize general relativity have led to many rival models of quantum gravity, which, however, generally lack experimental foundations. We report a quantum optical experimental test of event formalism of quantum fields, a theory that attempts to present a coherent description of quantum fields in exotic spacetimes containing closed timelike curves and ordinary spacetime. We experimentally test a prediction of the theory with the quantum satellite Micius that a pair of time-energy-entangled particles probabilistically decorrelate passing through different regions of the gravitational potential of Earth. Our measurement results are consistent with the standard quantum theory and hence do not support the prediction of event formalism.

Searching for Near-Horizon Quantum Structures in the Binary Black-Hole Stochastic Gravitational-Wave Background.

Quantum gravity corrections have been speculated to lead to modifications to space-time geometry near black-hole horizons. Such structures may reflect gravitational waves, causing echoes that follow the main gravitational waves from binary black-hole coalescence. By studying two phenomenological models of the near-horizon structures under the Schwarzschild approximation, we show that such echoes, if they exist, will give rise to a stochastic gravitational-wave background, which is very substantial if the near-horizon structure has a near-unity reflectivity for gravitational waves, readily detectable by Advanced LIGO. In case the reflectivity is much less than unity, the background will mainly be arising from the first echo, with a level proportional to the power reflectivity of the near-horizon structure, but robust against uncertainties in the location and the shape of the structure-as long as it is localized and close to the horizon. Sensitivity of third-generation detectors allows the detection of a background that corresponds to power reflectivity ∼3×10^{-3}, if uncertainties in the binary black-hole merger rate can be removed. We note that the echoes do alter the f^{2/3} power law of the background spectra at low frequencies, which is rather robust against uncertainties.

Towards the Fundamental Quantum Limit of Linear Measurements of Classical Signals.

The quantum Cramér-Rao bound (QCRB) sets a fundamental limit for the measurement of classical signals with detectors operating in the quantum regime. Using linear-response theory and the Heisenberg uncertainty relation, we derive a general condition for achieving such a fundamental limit. When applied to classical displacement measurements with a test mass, this condition leads to an explicit connection between the QCRB and the standard quantum limit that arises from a tradeoff between the measurement imprecision and quantum backaction; the QCRB can be viewed as an outcome of a quantum nondemolition measurement with the backaction evaded. Additionally, we show that the test mass is more a resource for improving measurement sensitivity than a victim of the quantum backaction, which suggests a new approach to enhancing the sensitivity of a broad class of sensors. We illustrate these points with laser interferometric gravitational-wave detectors.

Universal Decoherence under Gravity: A Perspective through the Equivalence Principle.

Pikovski et al. [Nat. Phys. 11, 668 (2015)] show that a composite particle prepared in a pure initial quantum state and propagated in a uniform gravitational field undergoes a decoherence process at a rate determined by the gravitational acceleration. By assuming Einstein's equivalence principle to be valid, we analyze a physical realization of the (1+1)D thought experiment of Pikovski et al. to demonstrate that the dephasing between the different internal states arises not from gravity but rather from differences in their rest mass, and the mass dependence of the de Broglie wave's dispersion relation. We provide an alternative view to the situation considered by Pikovski et al., where we propose that gravity plays a kinematic role by providing a relative velocity to the detector frame with respect to the particle; visibility can be easily recovered by giving the screen an appropriate uniform velocity. We then apply this insight to their thought experiment in (1+1)D to draw a direct correspondence, and obtain the same mathematical result for dephasing. We finally propose that dephasing due to gravity may in fact take place for certain modifications to the gravitational potential where the equivalence principle is violated.

Detecting Gravitational-Wave Memory with LIGO: Implications of GW150914.

It may soon be possible for Advanced LIGO to detect hundreds of binary black hole mergers per year. We show how the accumulation of many such measurements will allow for the detection of gravitational-wave memory: a permanent displacement of spacetime that comes from strong-field, general relativistic effects. We estimate that Advanced LIGO operating at design sensitivity may be able to make a signal-to-noise ratio 3 (5) detection of memory with ∼35 (90) events with masses and distance similar to GW150914. We highlight the importance of incorporating higher-order gravitational-wave modes for parameter estimation of binary black hole mergers, and describe how our methods can also be used to detect higher-order modes themselves before Advanced LIGO reaches design sensitivity.

Enhancing the Bandwidth of Gravitational-Wave Detectors with Unstable Optomechanical Filters.

Advanced interferometric gravitational-wave detectors use optical cavities to resonantly enhance their shot-noise-limited sensitivity. Because of positive dispersion of these cavities-signals at different frequencies pick up different phases, there is a tradeoff between the detector bandwidth and peak sensitivity, which is a universal feature for quantum measurement devices having resonant cavities. We consider embedding an active unstable filter inside the interferometer to compensate the phase, and using feedback control to stabilize the entire system. We show that this scheme in principle can enhance the bandwidth without sacrificing the peak sensitivity. However, the unstable filter under our current consideration is a cavity-assisted optomechanical device operating in the instability regime, and the thermal fluctuation of the mechanical oscillator puts a very stringent requirement on the environmental temperature and the mechanical quality factor.

[Clinical observation of recurrent oral ulcer of heat accumulation in the heart and spleen treated with acupoint injection and fire needling therapy].

OBJECTIVE: To compare the clinical efficacy between the combined acupuncture therapy of acupoint injection and fire needling and the oral administration of vitamin C and B2 as well as subcutaneous injection of transfer factor. METHODS: One hundred and fifty-eight patients of recurrent oral ulcer (ROU) differentiated as heat accumulation in the heart and spleen were randomized into an observation group and a control group, 79 cases in each, one. In the observation group, Xinshu (BL 15), Pishu (BL 20) and Zusanli (ST 36) were selected for acupoint injection of shuang huanglian injection, 1 mL at each point, three times a week, for 2 weeks totally. Additionally, fire needling was applied to the ulcer lesion and peripheral mucosa, once a day, totally for 3 times. In the control group, vitamin C 100 mg and vitamin B2 20 mg were prescribed for oral administration, three times a day; and subcutaneous injection of transfer factor was applied, 2 mL (3 mg), twice a week, for 2 weeks totally. The score of symptoms and physical signs and the visual analogue scale (VAS) were observed before and after treatment, as well as the time of ulcer healing and ulcer recurrence in the patients of the two groups. The clinical efficacy was compared between the two groups. RESULTS: The total effective rate was 92.4% (73/79) in the observation group, better than 77.2% (61/79) in the control group (P < 0.01). The differences in the score of symptoms and physical signs and VAS score before and after treatment were significant statistically in the observation group and the control group (all P < 0.01). The score of symptoms and physical signs and VAS score after treatment in the observation group were reduced significantly as compared with those in the control group (both P < 0.01). The time of ulcer healing in the observation group was earlier than that in the control group [(3.87 +/- 1.01) d vs. (6.22 +/- 0.53) d, P < 0.01]. The recurrence rate in the observation was lower than that in the control group [22.7% (17/75) vs. 50.0% (36/72), P < 0.01]. CONCLUSION: The combined therapy of acupoint injection and fire needling achieves the better efficacy on ROU compared with oral administration of vitamin and subcutaneous injection of transfer factor. This therapy has the good and quick effect of analgesia, relieves the relevant symptoms, shortens the time of ulcer healing and reduces the recurrence rate.

Narrowing the filter-cavity bandwidth in gravitational-wave detectors via optomechanical interaction.

We propose using optomechanical interaction to narrow the bandwidth of filter cavities for achieving frequency-dependent squeezing in advanced gravitational-wave detectors, inspired by the idea of optomechanically induced transparency. This can allow us to achieve a cavity bandwidth on the order of 100 Hz using small-scale cavities. Additionally, in contrast to a passive Fabry-Pérot cavity, the resulting cavity bandwidth can be dynamically tuned, which is useful for adaptively optimizing the detector sensitivity when switching amongst different operational modes. The experimental challenge for its implementation is a stringent requirement for very low thermal noise of the mechanical oscillator, which would need a superb mechanical quality factor and a very low temperature. We consider one possible setup to relieve this requirement by using optical dilution to enhance the mechanical quality factor.

Macroscopic quantum mechanics in a classical spacetime.

We apply the many-particle Schrödinger-Newton equation, which describes the coevolution of a many-particle quantum wave function and a classical space-time geometry, to macroscopic mechanical objects. By averaging over motions of the objects' internal degrees of freedom, we obtain an effective Schrödinger-Newton equation for their centers of mass, which can be monitored and manipulated at quantum levels by state-of-the-art optomechanics experiments. For a single macroscopic object moving quantum mechanically within a harmonic potential well, its quantum uncertainty is found to evolve at a frequency different from its classical eigenfrequency-with a difference that depends on the internal structure of the object-and can be observable using current technology. For several objects, the Schrödinger-Newton equation predicts semiclassical motions just like Newtonian physics, yet quantum uncertainty cannot be transferred from one object to another.