29 research outputs found
Elastic fractal higher-order topological states
In this work, elastic fractal higher-order topological states are
investigated. Bott index is adopted to characterize the topological property of
elastic fractal structures. The topological corner and edge states of elastic
waves in fractal structures are realized theoretically and experimentally.
Different from traditional two-dimension (2D) high-order topological insulators
based on periodic structures, the high-order topological states based on
elastic fractal structures in this work intuitively reflect the fractal
dimension in physics, supporting not only abundant topological outer corner
states, but also rich inner corner states. The richness of corner states is
much higher than that of topological insulators based on periodic structures.
The strong robustness of the topological corner states in the fractal structure
are verified by introducing disorders and defects. The topological phenomenon
of in elastic fractal structures revealed in this work enriches the topological
physics of elastic systems and breaks the limitation of that relies on periodic
elastic structures. The results have important application prospects in energy
harvesting, information transmissions, elastic energy acquisitions and
high-sensitivity detections
Anomalous size effects of effective stiffnesses in bistable counter-rotating mechanical metamaterials
Counter-rotating mechanical metamaterials have previously been found to have
anomalous characteristics or functions such as auxetics effects, shape
changers, and soliton transports, which are all under monostable conditions.
The properties of counter-rotating mechanical metamaterials under bistable
conditions have not yet been explored. Here, we found that for a bistable
counter-rotating metamaterial chain, the effective stiffnesses of the two
steady states are different in the chain with even-numbered nodes. For the
chain with odd-numbered nodes, the effective stiffnesses corresponding to the
two steady states are exactly the same. This special property is not
characterized by the characteristic attenuation lengths of the underlying
mechanism, but depends on the different symmetries of the underlying mechanism
of the chains with odd and even nodes. In addition, the relationship between
the abnormal non-monotonic size effect and equilibrium angle are clarified.
More interestingly, for one-dimensional chains with even-numbered nodes, the
size effect of effective stiffness bifurcates at a specific equilibrium angle,
and the according mechanisms are revealed
CRISPR-Cas and catalytic hairpin assembly technology for target-initiated amplification detection of pancreatic cancer specific tsRNAs
Transfer RNA-derived small RNAs (tsRNAs) tRF-LeuCAG-002 (ts3011a RNA) is a novel class of non-coding RNAs biomarker for pancreatic cancer (PC). Reverse transcription polymerase chain reaction (RT-qPCR) has been unfit for community hospitals that are short of specialized equipment or laboratory setups. It has not been reported whether isothermal technology can be used for detection, because the tsRNAs have rich modifications and secondary structures compared with other non-coding RNAs. Herein, we have employed a catalytic hairpin assembly (CHA) circuit and clustered regularly interspaced short palindromic repeats (CRISPR) to develop an isothermal and target-initiated amplification method for detecting ts3011a RNA. In the proposed assay, the presence of target tsRNA triggers the CHA circuit that transforms new DNA duplexes to activate collateral cleavage activity of CRISPR-associated proteins (CRISPR-Cas) 12a, achieving cascade signal amplification. This method showed a low detection limit of 88 aM at 37 °C within 2 h. Moreover, it was demonstrated for the first time that, this method is less likely to produce aerosol contamination than RT-qPCR by simulating aerosol leakage experiments. This method has good consistency with RT-qPCR in the detection of serum samples and showed great potential for PC-specific tsRNAs point-of-care testing (POCT)
Convergence and Privacy of Decentralized Nonconvex Optimization with Gradient Clipping and Communication Compression
Achieving communication efficiency in decentralized machine learning has been
attracting significant attention, with communication compression recognized as
an effective technique in algorithm design. This paper takes a first step to
understand the role of gradient clipping, a popular strategy in practice, in
decentralized nonconvex optimization with communication compression. We propose
PORTER, which considers two variants of gradient clipping added before or after
taking a mini-batch of stochastic gradients, where the former variant PORTER-DP
allows local differential privacy analysis with additional Gaussian
perturbation, and the latter variant PORTER-GC helps to stabilize training. We
develop a novel analysis framework that establishes their convergence
guarantees without assuming the stringent bounded gradient assumption. To the
best of our knowledge, our work provides the first convergence analysis for
decentralized nonconvex optimization with gradient clipping and communication
compression, highlighting the trade-offs between convergence rate, compression
ratio, network connectivity, and privacy
DESTRESS: Computation-optimal and communication-efficient decentralized nonconvex finite-sum optimization
Emerging applications in multi-agent environments such as internet-of-things,
networked sensing, autonomous systems and federated learning, call for
decentralized algorithms for finite-sum optimizations that are
resource-efficient in terms of both computation and communication. In this
paper, we consider the prototypical setting where the agents work
collaboratively to minimize the sum of local loss functions by only
communicating with their neighbors over a predetermined network topology. We
develop a new algorithm, called DEcentralized STochastic REcurSive gradient
methodS (DESTRESS) for nonconvex finite-sum optimization, which matches the
optimal incremental first-order oracle (IFO) complexity of centralized
algorithms for finding first-order stationary points, while maintaining
communication efficiency. Detailed theoretical and numerical comparisons
corroborate that the resource efficiencies of DESTRESS improve upon prior
decentralized algorithms over a wide range of parameter regimes. DESTRESS
leverages several key algorithm design ideas including randomly activated
stochastic recursive gradient updates with mini-batches for local computation,
gradient tracking with extra mixing (i.e., multiple gossiping rounds) for
per-iteration communication, together with careful choices of hyper-parameters
and new analysis frameworks to provably achieve a desirable
computation-communication trade-off
BEER: Fast O(1/T) rate for decentralized nonconvex optimization with communication compression
Communication efficiency has been widely recognized as the bottleneck for
large-scale decentralized machine learning applications in multi-agent or
federated environments. To tackle the communication bottleneck, there have been
many efforts to design communication-compressed algorithms for decentralized
nonconvex optimization, where the clients are only allowed to communicate a
small amount of quantized information (aka bits) with their neighbors over a
predefined graph topology. Despite significant efforts, the state-of-the-art
algorithm in the nonconvex setting still suffers from a slower rate of
convergence compared with their uncompressed counterpart,
where measures the data heterogeneity across different clients, and is
the number of communication rounds. This paper proposes BEER, which adopts
communication compression with gradient tracking, and shows it converges at a
faster rate of . This significantly improves over the state-of-the-art
rate, by matching the rate without compression even under arbitrary data
heterogeneity. Numerical experiments are also provided to corroborate our
theory and confirm the practical superiority of BEER in the data heterogeneous
regime.Comment: NeurIPS 202