On the efficiency of Hamiltonian-based quantum computation for low-rank matrices

We present an extension of Adiabatic Quantum Computing (AQC) algorithm for the unstructured search to the case when the number of marked items is unknown. The algorithm maintains the optimal Grover speedup and includes a small counting subroutine. Our other results include a lower bound on the amount of time needed to perform a general Hamiltonian-based quantum search, a lower bound on the evolution time needed to perform a search that is valid in the presence of control error and a generic upper bound on the minimum eigenvalue gap for evolutions. In particular, we demonstrate that quantum speedup for the unstructured search using AQC type algorithms may only be achieved under very rigid control precision requirements.Comment: 17 pages, no figures, to appear in JM

Predictive extended state observer-based repetitive controller for uncertain systems with input delay

This article presents a predictive extended state observer-based repetitive controller (PESO-RC) to simultaneously track and reject periodic signals on systems with long input delay and parameter uncertainties. First, a novel extended state observer (ESO) is proposed to tackle periodic signals on processes with input delay. Then a simple low pass filter is incorporated and tuned to improve robustness against modelling errors. Moreover, the modified repetitive controller (MRC) is integrated to enhance the performance when compensating periodic signals without affecting the overall system’s stability. Stability criteria and robust stability analysis under modelling errors are studied to develop tuning guidelines. Furthermore, validation of the proposed controller and comparison studies are simulated in MATLAB and tested on a brushless DC servo motor which highlight the superior performance of PESO-RC

A Step Closer to Comprehensive Answers: Constrained Multi-Stage Question Decomposition with Large Language Models

While large language models exhibit remarkable performance in the Question Answering task, they are susceptible to hallucinations. Challenges arise when these models grapple with understanding multi-hop relations in complex questions or lack the necessary knowledge for a comprehensive response. To address this issue, we introduce the "Decompose-and-Query" framework (D&Q). This framework guides the model to think and utilize external knowledge similar to ReAct, while also restricting its thinking to reliable information, effectively mitigating the risk of hallucinations. Experiments confirm the effectiveness of D&Q: On our ChitChatQA dataset, D&Q does not lose to ChatGPT in 67% of cases; on the HotPotQA question-only setting, D&Q achieved an F1 score of 59.6%. Our code is available at https://github.com/alkaidpku/DQ-ToolQA

Power Saving Experiments for Large Scale Global Optimization

Green computing, an emerging field of research that seeks to reduce excess power consumption in high performance computing (HPC), is gaining popularity among researchers. Research in this field often relies on simulation or only uses a small cluster, typically 8 or 16 nodes, because of the lack of hardware support. In contrast, System G at Virginia Tech is a 2592 processor supercomputer equipped with power aware components suitable for large scale green computing research. DIRECT is a deterministic global optimization algorithm, implemented in the mathematical software package VTDIRECT95. This paper explores the potential energy savings for the parallel implementation of DIRECT, called pVTdirect, when used with a large scale computational biology application, parameter estimation for a budding yeast cell cycle model, on System G. Two power aware approaches for pVTdirect are developed and compared against the CPUSPEED power saving system tool. The results show that knowledge of the parallel workload of the underlying application is beneficial for power management

The weak localization for the alloy-type Anderson model on a cubic lattice

We consider alloy type random Schr\"odinger operators on a cubic lattice whose randomness is generated by the sign-indefinite single-site potential. We derive Anderson localization for this class of models in the Lifshitz tails regime, i.e. when the coupling parameter $\lambda$ is small, for the energies $E \le -C \lambda^2$.Comment: 45 pages, 2 figures. To appear in J. Stat. Phy

Increased Basal Activity Is a Key Determinant in the Severity of Human Skeletal Dysplasia Caused by TRPV4 Mutations

TRPV4 is a mechanically activated Ca2+-passing channel implicated in the sensing of forces, including those acting on bones. To date, 33 mutations are known to affect human bone development to different extents. The spectrum of these skeletal dysplasias (SD) ranges from dominantly inherited mild brachylomia (BO) to neonatal lethal forms of metatropic dysplasia (MD). Complexities of the results from fluorescence and electrophysiological studies have led to questions on whether channel activity is a good predictor of disease severity. Here we report on a systematic examination of 14 TRPV4 mutant alleles covering the entire SD spectrum. Expressed in Xenopus oocyte and without any stimulation, the wild-type channel had a ∼1% open probability (Po) while those of most of the lethal MD channels approached 100%. All mutant channels had higher basal open probabilities, which limited their further increase by agonist or hypotonicity. The magnitude of this limitation revealed a clear correlation between the degree of over-activity (the molecular phenotype) and the severity of the disease over the entire spectrum (the biological phenotype). Thus, while other factors are at play, our results are consistent with the increased TRPV4 basal activity being a critical determinant of the severity of skeletal dysplasia. We discuss how the channel over-activity may lead to the “gain-of-function” phenotype and speculate that the function of wild-type TRPV4 may be secondary in normal bone development but crucial in an acute process such as fracture repair in the adult

Setup Background Assumptions

Statement of the result Proof of weak localization Wegner’s estimate Proof of lemma Zhenwei Cao Weak Localization for the alloy-type 3D Anderson Mode

Repetitive control and its applications (STEM Blitz August 2015)

Repetitive control and its applications. Recorded on 14 August 2015

Secure communication via multi-parameter modulation using Chua systems

In this paper, a multi-parameter modulation scheme is proposed for secure communication via Chua chaos using an adaptive learning mechanism. It is proved that under the scheme, the tracking performance of the communication scheme can be guaranteed. It is also shown that by incorporating a low pass filter structure into the structure of the receiver, good tracking performance can be achieved. A microprocessor experimental study is provided to demonstrate the effectiveness of the method proposed

Tracking variable periodic signals with fixed sampling rate: feedforward control

Recent research has shown that the feedback repetitive control is very efficient in tracking periodic signals. However, the existing repetitive control algorithms require an integer number of samples in each period. In some industry applications where the signal period varies but other requirements on the data acquisition system force a fixed sample rate, the number of samples per period may be a non-integer. To address this problem, adaptive feedback repetitive controllers have been proposed. Although the adaptive feedback repetitive control provides good steady state performance, the transient response is not fast. This paper presents a new adaptive feedforward control with fixed sampling rate to track periodic signals with variations in periods. The experimental result on a servomotor demonstrates that the proposed feedforward tracking controller has fast transient response