Recovery Threshold Research Articles

Adaptive Privacy-Preserving Coded Computing with Hierarchical Task Partitioning.

Coded computing is recognized as a promising solution to address the privacy leakage problem and the straggling effect in distributed computing. This technique leverages coding theory to recover computation tasks using results from a subset of workers. In this paper, we propose the adaptive privacy-preserving coded computing (APCC) strategy, designed to be applicable to various types of computation tasks, including polynomial and non-polynomial functions, and to adaptively provide accurate or approximated results. We prove the optimality of APCC in terms of encoding rate, defined as the ratio between the computation loads of tasks before and after encoding, based on the optimal recovery threshold of Lagrange Coded Computing. We demonstrate that APCC guarantees information-theoretical data privacy preservation. Mitigation of the straggling effect in APCC is achieved through hierarchical task partitioning and task cancellation, which further reduces computation delays by enabling straggling workers to return partial results of assigned tasks, compared to conventional coded computing strategies. The hierarchical task partitioning problems are formulated as mixed-integer nonlinear programming (MINLP) problems with the objective of minimizing task completion delay. We propose a low-complexity maximum value descent (MVD) algorithm to optimally solve these problems. The simulation results show that APCC can reduce the task completion delay by a range of 20.3% to 47.5% when compared to other state-of-the-art benchmarks.

Persistent (Nav1.9) sodium currents in human dorsal root ganglion neurons.

Nav1.9 is of interest to the pain community for a number of reasons, including the human mutations in the gene encoding Nav1.9, SCN11a, that are associated with both pain and loss of pain phenotypes. However, because much of what we know about the biophysical properties of Nav1.9 has been learned through the study of rodent sensory neurons, and there is only 76% identity between human and rodent homologs of SCN11a, there is reason to suggest that there may be differences in the biophysical properties of the channels in human and rodent sensory neurons, and consequently, the contribution of these channels to the control of sensory neuron excitability, if not pain. Thus, the purpose of this study was to characterize Nav1.9 currents in human sensory neurons and compare the properties of these currents with those in rat sensory neurons recorded under identical conditions. Whole-cell patch clamp techniques were used to record Nav1.9 currents in isolated sensory neurons in vitro. Our results indicate that several of the core biophysical properties of the currents, including persistence and a low threshold for activation, are conserved across species. However, we noted a number of potentially important differences between the currents in human and rat sensory neurons including a lower threshold for activation, higher threshold for inactivation, slower deactivation, and faster recovery from slow inactivation. Human Nav1.9 was inhibited by inflammatory mediators, whereas rat Nav1.9 was potentiated. Our results may have implications for the role of Nav1.9 in sensory, if not nociceptive signaling.

Assessment of the Restoration Potential of Forest Vegetation Coverage in the Alxa Desert Region of China.

To scientifically evaluate the sustainability of tree planting and afforestation in the Alxa Desert region, this study, grounded in the principles of water balance within the natural water cycle, employed multi-source remote sensing products and ground-based measurements to construct a quantitative response relationship model. This model links evapotranspiration (ET) with meteorological variables and the Enhanced Vegetation Index (EVI). Furthermore, the study estimated the recovery thresholds and potential of forest and grassland vegetation coverage in the Alxa Desert region under various precipitation scenarios. The findings reveal that ET exhibited an increasing trend in 84.17% of the Alxa Desert region, with a significant increase observed in 61.53% of the area, indicating positive outcomes from the implementation of the Three-North Shelterbelt Forest Program. Notably, however, ET in the southeastern plain region demonstrated a decreasing trend, which is strongly associated with human activities. The response relationship model demonstrated that linear relationship areas constituted 47.52%, while nonlinear relationship areas accounted for 45.51% of the total. The overall model exhibited an R2 value of 0.69, indicating a high level of predictive accuracy. Analysis of forest and grassland coverage revealed that, under wet year scenarios, the vegetation coverage showed a significant trend of recovery, with an average recovery threshold of (75.4 ± 12.5)% and an average recovery potential of (8.5 ± 3.6)%. It is noteworthy that the vegetation coverage in 31.25% of the area had already surpassed the recovery threshold. The outcomes of this study provide a theoretical foundation for the formulation of more scientifically rigorous ecological restoration strategies in the future.

Hysteretic and asynchronous regime shifts of bacterial and micro-eukaryotic communities driven by nutrient loading

Nutrient pollution is pervasive in many urban rivers, while restoration measures that reduce nutrient loading but fail to improve biological communities often lack effectiveness due to the indispensable role of biota, especially multi-taxa, in enhancing ecosystem stability and function. The investigation of the response patterns of multi-taxa to the nutrient loading in urban rivers is important for the recovery of biota structure and thus ecosystem function. However, little is known about the response patterns of multi-taxa and their impact on ecosystem structure and function in urban rivers. Here, the study, from the perspective of alternative stable states theory, showed the hysteretic response of both bacterial and micro-eukaryotic communities to nutrient loading based on the field investigation and environmental DNA metabarcoding. Bistability was shown to exist in both bacterial and micro-eukaryotic communities, demonstrating that the response of microbiota to nutrient loading was a regime shifts with hysteresis. Potential analysis then indicated that the increased nutrient loading drove regime shifts in the bacterial community and the micro-eukaryotic community towards a state dominated by anaerobic bacteria and benthic Bacillariophyta, respectively. High nutrient loading was found to reduce the relative abundance of metazoan, but increase that of eukaryotic algae, which made the trophic pyramid top-lighter and bottom-heavier, probably exacerbating the degradation of ecosystem function. It should be noted that, in response to the reduced nutrient loading, the recovery threshold of micro-eukaryotic communities (nutrient loading = ∼0.5) was lower than that of bacterial communities (nutrient loading = ∼1.2), demonstrating longer hysteresis of micro-eukaryotic communities. In addition, the markedly positive correlation between the status of microbial communities and N-related enzyme activities suggested the recovery of microbial communities probably will benefit the improvement of N-cycling functionality. The obtained results provide a deep insight into the collapse and recovery trajectories of multi-trophic microbiota to the nutrient loading gradient and their impact on the N transformation potential, therefore benefiting the restoration and management of urban rivers.

Detecting planted partition in sparse multilayer networks

Abstract Multilayer networks are used to represent the interdependence between the relational data of individuals interacting with each other via different types of relationships. To study the information-theoretic phase transitions in detecting the presence of planted partition among the nodes of a multilayer network with additional nodewise covariate information and diverging average degree, Ma and Nandy (2023, IEEE Trans. Inf. Theory, 69, 3203–3239) introduced Multi-Layer Contextual Stochastic Block Model. In this paper, we consider the problem of detecting planted partitions in the Multi-Layer Contextual Stochastic Block Model, when the average node degrees for each network are greater than $1$. We establish the sharp phase transition threshold for detecting the planted bi-partition. Above the phase-transition threshold testing the presence of a bi-partition is possible, whereas below the threshold no procedure to identify the planted bi-partition can perform better than random guessing. We further establish that the derived detection threshold coincides with the threshold for weak recovery of the partition and provides a quasi-polynomial time algorithm to estimate it.

Unmixing-based forest recovery indicators for predicting long-term recovery success

Recovery from forest disturbances is a pivotal metric of forest resilience. Forests globally are facing unprecedented levels of both natural and anthropogenic disturbances, yet our understanding of their recovery from these disturbances remains incomplete. Remote sensing is an effective tool for understanding post-disturbance recovery, but existing approaches largely rely on spectral recovery indicators that are difficult to interpret and require long time series after disturbance, which limits their applicability to recent disturbance pulses. We here introduce a novel, ecologically informed set of recovery indicators based on fractional cover maps derived from spectral unmixing analysis of Landsat and Sentinel-2 time series. We estimated annual pre- and post-disturbance tree cover and bare ground fractions over the eastern Alps (∼130,000 km2) for the period from 1990 to 2021. From these fraction time series, we derived recovery intervals defined as the time it takes to reach a pre-defined tree cover threshold after disturbance, referred to as canopy recovery. We found mean recovery intervals between 5.5 and 13.4 years, depending on recovery threshold and disturbance severity. Comparing our results to traditional remote sensing-based approaches of mapping forest recovery, we found that spectral unmixing-based recovery indicators give considerably more realistic recovery intervals than approaches based on spectral indices because they effectively distinguish tree regeneration from other post-disturbance vegetation (e.g., shrubs, grasses). Finally, we were able to accurately predict the long-term forest recovery success based on the information available only three years after disturbance, which underlines the high importance of a short window of reorganization post-disturbance, and highlights the utility of remote sensing to inform post-disturbance forest management (e.g., in identifying areas in need of tree planting). Our study thus provides an important step ahead in the remote sensing-based monitoring of forest recovery and resilience, which is urgently needed in a time of rapid forest change.

Effect of combining batroxobin with acupuncture treatment on hearing recovery in patients with sudden sensorineural hearing loss

Background The effect of batroxobin on hearing recovery in patients with Sudden Sensorineural Hearing Loss (SSNHL) is still controversial, and acupuncture shows auxiliary benefits for SSNHL Objectives To investigate the effectiveness of combining acupuncture with batroxobin therapy for patients with SSNHL. Material and Methods One hundred and fifty-six patients with SSNHL were retrospectively enrolled in this study, and categorized into the control group (only batroxobin treatment) and observation group (batroxobin and acupuncture treatment). Pure Tone Audiograms (PTA) threshold and clinical outcomes of hearing recovery were compared. Logistic regression analysis was used to evaluate the association between hearing recovery and potential risk factors. Results Compared to the control group, the observation group had a higher overall effective rate (p = 0.006) and improvement in PTA threshold (p = 0.007). Among SSNHL patients with high-frequency and flat-type hearing loss, observation group demonstrated superior hearing recovery post-treatment compared to the control group (p < 0.05). Additionally, hearing recovery in patient with SSNHL were associated with SSNHL types, disease duration, neutrophil count and acupuncture (p < 0.05). Conclusions and Significance Combining batroxobin and acupuncture treatments enhences the improvement of hearing recovery in SSNHL patients compared to only batroxobin treatments, especially high-frequency and flat-type hearing loss.

Learning Guarantee of SDP Relaxation on Directed Stochastic Block Models

Community detection in networks has been a focal point in various scientific domains, but the study of directed networks remains relatively under-explored despite their prevalence and importance in capturing real-world systems. This work addresses this research gap by focusing on Directed Stochastic Block Models (DSBMs), a natural extension of traditional Stochastic Block Models (SBMs) to directed graphs. The inherent complexity of directionality in DSBMs makes them challenging to analyze, requiring new mathematical frameworks and computational approaches. We introduce an augmented matrix to encapsulate the directional relationships within these networks, providing a nuanced perspective for further analysis. In this work, we prove the information-theoretical threshold for exact recovery in the DSBMs and propose an SDP relaxation that can achieve this threshold, thereby contributing to the theoretical understanding of community detection in the realm of directed graphs.

Community Detection in Censored Hypergraph

Community detection refers to the problem of clustering the nodes of a network (either graph or hypergrah) into groups. Various algorithms are available for community detection and all these methods apply to uncensored networks. In practice, a network may has censored (or missing) values and it is shown that censored values have non-negligible effect on the structural properties of a network. In this paper, we study community detection in censored $m$-uniform hypergraph from information-theoretic point of view. We derive the information-theoretic threshold for exact recovery of the community structure. Besides, we propose a polynomial-time algorithm to exactly recover the community structure up to the threshold. The proposed algorithm consists of a spectral algorithm plus a refinement step. It is also interesting to study whether a single spectral algorithm without refinement achieves the threshold. To this end, we also explore the semi-definite relaxation algorithm and analyze its performance.

Deep-sea macrofauna community recovery in Kaikōura canyon following an earthquake-triggered turbidity flow

Sediment density flows can transport massive amounts of sediment across large distances and can have dramatic, long-lasting impacts on deep-sea benthic communities. A canyon-flushing event in Kaikōura Canyon, New Zealand, triggered by the 2016 Mw 7.8 Kaikōura Earthquake, which included significant submarine mass wasting, debris and turbidity flows, provides an excellent opportunity to investigate the effects of this type of large-scale natural disturbance on benthic communities. The macrofauna community in the canyon was well characterised before the disturbance and the canyon described as a deep-sea benthic biomass hotspot. Macrofauna community structure before and after the event was analysed in a time series of sediment cores from 8 sites (∼400–1300 m water depth) collected 10 years and 6 years before, and 10 weeks, 10 months, and 4 years after the disturbance. The benthic community structure showed significant variability at all time points, but immediately after the 2016 disturbance abundances of all macrofauna dramatically decreased. Four years after the disturbance the benthic community was similar to, but not yet comparable to the pre-event community. The average abundances of most macrofauna increased over the 4 years post-earthquake, with polychaetes and bivalves being key taxa in the recovery process, especially 10 months and 4 years after the disturbance. Infauna abundances >5 cm below the seabed, remained low even 4 years after the event but the overall pattern of vertical faunal distribution was trending towards a pre-disturbance state. Community recovery was investigated in relation to changes in the physical characteristics of the habitat caused by the disturbance, using variables derived from sediment cores (e.g., sediment texture, organic matter, and pigment content). While the environmental variables explained relatively little of the overall variability in macrofauna community structure, key variables identified were related to particle size structure and food availability and quality. The minimum threshold time for the macrofauna community to fully recover, based on within-community similarity, was estimated to be between 5.6 and 6.7 years, although recovery was predicted to take up to 9 years if higher recovery thresholds were used. The management implications of this study are considered in comparison to the few studies of large-scale disturbances in the deep sea, in terms of their relevance to the efficacy of the marine reserve that encompasses Kaikōura Canyon, and potential implications for our understanding of the impacts of anthropogenic disturbances such as seabed mining.

Matching recovery threshold for correlated random graphs

Matching recovery threshold for correlated random graphs

Efficient Linear and Affine Codes for Correcting Insertions/Deletions

This paper studies linear and affine error-correcting codes for correcting synchronization errors such as insertions and deletions. We call such codes linear/affine insdel codes. Linear codes that can correct even a single deletion are limited to having an information rate at most (achieved by the trivial two fold repetition code). Previously, it was (erroneously) reported that more generally no nontrivial linear codes correcting deletions exist, i.e., that the -fold repetition codes and its rate of are basically optimal for any . We disprove this and show the existence of binary linear codes of length and rate just below capable of correcting insertions and deletions. This identifies rate as a sharp threshold for recovery from deletions for linear codes and reopens the quest for a better understanding of the capabilities of linear codes for correcting insertions/deletions. We prove novel outer bounds and existential inner bounds for the rate vs. (edit) distance trade-off of linear insdel codes. We complement our existential results with an efficient synchronization-string-based transformation that converts any asymptotically good linear code for Hamming errors into an asymptotically good linear code for insdel errors. Last, we show that the -rate limitation does not hold for affine codes by giving an explicit affine code of rate which can efficiently correct a constant fraction of insdel errors.

The potential benefits of assessing post-cardiopulmonary exercise testing (CPET) in aging: a narrative review

Cardiopulmonary exercise testing (CPET) is an important tool to measure the cardiopulmonary fitness of an individual and has been widely used in athletic, clinical and research settings. Most CPET focus on analyzing physiological responses during exercise. We contend that the post-CPET recovery physiological responses offer further diagnostic and prognostic information about the health of the cardiopulmonary and metabolic systems, especially when testing apparently healthy middle-aged and older adults. However, there are limited studies that investigate physiological responses during the post-CPET recovery, and even less so in middle-aged and older adults. Therefore, this current review is aimed at discussing the contribution of post-CPET recovery parameters to cardiopulmonary health and their potential applications in aging populations. In addition to the existing methods, we propose to examine the aerobic and anaerobic recovery threshold post-CPET as novel potential diagnostic and/or prognostic tools.

Stochastic Coded Offloading Scheme for Unmanned-Aerial-Vehicle-Assisted Edge Computing

Unmanned aerial vehicles (UAVs) have gained wide research interests due to their technological advancement and high mobility. The UAVs are equipped with increasingly advanced capabilities to run computationally intensive applications enabled by machine learning techniques. However, because of both energy and computation constraints, the UAVs face issues hovering in the sky while performing computation due to weather uncertainty. To overcome the computation constraints, the UAVs can partially or fully offload their computation tasks to the edge servers. In ordinary computation offloading operations, the UAVs can retrieve the result from the returned output. Nevertheless, if the UAVs are unable to retrieve the entire result from the edge servers, i.e., straggling edge servers, this operation will fail. In this article, we propose a coded distributed computing (CDC) approach for computation offloading to mitigate straggling edge servers. The UAVs can retrieve the returned result when the number of returned copies is greater than or equal to the recovery threshold. There is a shortfall if the returned copies are less than the recovery threshold. To minimize the cost of the network, energy consumption by the UAVs, and prevent over and under subscription of the resources, we devise a two-phase stochastic coded offloading scheme (SCOS). In the first phase, the appropriate UAVs are allocated to the charging stations amid weather uncertainty. In the second phase, we use the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$z$ </tex-math></inline-formula> -stage stochastic integer programming (SIP) to optimize the number of computation subtasks offloaded and computed locally, while taking into account the computation shortfall and demand uncertainty. By using a real data set, the simulation results show that our proposed scheme is fully dynamic and minimizes the cost of the network and UAV energy consumption amid stochastic uncertainties.

Straggler- and Adversary-Tolerant Secure Distributed Matrix Multiplication Using Polynomial Codes

Large matrix multiplications commonly take place in large-scale machine-learning applications. Often, the sheer size of these matrices prevent carrying out the multiplication at a single server. Therefore, these operations are typically offloaded to a distributed computing platform with a master server and a large amount of workers in the cloud, operating in parallel. For such distributed platforms, it has been recently shown that coding over the input data matrices can reduce the computational delay by introducing a tolerance against straggling workers, i.e., workers for which execution time significantly lags with respect to the average. In addition to exact recovery, we impose a security constraint on both matrices to be multiplied. Specifically, we assume that workers can collude and eavesdrop on the content of these matrices. For this problem, we introduce a new class of polynomial codes with fewer non-zero coefficients than the degree +1. We provide closed-form expressions for the recovery threshold and show that our construction improves the recovery threshold of existing schemes in the literature, in particular for larger matrix dimensions and a moderate to large number of colluding workers. In the absence of any security constraints, we show that our construction is optimal in terms of recovery threshold.

Community Detection With Known, Unknown, or Partially Known Auxiliary Latent Variables

Empirical observations suggest that in practice, community membership does not completely explain the dependency between the edges of an observation graph. The residual dependence of the graph edges are modeled in this paper, to first order, by auxiliary node latent variables that affect the statistics of the graph edges but <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">carry no information about the communities of interest.</i> We then study community detection in graphs obeying the stochastic block model and censored block model with auxiliary latent variables. We analyze the conditions for exact recovery when these auxiliary latent variables are unknown, representing unknown nuisance parameters or model mismatch. We also analyze exact recovery when these secondary latent variables have been either fully or partially revealed. Finally, we propose a semidefinite programming algorithm for recovering the desired labels when the secondary labels are either known or unknown. We show that exact recovery is possible by semidefinite programming down to the respective maximum likelihood exact recovery threshold.

Adaptive iterative hard thresholding for low-rank matrix recovery and rank-one measurements

In low-rank matrix recovery, many kinds of measurements fail to meet the standard restricted isometry property (RIP), such as rank-one measurements, that is, [A(X)]i=〈Ai,X〉 with rank(Ai)=1, i=1,...,m. Historical iterative hard thresholding sequence for low-rank matrix recovery and rank-one measurements was taken as Xn+1=Ps(Xn−μnPt(A⁎sign(A(Xn)−y))), which introduced the “tail” and “head” approximations Ps and Pt, respectively. In this paper, we remove the term Pt and provide a new iterative hard thresholding algorithm with adaptive step size (abbreviated as AIHT). The linear convergence analysis and stability results on AIHT are established under the ℓ1/ℓ2-RIP. Particularly, we discuss the rank-one Gaussian measurements under the tight upper and lower bounds on E‖A(X)‖1, and provide better convergence rate and sampling complexity. Besides, several empirical experiments are provided to show that AIHT performs better than the historical rank-one iterative hard thresholding method.

Diffusion-based Kalman iterative thresholding for compressed sampling recovery over network

Network-based CS recovery is used for faster processing of large-scale data, as well as for sensor networks where the observation vector and sampling matrix are distributed. In this paper, we propose a distributed CS recovery algorithm, called DKIST, which is based on three concepts: diffusion strategy, iterative thresholding, and extended Kalman filtering. We investigate that the estimation is unbiased and minimum variance, and the entire network is stable. Also, we proposed some modifications on DKIST to lower communication bit rate and computation of complexity. Simulation results show that the proposed algorithms outperform the competing distributed CS recovery methods performance in terms of accuracy and speed of convergence.

Distributed Random Beacon for Blockchain Based on Share Recovery Threshold Signature.

Random beacons play a crucial role in blockchains. Most random beacons in a blockchain are performed in a distributed approach to secure the generation of random numbers. However, blockchain nodes are in an open environment and are vulnerable to adversary reboot attacks. After such an attack, the number of members involved in a random number generation decreases. The random numbers generated by the system become insecure. To solve this problem while guaranteeing fast recovery of capabilities, we designed a threshold signature scheme based on share recovery. A bivariate polynomial was generated among the participants in the distributed key generation phase. While preserving the threshold signature key share, it can also help participants who lost their shares to recover. The same threshold setting for signing and recovery guarantees the security of the system. The results of our scheme show that we take an acceptable time overhead in distributed key generation and simultaneously enrich the share recovery functionality for the threshold signature-based random number generation scheme.

Settling the Sharp Reconstruction Thresholds of Random Graph Matching

This paper studies the problem of recovering the hidden vertex correspondence between two edge-correlated random graphs. We focus on the Gaussian model where the two graphs are complete graphs with correlated Gaussian weights and the Erdős-Rényi model where the two graphs are subsampled from a common parent Erdős-Rényi graph <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\mathcal {G}}(n,p)$ </tex-math></inline-formula> . For dense Erdős-Rényi graphs with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p=n^{-o(1)}$ </tex-math></inline-formula> , we prove that there exists a sharp threshold, above which one can correctly match all but a vanishing fraction of vertices and below which correctly matching any positive fraction is impossible, a phenomenon known as the “all-or-nothing” phase transition. Even more strikingly, in the Gaussian setting, above the threshold all vertices can be exactly matched with high probability. In contrast, for sparse Erdős-Rényi graphs with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p=n^{-\Theta (1)}$ </tex-math></inline-formula> , we show that the all-or-nothing phenomenon no longer holds and we determine the thresholds up to a constant factor. Along the way, we also derive the sharp threshold for exact recovery, sharpening the existing results in Erdős-Rényi graphs. The proof of the negative results builds upon a tight characterization of the mutual information based on the truncated second-moment computation and an “area theorem” that relates the mutual information to the integral of the reconstruction error. The positive results follows from a tight analysis of the maximum likelihood estimator that takes into account the cycle structure of the induced permutation on the edges.