Random Walk Research Articles

Shaping Quantum Noise through Cascaded Nonlinear Processes in a Dissipation-Engineered Multimode Cavity

Multimode quantum light is enticing for several applications, spanning imaging, spectroscopy, communication, and more. Parametric nonlinear processes have been vital in realizing squeezed and other quantum states of light. However, most work exploiting these processes has focused on generating multimode squeezed vacua and squeezing in mode superpositions (supermodes). Bright squeezing in multiple discrete frequency modes, if realized, could unlock novel applications in quantum-enhanced spectroscopy and optical quantum computing. Here, we show how dissipation engineering of a multimode nonlinear cavity with cascaded three-wave-mixing processes allows us to shape above-threshold frequency combs that feature strong single-mode output amplitude noise squeezing over 10 dB below the shot-noise limit, tunable across the comb. In addition, we demonstrate squeezing for multiple discrete frequency modes above threshold. This bright squeezing arises from enhancement of the (noiseless) nonlinear rate relative to decay rates in the system due to the cascaded generation of photons in a single idler “bath” mode. A natural consequence of the strong nonlinear coupling in our system is the creation of an effective cavity in the synthetic frequency dimension that sustains Bloch oscillations in the modal energy distribution. Bloch mode engineering could provide an opportunity to better control nonlinear energy flow in the synthetic frequency dimension, with exciting applications in quantum random walks and topological photonics. Lastly, we show evidence of long-range correlations in amplitude noise between discrete frequency modes, enabling long-range entanglement in a synthetic frequency dimension and providing a new resource for quantum communication. Published by the American Physical Society 2024

Means of Hitting Times for Random Walks on Graphs: Connections, Computation, and Optimization

For random walks on graph \(\mathcal{G}\) with \(n\) vertices and \(m\) edges, the mean hitting time \(H_{j}\) from a vertex chosen from the stationary distribution to vertex \(j\) measures the importance for \(j\) , while the Kemeny constant \(\mathcal{K}\) is the mean hitting time from one vertex to another selected randomly according to the stationary distribution. In this paper, we first establish a connection between the two quantities, representing \(\mathcal{K}\) in terms of \(H_{j}\) for all vertices. We then develop an efficient algorithm estimating \(H_{j}\) for all vertices and \(\mathcal{K}\) in nearly linear time of \(m\) . Moreover, we extend the centrality \(H_{j}\) of a single vertex to \(H(S)\) of a vertex set \(S\) , and establish a link between \(H(S)\) and some other quantities. We further study the NP-hard problem of selecting a group \(S\) of \(k\ll n\) vertices with minimum \(H(S)\) , whose objective function is monotonic and supermodular. We finally propose two greedy algorithms approximately solving the problem. The former has an approximation factor \((1-\frac{k}{k-1}\frac{1}{e})\) and \(O(kn^{3})\) running time, while the latter returns a \((1-\frac{k}{k-1}\frac{1}{e}-\epsilon)\) -approximation solution in nearly-linear time of \(m\) , for any parameter \(0 \lt \epsilon \lt 1\) . Extensive experiment results validate the performance of our algorithms.

Better power by design: Permuted-subblock randomization boosts power in repeated-measures experiments.

During an experimental session, participants adapt and change due to learning, fatigue, fluctuations in attention, or other physiological or environmental changes. This temporal variation affects measurement, potentially reducing statistical power. We introduce a restricted randomization algorithm, permuted-subblock randomization (PSR), that boosts power by balancing experimental conditions over the course of an experimental session. We used Monte Carlo simulations to explore the performance of PSR across four scenarios of time-dependent error: exponential decay (learning effect), Gaussian random walk, pink noise, and a mixture of the previous three. PSR boosted power by about 13% on average, with a range from 4% to 45% across a representative set of study designs, while simultaneously controlling the false positive rate when time-dependent variation was absent. An R package, explan, provides functions to implement PSR during experiment planning. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

How often can two independent elephant random walks on $\mathbf{Z}$ meet?

How often can two independent elephant random walks on $\mathbf{Z}$ meet?

TWIST1/miR-199a axis promotes tumor aggressiveness through inhibiting oxidative phosphorylation in carcinomas

Background Metabolic reprogramming has emerged as a key hallmark of cancer progression, though its role in tumor aggressiveness is still evolving. Here, using a pan-cancer genome approach, we aimed to comprehensively assess the metabolic reprogramming involved in tumor aggressiveness in carcinomas and identify metabolic hubs which can be therapeutically targeted to treat aggressive tumors in the clinic. Methods In this study, we employed a stringent pan-cancer multi-omic metabolism-targeted differential expression approach to identify the metabolic hubs regulating tumor aggressiveness. mRNA, miRNA, DNA methylation and mutation profiling data of tumors representing 14 different types of carcinomas was downloaded from TCGA database. Cell line expression profiling and drug response data was downloaded from CCLE database. Pathway enrichment, GSEA, String protein-protein interaction, miRNA-mRNA prediction, network random-walk and CCLE drug response analyses were carried out. Results We identified downregulated expression of enzymes involved in oxidative phosphorylation as a key common factor across carcinomas, aligning with the Warburg effect. Additionally, we established that the decreased dependence on oxidative phosphorylation is driven by elevated expression of miR-199 family miRNAs that inhibit their expression at the post-transcriptional level. Furthermore, we identified the epithelial-to-mesenchymal transition-related transcription factor, TWIST1, as a master regulator of tumor aggressiveness by controlling miR-199a-3p and -5p expression. Random walk analysis of established miRNA-mRNA network identified NDUFA2, DLD, COX15, NDUFB5, and TIMM13 as crucial metabolic hubs downregulated as tumors become aggressive. Drug response analysis suggested that targeting PDGFR signaling may offer a novel therapeutic approach to counteract the aggressiveness driven by the loss of oxidative phosphorylation. Conclusion We identified TWIST1/miR-199a axis mediated suppression of oxidative phosphorylation as major metabolic contributor towards tumor aggressiveness in carcinomas. These insights underscore the critical interplay between metabolic reprogramming and tumor aggressiveness, opening avenues for potential metabolic therapies in clinical settings.

Exiting measures for random walks on infinite rooted trees

Abstract We consider conformal iterated function systems (CIFS) that are induced by an infinite rooted tree T T , which we call T T -conformal iterated function systems ( T T -CIFS). We focus on the parameterized families of T T -CIFS that satisfy the trasversality condition and give a dimension formula for the exiting measure for a.e. parameter. We also give a sufficient condition that the exiting measure is absolutely continuous for a.e. parameter.

Exploring the value of arterial spin labeling and six diffusion MRI models in differentiating solid benign and malignant renal tumors

ObjectiveTo explore the value of three-dimensional arterial spin labeling (ASL) and six diffusion magnetic resonance imaging (MRI) models in differentiating solid benign and malignant renal tumors.MethodsThis retrospective study included 89 patients with renal tumors. All patients underwent ASL and ZOOMit diffusion-weighted imaging (DWI) examinations and were divided into three groups: clear cell renal cell carcinoma (ccRCC), non-ccRCC, and benign renal tumors (BRT). The mean and peak renal blood flow (RBFmean and RBFpeak) from ASL and fourteen diffusion parameters from mono-exponential DWI (Mono_DWI), intravoxel incoherent motion (IVIM), diffusion kurtosis imaging (DKI), stretched exponential model (SEM), fractional order calculus (FROC), and continuous-time random-walk (CTRW) model were analyzed. Binary logistic regression was used to determine the optimal parameter combinations. The diagnostic performance of various MRI-derived parameters and their combinations was compared.ResultsAmong the six diffusion models, the SEM model achieved the highest performance in differentiating ccRCC from non-ccRCC (area under the receiver operating characteristic curve [AUC] 0.880) and from BRT (AUC 0.891). IVIM model achieved the highest AUC (0.818) in differentiating non-ccRCC from BRT. Among all the MRI-derived parameters, RBFpeak combined with DKI_MK yielded the highest AUC (0.970) in differentiating ccRCC from non-ccRCC, and the combination of RBFpeak, SEM_DDC, and FROC_μ yielded the highest AUC (0.992) for differentiating ccRCC from BRT.ConclusionASL and all diffusion models showed similar diagnostic performance in differentiating ccRCC from non-ccRCC or BRT, while the IVIM model performed better in distinguishing non-ccRCC from BRT. Combining ASL with diffusion models can provide additional value in predicting ccRCC.Relevance statementConsidering the increasing detection rate of incidental renal masses, accurate discrimination of benign and malignant renal tumors is crucial for decision-making. Combining ASL with diffusion MRI models offers a promising solution to this clinical issue.Key PointsAll assessed models were effective for differentiating ccRCC from non-ccRCC or BRT.ASL and all diffusion models showed similar performance in differentiating ccRCC from non-ccRCC or BRT.Combining ASL with diffusion models significantly improved diagnostic efficacy in predicting ccRCC.IVIM model could better differentiate non-ccRCC from BRT.Graphical

Kalman filter time scale algorithm based on noise characteristics of optically pumped cesium clock

Abstract The time scale algorithm plays an important role in time keeping. Currently, the time scale algorithm primarily adopts the predictability weighting algorithm for microwave clocks. Due to the different working principles and performance of optically pumped small cesium clocks compared with microwave clocks, a new time scale algorithm must be developed to adapt to optically pumped clocks. Based on the noise characteristics of the optically pumped clocks, the state model is established and the time scale is calculated using the Kalman filtering algorithm. The state model of the optically pumped clocks simultaneously considers the effects of white frequency modulation, flicker frequency modulation, and random walk frequency modulation. The proposed algorithm models the flicker frequency modulation for filtering estimation, which effectively improves the stability of the time scale. Here, the flicker frequency modulation is modeled through the linear combination of Markov processes, and the impact of different numbers of Markov processes on the time scale stability is analyzed. Compared with the predictability weighted algorithm, the results obtained by the proposed algorithm demonstrate that the frequency stability of the Kalman filtering time scale based on the noise characteristics was better than that of the predictability algorithm. Taking rapid Coordinated Universal Time (UTCr) as a reference, the frequency stabilities of the time scale based on three optically pumped clocks obtained by the proposed algorithm were 1.14 × 10−14 for 15 days and 5.50 × 10−15 for 30 days.

Research on cross-provincial power trading strategy considering the medium and long-term trading plan

To accommodate China’s electricity market reforms integrating medium and long-term (MLT) transactions and spot transactions, and to boost renewable energy consumption through the spot market, this paper proposes an optimized cross-provincial electricity trading strategy model based on a two-layer game framework. The proposed model incorporates an MLT green certificate contract decomposition method, enabling nested optimization of green certificate contracts and scheduling plans for cross-provincial power transactions. To encourage broader participation, a bilateral green certificate trading framework is established, which globally optimizes green certificate allocation to increase benefits for market participants. A Nash-Stackelberg game model is introduced to address complex game interactions among multiple participants under the green certificate mechanism and the limitation of assuming complete rationality. The game model combines supply and demand sides with an embedded demand-side evolutionary game. Additionally, an improved Aquila optimization algorithm (IAOA) is developed to accurately calculate electricity supply and demand. The algorithm integrates a Circle chaotic map, Sobol sequence, random walk strategy, and filtering technology to enhance optimization capabilities and manage complex constraints. The algorithm is then embedded with a distributed iterative approach to achieve equilibrium strategies. A real-world case study was conducted to validate the feasibility and effectiveness of the proposed model. The results demonstrate that the proposed approach effectively achieves equilibrium, optimizes trading strategies, and fosters win-win, coordinated development among participants in the cross-provincial electricity market.

Larval source management in Ethiopia: modelling to assess its effectiveness in curbing malaria surge in dire Dawa and Batu Towns

BackgroundEthiopia faces several severe challenges in terms of malaria elimination, including drug resistance and diagnostic evasion in the Plasmodium falciparum parasite, insecticide resistance in the primary Anopheles malaria vector, and, most recently, the invasion of the Asian malaria vector Anopheles stephensi. Novel malaria control methods are therefore needed, and in this paper, we describe the evaluation of a larval source management (LSM) strategy implemented in response to An. stephensi. The primary outcome was the malaria incidence rate compared between intervention and non-intervention sites in the presence of An. stephensi.MethodsIntervention (Batu and Dire Dawa) and control (Metehara) towns were selected, and weekly malaria passive case detection data collected between 2014 and 2023 were obtained from the Oromia regional state and Dire Dawa City Administration Health Bureau. In addition, data regarding intervention were obtained from the President’s Malaria Initiative (PMI) reports. Weekly malaria passive case data were used to evaluate the change in the estimated malaria incidence rate and trends of temporal patterns of the estimated malaria incidence rate before and after interventions. An interrupted time series model with a cyclic second-order random walk structure periodic seasonal term was used to assess the impact of LSM on malaria incidence rate in the intervention and control settings.ResultsAn upsurge in malaria cases occurred after 2020 at both the intervention and control sites. The temporal patterns of malaria incidence rate showed an increasing trend after the intervention. The ITS model depicted that the LSM has no impact in reducing the malaria incidence rate at both intervention site Dire Dawa [immediate impact = 1.462 (0.891, 2.035)], [Lasting impact = 0.003 (− 0.012, 0.018)], and Batu [Immediate impact 0.007 (− 0.235, 0.249), [Lasting impact = 0.008 (− 0.003, 0.013)].ConclusionsAn overall increasing trend in the malaria incidence rate was observed irrespective of the implementation of LSM in the urban settings of Ethiopia, where An. stephensi has been found. Further investigations and validations of the incorporation of LSM into control activities are warranted.

On random sampling of supersingular elliptic curves

AbstractWe consider the problem of sampling random supersingular elliptic curves over finite fields of cryptographic size (SRS problem). The currently best-known method combines the reduction of a suitable complex multiplication (CM) elliptic curve and a random walk over some supersingular isogeny graph. Unfortunately, this method is not suitable when the endomorphism ring of the generated curve needs to be hidden, like in some cryptographic applications. This motivates a stricter version of the SRS problem, requiring that the sampling algorithm gives no information about the endomorphism ring of the output curve (cSRS problem). In this work we formally define the SRS and cSRS problems, which are both of theoretical interest. We discuss the relevance of the two problems for cryptographic applications, and we provide a self-contained survey of the known approaches to solve them. Those for the cSRS problem have exponential complexity in the characteristic of the base finite field (since they require computing and finding roots of polynomials of large degree), leaving the problem open. In the second part of the paper, we propose and analyse some alternative techniques—based either on the Hasse invariant or division polynomials—and we explain the reasons why they do not readily lead to efficient cSRS algorithms, but they may open promising research directions.

Convergence speed and approximation accuracy of numerical MCMC

Abstract When implementing Markov Chain Monte Carlo (MCMC) algorithms, perturbation caused by numerical errors is sometimes inevitable. This paper studies how the perturbation of MCMC affects the convergence speed and approximation accuracy. Our results show that when the original Markov chain converges to stationarity fast enough and the perturbed transition kernel is a good approximation to the original transition kernel, the corresponding perturbed sampler has fast convergence speed and high approximation accuracy as well. Our convergence analysis is conducted under either the Wasserstein metric or the $\chi^2$ metric, both are widely used in the literature. The results can be extended to obtain non-asymptotic error bounds for MCMC estimators. We demonstrate how to apply our convergence and approximation results to the analysis of specific sampling algorithms, including Random walk Metropolis, Metropolis adjusted Langevin algorithm with perturbed target densities, and parallel tempering Monte Carlo with perturbed densities. Finally, we present some simple numerical examples to verify our theoretical claims.

On the use of EBRSM turbulence model to improve continuous random walk model prediction in inhomogeneous turbulent flows

On the use of EBRSM turbulence model to improve continuous random walk model prediction in inhomogeneous turbulent flows

CC4S: Encouraging Certainty and Consistency in Scribble-Supervised Semantic Segmentation.

Deep learning-based solutions have achieved impressive performance in semantic segmentation but often require large amounts of training data with fine-grained annotations. To alleviate such requisition, a variety of weakly supervised annotation strategies have been proposed, among which scribble supervision is emerging as a popular one due to its user-friendly annotation way. However, the sparsity and diversity of scribble annotations make it nontrivial to train a network to produce deterministic and consistent predictions directly. To address these issues, in this paper we propose holistic solutions involving the design of network structure, loss and training procedure, named CC4S to improve Certainty and Consistency for Scribble-Supervised Semantic Segmentation. Specifically, to reduce uncertainty, CC4S embeds a random walk module into the network structure to make neural representations uniformly distributed within similar semantic regions, which works together with a soft entropy loss function to force the network to produce deterministic predictions. To encourage consistency, CC4S adopts self-supervision training and imposes the consistency loss on the eigenspace of the probability transition matrix in the random walk module (we named neural eigenspace). Such self-supervision inherits the category-level discriminability from the neural eigenspace and meanwhile helps the network focus on producing consistent predictions for the salient parts and neglect semantically heterogeneous backgrounds. Finally, to further improve the performance, CC4S uses the network predictions as pseudo-labels and retrains the network with an extra color constraint regularizer. From comprehensive experiments, CC4S achieves comparable performance to those from fully supervised methods and shows promising robustness under extreme supervision cases.

Compact Si-SiN photonic fiber optic gyroscope transceiver for large volume manufacturing

Miniaturized interferometric fiber optic gyroscopes (IFOGs) providing high-precision angular measurement are highly desired in various smart applications. In this work, we present a high-performance Si-SiN photonic FOG transceiver composed of an optical source, polarizer, splitter, and on-chip germanium (Ge) photodetector (PD). The transceiver is assembled in a standard butterfly package with a thermo-electric cooler (TEC). The optical loss (including two edge couplers, as well as one 3 dB splitter) and polarization extinction ratio (PER) are less than 7 dB and greater than 20 dB at room temperature, respectively. Built with the polarization maintaining (PM) fiber coil with 70 mm average diameter and 580 m length, the transceiver-based IFOG exhibits record-low bias stability of 0.022 deg/h at an integration time of 10 s, the angular random walk (ARW) of 0.0012 deg/h, and the bias instability of 0.003 deg/h, to the best of our knowledge. The preliminary reliability test agrees well with the practical requirements. Our work verifies that the on-chip Ge PD is eligible for high-performance FOG applications. Leveraged with the typical CMOS compatible 8-inch (200 mm diameter wafers) silicon photonics platform and decreased fiber splicing points, the presented transceiver provides a promising solution toward a low-loss and miniaturized FOG system with large volume manufacturing capability.

Gene prioritization-based Active Bio-module identification for Bioinformatics

Massive multi-omics data are being used to research cancer pathogenesis at the molecular level as high-throughput sequencing technology advances. Many present approaches frequently fail to detect strongly coupled modules that are intimately associated with cancer. By combining two forms of omics data, a technique to active bio-module identification known as IdeMod is proposed, which employs gene expression and protein-protein interaction networks. IdeMod is a p-step random walk kernel regression model-based gene activity score algorithm that uses the Pareto optimum consensus (POC) method's dominance connections to generate a prioritised list of genes. IdeMod uses the SA GPROX simulated annealing technique to identify the PPI network's most linked and high-priority bio-modules. The techniques RegMod, LEAN, SigMod, ModFinder, and IdeMod were experimentally tested on real-world cervical and BRCA datasets. These findings show that the IdeMod algorithm may identify a densely linked module containing multiple genes that either promote or hinder tumour growth. The BRCA1 gene increases the likelihood of developing hereditary breast cancer associated with BRCA mutations. As a result, the IdeMod technique can be used in conjunction with other tools to detect bio-modules.

Pore-scale T2-based numerical investigation on dynamics and wettability in mixed-wet shale oil reservoirs

Oil recovery in shale reservoirs is low due to the dynamics and wettability characteristics in mixed-wet shale oil reservoirs. Nuclear magnetic resonance (NMR) logging, a nondestructive and noninvasive technique, effectively evaluates the continuous dynamics and wettability in these reservoirs. The NMR numerical investigation can characterize the effects of dynamics and wettability, including varying wet regions and wet angles, on NMR responses, providing new insights into the frequency-dependent of T2-based petrophysical parameters. The NMR relaxation theory for mixed-wet shale oil reservoirs was proposed, and the relevant parameters were determined. The dynamics and wettability were characterized using the Shan Chen Lattice Boltzmann method, with constraints based on digital core technology. For the first time, the random walk method was employed to simulate the effects of water-wet regions with varying proportions, echo spacings, and wet angles on NMR responses in mixed-wet shale oil reservoirs at different frequencies. The proportions of water-wet regions, magnetic field frequencies, and echo spacings significantly influence porosity and T2LM, indicating that pore structure governs the dynamics and wettability and that petrophysical parameters can be characterized by their frequency dependence in mixed-wet shale oil reservoirs.

Evaluation of a Probabilistic Framework for Traffic Volume Forecasting Using Deep Learning and Traditional Models

Forecasting is a very important issue in the present times to optimize urban traffic management systems and their proper planning. It is often found that traditional forecasting models cannot fully approximate the non-linear and dynamic nature of traffic patterns. The presented paper proposes a framework that integrates multiple traditional models such as Autoregression (AR), Support Vector Regression (SVR), Exponential Smoothing, Historical Average, Random Walk and Artificial Neural Network (ANN) with deep learning models, especially Stacked Autoencoders, and enhances their predictive efficiency phenomenally. The forecast accuracy is then further enhanced through a dynamic probabilistic model integration strategy that adapts to real-time traffic conditions by dynamically weighting the models based on their performance. It is found that the hybrid framework proposed in the present paper performs much better than the traditional models in predicting traffic volume. Deep learning models with RMSE of 26.9976, AR (RMSE: 22.6679) and SVR (RMSE: 28.2221) provided remarkable prediction accuracy. Based on the results, the authors are confident that the integrated models are useful for real-time traffic management applications. However, they still have great potential for further refinement and optimization.

Determine a Performance Parameter by Using the IOTA Distributed Ledger Technology Method

This study aims to improve execution time, CPU utilization, network efficiency, and scalability while upholding robust security measures. The IOTA-DLT-based RA-WRW algorithm is developed in Python, considering node resources and transaction weights for optimal tip selection—verification procedures confirming tip authenticity and transaction validity. The algorithm significantly improves IOTA network transaction processing efficiency tips exhibit high authenticity and consistency, affirming the algorithm's effectiveness. The research presents the innovative IOTA-DLT RA-WRW algorithm, which integrates Resource Allocation (RA) and Weighted Random Walk strategies. This novel approach tackles challenges like lazy tip selection, network congestion, and double spending. By performance parameter and the tip selection process, the algorithm improves comparative analyses against existing methods and confirms the superior performance of our model, boasting high accuracy, f-measure, recall, precision, and scalability in distributed ledger transactions, significantly enhancing the IOTA network's transaction processing capabilities.

Random Walk on T-Fractal with Stochastic Resetting

In this study, we explore the impact of stochastic resetting on the dynamics of random walks on a T-fractal network. By employing the generating function technique, we establish a recursive relation between the generating function of the first passage time (FPT) and derive the relationship between the mean first passage time (MFPT) with resetting and the generating function of the FPT without resetting. Our analysis covers various scenarios for a random walker reaching a target site from the starting position; for each case, we determine the optimal resetting probability γ* that minimizes the MFPT. We compare the results with the MFPT without resetting and find that the inclusion of resetting significantly enhances the search efficiency, particularly as the size of the network increases. Our findings highlight the potential of stochastic resetting as an effective strategy for the optimization of search processes in complex networks, offering valuable insights for applications in various fields in which efficient search strategies are crucial.