Stochastic Map Research Articles

Exploring chaos and ergodic behavior of an inductorless circuit driven by stochastic parameters

There exist extensive studies on periodic and random perturbations of various smooth maps investigating their dynamics. Unlike smooth maps, non-smooth maps are yet to be studied extensively under a stochastic regime. This paper presents a stochastic piecewise-smooth map derived from a simple inductorless switching circuit. The stochasticity is introduced in parameter values. The distribution of the parameter values is bounded and randomly selected from uniform and triangular distributions and ranges between high and low bifurcation parameter values of the deterministic map. Due to this inherent stochasticity in parameter values, the time evolution of the state variable cannot be predicted at a specific time instant. We observe that the state variable exhibits completely ergodic behavior when the minimum value of the parameter is the same as the minimum bifurcation parameter of the deterministic system. However, the ensemble average of the state variable converges to a fixed value. The system demonstrates nonchaotic behavior for a particular range of parameter values but the deterministic map in that bifurcation range shows interplay between chaos and periodic orbits. The values of Lyapunov exponents decrease monotonically with increased asymmetry of the distribution from which the bifurcation parameter values are chosen. We determine the probability density function of the stochastic map and verify its invariance under initial conditions. The most noteworthy result is the disappearance of chaotic behavior when the lower range of the distribution is varied while maintaining a fixed upper threshold for a particular distribution, even though the deterministic map exhibits an array of periodic and chaotic behaviors within the range. As the period-incrementing cascade with chaotic inclusion only occurs in nonsmooth maps, this paper numerically shows the stochasticity of a piecewise-smooth map obtained from a practical system for the first time where randomness is introduced in the parameter space.

Co-seismic and rainfall-triggered landslide hazard susceptibility assessment for Uganda derived using fuzzy logic and geospatial modelling techniques

AbstractUganda has suffered from many damaging landslides like the 1966 Rwenzori, 1994 Kisomoro and 2010 Bududa events. Despite escalating landslide risks exacerbated by rapid deforestation, urbanization and population growth coupled with a substandard building stock, comprehensive national co-seismic and rainfall-induced landslide hazard and risk maps for Uganda do not exist. This study therefore aims to conduct landslide hazard assessment and zonation for Uganda using a geospatial-based fuzzy logic methodology. In this methodology, landslide frequency ratios obtained for the 1966 Toro and 1994 Kisomoro earthquakes are assigned to the stochastic event-based probabilistic seismic hazard map derived using OpenQuake-engine. The available co-seismic and rainfall-induced landslide inventory datasets are used to derive the distribution of landslide frequency ratios based on geology, topographic slope position index, slope aspect, slope angle, distance from streams, and proximity to major active faults. The spatial distribution of fuzzy membership functions obtained from frequency ratios are overlaid and aggregated to produce landslide susceptibility maps showing relative probabilities of landslide occurrences across Uganda. Results indicate that the highest overall landslide hazard susceptibility is expected in areas comprising highly weathered outcropping rocks of precambrian granites, dominantly metasedimentary, and granulites and gneisses geologies within 40 km from major active faults; where the bedrock peak ground acceleration ≥ 0.1 g, topographic position index ≥ 3.8, slope gradient ≥ 10°, and the distance from streams ≤ 1.25 km. These findings can inform Uganda’s directorate of disaster preparedness and management towards pioneering the development of co-seismic landslide risk mitigation measures for the country.

Entropic uncertainty principle for mixed states

The entropic uncertainty principle in the form proven by Maassen and Uffink yields a fundamental inequality that is prominently used in many places all over the field of quantum information theory. In this paper, we provide a family of versatile generalizations of this relation. Our proof methods build on a deep connection between entropic uncertainties and interpolation inequalities for the doubly stochastic map that links probability distributions in two measurement bases. In contrast to the original relation, our generalization also incorporates the von Neumann entropy of the underlying quantum state. These results can be directly used to bound the extractable randomness of a source-independent quantum random number generator in the presence of fully quantum attacks, to certify entanglement between trusted parties, or to bound the entanglement of a system with an untrusted environment. Published by the American Physical Society 2024

Uncertainty analysis of Altantic salmon fish scale’s acoustic impedance using 30 MHz C-Scan measurements

Understanding the biomechanics of fish scales is crucial for their survival and adaptation. Ultrasonic C-scan measurements offer a promising tool for non-invasive characterization, however, existing literature lacks uncertainty analysis while evaluating acoustic impedance. This article presents an innovative integration of uncertainty into the analytical framework for estimating stochastic specific acoustic impedance of salmon fish scale through ultrasonic C-scans. In this study, the various types of uncertainties arising due to variation in biological structures and aging, measurement errors, and analytical noises are combined together in the form of uncertain reflectance. This uncertain reflectance possesses a distribution which is derived using a theory of waves by assuming suitable stochasticity in wavenumber. This distribution helps in development of a stochastic-specific acoustic impedance map of the scales which demonstrates the possible deviations of impedance from mean value depending on uncertainties. Furthermore, maximal overlap discrete wavelet transform is employed for efficient time–frequency deconvolution and Kriging for spatial data interpolation to enhance the robustness of the impedance map, especially in scenarios with limited data. The framework is validated by accurately estimating the specific acoustic impedance of well-known materials like a pair of target medium (polyvinylidene fluoride) and reference medium (polyimide), achieving over 90% accuracy. Moreover, the accuracy of the framework is found superior when compared with an established approach in the literature. Applying the framework to salmon fish scales, we obtain an average specific acoustic impedance of 3.1 MRayl along with a stochastic map visualizing the potential variations arising from uncertainties. Overall, this work paves the way for more accurate and robust studies in fish scale biomechanics by incorporating a comprehensive uncertainty analysis framework.

Long-term averages of the stochastic logistic map

ABSTRACT The logistic map is a nonlinear difference equation well studied in the literature, used to model self-limiting growth in certain populations. It is known that, under certain regularity conditions, the stochastic logistic map, where the parameter is varied according to a specified distribution, has a unique invariant distribution. In these cases we can compare the long-term behaviour of the stochastic system with that of the deterministic system evaluated at the average parameter value. Here we examine the relationship between the mean of the stochastic logistic equation and the mean of orbits of the deterministic logistic equation at the expected value of the parameter. We formally prove that, in some cases, the addition of noise is beneficial to the populations, in the sense that it increases the mean, while for other ranges of parameters it is detrimental. A conjecture based on numerical evidence is presented at the end.

Development of a probabilistic seismic microzonation software considering geological and geotechnical uncertainties

ABSTRACT Modern seismic risk assessment software includes seismic hazard analysis algorithms or relies on precomputed hazard maps. In both cases, a major step is incorporating the impacts of the local geological and geotechnical conditions. The common practice to address this phenomenon, often referred to as site effect, is to use shear wave velocity (Vs)–depth correlations and a deterministic geological model as a proxy for Vs mapping. The Vs of the top 30 m (Vs30) and often the fundamental site period (T0) are then used as predictors of the potential amplification of seismic shaking. Recognising that uncertainty in local soil properties inevitably affects the seismic site response, a stochastic approach for evaluating Vs30 and T0 is proposed herein, considering a combination of probabilistic Vs–depth correlations and a probabilistic 3D geological model. Monte Carlo simulations are then applied to study the impact of the uncertainties on the seismic site characterisation model. The generated stochastic maps consist of Vs30 and T0 realisations accompanied with spatial distribution of uncertainty as an indication of areas where further fieldwork is needed to improve predictions. The developed methodology is currently being used in a homemade risk assessment software.

Exploring the uncertainty of machine learning models and geostatistical mapping of rare earth element potential in Indiana coals, USA

Rare earth elements and yttrium (REEs) have a wide range of applications in high- and low-carbon technologies. The strategic significance of REEs has grown due to their expanding applications in manufacturing industries and the constrained availability of these essential resources. This research explores the applicability of machine learning models and their uncertainty for assessing the REE potential in coal beds using various coal parameters as inputs. The work focuses on developing a predictive model based on geological variables, excluding considerations related to potential shifts in the commodities market. The Indiana Coal Quality Database was used as the data source. The promising and unpromising indicators derived from the outlook coefficient of samples from the database were used as the REE potential indicator for machine learning classification models. The filter-based approach with bootstrap was used to evaluate the importance of the coal parameters and their prediction uncertainties. Four machine learning methods (linear discriminant analysis (LDA), random forest (RF), support vector machine (SVM), and artificial neural networks (ANN), a data balancing and augmentation approach (Synthetic Minority Over-sampling Technique), and bootstrap resampling techniques were used for building the models and evaluating their prediction capabilities under uncertainty. It was determined that the SVM bootstrap model with ten-times balanced and augmented data provided superior results compared with other models. Finally, stochastic spatial maps of the REE potential within the coal basin were generated using sequential indicator simulation. The spatial maps of the REE potential showed that a 29% area of the Indiana section of the Illinois coal basin has economic potential of REEs, with 90% confidence.

Criteria for the Existence of Internal Fixed Points of Lotka-Volterra Quadratic Stochastic Mappings with Homogeneous Tournaments Acting in an (m−1) - Dimensional Simplex

Criteria for the Existence of Internal Fixed Points of Lotka-Volterra Quadratic Stochastic Mappings with Homogeneous Tournaments Acting in an (m−1) - Dimensional Simplex

Modeling annotator preference and stochastic annotation error for medical image segmentation

Manual annotation of medical images is highly subjective, leading to inevitable annotation biases. Deep learning models may surpass human performance on a variety of tasks, but they may also mimic or amplify these biases. Although we can have multiple annotators and fuse their annotations to reduce stochastic errors, we cannot use this strategy to handle the bias caused by annotators’ preferences. In this paper, we highlight the issue of annotator-related biases on medical image segmentation tasks, and propose a Preference-involved Annotation Distribution Learning (PADL) framework to address it from the perspective of modeling an annotator’s preference and stochastic errors so as to produce not only a meta segmentation but also the annotator-specific segmentation. Under this framework, a stochastic error modeling (SEM) module estimates the meta segmentation map and average stochastic error map, and a series of human preference modeling (HPM) modules estimate each annotator’s segmentation and the corresponding stochastic error. We evaluated our PADL framework on two medical image benchmarks with different imaging modalities, which have been annotated by multiple medical professionals, and achieved promising performance on all five medical image segmentation tasks. Code is available at https://github.com/Merrical/PADL.

ESPRESSO: topological clustering of single-cell transcriptomics data to reveal informative genes for spatio–temporal architectures of cells

BackgroundBioinformatics capability to analyze spatio–temporal dynamics of gene expression is essential in understanding animal development. Animal cells are spatially organized as functional tissues where cellular gene expression data contain information that governs morphogenesis during the developmental process. Although several computational tissue reconstruction methods using transcriptomics data have been proposed, those methods have been ineffective in arranging cells in their correct positions in tissues or organs unless spatial information is explicitly provided.ResultsThis study demonstrates stochastic self-organizing map clustering with Markov chain Monte Carlo calculations for optimizing informative genes effectively reconstruct any spatio–temporal topology of cells from their transcriptome profiles with only a coarse topological guideline. The method, eSPRESSO (enhanced SPatial REconstruction by Stochastic Self-Organizing Map), provides a powerful in silico spatio–temporal tissue reconstruction capability, as confirmed by using human embryonic heart and mouse embryo, brain, embryonic heart, and liver lobule with generally high reproducibility (average max. accuracy = 92.0%), while revealing topologically informative genes, or spatial discriminator genes. Furthermore, eSPRESSO was used for temporal analysis of human pancreatic organoids to infer rational developmental trajectories with several candidate ‘temporal’ discriminator genes responsible for various cell type differentiations.ConclusionseSPRESSO provides a novel strategy for analyzing mechanisms underlying the spatio–temporal formation of cellular organizations.

Sampling Complexity of Open Quantum Systems

Open quantum systems are ubiquitous in the physical sciences, with widespread applications in the areas of chemistry, condensed-matter physics, material science, optics, and many more. Not surprisingly, there is significant interest in their efficient simulation. However, direct classical simulation quickly becomes intractable with coupling to an environment with an effective dimension that grows exponentially. This raises the question: Can quantum computers help model these complex dynamics? A first step in answering this question requires an understanding of the computational complexity of this task. Here, we map the temporal complexity of a process to the spatial complexity of a many-body state using a computational model known as the process-tensor framework. With this, we are able to explore the simulation complexity of an open quantum system as a dynamic sampling problem: a system coupled to an environment can be probed at successive points in time—accessing multitime correlations. The complexity of multitime sampling, which is an important and interesting problem in its own right, contains the complexity of master equations and stochastic maps as a special case. Our results show how the complexity of the underlying quantum stochastic process corresponds to the complexity of the associated family of master equations for the dynamics. We present both analytical and numerical examples where the multitime sampling of an open quantum system is as complex as sampling from a many-body state that is classically hard. This also implies that the corresponding family of master equations is classically hard. Our results pave the way for studying open quantum systems from a complexity-theoretic perspective, highlighting the role quantum computers will play in our understanding of quantum dynamics.6 MoreReceived 13 October 2022Revised 12 February 2023Accepted 14 March 2023DOI:https://doi.org/10.1103/PRXQuantum.4.020310Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasComplex systemsComputational complexityOpen quantum systemsQuantum correlations in quantum informationQuantum Information

Sunda–Sahul floristic exchange and pathways into the Southwest Pacific: New insights from wet tropical forest trees

AbstractAimRecent investigations on the floristic exchange between Southeast Asia and Australia have shown a clear dispersal directionality bias (West to East) of wet‐adapted plant taxa. However, dispersal routes and directions of wet forest taxa into the South Pacific remain insufficiently known. We here aimed to establish the most likely routes and directions of plant dispersal into the Southwest Pacific islands.LocationSoutheast Asia, East Asia, Australia, Southwest Pacific.TaxonDysoxylum s.l. (Meliaceae). This includes Dysoxylum s.s., Didymocheton, Epicharis, Goniocheton, Pseudocarapa, and Prasoxylon.MethodWe sampled 75% of the species diversity in Dysoxylum s.l., covering the entire distribution range, all genera and major lineages. Phylogenetic relationships of 149 accessions were reconstructed using Bayesian Evolutionary Analysis and two internal constraints. The dispersal–extinction–cladogenesis variant, founder‐event speciation (DEC+J), was used for reconstructing the biogeographic history, and 100 Biogeographical Stochastic Mappings were simulated.ResultsDysoxylum s.l. originated and firstly diversified in the western part of its current distribution range (including Indochina) during the Miocene to Pliocene, followed by an overall eastern range expansion towards Malesia, Australia and the Southwest Pacific in the Pliocene.Main ConclusionsThe south‐eastward expansion of lineages into Wallacea and Australia is in temporal agreement with the convergence of the Asian and Australian tectonic plates since the Miocene. Long‐distance dispersal is the main mechanism that led to the current distribution. Two dispersal pathways into the Southwest Pacific are identified, (1) through New Guinea and the Solomon Islands to Fiji, and (2) from New Zealand to Fiji. For both routes, Fiji was an important secondary source area for dispersal into the Southwest Pacific.

A Novel Image Compression Algorithm Based on Autoencoder for Biometric Template Protection Scheme

Objectives: To evaluate the proposed deep learning-based method for biometric template protection schemes with other existing image compression methods. Methods: In this study, four image compression methods such as JPEG_LS, Vector quantization (VQ), Run-length encoding (RLE), and the Autoencoder methods are implemented. The experimental results are compared with the different performance parameters that are applied over the CASIA I iris dataset possessing 756 images. Findings: The proposed autoencoder method algorithm offered enhanced results in terms of PSNR, SSIM, MSE, and CR when compared to other transform methods. The deep neural network-based autoencoder algorithm achieved the highest compression ratio of 89.05 percent, while the conventional algorithms achieved the highest image quality rate of 94.05 percent. Novelty: A novel autoencoder-based image compression model has been proposed in this study. The proposed Autoencoder (AE) method incorporates five stages like Initialization, Learning compression representations, Generation of chaotic sequence, Image encryption and decryption, and Image reconstruction. The generation of the chaotic sequence using the stochastic logistic map, as well as the learning compression representations contributes towards the novelty of this study. Keywords: Image compression; Autoencoder; Runlength encoding (RLE); Vector quantization

Exploring the Limits of Controlled Markovian Quantum Dynamics with Thermal Resources

Our aim is twofold: First, we rigorously analyse the generators of quantum-dynamical semigroups of thermodynamic processes. We characterise a wide class of gksl-generators for quantum maps within thermal operations and argue that every infinitesimal generator of (a one-parameter semigroup of) Markovian thermal operations belongs to this class. We completely classify and visualise them and their non-Markovian counterparts for the case of a single qubit. Second, we use this description in the framework of bilinear control systems to characterise reachable sets of coherently controllable quantum systems with switchable coupling to a thermal bath. The core problem reduces to studying a hybrid control system (“toy model”) on the standard simplex allowing for two types of evolution: (i) instantaneous permutations and (ii) a one-parameter semigroup of [Formula: see text]-stochastic maps. We generalise upper bounds of the reachable set of this toy model invoking new results on thermomajorisation. Using tools of control theory we fully characterise these reachable sets as well as the set of stabilisable states as exemplified by exact results in qutrit systems.

Majorization and semidoubly stochastic operators on L^{1}(X)

This paper is devoted to a study of majorization based on semidoubly stochastic operators (denoted by Smathcal{D}(L^{1})) on L^{1}(X) when X is a σ-finite measure space. We answer Mirsky’s question and characterize the majorization by means of semidoubly stochastic maps on L^{1}(X). We prove some results on semidoubly stochastic operators such as a strong relation of semidoubly stochastic operators and integral stochastic operators and relatively weak compactness of S_{f}={Sf : Sin Smathcal{D}(L^{1})} for a fixed element fin L^{1}(X) by proving the equiintegrability of S_{f}. We present a full characterization of majorization on a σ-finite measure space X.

A hybrid particle-stochastic map filter

Filtering in nonlinear state-space models is known to be a challenging task due to the posterior distribution being either intractable or expressed in a complex form. One of the most successful methods, particle filtering (PF), although generally outperforming traditional filters, suffers from sample degeneracy. Drawing from optimal transport theory, the stochastic map filter (SMF) accommodates a solution to this problem, but its performance is influenced by the limited flexibility of nonlinear map parameterisation. To alleviate these drawbacks, we propose a hybrid filter which combines the PF and SMF, and hence call it PSMF. Specifically, the PSMF splits the likelihood into two parts, which are then updated by PF and SMF, respectively. The proposed approach adopts systematic resampling and smoothing to break the particle degeneracy caused by the PF. To investigate the influence of the nonlinearity of transport maps, we introduce two variants of the proposed filter, the PSMF-L and PSMF-NL, which are based on linear and nonlinear maps, respectively. The PSMF is tested on various nonlinear state-space models and a nonlinear non-Gaussian target tracking model. The proposed linear PSMF-L outperforms all the reference models for medium-to-large numbers of particles, whilst the PSMF-NL shows better resilience to parameter changes.

Conceptual design of narrow rectangular channel test section for research reactor application

Conceptual design was carried out on test section for studying heat transfer characteristics of narrow rectangular channel for research reactor application. Thermal hydraulic design requirements were specified through literature study on mid- to high-powered research reactors currently under operation or design. Engineering design was then carried out in streamlined fashion with help of in-house design code and computational fluid dynamics analysis. Considering various constraints and uncertainties in terms of engineering hot channel factors, sensitivity studies were performed and realistic test section design was obtained. For final design, stochastic operable heater power map is generated by merging individual operable ranges from each constraint, with random sampling of hot channel factors.

Some well known inequalities for $ (h_1, h_2) $-convex stochastic process via interval set inclusion relation

<abstract><p>This note introduces the concept of $ (h_1, h_2) $-convex stochastic processes using interval-valued functions. First we develop Hermite-Hadmard $ (\mathbb{H.H}) $ type inequalities, then we check the results for the product of two convex stochastic process mappings, and finally we develop Ostrowski and Jensen type inequalities for $ (h_1, h_2) $-convex stochastic process. Also, we have shown that this is a more generalized and larger class of convex stochastic processes with some remark. Furthermore, we validate our main findings by providing some non-trivial examples.</p></abstract>

Thermalization of Isolated Harmonic Networks Under Conservative Noise

We study a scalar harmonic network with pair interactions and a binary collision rule, exchanging the momenta of a randomly-chosen couple of sites. We consider the case of the isolated network where the total energy is conserved. In the first part, we recast the dynamics as a stochastic map in normal modes (or action-angle) coordinates and provide a geometric interpretation of it. We formulate the problem for generic networks but, for completeness, also reconsider the translation-invariant lattices. In the second part, we examine the kinetic limit and its range of validity. A general form of the linear collision operator in terms of eigenstates of the network is given. This defines an action network, whose connectivity gives information on the out-of-equilibrium dynamics. We present a few examples (ordered and disordered chains and elastic networks) where the topology of connections in action spaces can be determined in a neat way. As an application, we consider the classic problem of relaxation to equipartition from the point of view of the dynamics of linear actions. We compare the results based on the spectrum of the collision operator with numerical simulation, performed with a novel scheme based on direct solution of the equations of motion in normal modes coordinates.

Research Spotlights

The first Research Spotlights article in this issue is concerned with filtering, a task of paramount importance in a great many applications such as numerical weather prediction and geophysical data assimilation. Authors Alessio Spantini, Ricardo Baptista, and Youssef M. Marzouk, in their article “Coupling Techniques for Nonlinear Ensemble Filtering,” describe discrete-time filtering as the act of characterizing the sequence of conditional distributions of the latent field at observation times, given all currently available measurements. Despite the existing literature on filtering, issues such as high-dimensional state spaces and sparse (in both space and time) observations still prove formidable in practice. The traditional approach of ensemble-based data assimilation is the ensemble Kalman filter (EnKF), involving a prediction (forecasting) step followed by an analysis step. However, the authors note an intrinsic bias of EnKF due to the linearity of the transformation, estimated under Gaussian assumptions, that is used in the analysis step, which limits its accuracy. To overcome this, they propose two non-Gaussian generalizations of the EnKF---the so-called stochastic and deterministic map filters---using nonlinear transformations derived from couplings between the forecast distribution and the filtering distribution. What is crucial is that the transformations “can be estimated efficiently...perhaps using only convex optimization,” that they “are easy to `localize' in high dimensions,” and that their computation “should not become increasingly challenging as the variance of the observation noise decreases.” Following a comprehensive description of their new approaches, the authors demonstrate numerically the superiority of their stochastic map filter approach over traditional EnKF. The subsequent discussion offers the reader several jumping off points for future research. Recovery of a sparse solution to a large-scale optimization problem is another ubiquitous problem arising in many applications such as image reconstruction, signal processing, and machine learning. The cost functional typically includes a regularization term in the form of an $\ell_1$ norm term on the solution and/or regularized solution to enforce sparsity. Designing suitable algorithms for such recovery problems is the subject of our second Research Spotlights article. In “Sparse Approximations with Interior Point Methods,” authors Valentina De Simone, Daniela di Serafino, Jacek Gondzio, Spyridon Pougkakiotis, and Marco Viola set out to correct the misconception that first-order methods are to be preferred over second-order methods out of hand. Through case studies, they offer evidence that interior point methods (IPMs) which are constructed to “exploit special features of the problems in the linear algebra of IPMs” and which are designed “to take advantage of the expected sparsity of the optimal solution” can in fact be the method of choice for solving this class of optimization problems. The key to their approach is a reformulation of the original sparse approximation problem to one which is seemingly larger but which has properties upon which one can capitalize for computational gain. For each of four representative applications, the authors show how to take computational advantage of the problem-specific structure of the underlying linear systems involved at each iteration. These efforts are complemented by leveraging the expected sparsity: employing heuristics to drop near zero variables, thereby replacing very large, ill-conditioned intermediate systems by better conditioned, smaller systems. Their conclusion is that time invested in tailoring solvers to structure admitted by the reformulated variant, and in taking advantage of expected sparsity, may be well spent, since their demonstrations have shown it is possible for IPMs to have a “noticeable advantage” over state-of-the-art first-order methods for sparse approximation problems.