Path Properties Research Articles

Vector random fields on the arccos-quasi-quadratic metric space

An arccos-quasi-quadratic metric is defined as the composition of arccosine and quasi-quadratic functions over a subset of R d + 1 such as a ball, an ellipsoid, a simplex or a corner of the d-cube, a bounded solid cone, a bounded solid hyperboloid, or their surfaces. This metric is not only conditionally negative definite (or of negative type) but also a measure definite kernel, and the metric space incorporates several important cases in a unified framework so that we are able to study metric-dependent random fields on different metric spaces in a unified manner. This paper constructs the Gaussian vector random field on the arccos-quasi-quadratic metric space via an infinite series expression based on spherical harmonics, introduces a class of elliptically contoured vector random fields with metric-dependent covariance matrix functions that possess the ultraspherical polynomial expressions, and studies their sample path properties. In particular, the property of strong local nondeterminism and Hölder continuity are established, and Abelian and Tauberian theorems are derived.

Research on Mechanical Properties of a 3D Concrete Printing Component-Optimized Path by Multimodal Analysis

Three-dimensional concrete printing (3DCP) technology with solid wastes has significant potential for sustainable construction. However, the hardened mechanical properties of components manufactured using 3DCP technology are affected by weak interlayer interfaces, limiting the widespread application of 3DCP technology. To address the inherent limitations of 3DCP technology, conventional improvement strategies, such as external reinforcement and the optimization of material properties, lead to increased production costs, complex fabrication, and decreased automation. This study proposes an innovative spatial path optimization method to enhance the mechanical performance of 3D-printed, cement-based components. The novel S-path design introduces additional printed layers in the weak interlayer regions of the printed samples. This design improves the spatial distribution of fiber-reinforced filaments in continuous weak zones, thus enhancing the functional efficiency of fibers. This approach improves the mechanical performance of the printed samples, achieving compressive strengths close to those of cast samples and only a 20% reduction in average flexural strength. Compared to using a conventional printing path, the average compressive strength and flexural strength are improved by 30% and 55%, respectively, when the S-path layout is employed in 3DCP. Additionally, this method significantly reduces the anisotropy in compressive and flexural strengths to 26% and 28% of samples using conventional printing paths, respectively. Therefore, the proposed method can improve the mechanical properties and stability of the material, reducing the safety risks of printed structures.

Construction and sample path properties of Brownian house-moving between two curves

AbstractThis study aims to construct a stochastic process called “Brownian house-moving,” which is a Brownian bridge conditioned to stay between two curves. To construct this process, statements are prepared on the weak convergence of conditioned Brownian motions, conditioned Brownian bridges, and conditioned three-dimensional Bessel bridges. Moreover, the sample path properties of Brownian house-moving are studied as well.

Unified theory for the scaling of the crossover between strong and weak disorder behaviors of optimal paths and directed or undirected polymers in disordered media.

In this paper, we are concerned with the crossover between strong disorder (SD) and weak disorder (WD) behaviors in three well-known problems that involve minimal paths: directed polymers (directed paths with fixed starting point and length), optimal paths (undirected paths with a fixed end-to-end or spanning distance), and undirected polymers (undirected paths with a fixed starting point and length). We present a unified theoretical framework from which we can easily deduce the scaling of the crossover point of each problem in an arbitrary dimension. Our theory is based on the fact that the SD limit behavior of these systems is closely related to the corresponding percolation problem. As a result, the properties of those minimal paths are completely controlled by the so-called red bonds of percolation theory. Our model is first addressed numerically and then approximated by a two-term approach. This approach provides us with an analytical expression that seems to be reasonably accurate. The results are in perfect agreement with our simulations and with most of the results reported in related works. Our research also leads us to propose this crossover point as a universal measure of the disorder strength in each case. Interestingly, that measure depends on both the statistical properties of the disorder and the topological properties of the network.

General theory for extended-range percolation on simple and multiplex networks.

Extended-range percolation is a robust percolation process that has relevance for quantum communication problems. In extended-range percolation nodes can be trusted or untrusted. Untrusted facilitator nodes are untrusted nodes that can still allow communication between trusted nodes if they lie on a path of distance at most R between two trusted nodes. In extended-range percolation the extended-range giant component (ERGC) includes trusted nodes connected by paths of trusted and untrusted facilitator nodes. Here, based on a message-passing algorithm, we develop a general theory of extended-range percolation, valid for arbitrary values of R as long as the networks are locally treelike. This general framework allows us to investigate the properties of extended-range percolation on interdependent multiplex networks. While the extended-range nature makes multiplex networks more robust, interdependency makes them more fragile. From the interplay between these two effects a rich phase diagram emerges including discontinuous phase transitions and reentrant phases. The theoretical predictions are in excellent agreement with extensive Monte Carlo simulations. The proposed exactly solvable model constitutes a fundamental reference for the study of models defined through properties of extended-range paths.

Transition path properties for one-dimensional non-Markovian models

Transition path properties for one-dimensional non-Markovian models

Hurwitz enumeration problem through the perspective of Cayley graph

The Hurwitz enumeration problem studies how to determine the Hurwitz number for a branch profile, which counts the number of ways a per mutation can be factored into transpositions. In this paper, we consider the length of strictly monotone factorization from the perspective of Cayley graph theory. We represent the factorization problem using a Cayley graph, where vertices are permutations and edges are transpositions. Our focus is proving the unique monotone factorization theorem, which states that for a given permutation, there is only one monotone factorization of minimal length. To prove this, we employ inductive arguments on the structure of the Cayley graph. The key insight is using the connectivity of the graph and properties of shortest paths to characterize the uniqueness of the minimal factorization. This inductive approach allows us to rigorously connect the combinatorial Hurwitz problem to foundational graph concepts. Overall, this paper makes important theoretical advances in enumerating Hurwitz numbers by using Cayley graphs and induction to prove the novel unique monotone factorization theorem. The connections drawn between combinatorics, graphs, and inductive proofs are technically innovative. This theoretical foundation will hopefully stimulate further research into the deep links between the Hurwitz problem and other branches of mathematics.

NxtSPR: A deadlock-free shortest path routing dedicated to relaying for Triplet-Based many-core Architecture

Deadlock-free routing is a significant challenge in Network-on-Chip (NoC) design as it affects the network’s latency, power consumption, and load balance, impacting the performance of multi-processor systems-on-chip. However, achieving deadlock-free routing will routinely result in expensive overhead as previous solutions either sacrifice performance or power efficiency to proactively avoid deadlocks or impose high hardware complexity to resolve deadlocks when they occur reactively. Utilizing the various characteristics of NoC to implement deadlock-free routing can be significantly more cost-effective with less impact on performance. This paper proposes a relay routing algorithm (NxtSPR) with a shortest path property and a deadlock prevention mechanism based on a synchronized Hamiltonian ring. The proposal is based on an in-depth study of the characteristics of a Triplet-Based many-core Architecture (TriBA) NoC. We establish various important topology-related theories and perform a formal verification (proof-based) for them. By utilizing the critical subgraph and apex of TriBA, NxtSPR can pre-calculate downstream nodes forwarding ports for packets by using a concise judgment strategy. This significantly reduces the computational overhead required for data transmission while optimizing the pipeline design of routers to decrease packet transmission latency and power consumption compared to other TriBA routing algorithms. We group the data transmissions according to the levels of maximum Hamiltonian edges a packet will traverse during its transmission life cycle. Independent data transmissions between groups can avoid mutual interference and resource competition, eliminating potential deadlocks. Gem5 simulation results show that, under the synthetic traffic patterns, compared to the representative (Table) and up-to-date (SPR4T) routing algorithms, NxtSPR achieves a 20.19%, 14.76%, and 5.54%, 4.66% reduction in average packet latency and per-packet power consumption, respectively. Moreover, it has an average of 18.50% and 4.34% improvement in throughput, as compared to them. PARSEC benchmark results show that NxtSPR reduces application runtime by up to a maximum of 22.30% and 12.82% compared to Table and SPR4T, and running the same applications with TriBA results in a maximum runtime reduction of 10.77% compared to 2D-Mesh.

Three‐Dimensionally Arranged NiSe2 Nanosheets as an Efficient Electrocatalyst for Methanol Electrooxidation Reaction

Methanol oxidation stands out as a pivotal solution in addressing the global energy crisis and environmental pollution, owing to its practical applicability, high current density, and the ready availability of methanol as a fuel source. To effectively catalyze methanol oxidation, an electrocatalyst is imperious to overcome the activation energy barrier. Herein, a three‐dimensionally arranged NiSe2 nanosheet‐based electrocatalyst is synthesized through a facile solvothermal followed by an annealing method. The catalyst's porous structure enhances catalytic efficiency by providing a substantial electrochemical surface area (ECSA) equivalent to 0.121 mF cm−2. Notably, the electrocatalyst exhibits a remarkable response of 21.58 mA cm−2 at an overpotential of 1.70 V vs RHE, accompanied by the lowest Tafel slope recorded at 39.14 mV dec−1. The electronic circuit, represented by Rs(Qf(RfW(QdlRct)), aligns well with electrochemical impedance spectroscopy data, elucidating the reaction path and intrinsic properties. Furthermore, the catalytic performance is elucidated concerning ECSA and weight, revealing current densities of 5.60 mA cm−2 and 71.34 mA mg−1, respectively. Impressively, the catalyst demonstrates exceptional resistance to poisoning and sustained stability over a continuous 3600‐s operation. This comprehensive study underscores the promising potential of the NiSe2 nanosheet‐based electrocatalyst for efficient methanol oxidation, providing valuable insights for advancing clean energy technologies.

Closed paths in graphs vs. voting theory

Features of graphs that hinder finding closed paths with particular properties, as represented by the Traveling Salesperson Problem—TSP, are identified for three classes of graphs. Removing these terms leads to a companion graph with identical closed path properties that is easier to analyze. A surprise is that these troubling graph factors are precisely what is needed to analyze certain voting methods, while the companion graph’s terms are what cause voting theory complexities as manifested by Arrow’s Theorem. This means that the seemingly separate goals of analyzing closed paths in graphs and analyzing voting methods are complementary: components of data terms that assist in one of these areas are the source of troubles in the other. Consequences for standard decision methods are in Sects. 2.5, 3.7 and the companion paper (Saari in Theory Decis 91(3):377–402, 2021). The emphasis here is on paths in graphs; incomplete graphs are similarly handled.

The Euclidean $\phi^{4}_{2}$ theory as a limit of an interacting Bose gas

We prove that the complex Euclidean field theory with local quartic self-interaction in two dimensions arises as a limit of an interacting Bose gas at positive temperature, when the density of the gas becomes large and the range of the interaction becomes small. The field theory is supported on distributions of negative regularity, which requires a renormalization by divergent mass and energy counterterms. We obtain convergence of the relative partition function and uniform convergence of the renormalized reduced density matrices. The proof is based on three main ingredients: (a) a quantitative analysis of the infinite-dimensional saddle point argument for the functional integral introduced by Fröhlich et al. (2022) using continuity properties of Brownian paths, (b) a Nelson-type estimate for a general nonlocal field theory in two dimensions, and (c) repeated Gaussian integration by parts in field space to obtain uniform control on the renormalized correlation functions. As a byproduct of our proof, in two and three dimensions we also extend the results on the mean-field limit by Fröhlich et al. (2022) and Lewin et al. (2021) to unbounded interaction potentials satisfying the optimal integrability conditions proposed by Bourgain (1997).

HMSL: Source localization based on higher-order Markov propagation

The widespread use of the Internet and social media has brought us great convenience, but it has also exposed us to a lot of false information and malicious attacks. It is vital to accurately locate the source of the harmful spread to prevent it from spreading further. Most previous studies have assumed that the propagation path is memoryless and always the shortest path. This assumption implies the first-order Markov property of propagation paths. This paper takes into account the higher-order Markov property of propagation paths in the source localization problem. Firstly, the problem of source localization based on observers is formulated. Then, we introduce the higher-order Markov property of propagation paths into the problem and propose a reaction–synchronization–diffusion model to model the propagation process on the higher-order network. On this basis, we build a framework named source localization based on higher-order Markov propagation (HMSL), which is compatible with traditional algorithms for source localization. After that, we conducted experiments on a real dataset and found that the HMSL has significant improvement in the source localization compared to the first-order network. Sensitivity analysis indicates that the degree of improvement is significantly influenced by the probability of infection and the proportion of higher-order nodes. Furthermore, we investigated the reason behind the improvement and found that the first-order network creates paths that do not exist within the raw data. When these fake paths are shorter than actual propagation paths, the length of propagation paths and estimated activation time of observers will be underestimated, thus decreasing the accuracy of source localization. The HMSL framework can solve this problem effectively.

Weierstrass bridges

We introduce a new class of stochastic processes called fractional Wiener–Weierstraß bridges. They arise by applying the convolution from the construction of the classical, fractal Weierstraß functions to an underlying fractional Brownian bridge. By analyzing the p p -th variation of the fractional Wiener–Weierstraß bridge along the sequence of b b -adic partitions, we identify two regimes in which the processes exhibit distinct sample path properties. We also analyze the critical case between those two regimes for Wiener–Weierstraß bridges that are based on a standard Brownian bridge. We furthermore prove that fractional Wiener–Weierstraß bridges are never semimartingales, and we show that their covariance functions are typically fractal functions. Some of our results are extended to Weierstraß bridges based on bridges derived from a general continuous Gaussian martingale.

Analysis of the Methodology for Experimental Measuring of the Performance Criteria of the Laser-Using Collaborative Robot’s Path Accuracy

This study describes the design of an experimental methodology developed to measure the working properties of the accuracy of the path traversed by a collaborative robot. The methodology proposed here uses a collaborative robot and a laser measuring system Gepard from Raytec. The main parts of the measuring chain and the ISO 9283 standard are described. The proposed experimental methodology should examine the working properties of industrial robots, such as position and path. The focus of this study lies in the path accuracy of robots. Currently, interest in this topic is on the rise, and the measuring systems capable of recording this parameter are too costly. This study focuses on the experimental measuring of the path properties, describing them in more detail. The measuring and results were processed in the software tool developed for Gepard.

Stochastic model for barrier crossings and fluctuations in local timescale

The problem of computing the rate of diffusion-aided activated barrier crossings between metastable states is one of broad relevance in physical sciences. The transition path formalism aims to compute the rate of these events by analysing the statistical properties of the transition path between the two metastable regions concerned. In this paper, we show that the transition path process is a unique solution to an associated stochastic differential equation, with a discontinuous and singular drift term. The singularity arises from a local time contribution, which accounts for the fluctuations at the boundaries of the metastable regions. The presence of fluctuations at the local time scale calls for an excursion theoretic consideration of barrier crossing events. We show that the rate of such events, as computed from excursion theory, factorizes into a local time term and an excursion measure term, which bears empirical similarity to the transition state theory rate expression. Since excursion theory makes no assumption about the presence of a transition state in the potential energy landscape, the mathematical structure underlying this factorization ought to be general. We hence expect excursion theory (and local times) to provide some physical and mathematical insights in generic barrier crossing problems.

An Empirical Study on the Incubation Growth Path and Business Transformation of Cultural Intellectual Property for Chinese Tourism Destination Cities

This empirical study investigates the interplay between the incubation growth path, business transformation, and cultural intellectual property (IP) within Chinese tourism destination cities. With China's tourism industry experiencing rapid growth and cultural heritage playing a significant role in attracting visitors, understanding how startups leverage cultural IP and evolve over time is crucial for fostering sustainable tourism development. Through a mixed-methods approach incorporating interviews, surveys, and case studies, we examine the experiences of startups incubated in Chinese destination cities, focusing on their journey from inception within incubators to market maturity. The study explores the strategies employed by startups to integrate cultural elements into their products and services, the challenges they encounter in navigating cultural IP frameworks, and the impact of business transformation on their growth trajectories. Additionally, the research assesses the role of incubators, government policies, and industry collaborations in supporting startups and promoting responsible cultural stewardship. By shedding light on the dynamics between incubation, business transformation, and cultural IP, this study aims to provide valuable insights for policymakers, industry stakeholders, and academics seeking to foster innovation, preserve cultural heritage, and promote sustainable tourism in Chinese destination cities.

Necessary and sufficient conditions for continuity of hypercontractive processes and fields

Sample path properties of random processes are an interesting and extensively studied topic, especially in the case of Gaussian processes. In this article, we study the continuity properties of hypercontractive fields, providing natural extensions for some known Gaussian results beyond Gaussianity. Our results apply to both random processes and random fields alike.

Gct-TTE: graph convolutional transformer for travel time estimation

This paper introduces a new transformer-based model for the problem of travel time estimation. The key feature of the proposed GCT-TTE architecture is the utilization of different data modalities capturing different properties of an input path. Along with the extensive study regarding the model configuration, we implemented and evaluated a sufficient number of actual baselines for path-aware and path-blind settings. The conducted computational experiments have confirmed the viability of our pipeline, which outperformed state-of-the-art models on both considered datasets. Additionally, GCT-TTE was deployed as a web service accessible for further experiments with user-defined routes.

Enhanced thermoelectric performance of graphene at room temperature by cut-off phonon frequency

Based on the full electron-phonon interactions and temperature-induced phonon renormalization, both electrical transport and thermal transport of graphene are systematically studied under different cut-off phonon frequencies. When the electron concentration is less than 1013 cm−2, the electrical transport properties increase with the cut-off phonon frequency. Otherwise, the electrical transport properties are nearly the same between 1013 cm−2 and 1015 cm−2, indicating that the contribution of cut-off phonon frequency decreases with the electron concentration. Considering the three-phonon, four-phonon, and phonon-electron scattering processes, the lattice thermal conductivity is studied, showing a value of 1357 W/mK at room temperature. At Van Hove singularity (5 × 1014 cm−2), the lattice thermal conductivity changes from 1357 W/mK to 557 W/mK. The effect of cut-off phonon frequency on thermal transport is nearly negligible. The electrical/phonon transport property accumulation concerning the mean free path shows the quantitative relationship between the mean free path and transport property, indicating a key mean free path of 186 nm. With a grain boundary of 186 nm, the ZT changes from 0.22 to 0.56 under a cut-off phonon frequency of 0 cm−1, while increasing from 0.64 to 1.23 under a cut-off phonon frequency of 30 cm−1. This work provides a strategy to enhance the thermoelectric property by regulating the electron-phonon coupling strength through cut-off phonon frequency.

Sample path properties of multidimensional integral with respect to stochastic measure

Sample path properties of multidimensional integral with respect to stochastic measure