Path Space Research Articles

Modeling bundle-valued forms on the path space with a curved iterated integral

The usual iterated integral map given by Chen produces an equivalence between the two-sided bar complex on differential forms and the de Rham complex on the path space. This map fails to make sense when considering the curved differential graded algebra of bundle-valued forms with a covariant derivative induced by a connection. In this paper, we define a curved version of Chen’s iterated integral that incorporates parallel transport and maps an analog of the two-sided bar construction on bundle-valued forms to bundle-valued forms on the path space. This iterated integral is proven to be a homotopy equivalence of curved differential graded algebras, and for real-valued forms it factors through the usual Chen iterated integral.

Entropy-driven microstructure evolution predicted with the steepest-entropy-ascent quantum thermodynamic framework

A Potts model and the Replica Exchange Wang–Landau algorithm is used to construct an energy landscape for a crystalline solid containing surfaces and grain boundaries. The energy landscape is used by an equation of motion from the steepest-entropy-ascent quantum thermodynamic (SEAQT) framework to explore the kinetics of three distinct kinds of microstructural evolution: polycrystalline sintering, precipitate coarsening, and grain growth. The steepest-entropy-ascent postulate predicts unique kinetic paths for these non-equilibrium processes without needing any detailed information about the underlying physical mechanisms of the processes. A method is also proposed for associating the kinetic path in state space to a set of smoothly evolving microstructural descriptors. The SEAQT-predicted kinetics agree well with available experimental kinetics for ZrO2 sintering, Al3Li precipitate coarsening, and grain growth in nanocrystalline Pd. The computational cost associated with calculating the energy landscape needed by the approach is comparable to a Monte Carlo simulation. However, the subsequent kinetic calculations from the SEAQT equation of motion are quite modest and save considerable computational resources by obviating the need for averaging multiple kinetic Monte Carlo runs.

Rational motivic path spaces and Kim’s relative unipotent section conjecture

We develop the foundations of commutative algebra objects in the category of motives, which we call “motivic dga’s.” Works of White and Cisinski and Déglise provide us with a suitable model structure. This enables us to reconstruct the unipotent fundamental group of a pointed scheme from the associated augmented motivic dga and provides us with a factorization of Kim’s relative unipotent section conjecture into several smaller conjectures with a homotopical flavor.

Non-line-of-sight transient rendering

The capture and analysis of light in flight, or light in transient state, has enabled applications such as range imaging, reflectance estimation and especially non-line-of-sight (NLOS) imaging. For this last case, hidden geometry can be reconstructed using time-resolved measurements of indirect diffuse light emitted by a laser. Transient rendering is a key tool for developing such new applications, significantly more challenging than its steady-state counterpart. In this work, we introduce a set of simple yet effective subpath sampling techniques targeting transient light transport simulation in occluded scenes. We analyze the usual capture setups of NLOS scenes, where both the camera and light sources are focused on particular points in the scene. Also, the hidden geometry can be difficult to sample using conventional techniques. We leverage that configuration to reduce the integration path space. We implement our techniques in a modified version of Mitsuba 2 adapted for transient light transport, allowing us to support parallelization, polarization, and differentiable rendering.

Signal Processing-based Model for Primary User Emulation Attacks Detection in Cognitive Radio Networks

Cognitive Radio Networks (CRNs) have been conceived to improve the efficiency of accessing the spectrum. However, these networks are prone to various kinds of attacks and failures that can compromise the security and performance of their users. One of the notable malicious attacks in cognitive radio networks is the Primary User Emulation (PUE) attack, which results in underutilization and unavailability of the spectrum and low operational efficiency of the network. This study developed an improved technique for detecting PUE attacks in cognitive radio networks and further addressed the characteristics of sparsely populated cognitive radio networks and the mobility of the primary users. A hybrid signal processing-based model was developed using the free space path loss and additive Gaussian noise models. The free space path loss model was used to detect the position of the transmitter, while the additive Gaussian noise model was used to analyze the signal transmitted, i.e., energy detection in the spectrum at the detected location. The proposed model was benchmarked with an existing model using the number of secondary users and the velocity of the transmitter as performance parameters. The simulation results show that the proposed model has improved accuracy in detecting primary user emulation attacks. It was concluded that the proposed hybrid model with respect to the number of secondary users and the velocity of the transmitter can be used for primary user emulation attack detection in cognitive radio networks.

Synthesis of an algorithm for automatic control of the quadcopter position using the control force estimation method

A mathematical model of the quadcopter motion control system has been developed. A new algorithm for controlling the movement of the quadcopter is proposed, which, in combination with sliding modes for controlling the position and direction of movement, ensures stable movement of the quadcopter in space. The simulation of the quadcopter motion control system on the MATLAB SIMULINK software was performed. The proposed algorithm for controlling the movement of the quadcopter ensures its steady movement as a single quadcopter along a given flight path in space in the presence of interference, and the movement of a group of quadcopters

Prediction of surface roughness of CO2 laser modified poplar wood via response surface methodology

Due to the advantages of short treatment period, no wastewater and oil produced, the CO2 laser is applied as an environment friendly thermal treatment for wood materials to improve the wood properties, such as appearance, color and wettability, among others. However, the morphological features of treated wood surface are also changed, which have negative effects on wooden product properties. To reveal the change tendency of surface roughness during laser irradiation, the common indexes of average roughness (Ra) and mean peak-to-valley height (Rz) were chosen to evaluate the surface roughness. The response surface methodology was selected to arrange the experiments and analyze the influences of laser parameters on surface roughness. The results showed that the poplar wood got rougher with the increased laser power, but the surface roughness decreased with increased feed speed and path spacing, due to the total heat absorption varied under different combination of laser parameters. The ANOVA results showed that the selected quadratic models for Ra∥, Rz∥, Ra⊥and Rz⊥were significant due to the values of probability value (“Prob>F”) less than 0,05. In this case, all the input laser parameters were also the significant model terms for variation of surface roughness. The values of correlation coefficient were very close to 1, which meant the selected quadratic models could give accurate prediction of surface roughness for laser treated wood. Therefore, it is of great significance to predict the surface roughness of the modified wood surface scientifically and to guide the selection of reasonable modification process parameters.

Position-free multiple-bounce computations for smith microfacet BSDFs

Bidirectional Scattering Distribution Functions (BSDFs) encode how a material reflects or transmits the incoming light. The most commonly used model is the microfacet BSDF. It computes the material response from the microgeometry of the surface assuming a single bounce on specular microfacets. The original model ignores multiple bounces on the microgeometry, resulting in an energy loss, especially for rough materials. In this paper, we present a new method to compute the multiple bounces inside the microgeometry, eliminating this energy loss. Our method relies on a position-free formulation of multiple bounces inside the microgeometry. We use an explicit mathematical definition of the path space that describes single and multiple bounces in a uniform way. We then study the behavior of light on the different vertices and segments in the path space, leading to a reciprocal multiple-bounce description of BSDFs. Furthermore, we present practical, unbiased Monte Carlo estimators to compute multiple scattering. Our method is less noisy than existing algorithms for computing multiple scattering. It is almost noise-free with a very-low sampling rate, from 2 to 4 samples per pixel (spp).

Facile synthesis and efficient electrochemical water splitting of bifunctional nanostructured Ni-based layered double hydroxide/sulfide composite

The development of efficient, stable and low-cost bifunctional electrocatalyst for water splitting is of great practical significance for the industrial application of hydrogen production. In this paper, a well-aligned columnar nickel sulfide and NiAl layered double hydroxides composite (NiAl-LDH/Ni3S2) supported on Ni-foam substrate was successfully designed and prepared by successive hydrothermal processes. Ni3S2 nanorod arrays attached to Ni-foam could provide large open space and short ions diffusion path, and NiAl-LDH provides large contact area with electrolyte, thus enabling fast and reversible redox process, which together could promote electrocatalytic activity. Accordingly, the NiAl-LDH/Ni3S2/NF electrode shows excellent HER and OER performance, in which the low overpotentials of 53.6, 90.2 and 209.2 mV are needed to drive the current density of 10, 20 and 100 mA/cm2 for HER, and similarly for OER, it needs 350.4 mV low overvoltage to reach 100 mA/cm2. In the self-assembled device, the overall water splitting reaction can be driven at a cell voltage of 1.56 V when NiAl-LDH/Ni3S2/NF electrode used as cathode and anode, to achieve the current density of 10 mA/cm2, and the loss voltage is only 16.5 mV within 10 h, showing the excellent stability. The well-constructed NiAl-LDH/Ni3S2/NF is a promising material in the area of electrocatalytic water splitting, which is of practical significance to realize the industrial development of hydrogen production.

RRT*-based Path Planning for Continuum Arms.

Continuum arms are bio-inspired devices that exhibit continuous, smooth bending and generate motion through structural deformation. Rapidly-exploring random trees (RRT) is a traditional approach for performing efficient path planning. RRT approaches are usually based on exploring the configuration space (C-Space) of the robot to find a desirable work space (W-Space) path. Due to the complex kinematics and the highly non-linear mapping between the C-Space and W-Space of continuum arms, a high-quality path in the C-Space (e.g., a linear path) may not correspond to a desirable path/movement in the W-Space. Consequently, the C-Space RRT approaches that are based on C-Space cost functions do not lead to reliable and effective path planning when applied to continuum arms. In this paper, we propose a RRT* path planning approach for continuum arms that is based on exploring the W-Space of the robot as opposed to its C-Space. We show the successful applications of the proposed W-Space RRT* path planner in performing path planning with obstacle avoidance and in performing trajectory tracking. In all the aforementioned tasks, the quality of the paths generated by the proposed planner is superior to that of previous approaches and to its counterpart C-Space based RRT* approach, while the paths are generated in substantially less time.

Temporally sliced photon primitives for time‐of‐flight rendering

AbstractWe derive a class of new Monte Carlo estimators for volumetric time‐of‐flight rendering, generalizing prior work on transient photon points and beams. Conceptually, our method starts with any steady‐state photon primitive – like a photon plane, parallelepiped, or parallelotope – and slices it with a temporal wavefront, producing a primitive of one dimension lower. We show how different unbiased temporally sliced primitives arise by analytically integrating any four dimensions within a novel extended spatio‐temporal path space formulation. The differences between these estimators reduce to the determinant of a 4×4 Jacobian matrix, with columns dictated by the chosen dimensions. We then show how to combine the relative strengths of different sliced primitives using multiple importance sampling. Finally, we implement several of the new estimators enabled by our theory and compare them to each other as well as previous techniques.

Antenna for 5G Mobile Communication at 28 GHz

Fifth generation (5G) mobile communications has become one of the trendiest issues in recent years, especially in the development of wireless technology for communications. As such, 5G mobile communications will also suffer severe path loss, due to the high frequency bands. This work presents the antennas for 5G mobile communication at 28 GHz on Rogers RT5880 with a dielectric constant, εr of 2.2, loss tangent, tan δ of 0.0009 and thickness, h of 0.787 mm. A rectangular microstrip patch are proposed in this work which consist of a single element and array configurations with two and four elements. Microstrip feed line and inset feed line are implemented to observe their performances. It can be observed from the simulation results that the gain and directivity increase from a single element up until four elements array antenna for both the microstrip feed line and inset feed line of the rectangular microstrip patch antenna. This confirm to the fact that array antenna produces high gain and directivity which could overcome the challenge of high free space path loss in millimeter-wave. The spacing between each element in the array antenna are spaced accordingly and not so close with each other in order to suppress the mutual coupling between the elements. It is shown that the mutual coupling is greatly reduced based on the greater values of reflection coefficient in two-element and four-element array antennas. Based on the gain, directivity and reflection coefficient, inset feed line antennas perform better than microstrip feed line antennas. In terms of dimensions, the size of the antenna with an inset feed line reduces as compared to microstrip feed line as the number of elements increases. Thus, it is safe to conclude that inset feed line antennas outperform microstrip feed line antennas when it comes to gain, directivity, reflection coefficient, and dimensions of antennas. Therefore, the proposed array antennas in this work are suitable to be used in 5G mobile communications.

A quadratic Wiener path integral approximation for stochastic response determination of multi-degree-of-freedom nonlinear systems

A Wiener path integral (WPI) technique is developed for determining the stochastic response of multi-degree-of-freedom (MDOF) nonlinear systems. Specifically, the nonlinear system response joint transition probability density function (PDF) is expressed as a WPI over the space of paths satisfying the initial and final conditions in time. Next, a functional series expansion is considered for the WPI and a quadratic approximation is employed. Further, relying on a variational principle yields a functional optimization problem to be solved for the most probable path, which is used for determining approximately the joint response transition PDF. It is shown that compared to the standard (semiclassical) WPI solution approach, which accounts only for the most probable path, the quadratic approximation developed herein exhibits enhanced accuracy. This is due to the fact that fluctuations around the most probable path are also accounted for by considering a localized state-dependent factor in the calculation of the WPI. Furthermore, the PDF normalization step of the most probable path approach is bypassed, and thus, probabilities of rare events (e.g., failures) can be determined in a direct manner without the need for obtaining the complete joint response PDF first. The herein developed technique can be construed as an extension of earlier efforts in the literature to account for MDOF systems. Several numerical examples are considered for demonstrating the accuracy of the technique. These pertain to various dynamical systems exhibiting diverse nonlinear behaviors. Comparisons with pertinent Monte Carlo simulation data are included as well.

Prediction of Gaseous Attenuation of Satellite Signal in Nigeria

It would be noticed that the rate at which people are demanding for satellite services has drastically increased due to increment in population. However, one of the apprehensions of satellite telecommunication engineer is the effects imposed on the earth-to space path link by gaseous attenuation. The research conducted in this paper bordered about investigation with comparison of prediction models for gas attenuation in the six locations in Nigeria, with each of the location taken from six geopolitical within the country. The cities considered for the analysis are: Kaduna (), Lagos (), Abuja (), Portharcort (), Enugu () and Bauchi (). Five-year radiosonde data were used in predicting gas attenuation in the cities selected which represent the geographical characteristics of each zone. Monthly variation of tropospheric components for each zone were computed. Influence of gas attenuation at different frequency bands for each zone were analysed. The results indicated that at clear-sky scenario, gas attenuation effects are still seen on satellite communication. Therefore, this research work would provide the needed statistical data of gas attenuation which would be of tremendous advantage for the link designers for their subsequent planning and design of good telecommunication systems in the six geopolitical zones of Nigeria.

Cognitive characteristics in firefighter wayfinding Tasks: An Eye-Tracking analysis

During search and rescue, firefighters need to find paths in an unfamiliar space with minimum time and information available. The effective memorization and retrieval of critical spatial information can help reduce risks and increase mission efficiency. Although evidence has shown that different formats of wayfinding information, including landmarks, routes, and surveys, can impact search and rescue performance in different manners, a deeper understanding of the characteristics of firefighters’ cognitive processes related to the varying wayfinding information formats is less explored. To evaluate firefighters’ performance and cognitive characteristics in search and rescue, a firefighter experiment in Virtual Reality (VR) was conducted. Firefighters (n = 40) were recruited to participate in the simulated rescue task. After reviewing the spatial information in different formats, firefighters were requested to find three victims inside a VR maze as quickly as possible. Task performance was evaluated by the number of victims found and the time spent. Firefighters’ gaze patterns were analyzed to evaluate their cognitive status. The result showed that although the cognitive load under the survey and route conditions was significantly higher than under the landmark condition (p < 0.001), the decision-making involved a more effective cognitive process related to choosing the right path at critical waypoints such as where a turning decision must be made. Thus, the perceived workload and fatigue levels of the two conditions were lower, and the wayfinding performance was better. In contrast, with landmark information, the cognitive load levels were consistently high, along with increased mental fatigue.The findings reveal a series of cognitive features related to a more effective spatial decision-making in search and rescue. In the future, it is expected that these cognitive features can be used to develop real-time monitoring and prediction models for wayfinding performance.

Monotone convex order for the McKean–Vlasov processes

This paper is a continuation of our previous paper (Liu and Pagès, 2020). In this paper, we establish the monotone convex order (see further (1.1)) between two R-valued McKean–Vlasov processes X=(Xt)t∈[0,T] and Y=(Yt)t∈[0,T] defined on a filtered probability space (Ω,F,(Ft)t≥0,P) by dXt=b(t,Xt,μt)dt+σ(t,Xt,μt)dBt,X0∈Lp(P)withp≥2,dYt=β(t,Yt,νt)dt+θ(t,Yt,νt)dBt,Y0∈Lp(P),where∀t∈[0,T],μt=P∘Xt−1,νt=P∘Yt−1.If we make the convexity and monotony assumption (only) on b and |σ| and if b≤β and |σ|≤|θ|, then the monotone convex order for the initial random variable X0⪯mcvY0 can be propagated to the whole path of processes X and Y. That is, if we consider a non-decreasing convex functional F defined on the path space with polynomial growth, we have EF(X)≤EF(Y); for a non-decreasing convex functional G defined on the product space involving the path space and its marginal distribution space, we have EG(X,(μt)t∈[0,T])≤EG(Y,(νt)t∈[0,T]) under appropriate conditions. The symmetric setting is also valid, that is, if Y0⪯mcvX0 and |θ|≤|σ|, then EF(Y)≤EF(X) and EG(Y,(νt)t∈[0,T])≤EG(X,(μt)t∈[0,T]). The proof is based on several forward and backward dynamic programming principles and the convergence of the truncated Euler scheme of the McKean–Vlasov equation.

Effects of Landscape Types and Complexity Along Path on Mental Restoration.

This study checked the effects of landscape types and complexity along path in urban green spaces on perceived restorativeness, so as to provide guidance for path landscape design. Paths in urban green spaces are not only the connections between places but also places for visitors reducing mental stress and seeking psychological well-being. However, there is a lack of evidence-based research on the effects of landscape composition along the path on restorative quality, failing to provide a cohesive guideline for practice. Fourteen videos representing the popular path landscapes in urban green spaces were produced using computer software by adding or/and deleting elements and controlling environmental components. The restorative quality of these videos was measured by Short-version Revised Restoration Scale (SRRS). Statistical analysis was employed to treat the data and checked the effects of different landscape types and complexity on restorative quality. (1) A significant difference in restorative quality between 14 path landscapes was found, comparatively, the path containing lawn or(and) forest was much better than that containing bamboo and waterscape, and bamboo was a negative predictor of restorative quality; (2) waterscape generally reduced the restorative quality of vegetated path landscape, especially when the landscape possessed higher restorative quality; (3) path landscape complexity had a weak influence on restorative quality. This study explains how path landscapes affect mental restoration of users, and these findings contribute to enhancing the restorative quality of urban green spaces and have applications for path landscape design.

Analysis and visualization of traceless symmetric tensors. Application to the Hencky strain tensor for large strain tension–torsion

Cyclic multiaxial loadings of soft materials are usually studied throughout experiments involving machines that prescribe a combination of uniaxial tension and torsion. Due to the large strain framework, classical kinematic analyses of strain in uniaxial tension–torsion are usually very complex. Based on this observation, the present paper proposes a method to both analyze and visualize a strain measure during a duty cycle of uniaxial tension–torsion in large strain: based on the mathematical properties of the Hencky strain tensor h, the method consists in projecting h onto a well-chosen tensor basis, whose constituting elements are described in terms of physical meaning. Thanks to this decomposition, the history of h reduces to the time evolution of a 3-component vector α(t). This vector history can then be visualized as a path in 3D space, rendering very visual the complex kinematic phenomenon. As a second result, an original definition of the mean and the amplitude of a strain path, based on the theory of the Minimum Circumscribed Spheres, is proposed. This definition could be useful for fatigue studies, for instance.

Narrative Activism: Writing Desire For Injury-Bound Individuals

Narrative Activism: Writing Desire For Injury-Bound Individuals

Crossing the boundaries: reimagining innovation and diffusion

Boundaries represent separation and the end of one thing and the beginning of another. The diffusion of innovations represents a transmission of information, personal relationships, creativity and similarities across boundaries. While policy and management innovation and diffusion studies began as an American state policy field, over the last 20 years the studies have expanded to include new frameworks for Chinese, Korean and other countries’ innovation and diffusion studies. Using an expanded range of institutional structures, leadership, and factors that impact innovation and diffusion, these studies embrace more comparative studies of policy diffusion across countries. In this paper, we lay out key topics in organizational and policy innovation studies, and independent variables found to lead to innovation and diffusion. In addition, we argue we should expand the types of variables included in multivariate models to empirically test questions related to which innovations diffuse rapidly or incompletely, why governments adopt innovations, and what barriers and resources are present across types of innovations. We introduce three types of boundaries—space boundaries, time and path dependency boundaries, and actors boundaries that we believe should be more regularly and broadly included in innovation and diffusion studies, and we conclude by defining how these boundaries can be operationalized.