Mobile manipulators, which are robotic systems integrating an automatic or autonomous mobile base with a manipulator, can potentially enhance automation in many industrial and unstructured environments. Namely, large-scale manufacturing processes, typical in the aerospace, energy, transportation, and conformal additive manufacturing fields, encompass a notable subset of potential future mobile manipulator use-cases. Utilizing autonomous mobility for manipulator re-positioning could allow for continuous, simultaneous arm and mobile base cooperation, which is referred to as i.e., continuous performance. Continuous mobile manipulator capabilities may hold particular benefit for large, curved, and complex workpieces. However, such flexibility can also introduce additional sources of performance uncertainty, preventing mobile manipulators from satisfying stringent pose repeatability and accuracy requirements. To identify and quantify this uncertainty, the Configurable Mobile Manipulator Apparatus (CMMA) was developed by the National Institute of Standards and Technology. Previous test implementations with the apparatus included non-continuous mobile manipulator performance, such as static and indexed performance, but continuous performance measurement had only been previously demonstrated in simulation and on proof-of-concept hardware. This dataset was obtained through the transfer of simulations and algorithms for continuous registration to an industrial mobile manipulator platform and through a subsequent 2^3 factorial designed experiment to compare the performance and robustness of two continuous localization methods: 1) A deterministic spiral search and 2) A stochastic Unscented Kalman Filter (UKF) search across two selected mobile base speeds and sides of the CMMA. Supplementary data obtained prior to the experiment, such as source code, calibration data, mobile base map and configuration data, coordinate system measurements, and robot/client to ground-truth system time synchronization is also included, along with the analysis source code and results files generated in conducting the performance evaluation. The experiment included the following improvements from the prior experiment conducted in February 2022: 1) Further manual tuning of the UKF hyper-parameters, 2) added retro-reflective tape edge detection to assist initial coordinate registration and to eliminate anomalies where the first fiducial was not detected, 3) eliminated infrared reflections on the CMMA and from the lab windows to improve ground-truth data capture quality, and 4) the coordinate system measurement between the cart transporter map and the ground truth system was re-done.*Certain commercial equipment, instruments, or materials are identified in this dataset to foster understanding. Such identification does not imply recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that the materials or equipment identified are necessarily the best available for the purpose.

Suppose we observe a random vector X from some distribution in a known family with unknown parameters. We ask the following question: when is it possible to split X into two pieces f(X) and g(X) such that neither part is sufficient to reconstruct X by itself, but both together can recover X fully, and their joint distribution is tractable? One common solution to this problem when multiple samples of X are observed is data splitting, but Rasines and Young offers an alternative approach that uses additive Gaussian noise—this enables post-selection inference in finite samples for Gaussian distributed data and asymptotically when errors are non-Gaussian. In this article, we offer a more general methodology for achieving such a split in finite samples by borrowing ideas from Bayesian inference to yield a (frequentist) solution that can be viewed as a continuous analog of data splitting. We call our method data fission, as an alternative to data splitting, data carving and p-value masking. We exemplify the method on several prototypical applications, such as post-selection inference for trend filtering and other regression problems, and effect size estimation after interactive multiple testing. Supplementary materials for this article are available online.

This code estimates the generalized continuous-discrete model with a t-distributed error kernel. It also replicates the Monte Carlo study of this paper. If you use any part of this code in any form, please cite this paper.

A new approach to the validation of surface texture form removal methods is introduced. A linear algebra technique is presented that obtains total least squares (TLS) model fits for a continuous mathematical surface definition. This model is applicable to both profile and areal form removal, and can be used for a range of form removal models including polynomial and spherical fits. The continuous TLS method enables the creation of mathematically traceable reference pairs suitable for the assessment of form removal algorithms in surface texture analysis software. Multiple example reference pairs are presented and used to assess the performance of four tested surface texture analysis software packages. The results of each software are compared against the mathematical reference, highlighting their strengths and weaknesses.

All the randomly generated problems in this data set involve a number A of aircraft passing through a square multi-sector area (MSA) of side 600 km. This MSA is composed of four square adjacent sectors of side 300 km. The aircraft use four different flight levels that belong to the same MSA. The aircraft trajectories are randomly generated in such a way that all aircraft are either flying from bottom to upper MSA borders, or from left to right borders. Taking the origin at the bottom left corner of the MSA, the distance between the first waypoint and the origin is randomly generated using the continuous uniform distribution U[75 km, 595 km]. Each trajectory is composed of three waypoints located on the MSA edges. The first waypoint is located on either the bottom or the left MSA border. The other two waypoints are generated randomly along the opposing sector borders using a uniform distribution. The cruise speeds of the aircraft are randomly generated using the continuous uniform distribution U[458 knots, 506 knots]. The time at which the aircraft enters the MSA follows the continuous uniform distribution U[20 min, 90 min]. The flight level used for each trajectory is randomly generated using a discrete uniform distribution U{1, K}. A constant flight level is used by 90% of the aircraft. The others undergo one flight level change at the internal boundary. For these aircraft, the second flight level is randomly generated using U{1, K} while excluding the first sector flight level.

The association between working memory and word reading or mathematics skills have been extensively explored. However, the existing evidence has predominantly relied on WM span-based tasks that measure the quantity of items stored in WM, neglecting the quality of stored item representations, i.e., WM precision. This limitation is particularly important in understanding the shared and distinct cognitive mechanisms underlying reading difficulties (RD), mathematics difficulties (MD), and their comorbidity (RDMD). Therefore, using a continuous report paradigm to assess WM precision, this thesis addressed this gap by investigating the distinct roles of WM span and WM precision in word reading and mathematics skills among Chinese third graders, and examined WM precision profiles across learning difficulty subgroups.Study 1 examined the distinct and interactive contributions of WM span and WM precision to Chinese word reading, considering the phonetic regularity and character frequency. Results from a generalized linear mixed model indicated that WM precision was positively correlated with irregular characters reading across children with all WM span levels, whereas such positive association with regular characters reading only observed for those with low WM span. For two-character words, WM precision was positively correlated with word reading, while WM span was only positively correlated with irregular but not regular characters. These findings highlight the importance of WM precision for phonetic irregular characters, especially for those with limited WM span.Study 2 investigated the effects of WM span and WM precision on math facts fluency and word problems, through the interplay with number sense based on the Pathways to Mathematics Model and Hierarchical framework underpinning mathematics skills. After controlling for nonverbal intelligence and language skills, results from structure equation model analyses showed that WM span directly predicted mathematics skills, while WM precision operated indirectly through number line estimation for word problems or conditionally for math facts, interacting with non-symbolic comparison, with stronger positive association in children with high WM precision. This demonstrates that WM precision supports mathematics skills through foundational number sense.Study 3 characterized WM precision profiles across children with RD, MD, comorbid RDMD, and typically achieving peers using continuous report tasks under varying cognitive loads (the number of items to be remembered: set sizes 1-4). Children with RD exhibited comparable WM precision to TA peers. Those with MD showed deficits only under high cognitive load conditions. Critically, the RDMD group demonstrated severe, generalized impairments across all set sizes, with a steeper increase in WM precision errors as cognitive load increased, indicating a fundamental deficit in their WM representational quality.In conclusion, this thesis demonstrated WM precision as a distinct cognitive factor from WM span with unique contributions to academic skills. The findings reveal heterogeneous profiles across learning difficulties, highlighting that comorbidity is not merely additive but may represent a unique phenotype with severe WM precision deficits. These results provide a more nuanced cognitive account of learning difficulties, suggesting that WM precision may serve as a critical diagnostic and intervention target, especially for children with comorbid RDMD.

Adaptive Math Practice Apps Market Outlook

According to our latest research, the global adaptive math practice apps market size reached USD 2.14 billion in 2024, reflecting the sector’s robust expansion and growing significance in the educational technology landscape. The market is poised for substantial growth, with a projected CAGR of 13.2% from 2025 to 2033. By the end of 2033, the market is forecasted to attain a value of USD 6.24 billion. This impressive growth trajectory is primarily driven by the increasing integration of artificial intelligence and machine learning algorithms in educational tools, which are fundamentally transforming how students engage with mathematics and how educators tailor instruction to individual needs.

One of the primary growth factors propelling the adaptive math practice apps market is the global shift toward personalized learning experiences. As educational institutions and parents alike recognize the limitations of traditional, one-size-fits-all teaching approaches, there is a growing demand for digital solutions that can adapt in real time to a learner’s strengths, weaknesses, and pace. Adaptive math practice apps harness advanced analytics and AI to create customized learning pathways, offering targeted practice and instant feedback. This capability not only enhances student engagement but also improves learning outcomes, making these apps particularly attractive in both formal education settings and for supplementary home learning. The proliferation of smart devices and increased internet penetration worldwide further supports the widespread adoption of these apps, making high-quality, adaptive math practice accessible to a broader audience than ever before.

Another significant factor driving market growth is the increasing emphasis on STEM (Science, Technology, Engineering, and Mathematics) education across the globe. Governments, educational organizations, and private sector stakeholders are investing heavily in digital tools that can help bridge learning gaps and prepare students for future careers in technology-driven fields. Adaptive math practice apps are uniquely positioned to address diverse learning needs, providing differentiated instruction that supports students at all proficiency levels. The COVID-19 pandemic accelerated the adoption of e-learning solutions, highlighting the importance of flexible, scalable, and effective digital education tools. As hybrid and remote learning models become more prevalent, adaptive math practice apps are expected to play a central role in supporting continuous, uninterrupted math education.

Furthermore, the market is benefiting from growing awareness among parents, teachers, and educational institutions regarding the advantages of data-driven instruction. Adaptive math practice apps offer valuable insights into student progress, identifying areas of struggle and enabling timely intervention. This data-centric approach aligns with the increasing demand for measurable educational outcomes and accountability in both public and private education sectors. Strategic partnerships between edtech companies, schools, and government agencies are also fostering innovation, leading to the development of more sophisticated and accessible adaptive math solutions. As regulatory frameworks evolve to support digital learning, the market is expected to witness sustained investment and innovation, further fueling its growth.

From a regional perspective, North America currently dominates the adaptive math practice apps market, owing to its advanced technological infrastructure, high levels of digital literacy, and significant investments in educational technology. However, the Asia Pacific region is emerging as a key growth area, driven by large student populations, increasing smartphone adoption, and government initiatives to modernize education. Europe also represents a substantial market, with a strong focus on lifelong learning and digital inclusion. Latin America and the Middle East & Africa, while still developing, are experiencing rising demand as internet access improves and educational reforms take root. These regional dynamics underscore the global nature of the adaptive math practice apps market and its potential for continued expansion.

Product Type Analysis

The adaptive math practice apps market is segmented by product type into K-12 adaptive math apps, higher education adaptive math apps, adult learning adaptive math apps, and others. The

The Rwanda Quality Basic Education for Human Capital Development (RQBEHCD) is a World Bank Group financed project through the government of Rwanda to support Mathematics and Science teachers from upper primary and lower secondary schools. The project was confirmed in 2019 and initiated in 2020. The dataset deposited here comprises two types of data; (1) teacher performance scores per subject taught [Math (for both primary and secondary school teachers), Physics, Chemistry, Biology taught in secondary, and Science and Elementary Technology (SET) taught in upper primary school], (2) teacher belief scores. The data were collected before and after a continuous profession development (CPD) training program of five months starting from March to July 2023. The training program comprised four channels that are ICT integration in teaching math and science, content knowledge (SCK), Math and Science laboratory activities, and innovative pedagogy. The data are collected from seven districts of Rwanda that were involved in the second cohort of training (2022-2023).

Replication data for the publication Integrated photonics enables continuous-beam electron phase modulation available at https://zenodo.org/record/5575752#.ZEu7Cy9BwrM

Abstract We investigate the use of the Probabilistic Incremental Programming Evolution (PIPE) algorithm as a tool to construct continuous cumulative distribution functions to model given data sets. The PIPE algorithm can generate several candidate functions to fit the empirical distribution of data. These candidates are generated by following a set of probability rules. The set of rules is then evolved over a number of iterations to generate better candidates regarding some optimality criteria. This approach rivals that of generated distribution, obtained by adding parameters to existing probability distributions. There are two main advantages for this method. The first is that it is possible to explicitly control the complexity of the candidate functions, by specifying which mathematical functions and operators can be used and how lengthy the mathematical expression of the candidate can be. The second advantage is that this approach deals with model selection and estimation at the same time. The overall performance in both simulated and real data was very satisfying. For the real data applications, the PIPE algorithm obtained better likelihoods for the data when compared to existing models, but with remarkably simpler mathematical expressions.

Adaptive Learning Math Platform Market Outlook

As per our latest research, the global adaptive learning math platform market size reached USD 2.4 billion in 2024, demonstrating robust expansion driven by the increasing digitization of education. The market is expected to register a remarkable CAGR of 18.2% during the forecast period, with projections indicating it will attain a value of USD 11.5 billion by 2033. This growth is primarily fueled by the widespread adoption of personalized learning technologies, the rising demand for data-driven educational tools, and the growing emphasis on improving student outcomes through adaptive methodologies.

A key driver for the adaptive learning math platform market is the escalating demand for individualized learning experiences across educational institutions and corporate training environments. Traditional one-size-fits-all teaching models are increasingly being replaced by adaptive solutions that utilize artificial intelligence and machine learning to tailor content and pace according to each learnerÂ’s needs. With mathematics being a foundational subject for academic and professional success, schools and organizations are investing in platforms that can identify knowledge gaps, adjust learning paths in real-time, and provide targeted feedback. This enhances student engagement and retention, while also enabling educators to focus on high-impact interventions, thus significantly contributing to the marketÂ’s expansion.

Another significant growth factor is the proliferation of digital devices and the increasing penetration of high-speed internet, which have made e-learning more accessible globally. The COVID-19 pandemic accelerated the transition to remote and hybrid learning models, prompting educational institutions and corporations to adopt advanced digital solutions for continuous learning. Adaptive learning math platforms, which can be seamlessly integrated into both classroom and remote settings, emerged as essential tools for delivering uninterrupted, personalized education. Furthermore, the integration of analytics and reporting features within these platforms allows for real-time performance tracking, empowering educators and administrators to make data-driven decisions that further enhance learning outcomes.

The market is also being propelled by ongoing advancements in artificial intelligence, natural language processing, and big data analytics, which have significantly improved the efficacy and scalability of adaptive learning technologies. Vendors are continuously innovating to offer platforms that not only adapt to individual learning styles but also provide predictive insights and automated content recommendations. Governments and educational agencies are increasingly supporting digital transformation initiatives, including grants and funding for schools to adopt adaptive learning solutions. This favorable policy environment, combined with growing awareness of the benefits of personalized education, is expected to sustain the upward trajectory of the adaptive learning math platform market over the coming years.

Math Enrichment programs are becoming an integral part of the adaptive learning math platform landscape. These programs are designed to go beyond traditional curricula, offering students opportunities to explore mathematical concepts in greater depth and with more complexity. By incorporating Math Enrichment into adaptive platforms, educators can provide students with challenges that stimulate critical thinking and problem-solving skills. This approach not only caters to advanced learners but also helps in identifying and nurturing potential talent in mathematics. As schools and educational institutions strive to foster a love for math and prepare students for future academic pursuits, the integration of Math Enrichment into adaptive learning solutions is gaining traction. This trend is expected to enhance student engagement and achievement, contributing to the overall growth of the adaptive learning math platform market.

From a regional perspective, North America currently dominates the adaptive learning math platform market, accounting for the largest share in 2024, followed by Europe and Asia Pacific. The strong presence of leading technology providers, high digital literacy rates, and substantial investments in educational technology infrastructure are key

The used dataset contained information about:

students' gender (1 = male, 2 = female);

schools' type (1 = scientific lyceums, 2 = other lyceums, 3 = technical schools, 4 = vocational schools);

schools' macreregion (1 = Northwester Italy, 2 = Northeastern Italy, 3 = Central Italy, 4 = Southern Italy, 5 = Southern Italy and Isles);

students' origin (1 = native Italian student, 2 = first-generation immigrant student, 3 = second-generation immigrant student);

students' ESCS (continuous data);

teacher-given grades in mathematics (from 1 to 10);

students' achievements on the INVALSI mathematics test (continuous data);

students' fuzzy grade, obtained as a combination of teacher-given grades and achievements in mathematics (from 1 to 10).

Result sets produced in the application of Differential Evolution to the problem of meander line RFID antenna design, as reported in the in prep. paper "Integrating Continuous Differential Evolution with Discrete Local Search for Meander Line RFID Antenna Design". Two files of generated solutions are included: the eight local search variants applied to the 7x7 instance (7x7_ls_study.txt.zip); and all other results for variants of DE applied to 5x5 to 10x10 problems, plus the results of the prior ACO (de_w_ls_for_RFID_results.txt.zip). Results are grouped by the algorithm composition used to generated them. Also included is C++ source code for a version of the NEC++ antenna evaluator, a Linux executable for the NEC evaluator (mynec), and a Python script for transforming node paths into input files for NEC++ (evaluate.py).

The two data files are tab-delimited with the following columns: alg: the algorithm combination used size: grid size (5-10) trial: for DE this is the random seed, for ACO this is the value of the q0 parameter f0: solution's resonant frequency e: solution's efficiency (%) length: number of nodes in the antenna path path: node path as a space-delimited list

Values for alg include: DE: the multiobjective DE 'control' DE + bias: DE with solution archive selection bias DE + bias + ls x/y/n: DE with bias and backbite local search, using the x/y/n solution reintegration strategy (see paper for details) DE + bias + (uncounted) ls, regen/det/3: DE with best-performing local search strategy run under similar conditions to prior ACO ACO: the prior Ant Colony System algorithm; due to the way solutions were represented in that work some duplicate solutions were produced

The Python evaluation script can be used interactively to generate the input used by NEC or, at the command line, it will also attempt to run the NEC simulator and report the objective values for the given solution.

Equation Editors Market Outlook

The global equation editors market size was valued at USD 270 million in 2023 and is projected to reach USD 450 million by 2032, exhibiting a CAGR of 5.5% during the forecast period from 2024 to 2032. The increasing demand for advanced mathematical and scientific computation tools in various sectors such as education, research, and engineering is a significant growth factor propelling the equation editors market.

One of the primary growth factors for the equation editors market is the rising adoption of digital tools in educational institutions. The increasing utilization of e-learning platforms has led to a higher demand for sophisticated equation editors that can seamlessly integrate with these tools. Moreover, the burgeoning trend of remote learning and online education during and post the COVID-19 pandemic has further accelerated the need for advanced equation editor software. Additionally, the push for STEM (Science, Technology, Engineering, and Mathematics) education across various regions has necessitated the use of precise and user-friendly mathematical tools, thereby bolstering market growth.

In the research and publishing sectors, the need for accurate and efficient equation editors is paramount. Researchers and scientists require tools that can facilitate the easy input, editing, and sharing of complex mathematical formulas. The rise in scientific publications and research activities globally has resulted in a heightened demand for equation editors. These tools enable researchers to present their findings clearly and concisely, ensuring that complex mathematical data is accurately communicated. The continuous advancements in artificial intelligence and machine learning are further enhancing the capabilities of equation editors, making them more intuitive and user-friendly, thereby driving market growth.

The engineering sector is another significant contributor to the growth of the equation editors market. Engineers often deal with complex mathematical calculations and simulations, making the use of robust equation editors essential. The increasing adoption of computer-aided design (CAD) and simulation software in engineering projects necessitates the integration of powerful equation editors. These tools not only enhance the accuracy of mathematical calculations but also improve the overall efficiency of engineering processes. As industries continue to adopt more sophisticated engineering tools, the demand for advanced equation editors is expected to rise.

In the realm of digital tools for mathematical computations, Coalescent For Latex has emerged as a noteworthy development. This innovative approach allows for the seamless integration of complex mathematical expressions into digital documents, enhancing the capabilities of traditional equation editors. By leveraging the power of LaTeX, a typesetting system widely used for technical and scientific documentation, Coalescent For Latex offers users the ability to create highly precise and visually appealing mathematical content. This advancement is particularly beneficial for researchers and educators who require sophisticated tools to convey complex mathematical ideas effectively. As the demand for advanced equation editors continues to grow, the integration of Coalescent For Latex into existing platforms is expected to provide users with enhanced functionality and greater flexibility in their work.

Regionally, North America holds a dominant position in the equation editors market, owing to the high adoption of advanced educational tools and technologies. The presence of leading software companies and a well-established educational infrastructure further supports market growth in this region. Europe follows closely, driven by significant investments in educational technology and research activities. The Asia Pacific region is expected to witness the highest growth rate during the forecast period, attributed to the rapid digital transformation in the education sector and increasing government initiatives to promote STEM education. Latin America and the Middle East & Africa are also anticipated to experience steady growth, supported by the gradual adoption of digital tools in education and research.

Component Analysis

The component segment of the equation editors market is bifurcated into software and services. The software segment dominates the market, driven by the increasing demand for robust and user-friendly equation editor software across various a

We consider a neighborhood random walk on a quadrant {(X1(t),X2(t),φ(t)):t≥0} with environment phase variable φ(t) modeled by a continuous-time Markov chain with φ(t)∈Snm when X1(t) = n, X2(t) = m. We describe this random walk using a two-dimensional level-dependent Quasi-Birth-and-Death process (2D-LD-QBD) with phase variable φ(t) and level variables X1(t),X2(t)∈{0,1,2,…} which change in a skip-free manner at the moments of jump in the process. We transform this random walk into a one-dimensional LD-QBD {(Z(t),χ(t)):t≥0} with level variable Z(t)∈{0,1,2,…} recording the maximum of the two level variables and phase variable χ(t)=(χ1(t),χ2(t),φ(t)) recording the remaining information about the random walk. Using this transformation, we perform transient and stationary analysis of the random walk, including first hitting times for various sample paths, using matrix-analytic methods. We also construct a sequence of neighborhood random walks, represented as two-dimensional QBDs ({(X1(k)(t),X2(k)(t),φ(t)):t≥0})k=1,2,…, converging in distribution to a two-dimensional stochastic fluid model (SFM) {(Y1(t),Y2(t),φ(t)):t≥0}, which describes a movement on a quadrant in which the position changes in a continuous manner according to rates dY1(t)/dt=c1,φ(t) and dY2(t)/dt=c2,φ(t) modulated by the underlying phase process {φ(t):t≥0}. Numerical examples are provided to illustrate the application of the methodology.

Matlab data file gathering continuous measures of emotion, subjective and physiological, to repeated listenings of stimulus 25 (Origin - Portal) in the solo response project. Please refere to Readme.txt for more details, and http://soloresponseproject.com/ for related research.

The strong relationship between socioeconomic status (SES) and academic achievement has been the focus of much research over the last fifty years. However, there is a very limited number of studies that examine the SES of individual students and the SES of their peers in a disaggregated manner. This study examines the relationship between SES and academic achievement at both the student and school levels, using data from 54 countries from six cycles of the Trends in International Mathematics and Science Study (TIMSS) assessment over the past two decades. Integrative Data Analysis (IDA) is used to synthesize data across cycles and countries, and Hierarchical Linear Modeling (HLM) is used to account for the nested nature of students within schools. The results show that both individual and school SES have a significant positive effect on academic achievement, with school SES having a stronger effect. Moreover, most of the variance in the effects of individual and school SES is due to differences between countries. Income inequality reduces the effect of individual SES and leads to differences in SES and achievement between schools. On the other hand, an increase in individual SES increases the academic achievement of female students more, while male students attending schools with higher SES levels improve their academic achievement more. Increasing the individual or school SES of migrant students helps them reduce their academic achievement gaps. Moreover, the relationship between school SES and achievement was stronger in densely populated cities and large metropolitan areas. In line with the research findings, several recommendations are made to researchers and policy makers.

QSW_MPI is a Python package developed for time-series simulation of continuous-time quantum stochastic walks. This model allows for the study of Markovian open quantum systems in the Lindblad formalism, including a generalisation of the continuous-time random walk and continuous-time quantum walk. Consisting of a Python interface accessing parallelised Fortran libraries utilising sparse data structures, QSW_MPI is scalable to massively parallel computers, which makes possible the simulation of a wide range of walk dynamics on directed and undirected graphs of arbitrary complexity.

This is the dataset for the following manuscript "Continuous Flow Synthesis and Simulation-Supported Investigation of Tunable Plasmonic Gold Patchy Nanoparticles".

Abstract

Plasmonic nanoparticles have intriguing optical properties which make them suitable candidates for sensing or theranostic applications. Anisotropic patchy particles, where metal is locally deposited on the surface of a core particle, exhibit plasmon resonances that can be specifically adjusted for these applications. However, many existing synthesis routes are complex, yield too little material, or provide particles with limited optical tunability. In this work, we present a simple and scalable continuous flow synthesis of gold-on-polystyrene patchy particles with widely adjustable optical properties. By increasing the chloride concentration in the electroless deposition of gold, we slow down the redox reduction kinetics and obtain a dense patch morphology as well as a reduced nucleation rate. The latter is counteracted by introducing a low-level seeding approach where a small number of gold nanocrystals heterocoagulate with the core particles prior to patch growth. Seeding and patch growth are performed in a continuous flow set-up with two T-shaped milli-mixers. The resulting patchy particle samples exhibit a tunable dipolar plasmon peak between 600 nm and 1100 nm. We also investigate the structure-property relationship for our gold patchy particles using Finite Element Method simulations. After identifying a suitable patch shape model, we elucidate the influence of individual geometric parameters on the optical properties and show that the relationship holds true for a large range of patch coverages. Finally, we apply the relationship to explain the time-dependent change in the optical properties of as-synthesized patches by correlating it with the patch shape transformation revealed by electron microscopy.

The uploaded data are sorted by figure.

Correction of out-of-service rate based on the previous day’s mobile terminal location data.