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Robust control of a quantum system is essential to utilize the current noisy quantum hardware to its full potential, such as quantum algorithms. To achieve such a goal, a systematic search for an optimal control for any given experiment is essential. The design of optimal control pulses requires accurate numerical models and, therefore, accurate characterization of the system parameters. We present an online Bayesian approach for quantum characterization of qutrit systems, which automatically and systematically identifies optimal experiments that provide maximum information on the system parameters, thereby greatly reducing the number of experiments that need to be performed on the quantum testbed. Unlike most characterization protocols that provide point-estimates of the parameters, the proposed approach is able to estimate their probability distribution. The applicability of the Bayesian experimental design technique was demonstrated on test problems, where each experiment was defined by a parameterized control pulse. In addition to this, we also present an approach for iterative pulse extension, which is robust under uncertainties in transition frequencies and coherence times, and shot noise, despite being initialized with wide uninformative priors. Furthermore, we provide a mathematical proof of the theoretical identifiability of the model parameters and present conditions on the quantum state under which the parameters are identifiable. The proof and conditions for identifiability are presented for both closed and open quantum systems using the Schrödinger equation and the Lindblad master equation, respectively. [ABSTRACT FROM AUTHOR]

A coloring C = (V1,...,Vk) of G partitions the vertex set V (G) into independent sets Vi which are said to be color classes with respect to the coloring C. A vertex v is said to have a dominator (dom) color class in C if there is color class Vi such that v is adjacent to all the vertices of Vi and v is said to have an anti-dominator (anti-dom) color class in C if there is color class Vj such that v is not adjacent to any vertex of Vj. Dominator coloring of G is a coloring C of G such that every vertex has a dom color class. The minimum number of colors required for a dominator coloring of G is called the dominator chromatic number of G, denoted by χd(G). Global Dominator coloring of G is a coloring C of G such that every vertex has a dom color class and an anti-dom color class. The minimum number of colors required for a global dominator coloring of G is called the global dominator chromatic number of G, denoted by χgd(G). In this paper, we give a counterexample for the conjecture posed in [I. Sahul Hamid, M.Rajeswari, Global dominator coloring of graphs, Discuss. Math. Graph Theory 39 (2019), 325-339] that for a graph G, if Xgd(G) = 2χd(G), then G is a complete multipartite graph. We deduce upper and lower bound for the global dominator chromatic number of Mycielskian of the graph G in terms of dominator chromatic number of G. [ABSTRACT FROM AUTHOR]

This article evaluates select Mangave cultivars, which are a new addition to the horticultural scene. Mangaves are low-maintenance, versatile plants that can withstand various temperatures and are suitable for landscapes and containers. The article provides information on the breeding of Mangaves and the trial details of the evaluated cultivars. It also includes evaluations of the cultivars based on their appearance, growth habits, and flowering characteristics, categorizing them into excellent, fair, and poor ratings. The document emphasizes the importance of considering a mangave's flowering age and response to environmental conditions when selecting a cultivar. [Extracted from the article]

The plasticity of the conduction delay between neurons plays a fundamental role in learning temporal features that are essential for processing videos, speech, and many high-level functions. However, the exact underlying mechanisms in the brain for this modulation are still under investigation. Devising a rule for precisely adjusting the synaptic delays could eventually help in developing more efficient and powerful brain-inspired computational models. In this article, we propose an unsupervised bioplausible learning rule for adjusting the synaptic delays in spiking neural networks. We also provide the mathematical proofs to show the convergence of our rule in learning spatiotemporal patterns. Furthermore, to show the effectiveness of our learning rule, we conducted several experiments on random dot kinematogram and a subset of DVS128 Gesture data sets. The experimental results indicate the efficiency of applying our proposed delay learning rule in extracting spatiotemporal features in an STDP-based spiking neural network. [ABSTRACT FROM AUTHOR]

Accelerometers, devices that measure body movements, have become valuable tools for studying the fragmentation of rest-activity patterns, a core circadian rhythm dimension, using metrics such as inter-daily stability (IS), intradaily variability (IV), transition probability (TP), and self-similarity parameter (named α ). However, their use remains mainly empirical. Therefore, we investigated the mathematical properties and interpretability of rest-activity fragmentation metrics by providing mathematical proofs for the ranges of IS and IV, proposing maximum likelihood and Bayesian estimators for TP, introducing the activity balance index (ABI) metric, a transformation of α , and describing distributions of these metrics in real-life setting. Analysis of accelerometer data from 2,859 individuals (age=60-83 years, 21.1% women) from the Whitehall II cohort (UK) shows modest correlations between the metrics, except for ABI and α . Sociodemographic (age, sex, education, employment status) and clinical (body mass index (BMI), and number of morbidities) factors were associated with these metrics, with differences observed according to metrics. For example, a difference of 5 units in BMI was associated with all metrics (differences ranging between -0.261 (95% CI -0.302, -0.220) to 0.228 (0.18, 0.268) for standardised TP rest to activity during the awake period and TP activity to rest during the awake period, respectively). These results reinforce the value of these rest-activity fragmentation metrics in epidemiological and clinical studies to examine their role for health. This paper expands on a set of methods that have previously demonstrated empirical value, improves the theoretical foundation for these methods, and evaluates their empirical use in a large dataset. [ABSTRACT FROM AUTHOR]

This paper considers pure strategy Nash equilibria of non-cooperative legislative bargaining models. In contrast to existing legislative bargaining models, we derive legislators behavior from stochastic utility maximization. This approach allows us to prove the existence of a stationary Pure Local and Global Nash Equilibrium under rather general settings. The mathematical proof is based on a fixed point argument, which can also be used as a numerical method to determine an equilibrium. We characterize the equilibrium outcome as a lottery of legislators' proposals and prove a Mean Voter Theorem, i.e., proposals result dimension-by-dimension as a weighted mean of legislators' ideal points and are Pareto-optimal. Based on a simple example, we illustrate different logic of our model compared to mixed strategy equilibrium of the legislative bargaining model suggested by Banks and Duggan (Am Polit Sci Rev 94(1):73–88. https://doi.org/10.2307/2586381, 2000). [ABSTRACT FROM AUTHOR]

Urban development is a key driver of global biodiversity loss. "Green" infrastructure is integrated to offset some impacts of development on ecosystem quality by supporting urban biodiversity, a prominent example being green roofs. The effects of green infrastructures on urban biodiversity are not well understood and poorly included in life cycle assessment (LCA) methodology. Here, we present a novel methodology that quantifies the local impact of green infrastructures on terrestrial biodiversity—demonstrated here for sedum roofs in London, UK—and integrates within LCA. It relates energy provision by plants to the metabolic requirements of animals to determine what species richness (number of species) and species abundance (number of individuals) are supported. We demonstrate this methodology using a case study, comparing the life cycle impact of developing 18 buildings, with either asphalt concrete or sedum roofs, on ecosystem quality. We found the sedum roofs (0.018 km2) support 53 species (673 individuals), equivalent to 1.3% of the development's life cycle impacts on ecosystem quality. Complete offsetting requires considerable reduction in transport use throughout the development's lifetime, and lower environmental impact material selection during construction (contributing 98% and 2%, respectively). The results indicate sedum roofs offer minor impact mitigation capacities in the context of urban development, and this capacity is limited for all green infrastructures by species richness in local species pools. This paper demonstrates the potential and limitations of quantifying terrestrial biodiversity offsets offered by green infrastructures alongside urbanization, and the need for realistic expectations of what role it might play in sustainable urban design. [ABSTRACT FROM AUTHOR]

Purity is known as an ideal of proof that restricts a proof to notions belonging to the 'content' of the theorem. In this paper, our main interest is to develop a conception of purity for formal (natural deduction) proofs. We develop two new notions of purity: one based on an ontological notion of the content of a theorem, and one based on the notions of surrogate ontological content and structural content. From there, we characterize which (classical) first-order natural deduction proofs of a mathematical theorem are pure. Formal proofs that refer to the ontological content of a theorem will be called 'fully ontologically pure'. Formal proofs that refer to a surrogate ontological content of a theorem will be called 'secondarily ontologically pure', because they preserve the structural content of a theorem. We will use interpretations between theories to develop a proof-theoretic criterion that guarantees secondary ontological purity for formal proofs. [ABSTRACT FROM AUTHOR]

This text explores the relationship between mathematicians Georg Cantor and Richard Dedekind and their differing perspectives on set theory. Cantor saw sets as vast and infinite, while Dedekind viewed them as closed and finite. Cantor sought Dedekind's support for his ideas on inconsistent sets, but Dedekind was not interested. Cantor's mental health declined, and he sought a position outside of academia. Despite their differences, both mathematicians made important contributions to the field of set theory. [Extracted from the article]

With the rapid development of modern medical technology and the dramatic increase in the amount of medical data, traditional centralized medical information management is facing many challenges. In recent years blockchain, which is a peer-to-peer distributed database, has been increasingly accepted and adopted by different industries and use cases. Key areas of healthcare blockchain applications include electronic medical record (EMR) management, medical device supply chain management, remote condition monitoring, insurance claims and personal health data (PHD) management, among others. Even so, there are a number of challenges in applying blockchain concepts to healthcare and its data, including interoperability, data security privacy, scalability, TPS and so on. While these challenges may hinder the development of blockchain in healthcare scenarios, they can be improved with existing technologies In this paper, we propose a blockchain-based healthcare operations management framework that is combined with the Interplanetary File System (IPFS) for managing EMRs, protects data privacy through a distributed approach while ensuring that this medical ledger is tamper-proof. Doctors act as full nodes, patients can participate in network maintenance either as light nodes or as full nodes, and the hospital acts as the endpoint database of data, i.e., the IPFS node, which saves the arithmetic power of nodes and allows the data stored in the hospitals and departments to be shared with the other organizations that have uploaded the data. Therefore, the integration of blockchain and zero-knowledge proof proposed in this paper helps to protect data privacy and is efficient, better scalable, and more throughput. [ABSTRACT FROM AUTHOR]

Summary: Communities of arbuscular mycorrhizal (AM) fungi assemble passively over time via biotic and abiotic mechanisms. In degraded soils, AM fungal communities can assemble actively when humans manage mycorrhizas for ecosystem restoration.We investigated mechanisms of urban AM fungal community assembly in a 2‐yr green roof experiment. We compared AM fungal communities in inoculated and uninoculated trays to samples from two potential sources: the inoculum and air.Active inoculation stimulated more distinct and diverse AM fungal communities, an effect that intensified over time. In the treatment trays, 45% of AM fungal taxa were detected in the inoculum, 2% were detected in aerial samples, 23% were detected in both inoculum and air, and 30% were not detected in either source.Passive dispersal of AM fungi likely resulted in the successful establishment of a small number of species, but active inoculation with native AM fungal species resulted in an immediate shift to a diverse and unique fungal community. When urban soils are constructed or modified by human activity, this is an opportunity for intervention with AM fungi that will persist and add diversity to that system. [ABSTRACT FROM AUTHOR]

'We are convinced most of all whenever we take something to have been demonstrated' (1355a5-6). The meaning and significance of this claim is a key point of dispute between those who take Aristotle's project in the Rhetoric to be defending his distinctively argument-centred kind of rhetoric on the grounds that it is most persuasively effective, and those for whom he does so on the more normatively-charged grounds that this is the most valuable kind of rhetoric, and best delivers rhetoric's distinctive benefits to civic communities. On the interpretation defended, the claim links being convinced (πιστεύειν) and the things that get us convinced (πίστεις) to the kind of epistemic merits possessed above all by demonstrations. This saves Aristotle from an implausible generalisation about the persuasive supremacy of deductive arguments. Since πίστεις are clearly central to Aristotelian rhetoric, this interpretation also lends support to the more normative understanding of Aristotle's project overall. [ABSTRACT FROM AUTHOR]

Ensuring safety for vehicle overtaking systems is one of the most fundamental and challenging tasks in autonomous driving. This task is particularly intricate when the vehicle must not only overtake its front vehicle safely but also consider the presence of potential opposing vehicles in the opposite lane that it will temporarily occupy. In order to tackle the overtaking task in such challenging scenarios, we introduce a novel integrated framework tailored for vehicle overtaking manoeuvres. Our approach integrates the theories of varying-level control barrier functions (CBF) and time-optimal model predictive control (MPC). The main feature of our proposed overtaking strategy is that it is safe-by-construction, which enables rigorous mathematical proof and validation of the safety guarantees. We show that the proposed framework is applicable when the opposing vehicle is either fully autonomous or driven by human drivers. To demonstrate our framework, we perform a set of simulations for overtaking scenarios under different settings. The simulation results show the superiority of our framework in the sense that it ensures collision-free and achieves better safety performance compared with the standard MPC-based approach without safety guarantees. [ABSTRACT FROM AUTHOR]

The building envelope is the interface between the external atmospheric conditions and the indoor environment. It contributes to approximately 60%-70% of the heating and cooling load. The building envelope constitutes walls, fenestrations, and roofs from which thermal transfer from the roof is significantly very high compared to walls in low-rise buildings. This research paper aims to provide recommendations for energy-efficient roof design considering roof form, material, and external coating suitable for various climate conditions of India. The paper's methodology consists of a literature review of related research papers, learnings from the roofing system of energy-efficient building case studies, and all possible energy-efficient roofing systems that would be simulated for energy efficiency and thermal comfort in five climate types of India. The expected outcome of this paper would be in the form of recommendations for roofing systems in different climate type and their potential for energy saving from the highest to the lowest. This research would be done in three stages viz, Step-1: Literature Review and case study of best practices: A review of the related literature and best practices examples would be done to formulate the maximum possible cases for the simulation. Step-2: The roofing systems, including building form, material (Thermal and insulation), and finishes (reflectance), would be simulated one by one for various climate types of India (composite, hot & dry, warm and humid, moderate and cold) to optimize energy efficiency and payback period. Step-3: Special roof types like Green roofs, cool roofs, Photovoltaic roofs, roof ponds, and the like are simulated and compared for their effectiveness in selected climate types. Based on the literature review, simulation results, and analysis, the recommendations are framed for energy-efficient roofing systems in the selected climate type with respect to heat transfer through the roof and thermal comfort. [ABSTRACT FROM AUTHOR]

Nature-based solutions have appeared as relevant solutions to mitigate urban heat islands. To improve our knowledge of the assessment of this ecosystem service and the related physical processes (evapotranspiration), monitoring campaigns are required. This was the objective of several experiments carried out on the Blue Green Wave, a large green roof located in Champs-sur-Marne (France). Three different protocols were implemented and tested to assess the evapotranspiration flux at different scales: the first one was based on the surface energy balance (large scale); the second one was carried out using an evapotranspiration chamber (small scale); and the third one was based on the water balance evaluated during dry periods (point scale). In addition to these evapotranspiration estimates, several hydrometeorological variables (especially temperature) were measured. Related data and Python programs providing preliminary elements of the analysis and graphical representation have been made available. They illustrate the space–time variability in the studied processes regarding their observation scale. The dataset is available at 10.5281/zenodo.8064053 (Versini et al., 2023). [ABSTRACT FROM AUTHOR]

Memristors have several chaotic dynamic models and have been used successfully in various fields, including secure communication systems, information storage, and artificial neural networks. The memristor-based four-dimensional chaotic (FDMC) systems generate unpredictable and intricate time domain signals. Parameter fluctuations in the FDMC system may give birth to chaos, making it difficult to suppress. Stabilizing chaos in the FDMC system improves the circuit's performance. This paper synthesizes a novel time-efficient chatter-free nonlinear robust adaptive control (NLRAC) technique that stabilizes chaos in the FDMC system affected by time-varying unknown bounded exogenous disturbances and model uncertainties. The proposed NLRAC strategy decimates the time-varying unknown bounded exogenous disturbances and model uncertainties effects; it establishes a faster, smoother state-variable trajectories convergence to the zero vicinity. The theoretical analysis and mathematical proofs are based on the Lyapunov stability technique. Computer simulation results show that the proposed NLRAC technique effectively brings the FDMC system's state-variable trajectories to zero with reduced fluctuations for control input signals and state-variable trajectories. This feedback controller's attribute enhances closed-loop stability performance, improves precision, and reduces risk overshoot. The paper includes comparative computer simulation results to endorse the proposed controller performance. [ABSTRACT FROM AUTHOR]

This work focuses on the issue of designing a fixed-time fuzzy adaptive controller for variable-speed doubly fed induction generator-based wind turbine. The main goal is to optimize the wind turbine power production, while improving the performance of the overall control system such as, convergence speed, tracking accuracy, and robustness. For the control design, the backstepping technique is adopted, and fuzzy adaptive systems are employed as universal approximators to estimate continuous functional uncertainties. Using fixed–time stability concept, a detailed mathematical stability proof of the closed-loop control system is performed. Simulation results are presented to testify the efficiency of the designed control approach. [ABSTRACT FROM AUTHOR]

This work is devoted to exploring proof abilities in Graph Theory of undergraduate students of the Degree in Computer Engineering and Technology of the University of Seville. To do this, we have designed a questionnaire consisting of five open-ended items that serve as instrument to collect data concerning their proof skills when dealing with graphs. We have thus analysed them adapting the methodology for computing the degrees of acquisition of the Van Hiele levels. Our analysis leads to different proof profiles of Graph Theory students whose characteristics provide empirical support to consider proof levels in Graph Theory from the perspective of the Van Hiele model. [ABSTRACT FROM AUTHOR]

We report findings from a longitudinal study of students' beliefs about empirical arguments and mathematical proof. We consider the influence of an 'Introduction to Proof (ITP)' course and the consequences of the observed changes in behaviour. Consistent with recent literature, our findings suggest that a majority of the thirty-eight undergraduate students in this study do not find empirical arguments convincing, even at the beginning of their ITP course. We use Sankey diagrams to show that, while many were unconvinced by these arguments at the start and end of the course, others began the course endorsing empirical arguments as similar to their own, shifting toward deductive-symbolic arguments by the end. Finally, we consider the value of Sankey diagrams for understanding changes in population behaviours, and the consequences of our work for future research on the role of empirical arguments in the classroom. [ABSTRACT FROM AUTHOR]

Aims: Post‐analyses of digital red, green, blue (RGB) and thermal images have become increasingly popular as modern approaches to plant cover analysis. Image analyses are often coupled with semi‐automated or automated workflows to reduce the amount of human labor input compared with traditional manual procedures. This study aims to evaluate and compare different image segmentation methods for plant cover analysis using digital RGB and thermal images, focusing on the effectiveness of semi‐automated and manual segmentation techniques in monitoring plant cover on green roofs. Location: An Extensive green roof in the City of Toronto. Methods: We surveyed the plant cover of an extensive green roof using digital and thermal imagery. The plant cover values were obtained using three methods: traditional manual segmentation based on a visual examination (MS), ImageJ Color Threshold (CT) and Trainable Weka Segmentation (TWS), all performed within FIJI (a distribution of ImageJ). Manual segmentation based on visual examination was used as a reference standard. Results: Significant correlation was found between the cover estimation using the CT and TWS methods relative to MS, and between cover estimation using the thermal image and the RGB image. TWS overestimated plant cover on thermal images while producing an underestimation on RGB images. CT demonstrated a performance closer to MS than TWS, indicating that manually customized methods produced results more aligned with MS. The estimated cover values by MS were not significantly affected by the image type (digital RGB or thermal). Conclusions: Results suggest that RGB and thermal imaging techniques may provide complementary results and reveal unique information regarding the functioning of green roofs. The accuracy of supervised machine‐learning methods could be enhanced with site‐specific data to provide a more accurate and efficient estimation of plant cover, which might be beneficial for long‐term studies on green roofs and ecological sites in remote locations. [ABSTRACT FROM AUTHOR]

Existing computer programs called proof assistants can verify the correctness of mathematical proofs but their specialized proof languages present a barrier to entry for many mathematicians. Large language models have the potential to lower this barrier, enabling mathematicians to interact with proof assistants in a more familiar vernacular. Among other advantages, this may allow mathematicians to explore radically new kinds of mathematics using an LLM-powered proof assistant to train their intuitions as well as ensure their arguments are correct. Existing proof assistants have already played this role for fields such as homotopy type theory. [ABSTRACT FROM AUTHOR]

Since the early twentieth century, it has been understood that mathematical definitions and proofs can be represented in formal systems with precise grammars and rules of use. Building on such foundations, computational proof assistants now make it possible to encode mathematical knowledge in digital form. This article enumerates some of the ways that these and related technologies can help us do mathematics. [ABSTRACT FROM AUTHOR]

The investigation into the domination problem and the associated subset problem of graphs is a focal point in graph theory research, sparking widespread interest and extensive exploration. This paper mainly studies the Italian domination of the strong product of two cycles. By constructing recursive Italian dominating functions, a well-defined bound for the Italian domination number in Cn Cm is obtained. Furthermore, through mathematical derivation and proof, the precise Italian domination number of C3 Cm is determined. [ABSTRACT FROM AUTHOR]

In most wireless networks, users/peers are connected to backbone networks using access links. The access link capacity is divided into upload and download capacity, and these capacities are used for upload and download of data, respectively. A peer can modify this division of link capacity between upload and download. A peer will allocate its entire link capacity for download to maximize utility. But incentive mechanism forces them to allocate some portion of capacity for upload. This paper investigates how to optimally divide link capacity so that peers receive maximum utility in a P2P network. We model this scenario as a game and determine capacity partitioning of peers during the Nash equilibrium NE. We also prove the social optimality of NE. As this portioning maximizes individual as well as social benefit, so NE is an optimal state of capacity partition. Using simulation, we verify that NE is an optimal state. BitTorrent network and a distributed algorithm for dividing access capacities are simulated, and partition providing maximum utility is compared with NE. This work provides a generalized expression and the mathematical proof for capacity partitioning at which peers receive maximum utility. [ABSTRACT FROM AUTHOR]

Mathematics is often treated as different from other disciplines, since arguments in the field rely on deductive proof rather than empirical evidence as in the natural sciences. A mathematical paper can therefore, at least in principle, be replicated simply by reading it. While this distinction is sometimes taken as the basis to claim that the results in mathematics are therefore certain, mathematicians themselves know that the published literature contains many mistakes. Reading a proof is not easy, and checking whether an argument constitutes a proof is surprisingly difficult. This article uses peer review of submissions to mathematics journals as a site where referees are explicitly concerned with checking whether a paper is correct and therefore could be published. Drawing on 95 qualitative interviews with mathematics journal editors, as well as a collection of more than 100 referee reports and other correspondence from peer review processes, this article establishes that while mathematicians acknowledge that peer review does not guarantee correctness, they still value it. For mathematicians, peer review 'adds a bit of certainty', especially in contrast to papers only submitted to preprint servers such as arXiv. Furthermore, during peer review there can be disagreements not just regarding the importance of a result, but also whether a particular argument constitutes a proof or not (in particular, whether there are substantial gaps in the proof). Finally, the mathematical community is seen as important when it comes to accepting arguments as proofs and assigning certainty to results. Publishing an argument in a peer-reviewed journal is often only the first step in having a result accepted. Results get accepted if they stand the test of time and are used by other mathematicians. [ABSTRACT FROM AUTHOR]

Green roofs' (GR) positive impact on indoor thermal conditions in hot areas may have possible negative impacts during hot and cold weather. Most previous studies have focused on GR's positive effects as a standalone strategy without mitigating these side effects of GR application. This study contributes to a more comprehensive understanding of the impact of GR and how to mitigate the negative aspects by integrating it with other passive techniques (natural ventilation and thermal insulation). Therefore, this study experimentally compares the seasonal impact of various soil layer configurations, integrated with natural ventilation, on improving Indoor Thermal Comfort (ITC) throughout the day in summer and winter. Field experiments were conducted using two identical validated test boxes. The results revealed that clay soil reduced Indoor Air Temperature (IAT) during the daytime in summer by up to 4.7 and 4°C for low and high soil thickness, respectively. Increasing clay soil thickness improved average IAT during the daytime in summer and winter by up to 6.49% and 2.61%, respectively. Additionally, adding thermal insulation is preferred in winter, while uninsulated soil had a slight positive effect on IAT and Indoor Relative Humidity (IRH) in summer. The use of natural ventilation at night and closed-ventilated systems during the daytime in summer and winter is recommended. Clay soil could save cooling and heating energy by up to 34.8% and 12.18%, respectively. These findings might inform designers by adjusting different GR soil parameters and the importance of natural ventilation in improving multi-seasonal thermal and energy performance. [ABSTRACT FROM AUTHOR]

Biochar is widely used as a soil amendment in green roofs because it can increase the soil's water-holding capacity, inhibit cracking, and provide nutrients for vegetation. The interaction mechanism between biochar and expansive soil is a significant factor in the performance of green roofs. However, research mainly focused on the hydrological scale (i.e. runoff regulation and rainwater storage), and there is a lack of research on the hydrological properties (i.e. hysteresis of soil–water characteristic curves, changes in soil pore size and pore distribution, formation and development of cracks and swelling–shrinking characteristics) of biochar-amended expansive soils under dynamic water environment. This test was conducted out on soil columns with expansive soil and 5% (by mass) biochar-amended under 5 drying–wetting cycles. The results showed that within the range of water content suitable for plant growth (i.e. between the anaerobic point and wilting point), the hysteresis area of soil–water characteristic curves of the amended soil is smaller than the bare soil at each drying–wetting cycle. The addition of biochar changes the pore size distribution of the soil, reduces the pore size and swelling–shrinking characteristics of the expansive soil, and inhibits the development of cracks. Therefore, the addition of biochar significantly attenuates the hysteresis characteristics of the soil–water characteristic curves of expansive soils, which may improve the stability of the hydraulic performance of green roofs. The results contribute to the understanding of the physicochemical and water properties of biochar-amended expansive soil and provide theoretical support for the application of biochar to green roofs. [ABSTRACT FROM AUTHOR]

Combinatorial proofs of binomial identities involve establishing an identity by arguing that each side enumerates a certain set of outcomes. In this paper, we share results from interviews with experienced provers (mathematicians and upper-division undergraduate mathematics students) and examine one particular aspect of combinatorial proof, namely the kinds of contexts that experienced provers used to establish combinatorial proofs of binomial identities. Our findings show that overall, our participants used a variety of contexts in their work; we also demonstrate ways in which previous experiences influenced the contexts they chose, and we offer some instances in which features of a context supported their combinatorial proof production. We offer some theoretical implications of our work, and we conclude with a discussion of limitations and avenues for future work. [ABSTRACT FROM AUTHOR]

In this note we demonstrate two instances where matrix multiplication can be easily verified. In the first setting, the matrix product appears as matrix element concatenation, and in the second, the product coincides with matrix addition. General proofs for some results are provided with a more complete description for $ 2 \times 2 $ 2 × 2 matrices. Suggested for consolidation of the algorithm rather than as an introduction, we believe the example base that can be created, combined with an analysis for understanding the context, acts as a positive motivator to secure mastery as it needs to be practised. [ABSTRACT FROM AUTHOR]

For a given rational number r, a classical theorem of Niven asserts that if $ \cos (r\pi) $ cos ⁡ (rπ) is rational, then $ \cos (r\pi)\in \{0, \pm 1, \pm 1/2\}. $ cos ⁡ (rπ) ∈ { 0 , ± 1 , ± 1 / 2 }. In this note, we extend Niven's theorem to quadratic irrationalities and present an elementary proof of that. [ABSTRACT FROM AUTHOR]

Providing trust in machine learning (ML) systems and their fairness is a socio-technical challenge, and while the use of ML continues to rise, there is lack of adequate processes and governance practices to assure their fairness. In this paper, we propose FaaS, a novel privacy-preserving, end-to-end verifiable solution, that audits the algorithmic fairness of ML systems. FaaS offers several features, which are absent from previous designs. The FAAS protocol is model-agnostic and independent of specific fairness metrics and can be utilised as a service by multiple stakeholders. FAAS uses zero knowledge proofs to assure the well-formedness of the cryptograms and provenance in the steps of the protocol. We implement a proof of concept of the FaaS architecture and protocol using off-the-shelf hardware, software, and datasets and run experiments to demonstrate its practical feasibility and to analyse its performance and scalability. Our experiments confirm that our proposed protocol is scalable to large-scale auditing scenarios (e.g. over 1000 participants) and secure against various attack vectors. [ABSTRACT FROM AUTHOR]

This paper presents a new fuzzy non‐singular fast terminal decoupled sliding mode control based on the finite‐time extended state observer for trajectory tracking control of flexible joint robot manipulators under chaos and uncertainty. First, a suitable chaotic reference is used in a synchronization mechanism to create chaos in the dynamics. Then, the essential modifications made to the conventional decoupled sliding mode control are introduced. A new coupling variable and a non‐singular fast terminal sliding surface are proposed in combination with an extended state observer. A complete convergence analysis is also performed for all the sliding surfaces. Furthermore, two fuzzy systems are designed in such a way that not only they can eliminate the chattering phenomenon but can also improve the convergence time without increasing the control input in a voltage‐based manner. The mathematical proof guarantees the finite‐time asymptotic stability of the closed‐loop control system under the proposed scheme for a class of under‐actuated systems in the presence of structured and un‐structured uncertainties. Finally, some simulations and experimental implementations as hardware‐in‐the‐loop are performed to evaluate the proposed method's performance. The proposed controller is an effective method, as confirmed by the numerical simulation results and experimental validation. [ABSTRACT FROM AUTHOR]

The significance of green roofs in stormwater management cannot be overlooked, as they have become an integral component in the creation of sustainable cities. This study not only examined the purifying effects of substrates, but also explored the interplay between substrate and vegetation through a combination planting approach, resulting in an innovative roof greening and planting method that incorporates both substrate and vegetation. In the experiment, 16 planting combinations of green roofs were created by cross-planting four proportioned substrates and four proportioned turfgrass. Subsequently, the outflow water quality indexes including ammonium nitrogen (NH4+-N), suspended solids (SS), chemical oxygen demand (COD), total nitrogen (TN) and total phosphorus (TP) were analyzed individually. The study findings indicate significant variations in the rainwater quality improvement capacity among the 16 green roof planting combinations, with both exhibiting effective purification of NH4+-N and SS. However, all 16 planting combinations were identified as sources of pollution for TP, TN and COD in rainwater. Among the four proportioned substrates, the combination of planting and B substrate (field soil: turfy soil: vermiculite: perlite: zeolite = 5:2:1:1:1) exhibits a superior purification effect with minimal variance. Therefore, it is recommended to promote and apply B substrate in large-scale green roofs. The A2 combination (field soil: turfy soil: perlite: vermiculite = 5:3:1:1 and Poa pratensis: Agrostis matsumurae: Lolium perenne = 5:4:1) e xhibited the highest effluent water quality among the 16 combinations tested, while other planting combinations utilizing substrate A did not perform as well. In summary, green roofs have the potential to purify rainwater but also pose a certain risk of pollution. [ABSTRACT FROM AUTHOR]

This paper is concerned with the propagation phenomena for a nonlocal dispersal Lotka–Volterra competition model with shifting habitats. It is assumed that the growth rate of each species is nondecreasing along the x-axis, positive near ∞ and nonpositive near - ∞ , and shifting rightward with a speed c > 0 . In the case where both species coexist near ∞ , we established three types of forced waves connecting the origin, respectively to the coexistence state with any forced speed c; to itself with forced speed c > c ∗ (∞) ; and to a semi-trivial steady state with forced speed c > c ¯ (∞) , where c ∗ (∞) and c ¯ (∞) are two positive numbers. In the case where one species is competitively stronger near ∞ , we also obtain the existence and nonexistence of forced waves connecting the origin to the semi-trivial steady state. Our results show the existence of multiple types of forced waves with the same forced speed. The mathematical proofs involve integral equations and Schauder's fixed point theorem, and heavily rely on the construction of various upper-lower solutions, which adds new techniques to deal with the "shifting environments" problem. [ABSTRACT FROM AUTHOR]

Green roofing technologies have been developed and implemented worldwide as they bring with them thermal, hydrological, and environmental benefits, especially in urbanized areas. Many studies have been conducted to investigate the thermal performance of green roofs over reinforced cement concrete (RCC) structural bases but there is a lacuna of experimental evaluation of the thermal performance of green roofs on sloping galvanized iron (GI) sheet truss type roof structures. In this paper, the thermal performance of a retrofitted extensive green roof is quantified; this is challenging in subtropical climates because of extreme seasonal and diurnal variations. The thermal performance of the green roof system was assessed using a life-size experiment setup followed by a whole-building simulation using Design Builder, which runs on the EnergyPlus simulation engine. Two prototype roofs were analyzed and the performance of the retrofitted extensive green roof was compared with that of a conventional RCC roof solution. To validate the results, two prototype buildings were constructed at a university campus and their thermal and energy performance analyzed for two observation periods, one during a typical summer week and the other during a typical winter week. The extensive retrofitted green roof displayed enhanced thermal and energy performance at a nominal additional cost. The findings of this study can be deployed in the development of a retrofitted extensive green roof module for sloped GI sheet roofs for better thermal performance, and hence reduced energy loads, and meet the sustainable development goals. [ABSTRACT FROM AUTHOR]

In response to Felix Mühlhölzer's critical discussion of my book Wittgenstein on Mathematics (2021), I argue against his main objections, in particular his view that one shouldn't even look for coherence in Wittgenstein's philosophy of mathematics, and his claim that Wittgenstein's insistence on the empirical applicability of mathematical concepts need not be taken seriously because in one passage it is prefaced by the words 'I want to say'. I also correct a number of irksome misunderstandings in Mühlhölzer's review. Repeatedly he ascribes to me a position that I merely present for discussion – and reject or qualify in the end. In particular, he wrongly ascribes to me the empiricist view that mathematical propositions are derived from experience. Some of Wittgenstein's remarks seem to express such a view, so I discuss it but conclude that, some exceptions apart, it is untenable and also inconsistent with Wittgenstein's key ideas about mathematical proof. [ABSTRACT FROM AUTHOR]

We introduce a variant of PCPs, that we refer to as rectangular PCPs, wherein proofs are thought of as square matrices, and the random coins used by the verifier can be partitioned into two disjoint sets, one determining the row of each query and the other determining the column. We construct PCPs that are efficient, short, smooth and (almost-)rectangular. As a key application, we show that proofs for hard languages in NTIME(2n), when viewed as matrices, are rigid infinitely often. This strengthens and simplifies a recent result of Alman and Chen [FOCS, 2019] constructing explicit rigid matrices in FNP. Namely, we prove the following theorem: - There is a constant δ∈(0,1) such that there is an FNP-machine that, for infinitely many N, on input 1N outputs NXN matrices with entries in F2 that are δN²-far (in Hamming distance) from matrices of rank at most 2logN/Ω(loglogN). Our construction of rectangular PCPs starts with an analysis of how randomness yields queries in the Reed--Muller-based outer PCP of Ben-Sasson, Goldreich, Harsha, Sudan and Vadhan [SICOMP, 2006; CCC, 2005]. We then show how to preserve rectangularity under PCP composition and a smoothness-inducing transformation. This warrants refined and stronger notions of rectangularity, which we prove for the outer PCP and its transforms. [ABSTRACT FROM AUTHOR]

Space availability is one of the largest barriers to urban agriculture. One way around this issue that urban farmers in some parts of the world are exploring is moving their farming activities to building rooftops. One method of rooftop farming in use is row agriculture using green roof technology. Vegetable crop plants, which typically require more water and more nutrients than the ornamental species found on green roofs, require irrigation and the use of fertilizers. One nutrient management practice that some rooftop farmers are using is the addition of compost, which could lead to changes over time in the water-holding capacity, organic matter content, and weight of green roof media. This practice and its long-term implications have not been well-studied. Green roof platforms were created to examine how the annual additions of compost in quantities of 0, 0.33, 0.66, and 1 kg/m2 affect runoff water quality and green roof media properties. Runoff water samples were collected and analyzed for pH, conductivity, color, turbidity, and nitrate nitrogen, ammonia nitrogen, total phosphorus, and potassium contents. Compost treatment had no effect on any water quality metric except for color, which had slightly different changes over time in the different compost treatments. The lack of difference among the treatments may be attributed to the low nutrient content of the compost and continued use of fertilizers to provide nutrients. Most samples observed in this study exceeded the US Environmental Protection Agency water quality guidelines for nitrate nitrogen and phosphorus and were similar to values observed in the green roof literature regarding agricultural and ornamental green roofs. This has potential implications for surface water quality and eutrophication, especially as green roof agriculture increases. [ABSTRACT FROM AUTHOR]