Additive Functions Research Articles

A ranking approach for robust portfolio decision analysis based on multilinear portfolio utility functions and incomplete preference information

Uncertainties are often present in typical portfolio decision analysis (PDA), and it is prudent to conduct a robust PDA to identify project portfolios that perform reasonably well across the entire range of uncertain parameter values. Previous research on robust PDA and applications has almost entirely relied on additive portfolio preference functions, with little research on robustness under multilinear portfolio utility functions (PUFs). A ranking approach for robust PDA is proposed based on multilinear PUFs, incomplete preference information, and the algorithm for accelerating stochastic multicriteria acceptability analysis (SMAA). First, the initial set of portfolios is screened through various constraints to produce a smaller set of desirable portfolios. Second, several types of incomplete preference information are thought to be elicited with regard to multilinear PUFs, including preference information on coefficients, portfolios, and uncertainties on preference elicitation techniques. Third, the SMAA decomposition algorithm is implemented as a ranking approach to perform robust PDA on the basis of multilinear PUFs, incomplete preference information, and potentially numerous portfolios in the set of desirable portfolios. Finally, the approach is applied to a case to validate its effectiveness, and comparisons among additive, multiplicative, and multilinear PUFs in terms of decision recommendations are performed.

Phenology-Based Maximum Light Use Efficiency for Modeling Gross Primary Production across Typical Terrestrial Ecosystems

The maximum light use efficiency (LUE) (ε0) is a key essential parameter of the LUE model, and its accurate estimation is crucial for quantifying gross primary production (GPP) and better understanding the global carbon budget. Currently, a comprehensive understanding of the potential of seasonal variations of ε0 in GPP estimation across different plant functional types (PFTs) is still lacking. In this study, we used a phenology-based strategy for the estimation of ε0 to find the optimal photosynthetic responses of the parameter in different phenological stages. The start and end of growing season (SOS and EOS) from time series vegetation indices and the camera-derived greenness index were extracted across seven PFT flux sites using the methods of the hybrid generalized additive model (HGAM) and double logistic function (DLF). Optimal extractions of SOS and EOS were evaluated, and the ε0 was estimated from flux site observations during the optimal phenological stages with the light response equation. Coupled with other obligatory parameters of the LUE model, phenology-based GPP (GPPphe-based) was estimated over 21 site-years and compared with vegetation photosynthesis model (VPM)-based GPP (GPPVPM) and eddy covariance-measured GPP (GPPEC). Generally, GPPphe-based basically tracked both the seasonal dynamics and inter-annual variation of GPPEC well, especially at forest, cropland, and wetland flux sites. The R2 between GPPphe-based and GPPEC was stable between 0.85 and 0.95 in forest ecosystems, between 0.75 and 0.85 in cropland ecosystems, and around 0.9 in wetland ecosystems. Furthermore, we found that GPPphe-based was significantly improved compared to GPPVPM in cropland, grassland, and wetland ecosystems, implying that phenology-based ε0 is more appropriate in the GPP estimation of herbaceous plants. In addition, we found that GPPphe-based was significantly improved over GPPVPM in cropland, grassland, and wetland ecosystems, and the R2 between GPPphe-based and GPPEC was improved by up to 0.11 in cropland ecosystems and 0.05 in wetland ecosystems compared to GPPVPM, and RMSE was reduced by up to 5.90 and 2.11 g C m−2 8 day−1, respectively, implying that phenology-based ε0 in herbaceous plants is more appropriate for GPP estimation. This work highlights the potential of phenology-based ε0 in understanding the seasonal variation of vegetation photosynthesis and production.

Metric Learning-Guided Semi-Supervised Path-Interaction Fault Diagnosis Method for Extremely Limited Labeled Samples under Variable Working Conditions.

The lack of labeled data and variable working conditions brings challenges to the application of intelligent fault diagnosis. Given this, extracting labeled information and learning distribution-invariant representation provides a feasible and promising way. Enlightened by metric learning and semi-supervised architecture, a triplet-guided path-interaction ladder network (Tri-CLAN) is proposed based on the aspects of algorithm structure and feature space. An encoder-decoder structure with path interaction is built to utilize the unlabeled data with fewer parameters, and the network structure is simplified by CNN and an element additive combination activation function. Metric learning is introduced to the feature space of the established algorithm structure, which enables the mining of hard samples from extremely limited labeled data and the learning of working condition-independent representations. The generalization and applicability of Tri-CLAN are proved by experiments, and the contribution of the algorithm structure and the metric learning in the feature space are discussed.

VERBAL DESCRIPTION OF THE TECHNOLOGY FOR PLANNING THE QUALITY IMPROVEMENT OF A SUBSET OF THE PROCESSES OF THE SPICE MATURITY REFERENCE MODEL

It is noted that to solve the problem of developing information technology for planning the increase of maturity level of a subset of the processes of the SPICE reference maturity model, this issue must first be considered at the verbal level as a technology (sequence of stages) for the implementation of the given problem. At the first stage, the structure of the SPICE reference model, which consists of a number of separate processes, was formalized. This set is presented as a hierarchical structure: the first level is a set of processes and subprocesses; the second level is a set of process groups; the third level is a set of process categories. At the second stage, the method of assessing the level of possibility of a separate process/sub-process of the reference maturity model SPICE is considered. It is given from the point of view of two dimensions of the SPICE model: the purpose of the processes; the attributes of the processes (measurable characteristics necessary for managing the process and increasing the possibility of its execution). The third stage of the technology is focused on the synthesis of planning model of the subset development processes for the SPICE model, which determines the quality level of a separate component of the software development process (SDP), which in turn has a positive effect on the level of development of software systems. Assessment and planning of the possibility level of a subset of processes is implemented during a certain planning period under conditions of limited resources based on their optimal distribution, taking into account the importance of individual processes and their practices during the planning period. At the fourth stage of the technology, an algorithm for planning the development of a subset of processes of the reference maturity model SPICE is considered based on the method of sequential analysis of options. This is primarily due to the fact that the optimization model has an additive objective function. The method allows discarding those appropriate solutions that do not contain optimal solutions. In the future, when specifying the model, it is planned to choose an algorithm that belongs to this method and adapt it to the solution of the given problem. The fifth stage is devoted to information technology implementation of the developed model and algorithm. At this stage, the following set of problems is solved. Analysis of business processes of the technology of improving the quality of software development process. Definition of software requirements. Forming a diagram of use cases. Development of data models. Justification of the choice of tools for software development. Selection of reference system architecture. Next, software coding and testing. At the sixth stage, based on information technology, a number of variants of the plan for improving the quality of a subset of the processes of the SPICE maturity model are formed in order to support decision-making by the management of the IT company. For this, a set of effective solutions is preliminarily determined, which is proposed to determine the final option, which is implemented later.

On simply normal numbers with digit dependencies

AbstractGiven an integer and a set of prime numbers, the set of Toeplitz numbers comprises all elements of [0, b[ whose digits in the base‐b expansion satisfy for all and . Using a completely additive arithmetical function, we construct a number in that is simply Borel normal if, and only if, . We then provide an effective bound for the discrepancy.

An Adaptive IPM-Based HEVC Video Steganography via Minimizing Non-Additive Distortion

Recently, almost all the proposed adaptive video steganographic schemes are based on minimizing an additive embedding distortion. However, they ignore the hard fact that the additive embedding distortion is not quite suitable for video steganography because of the interplay of cover elements in video steganography. In this paper, an adaptive intra prediction mode based (IPM-based) video steganography is proposed by minimizing the non-additive distortion in HEVC. To reduce the complexity of minimizing the non-additive distortion, a multi-layered embedding structure combined with a proposed embed-ding distortion updating strategy is adopted to approximate the non-additive distortion in an additive form. Firstly, all IPMs are decomposed into multiple layers based on the distortion drift graph to offer multi-layered embedding. Each IPM in the same layer is considered to be independent, and syndrome-trellis code (STC) can be applied to embed the message segment into each layer with an additive distortion function sequentially. Then, a distortion function composed of self-distortion and drift-distortion is proposed to initialize the distortion of modifying each IPM. Finally, after embedding the first message segment into the IPMs in the first layer with the initialized distortions, an embedding distortion updating strategy is applied to update the distortions of the IPMs in the remaining layers dynamically. Ex-perimental results demonstrate that the proposed adaptive IPM-based video steganography can achieve much better perceptual quality and security performance than the state-of-the-art.

Questionable stepwise explanations for a robust additive preference model

In this paper, we study Multiple Criteria Decision Aiding (MCDA) problems modeled using an additive value function. We consider an epistemic framework in which the preferences of the decision-maker are imprecisely specified, yielding a robust additive preference model. In this context, we are interested in explaining recommendations derived from such robust model using a transitive sequence of preference swaps. Previous work laid the foundations for explaining the necessary preference relation through a sequence of necessary preference swaps. We extend this to take into account non-necessary preference, yielding to so-called “questionable explanations”: a chain of alternatives which is non-increasing w.r.t. preference of the decision-maker. This approach provides additional descriptive power for explaining robust recommendations. We propose an efficient resolution engine based on Mixed-Integer Linear Programs, and we conduct numerical experiments to assess the benefit of our explanation strategy.

A unified model specification for sparse and dense functional/longitudinal data

The semi varying-coefficient additive model is a flexible nonparametric regression method, including varying-coefficient model and additive model as its special cases. However, a complex model may lead over-fitting phenomenon, which motivates us to develop a set of testing procedure to judge whether a parsimonious submodel is sufficient or not. Specifically, we propose hypothesis testings to check time-varying property of varying-coefficient component functions and linearity of additive component functions, respectively. For repeated measurements data, it is a subjective choice between sparse and dense case, which may lead to wrong statistical inference. One major contribution of this paper is to introduce consistent testing methodologies in a unified framework of sparse, dense and ultra dense cases of the data, which avoids a subjective choice of data types in practical applications. Extensive Monte Carlo simulation studies investigating the finite sample performance of the proposed methodologies confirm our asymptotic results. We further illustrate our methodologies via two real-life data applications.

Using multi-criteria decision analysis to describe stakeholder preferences for new quality improvement initiatives that could optimise prescribing in England.

Hospital decision-makers have limited resources to implement quality improvement projects. To decide which interventions to take forward, trade-offs must be considered that inevitably turn on stakeholder preferences. The multi-criteria decision analysis (MCDA) approach could make this decision process more transparent. An MCDA was conducted to rank-order four types of interventions that could optimise medication use in England's National Healthcare System (NHS) hospitals, including Computerised Interface, Built Environment, Written Communication, and Face-to-Face Interactions. Initially, a core group of quality improvers (N = 10) was convened to determine criteria that could influence which interventions are taken forward according to the Consolidated Framework for Implementation Research. Next, to determine preference weightings, a preference survey was conducted with a diverse group of quality improvers (N = 356) according to the Potentially All Pairwise Ranking of All Possible Alternatives method. Then, rank orders of four intervention types were calculated according to models with criteria unweighted and weighted according to participant preferences using an additive function. Uncertainty was estimated by probabilistic sensitivity analysis using 1,000 Monte Carlo Simulation iterations. The most important criteria influencing what interventions were preferred was whether they addressed "patient needs" (17.6%)' and their financial "cost (11.5%)". The interventions' total scores (unweighted score out of 30 | weighted out of 100%) were: Computerised Interface (25 | 83.8%), Built Environment (24 | 79.6%), Written Communication (22 | 71.6%), and Face-to-Face (22 | 67.8%). The probabilistic sensitivity analysis revealed that the Computerised Interface would be the most preferred intervention over various degrees of uncertainty. An MCDA was conducted to rank order intervention types that stand to increase medication optimisation across hospitals in England. The top-ranked intervention type was the Computerised Interface. This finding does not imply Computerised Interface interventions are the most effective interventions but suggests that successfully implementing lower-ranked interventions may require more conversations that acknowledge stakeholder concerns.

Interpretable Machine Learning for Choosing Radiation Dose-volume Constraints on Cardio-pulmonary Substructures Associated with Overall Survival in NRG Oncology RTOG 0617

Our objective was to use interpretable machine learning for choosing dose-volume constraints on cardiopulmonary substructures (CPSs) associated with overall survival (OS) in radiation therapy for locally advanced non-small cell lung cancer. A total of 428 patients with non-small cell lung cancer were randomly divided into training/validation/test subsets (n=230/149/49) in Radiation Therapy Oncology Group 0617. Manual or automated contouring was performed to segment CPSs, including heart, atria, ventricles, aorta, left/right ventricle/atrium (LV+RV+LA+RA), inferior/superior vena cava, pulmonary artery, and pericardium. Peri (pericardium-heart), rest (heart-[LV+RV+LA+RA]), clinical target volume (CTV), and lungs-CTV contours were also obtained. Dose-volume histogram features were extracted, including minimum/mean dose to the hottest x% volume (Dx%[Gy]/MOHx%[Gy]), minimum/mean/maximum dose, percent volume receiving at least xGy (VxGy[%]), and overlapping volume of each CPS with planning target volume (PTV_Voverlap[%]). Clinical parameters were collected from the National Clinical Trials Network/Community oncology research program data archive. Feature selection was performed using a series of multiblock sparse partial least squares regression, stability selection supervised principal component analysis, and Boruta. Explainable boosting machine (EBM) was trained using a conditional survival distribution-based approach for imputing censored data, treating survival analysis as a regression problem. Harrell's C-index was used to evaluate OS discrimination performance of EBM, Cox proportional hazards (CPH), random survival forest, extreme gradient boosting survival embeddings, and CPH deep neural network (DeepSurv) models in the test set. Dose-volume constraints were selected using the binary change point detection algorithm in Shapley additive explanations-based partial dependence functions. Selected features included LA_V60Gy(%), pericardium_D30%(Gy), lungs-CTV_PTV_Voverlap(%), RA_V55Gy(%), and received_cons_chemo. All models ranked LA_V60Gy(%) as the most important feature. EBM achieved the best performance for predicting OS, followed by extreme gradient boosting survival embeddings, random survival forest, DeepSurv, and CPH (C-index=0.653, 0.646, 0.642, 0.638, and 0.632). EBM global explanations suggested that LA_V60Gy(%) < 25.6, lungs-CTV_PTV_Voverlap(%) < 1.1, pericardium_D30%(Gy) < 18.9, RA_V55Gy(%) < 19.5, and received_cons_chemo='Yes' for improved OS. EBM can be used to discriminate OS while also guiding dose-volume constraint selection for optimal management of cardiac toxicity in lung cancer radiation therapy.

Development and application of fruit and vegetable based green films with natural bio-actives in meat and dairy products: A review.

In recent years, food-borne outbreaks and food plastic waste accumulation in the environment have impelled a hunt for new, sustainable, novel and innovatory food packaging interventions to face microbial contamination, food quality and safety. Pollution caused from wastes generated by agricultural activities is one of chief rising concerns of the environmentalists across the globe. A solution to this problem is effective and economic valorization of residues from agriculture sector. It would ensure that the by-products / residues from one activity act as ingredients/ raw materials for another industry. An example is fruit and vegetable waste based green films for food packaging. Edible packaging is a well-researched area of science where numerous biomaterials have been already explored. Along with dynamic barrier properties, these biofilms often exhibit antioxidant and antimicrobial properties as function of the bioactive additives (like essential oils) often incorporated in them. Additionally, these films are made competent by use of recent technologies (like encapsulation, nano-emulsions, radio-sensors) to ensure high end performance and meet the principles of sustainability. Livestock products like meat, poultry and dairy products are highly perishable and depend largely upon the mercy of packaging materials to enhance their shelf life. In this review, all the above-mentioned aspects are thoroughly covered with a view to project FVBGFs as a potential and viable packaging material for livestock products, along with a discussion on role of bio-additives, technological interventions, properties and potential applications of FVBGFs in livestock products. This article is protected by copyright. All rights reserved.

Probabilistic ordinal regression methods for multiple criteria sorting admitting certain and uncertain preferences

We propose a family of probabilistic ordinal regression methods for multiple criteria sorting. They employ an additive value function model to aggregate the performances on multiple criteria and the threshold-based procedure to derive the class assignments of alternatives. The Decision Makers (DMs) can provide certain and uncertain assignment examples concerning a subset of reference alternatives, expressing the confidence levels using linguistic descriptions. On the one hand, we introduce Bayesian Ordinal Regression to derive a posterior distribution over a set of all potential sorting models by defining a likelihood for the provided preference information and specifying a prior of the preference model. This distribution emphasizes the potential differences in the models’ abilities to reconstruct the DM’s classification examples and thus is robust to the DM’s potential cognitive biases in her judgments. We also develop a Markov Chain Monte Carlo algorithm to summarize the posterior distribution of the preference model. On the other hand, we adapt Subjective Stochastic Ordinal Regression to sorting problems. It builds a probability distribution over the space of all value functions and class thresholds compatible with the DM’s certain holistic judgments. The ambiguity in representing incomplete and potentially uncertain preference information by the assumed sorting model is quantified using class acceptability indices. We investigate the performance and robustness of the introduced approaches through an extensive experimental study involving real-world datasets. We also compare them against novel methods based on mathematical programming that handle potential inconsistencies in uncertain preferences in the traditional way by minimizing the misclassification error or the number of misclassified reference alternatives.

Robust optimization for functional multiresponse in 3D printing process

Computer models are commonly used to simulate the functional relationships between inputs and outputs for quality design in 3D printing. However, the high-dimensional outputs of functional multiresponse make it challenging to develop the simulation model and perform robust optimization. This paper proposes a novel optimization method with an additive multiresponse Gaussian process model for dealing with functional multiresponse optimization problems. First, an additive covariance function is constructed to capture the correlation of the temporal inputs. Second, the Markov Chain Monte Carlo sampling technique is adopted to determine the simulation model and quantify the uncertainty. Finally, the optimization model is constructed by integrating the quality loss function and interval analysis method, and the Bayesian optimization algorithm is used to obtain the optimal solution. A numerical simulation example and a 3D printing case study are used to illustrate the effectiveness of the proposed method. The comparison results show that the responses of the proposed method are closer to the targets than the current ones, and all fall within the specified interval.

Scoring from pairwise winning indices

The pairwise winning indices, computed in the Stochastic Multicriteria Acceptability Analysis, give the probability with which an alternative is preferred to another. They are computed taking into account all the instances of the assumed preference model compatible with the preference information provided by the Decision Maker mainly, but not exclusively, in terms of pairwise preference comparisons of reference alternatives. In this paper we present a new scoring method assigning a value to each alternative summarizing the results of the pairwise winning indices. Several procedures of this type have been provided in literature. However, our method, expressing the score in terms of a representative additive value function, permits to disaggregate the overall evaluation of each alternative in the sum of contributions of considered criteria. This permits not only to rank the alternatives but also to explain the reasons for which an alternative obtains its evaluation and, consequently, fills a certain ranking position. We also present a probabilistic model underlying our methodology. This probabilistic model is based on a simple piecewise linear approximation of the cumulative normal distribution, which allows the use of linear programming. To prove the efficiency of the method in representing the preferences of the Decision Maker, we performed an extensive set of simulations varying the number of alternatives and criteria. The results of the simulations, analyzed from a statistical point of view, prove the reliability of our procedure. The applicability of the method to decision making problems is explained by means of a case study related to the evaluation of financial funds.

Complementarity between quantum coherence and mixedness: a majorization approach

Quantum coherence is a relevant resource for various quantum information processing tasks, but it is fragile since it is generally affected by environmental noise. This is reflected in the loss of purity of the system, which in turn limits the amount of quantum coherence of it. As a consequence, a complementarity relation between coherence and mixedness arises. Previous works characterize this complementarity through inequalities between the ℓ 1-norm of coherence and linear entropy, and between the relative entropy of coherence and von Neumann entropy. However, coherence–mixedness complementarity is expected to be a general feature of quantum systems, regardless of the measures used. Here, an alternative approach to coherence–mixedness complementarity, based on majorization theory, is proposed. Vectorial quantifiers of coherence and mixedness, namely the coherence vector and the spectrum, respectively, are used, instead of scalar measures. A majorization relation for the tensor product of both vectorial quantifiers is obtained, capturing general aspects of the trade-off between coherence and mixedness. The optimal bound for qubit systems and numerical bounds for qutrit systems are analyzed. Finally, coherence–mixedness complementarity relations are derived for a family of symmetric, concave and additive functions. These results provide a deeper insight into the relation between quantum coherence and mixedness.

SiO2 cryogel – cellulose composite thin layer

This study proposed the preparation of light, thin insulating composite layers from potential biocompatible components such as highly porous silica cryogels and cellulose fibers. One of the novelties in this work is the application of cellulose fibers as matrix, and the silica cryogel particles provide the reinforcing phase. The synthesis of silica cryogel was carried out by means of sol-gel chemistry and freeze drying process. The function of additives (NaOH, carbamide, hydroxyethyl cellulose) was to create connections between the components in the composites. The study extended to the investigation of chemical compositions, the time of treatment, as well as the measurements of the dust loss, thermal conductivity, and the adhesion of composites to the various substrates. The bond system of composites was controlled by FTIR, the morphology by SEM. The composites can be characterised by excellent thermal insulation properties (0.048 W/(m⋅K), very low dust loss (0.01 w/w%), and good adhesion to various surfaces.

Additive energy functions have predictable landscape topologies.

Recent work [Mirth et al., J. Chem. Phys. 154, 114114 (2021)] has demonstrated that sublevelset persistent homology provides a compact representation of the complex features of an energy landscape in 3 N-dimensions. This includes information about all transition paths between local minima (connected by critical points of index ≥1) and allows for differentiation of energy landscapes that may appear similar when considering only the lowest energy pathways (as tracked by other representations, such as disconnectivity graphs, using index 1 critical points). Using the additive nature of the conformational potential energy landscape of n-alkanes, it became apparent that some topological features-such as the number of sublevelset persistence bars-could be proven. This work expands the notion of predictable energy landscape topology to any additive intramolecular energy function on a product space, including the number of sublevelset persistent bars as well as the birth and death times of these topological features. This amounts to a rigorous methodology to predict the relative energies of all topological features of the conformational energy landscape in 3N dimensions (without the need for dimensionality reduction). This approach is demonstrated for branched alkanes of varying complexity and connectivity patterns. More generally, this result explains how the sublevelset persistent homology of an additive energy landscape can be computed from the individual terms comprising that landscape.

Risk Assessment of Water Transport Enterprises by Modeling Direct and Indirect Threats

Introduction. The methods of traffic modeling by water transport and assessing the risks associated with it is needed to identify the issues of the past period, proposing methods for assessing not only direct but also indirect risks to form the preconditions for preventing them in the postwar reconstruction. The coordination of different transport type’s actions of transport requires an assessment of risks impact of the previous stages of mixed transportation on the formation of the following risks’ stages. Existing methods of assessing such impact need to be improved.&#x0D; Aim and tasks. The aim of this study is creation of methodological approach to risk management in water transport based on a mathematical model for assessing the impact of both direct and indirect risks. The tasks are: to prove that the additive approach of taking risks into account leads to the systematic deviation appearance from the result; take into account the impact on the risk of cargo transportation.&#x0D; Results. It has proved that the calculation of risk as an additive function leads to a systematic deviation from the relevant result. It stated that the risk of each of the next stages of transportation depends on the risks of the previous stages. To increase risk analysis relevance in water transport, the use of an oriented graph in a multidimensional parameter space proposed. It stated that in order to calculate the integrated risk, it is essential building not only the risk matrix but also the risk incidence matrix to take into account their relation to business entities. It established the impact of even minor risks could take the form of a catastrophe, which leads to cargo flows reorientation. It established that: for calculation of integral risk, it is crucial consider direct and indirect influences of risks; risk calculation for water transport also requires risk analysis in related modes of transport.&#x0D; Conclusions. It was established that, when calculating integral risk, it is necessary to consider direct and indirect influences on risks and that the risk calculation for water transport also requires risk analysis in related modes of transport. The proposed approach significantly increases the relevance of water transport risk analysis and allows for managing changes in transportation routes in real time.

Transmission of information in automated special purpose systems

This paper is devoted to solving the problem of optimizing the message transport service, which is one of the basic for automated special purpose systems. The NATO model of network-centric transformation of automated control and communication systems, which is presented in the form of a general plan for the development of information systems, was taken as the basis for the construction of special-purpose systems. An analysis of the development of information systems was carried out within the framework of the program of modernization and improvement of automated management systems. Under this program, large-scale work was carried out on the creation of new mobile nodes and means of communication for the perspective automated communication system at the tactical level Warfighter Information Network-Tactical. Therefore, it is proposed to use wireless, decentralized, mobile IP networks such as MANET (Mobile Ad hoc Network) for automated special purpose systems at the tactical level. Each of the mobile devices of such network can move independently in any direction, and, as a result, often break and establish connections with neighbors. For the MANET network the messaging service is considered in the context of: one automated workplace, one domain and interconnection between domains. The efficiency of information transmission systems is considered. Circular transmission algorithms for messages with the highest urgency category are defined and a control algorithm is provided for selecting the optimal message transmission channel in which the time spent on message transmission between these subscribers is minimal (dynamic programming problem with additive effect function). Bellman's functional equation for the conditional optimization stage was adapted for this problem.

Deciphering the Roles of MA-Based Volatile Additives for α-FAPbI3 to Enable Efficient Inverted Perovskite Solar Cells

Functional additives that can interact with the perovskite precursors to form the intermediate phase have been proven essential in obtaining uniform and stable α-FAPbI3 films. Among them, Cl-based volatile additives are the most prevalent in the literature. However, their exact role is still unclear, especially in inverted perovskite solar cells (PSCs). In this work, we have systematically studied the functions of Cl-based volatile additives and MA-based additives in formamidinium lead iodide (FAPbI3)-based inverted PSCs. Using in situ photoluminescence, we provide clear evidence to unravel the different roles of volatile additives (NH4Cl, FACl, and MACl) and MA-based additives (MACl, MABr, and MAI) in the nucleation, crystallization, and phase transition of FAPbI3. Three different kinds of crystallization routes are proposed based on the above additives. The non-MA volatile additives (NH4Cl and FACl) were found to promote crystallization and lower the phase-transition temperatures. The MA-based additives could quickly induce MA-rich nuclei to form pure α-phase FAPbI3 and dramatically reduce phase-transition temperatures. Furthermore, volatile MACl provides a unique effect on promoting the growth of secondary crystallization during annealing. The optimized solar cells with MACl can achieve an efficiency of 23.1%, which is the highest in inverted FAPbI3-based PSCs.