OLITICS and business are considered traditional spheres of human negotiation. The internet and modern goods/service characterised by several, possibly interrelated, means of communication have extended human negotiation attributes (say price of a product and terms of its delivery); ii) to new domains such as social networks, deliberative democracy, limited negotiation time as no agent can deliberate infinitely; e-commerce, cloud-based applications, [1], [2]. Besides, iii) absence of moderator to coordinate the negotiation, so the automatic bargaining and negotiation, being inevitable agents must reach agreement themselves [11]. in modern cyber-physical-social systems [3], have been established The negotiation has been widely addressed in diverse fields in variety of applications, like network negotiation, ranging from economy and sociology to computer science.

Diffusion Models (DMs) iteratively denoise random samples to produce high-quality data. The iterative sampling process is derived from Stochastic Differential Equations (SDEs), allowing a speed-quality trade-off chosen at inference. Another advantage of sampling with differential equations is exact likelihood computation. These likelihoods have been used to rank unconditional DMs and for out-of-domain classification. Despite the many existing and possible uses of DM likelihoods, the distinct properties captured are unknown, especially in conditional contexts such as Text-To-Image (TTI) or Text-To-Speech synthesis (TTS). Surprisingly, we find that TTS DM likelihoods are agnostic to the text input. TTI likelihood is more expressive but cannot discern confounding prompts. Our results show that applying DMs to conditional tasks reveals inconsistencies and strengthens claims that the properties of DM likelihood are unknown. This impact sheds light on the previously unknown nature of DM likelihoods. Although conditional DMs maximise likelihood, the likelihood in question is not as sensitive to the conditioning input as one expects. This investigation provides a new point-of-view on diffusion likelihoods.

This paper introduces a generalized ps-BART model for the estimation of Average Treatment Effect (ATE) and Conditional Average Treatment Effect (CATE) in continuous treatments, addressing limitations of the Bayesian Causal Forest (BCF) model. The ps-BART model's nonparametric nature allows for flexibility in capturing nonlinear relationships between treatment and outcome variables. Across three distinct sets of Data Generating Processes (DGPs), the ps-BART model consistently outperforms the BCF model, particularly in highly nonlinear settings. The ps-BART model's robustness in uncertainty estimation and accuracy in both point-wise and probabilistic estimation demonstrate its utility for real-world applications. This research fills a crucial gap in causal inference literature, providing a tool better suited for nonlinear treatment-outcome relationships and opening avenues for further exploration in the domain of continuous treatment effect estimation.

Estimating a distribution given access to its unnormalized density is pivotal in Bayesian inference, where the posterior is generally known only up to an unknown normalizing constant. Variational inference and Markov chain Monte Carlo methods are the predominant tools for this task; however, both are often challenging to apply reliably, particularly when the posterior has complex geometry. Here, we introduce Soft Contrastive Variational Inference (SoftCVI), which allows a family of variational objectives to be derived through a contrastive estimation framework. The approach parameterizes a classifier in terms of a variational distribution, reframing the inference task as a contrastive estimation problem aiming to identify a single true posterior sample among a set of samples. Despite this framing, we do not require positive or negative samples, but rather learn by sampling the variational distribution and computing ground truth soft classification labels from the unnormalized posterior itself. The objectives have zero variance gradient when the variational approximation is exact, without the need for specialized gradient estimators. We empirically investigate the performance on a variety of Bayesian inference tasks, using both simple (e.g. normal) and expressive (normalizing flow) variational distributions. We find that SoftCVI can be used to form objectives which are stable to train and mass-covering, frequently outperforming inference with other variational approaches.

Variational inference (VI) is a computationally efficient and scalable methodology for approximate Bayesian inference. It strikes a balance between accuracy of uncertainty quantification and practical tractability. It excels at generative modelling and inversion tasks due to its built-in Bayesian regularisation and flexibility, essential qualities for physics related problems. Deriving the central learning objective for VI must often be tailored to new learning tasks where the nature of the problems dictates the conditional dependence between variables of interest, such as arising in physics problems. In this paper, we provide an accessible and thorough technical introduction to VI for forward and inverse problems, guiding the reader through standard derivations of the VI framework and how it can best be realized through deep learning. We then review and unify recent literature exemplifying the creative flexibility allowed by VI. This paper is designed for a general scientific audience looking to solve physics-based problems with an emphasis on uncertainty quantification.

In cognitive systems, recent emphasis has been placed on studying the cognitive processes of the subject whose behavior was the primary focus of the system's cognitive response. This approach, known as inverse cognition, arises in counter-adversarial applications and has motivated the development of inverse Bayesian filters. In this context, a cognitive adversary, such as a radar, uses a forward Bayesian filter to track its target of interest. An inverse filter is then employed to infer the adversary's estimate of the target's or defender's state. Previous studies have addressed this inverse filtering problem by introducing methods like the inverse Kalman filter (I-KF), inverse extended KF (I-EKF), and inverse unscented KF (I-UKF). However, these filters typically assume additive Gaussian noise models and/or rely on local approximations of non-linear dynamics at the state estimates, limiting their practical application. In contrast, this paper adopts a global filtering approach and presents the development of an inverse particle filter (I-PF). The particle filter framework employs Monte Carlo (MC) methods to approximate arbitrary posterior distributions. Moreover, under mild system-level conditions, the proposed I-PF demonstrates convergence to the optimal inverse filter. Additionally, we propose the differentiable I-PF to address scenarios where system information is unknown to the defender. Using the recursive Cramer-Rao lower bound and non-credibility index (NCI), our numerical experiments for different systems demonstrate the estimation performance and time complexity of the proposed filter.

Numerous techniques of multi-criteria decision-making (MCDM) have been proposed in a variety of business domains. One of the well-known methods is the Analytical Hierarchical Process (AHP). Various uncertain numbers are commonly used to represent preference values in AHP problems. In the case of multi-granularity linguistic information, several methods have been proposed to address this type of AHP problem. This paper introduces a novel method to solve this problem using shadowed fuzzy numbers (SFNs). These numbers are characterized by approximating different types of fuzzy numbers and preserving their uncertainty properties. The new Shadowed AHP method is proposed to handle preference values which are represented by multi-types of uncertain numbers. The new approach converts multi-granular preference values into unified model of shadowed fuzzy numbers and utilizes their properties. A new ranking approach is introduced to order the results of aggregation preferences. The new approach is applied to solve a supplier selection problem in which multi-granular information are used. The features of the new approach are significant for decision-making applications.

Adjusting the control actions of a wheeled robot to eliminate oscillations and ensure smoother motion is critical in applications requiring accurate and soft movements. Fuzzy controllers enable a robot to operate smoothly while accounting for uncertainties in the system. This work uses fuzzy theories and parallel distributed compensation to establish a robust controller for wheeled mobile robots. The use of fuzzy logic type I and type II controllers are covered in the study, and their performance is compared with a PID controller. Experimental results demonstrate that fuzzy logic type II outperforms type I and the classic controller. Further, we deploy parallel distributed compensation, sector of nonlinearity, and local approximation strategy in our design. These strategies help analyze the stability of each rule of the fuzzy controller separately and map the if-then rules of the fuzzy box into parallel distributed compensation using Linear Matrix Inequalities (LMI) analysis. Also, they help manage the uncertainty flow in the equations that exist in the kinematic model of a robot. Last, we propose a Bezier curve to represent the different pathways for the wheeled mobile robot.

Wind power is one of the fastest-growing renewable energy sectors and a key pillar for the transition to a carbon-free economy. In 2023, energy from wind accounted for 10.2% of all U.S. utility-scale electricity generation [54]. Being intrinsically weather-driven, wind power injects uncertainty into the balancing of power demand and generation. On the daily operational time scale, quantifying the asset-specific and area-wide uncertainty of renewable generation for the next day is an essential ingredient of grid management. Specifically, grid operators need probabilistic spatiotemporal forecasting of wind power in order to appropriately set grid reserves, ensure grid stability, and optimize dispatch of grid resources. Our goal is to develop a statistical framework for short-term wind power generation simulations across space and time. This project is motivated by working with a large dataset of wind generation in the Electric Reliability Council of Texas (ERCOT) region and is geared to the concrete practical concerns faced by electricity grid operators. We refer to our team's related publications [8, 7, 52, 38] that employ similar simulations for various downstream risk management tasks; other use cases are discussed, among others, in [27, 33, 35, 58].

The damage detection problem in mechanical systems, using vibration measurements, is commonly called Structural Health Monitoring (SHM). Many tools are able to detect damages by changes in the vibration pattern, mainly, when damages induce nonlinear behavior. However, a more difficult problem is to detect structural variation associated with damage, when the mechanical system has nonlinear behavior even in the reference condition. In these cases, more sophisticated methods are required to detect if the changes in the response are based on some structural variation or changes in the vibration regime, because both can generate nonlinearities. Among the many ways to solve this problem, the use of the Volterra series has several favorable points, because they are a generalization of the linear convolution, allowing the separation of linear and nonlinear contributions by input filtering through the Volterra kernels. On the other hand, the presence of uncertainties in mechanical systems, due to noise, geometric imperfections, manufacturing irregularities, environmental conditions, and others, can also change the responses, becoming more difficult the damage detection procedure. An approach based on a stochastic version of Volterra series is proposed to be used in the detection of a breathing crack in a beam vibrating in a nonlinear regime of motion, even in reference condition (without crack). The system uncertainties are simulated by the variation imposed in the linear stiffness and damping coefficient. The results show, that the nonlinear analysis done, considering the high order Volterra kernels, allows the approach to detect the crack with a small propagation and probability confidence, even in the presence of uncertainties.