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Audio-driven talking face generation is a widely researched topic due to its high applicability. Reconstructing a talking face using audio significantly contributes to fields such as education, healthcare, online conversations, virtual assistants, and virtual reality. Early studies often focused solely on changing the mouth movements, which resulted in outcomes with limited practical applications. Recently, researchers have proposed a new approach of constructing the entire face, including face pose, neck, and shoulders. To achieve this, they need to generate through landmarks. However, creating stable landmarks that align well with the audio is a challenge. In this paper, we propose the KFusion of Dual-Domain model, a robust model that generates landmarks from audio. We separate the audio into two distinct domains to learn emotional information and facial context, then use a fusion mechanism based on the KAN model. Our model demonstrates high efficiency compared to recent models. This will lay the groundwork for the development of the audio-driven talking face generation problem in the future.

Reward shaping is effective in addressing the sparse-reward challenge in reinforcement learning by providing immediate feedback through auxiliary informative rewards. Based on the reward shaping strategy, we propose a novel multi-task reinforcement learning framework, that integrates a centralized reward agent (CRA) and multiple distributed policy agents. The CRA functions as a knowledge pool, which aims to distill knowledge from various tasks and distribute it to individual policy agents to improve learning efficiency. Specifically, the shaped rewards serve as a straightforward metric to encode knowledge. This framework not only enhances knowledge sharing across established tasks but also adapts to new tasks by transferring valuable reward signals. We validate the proposed method on both discrete and continuous domains, demonstrating its robustness in multi-task sparse-reward settings and its effective transferability to unseen tasks.

Reward shaping addresses the challenge of sparse rewards in reinforcement learning by constructing denser and more informative reward signals. To achieve self-adaptive and highly efficient reward shaping, we propose a novel method that incorporates success rates derived from historical experiences into shaped rewards. Our approach utilizes success rates sampled from Beta distributions, which dynamically evolve from uncertain to reliable values as more data is collected. Initially, the self-adaptive success rates exhibit more randomness to encourage exploration. Over time, they become more certain to enhance exploitation, thus achieving a better balance between exploration and exploitation. We employ Kernel Density Estimation (KDE) combined with Random Fourier Features (RFF) to derive the Beta distributions, resulting in a computationally efficient implementation in high-dimensional continuous state spaces. This method provides a non-parametric and learning-free approach. The proposed method is evaluated on a wide range of continuous control tasks with sparse and delayed rewards, demonstrating significant improvements in sample efficiency and convergence stability compared to relevant baselines.

In this note, we establish the Lipschitz continuity of finite-dimensional globally convex functions on all given balls and global Lipschitz continuity for eligible functions of that type. The Lipschitz constants in both situations draw information solely from function values, and the global Lipschitz modulus is found when it exists. Some examples of classes of globally Lipschitz continuous convex functions beside the norms are also provided along with their global Lipschitz modulus.

Action recognition technology plays a vital role in enhancing security through surveillance systems, enabling better patient monitoring in healthcare, providing in-depth performance analysis in sports, and facilitating seamless human-AI collaboration in domains such as manufacturing and assistive technologies. The dynamic nature of data in these areas underscores the need for models that can continuously adapt to new video data without losing previously acquired knowledge, highlighting the critical role of advanced continual action recognition. To address these challenges, we propose Decoupled Prompt-Adapter Tuning (DPAT), a novel framework that integrates adapters for capturing spatial-temporal information and learnable prompts for mitigating catastrophic forgetting through a decoupled training strategy. DPAT uniquely balances the generalization benefits of prompt tuning with the plasticity provided by adapters in pretrained vision models, effectively addressing the challenge of maintaining model performance amidst continuous data evolution without necessitating extensive finetuning. DPAT consistently achieves state-of-the-art performance across several challenging action recognition benchmarks, thus demonstrating the effectiveness of our model in the domain of continual action recognition.

To address the challenges of providing quick and plausible explanations in Explainable AI (XAI) for object detection models, we introduce the Gaussian Class Activation Mapping Explainer (G-CAME). Our method efficiently generates concise saliency maps by utilizing activation maps from selected layers and applying a Gaussian kernel to emphasize critical image regions for the predicted object. Compared with other Region-based approaches, G-CAME significantly reduces explanation time to 0.5 seconds without compromising the quality. Our evaluation of G-CAME, using Faster-RCNN and YOLOX on the MS-COCO 2017 dataset, demonstrates its ability to offer highly plausible and faithful explanations, especially in reducing the bias on tiny object detection., Comment: Canadian AI 2024

This paper proposes and develops new Newton-type methods to solve structured nonconvex and nonsmooth optimization problems with justifying their fast local and global convergence by means of advanced tools of variational analysis and generalized differentiation. The objective functions belong to a broad class of prox-regular functions with specification to constrained optimization of nonconvex structured sums. We also develop a novel line search method, which is an extension of the proximal gradient algorithm while allowing us to globalize the proposed coderivative-based Newton methods by incorporating the machinery of forward-backward envelopes. Further applications and numerical experiments are conducted for the $\ell_0$-$\ell_2$ regularized least-square model appearing in statistics and machine learning.

LangXAI is a framework that integrates Explainable Artificial Intelligence (XAI) with advanced vision models to generate textual explanations for visual recognition tasks. Despite XAI advancements, an understanding gap persists for end-users with limited domain knowledge in artificial intelligence and computer vision. LangXAI addresses this by furnishing text-based explanations for classification, object detection, and semantic segmentation model outputs to end-users. Preliminary results demonstrate LangXAI's enhanced plausibility, with high BERTScore across tasks, fostering a more transparent and reliable AI framework on vision tasks for end-users.

Cheating in online exams has become a prevalent issue over the past decade, especially during the COVID-19 pandemic. To address this issue of academic dishonesty, our "Exam Monitoring System: Detecting Abnormal Behavior in Online Examinations" is designed to assist proctors in identifying unusual student behavior. Our system demonstrates high accuracy and speed in detecting cheating in real-time scenarios, providing valuable information, and aiding proctors in decision-making. This article outlines our methodology and the effectiveness of our system in mitigating the widespread problem of cheating in online exams.

The paper is devoted to deriving novel second-order necessary and sufficient optimality conditions for local minimizers in rather general classes of nonsmooth unconstrained and constrained optimization problems in finite-dimensional spaces. The established conditions are expressed in terms of second-order subdifferentials of lower semicontinuous functions and mainly concern prox-regular objectives that cover a large territory in nonsmooth optimization and its applications. Our tools are based on the machinery of variational analysis and second-order generalized differentiation. The obtained general results are applied to problems of nonlinear programming, where the derived second-order optimality conditions are new even for problems with twice continuously differential data, being expressed there in terms of the classical Hessian matrices.

This paper is devoted to a systematic study and characterizations of the fundamental notions of variational and strong variational convexity for lower semicontinuous functions. While these notions have been quite recently introduced by Rockafellar, the importance of them has been already recognized and documented in finite-dimensional variational analysis and optimization. Here we address general infinite-dimensional settings and derive comprehensive characterizations of both variational and strong variational convexity notions by developing novel techniques, which are essentially different from finite-dimensional counterparts. As a consequence of the obtained characterizations, we establish new quantitative and qualitative relationships between strong variational convexity and tilt stability of local minimizers in appropriate frameworks of Banach spaces.

The paper is devoted to a systematic study and characterizations of notions of local maximal monotonicity and their strong counterparts for set-valued operators that appear in variational analysis, optimization, and their applications. We obtain novel resolvent characterizations of these notions together with efficient conditions for their preservation under summation in broad infinite-dimensional settings. Further characterizations of these notions are derived by using generalized differentiation of variational analysis in the framework of Hilbert spaces.

Decentralized data sources are prevalent in real-world applications, posing a formidable challenge for causal inference. These sources cannot be consolidated into a single entity owing to privacy constraints. The presence of dissimilar data distributions and missing values within them can potentially introduce bias to the causal estimands. In this article, we propose a framework to estimate causal effects from decentralized data sources. The proposed framework avoid exchanging raw data among the sources, thus contributing towards privacy-preserving causal learning. Three instances of the proposed framework are introduced to estimate causal effects across a wide range of diverse scenarios within a federated setting. (1) FedCI: a Bayesian framework based on Gaussian processes for estimating causal effects from federated observational data sources. It estimates the posterior distributions of the causal effects to compute the higher-order statistics that capture the uncertainty. (2) CausalRFF: an adaptive transfer algorithm that learns the similarities among the data sources by utilizing Random Fourier Features to disentangle the loss function into multiple components, each of which is associated with a data source. It estimates the similarities among the sources through transfer coefficients, and hence requiring no prior information about the similarity measures. (3) CausalFI: a new approach for federated causal inference from incomplete data, enabling the estimation of causal effects from multiple decentralized and incomplete data sources. It accounts for the missing data under the missing at random assumption, while also estimating higher-order statistics of the causal estimands. The proposed federated framework and its instances are an important step towards a privacy-preserving causal learning model., Comment: Preprint. arXiv admin note: substantial text overlap with arXiv:2301.00346

This paper proposes and develops inexact proximal methods for finding stationary points of the sum of a smooth function and a nonsmooth weakly convex one, where an error is present in the calculation of the proximal mapping of the nonsmooth term. A general framework for finding zeros of a continuous mapping is derived from our previous paper on this subject to establish convergence properties of the inexact proximal point method when the smooth term is vanished and of the inexact proximal gradient method when the smooth term satisfies a descent condition. The inexact proximal point method achieves global convergence with constructive convergence rates when the Moreau envelope of the objective function satisfies the Kurdyka-Lojasiewicz (KL) property. Meanwhile, when the smooth term is twice continuously differentiable with a Lipschitz continuous gradient and a differentiable approximation of the objective function satisfies the KL property, the inexact proximal gradient method achieves the global convergence of iterates with constructive convergence rates., Comment: 26 pages, 3 tables

In recent years, artificial intelligence is increasingly being applied widely in many different fields and has a profound and direct impact on human life. Following this is the need to understand the principles of the model making predictions. Since most of the current high-precision models are black boxes, neither the AI scientist nor the end-user deeply understands what's going on inside these models. Therefore, many algorithms are studied for the purpose of explaining AI models, especially those in the problem of image classification in the field of computer vision such as LIME, CAM, GradCAM. However, these algorithms still have limitations such as LIME's long execution time and CAM's confusing interpretation of concreteness and clarity. Therefore, in this paper, we propose a new method called Segmentation - Class Activation Mapping (SeCAM) that combines the advantages of these algorithms above, while at the same time overcoming their disadvantages. We tested this algorithm with various models, including ResNet50, Inception-v3, VGG16 from ImageNet Large Scale Visual Recognition Challenge (ILSVRC) data set. Outstanding results when the algorithm has met all the requirements for a specific explanation in a remarkably concise time., Comment: Published in the Proceedings of FAIC 2021

Nowadays, deep neural networks for object detection in images are very prevalent. However, due to the complexity of these networks, users find it hard to understand why these objects are detected by models. We proposed Gaussian Class Activation Mapping Explainer (G-CAME), which generates a saliency map as the explanation for object detection models. G-CAME can be considered a CAM-based method that uses the activation maps of selected layers combined with the Gaussian kernel to highlight the important regions in the image for the predicted box. Compared with other Region-based methods, G-CAME can transcend time constraints as it takes a very short time to explain an object. We also evaluated our method qualitatively and quantitatively with YOLOX on the MS-COCO 2017 dataset and guided to apply G-CAME into the two-stage Faster-RCNN model., Comment: 10 figures

Recent advances in Artificial Intelligence (AI) technology have promoted their use in almost every field. The growing complexity of deep neural networks (DNNs) makes it increasingly difficult and important to explain the inner workings and decisions of the network. However, most current techniques for explaining DNNs focus mainly on interpreting classification tasks. This paper proposes a method to explain the decision for any object detection model called D-CLOSE. To closely track the model's behavior, we used multiple levels of segmentation on the image and a process to combine them. We performed tests on the MS-COCO dataset with the YOLOX model, which shows that our method outperforms D-RISE and can give a better quality and less noise explanation., Comment: 9 pages, 10 figures

The ability to explain the prediction of deep learning models to end-users is an important feature to leverage the power of artificial intelligence (AI) for the medical decision-making process, which is usually considered non-transparent and challenging to comprehend. In this paper, we apply state-of-the-art eXplainable artificial intelligence (XAI) methods to explain the prediction of the black-box AI models in the thyroid nodule diagnosis application. We propose new statistic-based XAI methods, namely Kernel Density Estimation and Density map, to explain the case of no nodule detected. XAI methods' performances are considered under a qualitative and quantitative comparison as feedback to improve the data quality and the model performance. Finally, we survey to assess doctors' and patients' trust in XAI explanations of the model's decisions on thyroid nodule images., Comment: Accepted by AAAI 2023 The 7th International Workshop on Health Intelligence (W3PHIAI-23)

We propose a new causal inference framework to learn causal effects from multiple, decentralized data sources in a federated setting. We introduce an adaptive transfer algorithm that learns the similarities among the data sources by utilizing Random Fourier Features to disentangle the loss function into multiple components, each of which is associated with a data source. The data sources may have different distributions; the causal effects are independently and systematically incorporated. The proposed method estimates the similarities among the sources through transfer coefficients, and hence requiring no prior information about the similarity measures. The heterogeneous causal effects can be estimated with no sharing of the raw training data among the sources, thus minimizing the risk of privacy leak. We also provide minimax lower bounds to assess the quality of the parameters learned from the disparate sources. The proposed method is empirically shown to outperform the baselines on decentralized data sources with dissimilar distributions., Comment: NeurIPS 2022

This paper addresses the study and characterizations of variational convexity of extended-real-valued functions on Banach spaces. This notion has been recently introduced by Rockafellar, and its importance has been already realized and applied to continuous optimization problems in finite-dimensional spaces. Variational convexity in infinite-dimensional spaces, which is studied here for the first time, is significantly more involved and requires the usage of powerful tools of geometric functional analysis together with variational analysis and generalized differentiation in Banach spaces.

The paper is devoted to the study, characterizations, and applications of variational convexity of functions, the property that has been recently introduced by Rockafellar together with its strong counterpart. First we show that these variational properties of an extended-real-valued function are equivalent to, respectively, the conventional (local) convexity and strong convexity of its Moreau envelope. Then we derive new characterizations of both variational convexity and variational strong convexity of general functions via their second-order subdifferentials (generalized Hessians), which are coderivatives of subgradient mappings. We also study relationships of these notions with local minimizers and tilt-stable local minimizers. The obtained results are used for characterizing related notions of variational and strong variational sufficiency in composite optimization with applications to nonlinear programming.

This paper proposes and justifies two globally convergent Newton-type methods to solve unconstrained and constrained problems of nonsmooth optimization by using tools of variational analysis and generalized differentiation. Both methods are coderivative-based and employ generalized Hessians (coderivatives of subgradient mappings) associated with objective functions, which are either of class $\mathcal{C}^{1,1}$, or are represented in the form of convex composite optimization, where one of the terms may be extended-real-valued. The proposed globally convergent algorithms are of two types. The first one extends the damped Newton method and requires positive-definiteness of the generalized Hessians for its well-posedness and efficient performance, while the other algorithm is of {the regularized Newton type} being well-defined when the generalized Hessians are merely positive-semidefinite. The obtained convergence rates for both methods are at least linear, but become superlinear under the semismooth$^*$ property of subgradient mappings. Problems of convex composite optimization are investigated with and without the strong convexity assumption {on smooth parts} of objective functions by implementing the machinery of forward-backward envelopes. Numerical experiments are conducted for Lasso problems and for box constrained quadratic programs with providing performance comparisons of the new algorithms and some other first-order and second-order methods that are highly recognized in nonsmooth optimization., Comment: arXiv admin note: text overlap with arXiv:2101.10555

Many modern applications collect data that comes in federated spirit, with data kept locally and undisclosed. Till date, most insight into the causal inference requires data to be stored in a central repository. We present a novel framework for causal inference with federated data sources. We assess and integrate local causal effects from different private data sources without centralizing them. Then, the treatment effects on subjects from observational data using a non-parametric reformulation of the classical potential outcomes framework is estimated. We model the potential outcomes as a random function distributed by Gaussian processes, whose defining parameters can be efficiently learned from multiple data sources, respecting privacy constraints. We demonstrate the promise and efficiency of the proposed approach through a set of simulated and real-world benchmark examples., Comment: Preprint

Data scarcity is a tremendous challenge in causal effect estimation. In this paper, we propose to exploit additional data sources to facilitate estimating causal effects in the target population. Specifically, we leverage additional source datasets which share similar causal mechanisms with the target observations to help infer causal effects of the target population. We propose three levels of knowledge transfer, through modelling the outcomes, treatments, and confounders. To achieve consistent positive transfer, we introduce learnable parametric transfer factors to adaptively control the transfer strength, and thus achieving a fair and balanced knowledge transfer between the sources and the target. The proposed method can infer causal effects in the target population without prior knowledge of data discrepancy between the additional data sources and the target. Experiments on both synthetic and real-world datasets show the effectiveness of the proposed method as compared with recent baselines., Comment: Preprint

The paper proposes and develops new globally convergent algorithms of the generalized damped Newton type for solving important classes of nonsmooth optimization problems. These algorithms are based on the theory and calculations of second-order subdifferentials of nonsmooth functions with employing the machinery of second-order variational analysis and generalized differentiation. First we develop a globally superlinearly convergent damped Newton-type algorithm for the class of continuously differentiable functions with Lipschitzian gradients, which are nonsmooth of second order. Then we design such a globally convergent algorithm to solve a structured class of nonsmooth quadratic composite problems with extended-real-valued cost functions, which typically arise in machine learning and statistics. Finally, we present the results of numerical experiments and compare the performance of our main algorithm applied to an important class of Lasso problems with those achieved by other first-order and second-order optimization algorithms.

This paper proposes and develops a new Newton-type algorithm to solve subdifferential inclusions defined by subgradients of extended-real-valued prox-regular functions. The proposed algorithm is formulated in terms of the second-order subdifferential of such functions that enjoys extensive calculus rules and can be efficiently computed for broad classes of extended-real-valued functions. Based on this and on metric regularity and subregularity properties of subgradient mappings, we establish verifiable conditions ensuring well-posedness of the proposed algorithm and its local superlinear convergence. The obtained results are also new for the class of equations defined by continuously differentiable functions with Lipschitzian gradients (${\cal C}^{1,1}$ functions), which is the underlying case of our consideration. The developed algorithms for prox-regular functions and its extension to a structured class of composite functions are formulated in terms of proximal mappings and forward-backward envelopes. Besides numerous illustrative examples and comparison with known algorithms for ${\cal C}^{1,1}$ functions and generalized equations, the paper presents applications of the proposed algorithms to regularized least square problems arising in statistics, machine learning, and related disciplines., Comment: 46 pages

This work extends causal inference with stochastic confounders. We propose a new approach to variational estimation for causal inference based on a representer theorem with a random input space. We estimate causal effects involving latent confounders that may be interdependent and time-varying from sequential, repeated measurements in an observational study. Our approach extends current work that assumes independent, non-temporal latent confounders, with potentially biased estimators. We introduce a simple yet elegant algorithm without parametric specification on model components. Our method avoids the need for expensive and careful parameterization in deploying complex models, such as deep neural networks, for causal inference in existing approaches. We demonstrate the effectiveness of our approach on various benchmark temporal datasets., Comment: AISTATS 2021

In this paper, we present some properties of Lead Zirconate Titanate - Poly Vinylidene Flouride composites. The obtained results indicate that PZT-PVDF fibers involved firms were achieved using electrospining method. In other hand, the effect of grain size, content and other factors under the purview of Young's modulus and ferroelectric properties., Comment: 12 pages, 06 figures

We simulate the granulation process of solid spherical particles in the presence of a viscous liquid in a horizontal rotating drum by using molecular dynamics simulations in three dimensions. The numerical approach accounts for the cohesive and viscous effects of the binding liquid, which is assumed to be transported by wet particles and re-distributed homogeneously between wet particles in contact. We investigate the growth of a single granule introduced into the granular bed and the cumulative numbers of accreted and eroded particles as a function of time for a range of values of material parameters such as mean particle size, size polydispersity, friction coefficient, and liquid viscosity. We find that the granule growth is an exponential function of time, reflecting the decrease of the number of free wet particles. The influence of material parameters on the accretion and erosion rates reveals the nontrivial dynamics of the granulation process. It opens the way to a granulation model based on the realistic determination of particle-scale mechanisms of granulation.

For a $\mathcal{C}^2$-smooth function on a finite-dimensional space, a necessary condition for its quasiconvexity is the positive semidefiniteness of its Hessian matrix on the subspace orthogonal to its gradient, whereas a sufficient condition for its strict pseudoconvexity is the positive definiteness of its Hessian matrix on the subspace orthogonal to its gradient. Our aim in this paper is to extend those conditions for $\mathcal{C}^{1,1}$-smooth functions by using the Fr\'echet and Mordukhovich second-order subdifferentials., Comment: 14 pages

The ability of curved gratings as sectors of concentric circular gratings to couple linearly polarized light into focused surface plasmons is investigated by theory, simulation and experiment. Curved gratings, as sectors of concentric circular gratings with four different sector angles, are etched into a 30-nm thick gold layer on a glass coverslip and used to couple linearly-polarised free space light at nm into surface plasmons. The experimental and simulation results show that increasing the sector angle of the curved gratings decreases the lateral spotsize of the excited surface plasmons, resulting in focussing of surface plasmons which is analogous to the behaviour of classical optical lenses. We also show that two faced curved gratings, with their groove radius mismatched by half of the plasmon wavelength (asymmetric configuration), can couple linearly-polarised light into a single focal spot of concentrated surface plasmons with smaller depth of focus and higher intensity in comparison to single-sided curved gratings. The major advantage of these structures is the coupling of linearly-polarised light into focused surface plasmons with access to and control of the plasmon focal spot, which facilitates potential applications in sensing, detection and nonlinear plasmonics., Comment: 15 pages and 12 figures

We consider the EWPT in the economical 3-3-1 (E331) model. Our analysis shows that the EWPT in the model is a sequence of two first-order phase transitions, $SU(3) \rightarrow SU(2)$ at the TeV scale and $SU(2) \rightarrow U(1)$ at the $100$ GeV scale. The EWPT $SU(3) \rightarrow SU(2)$ is triggered by the new bosons and the exotic quarks; its strength is about $1 - 13$ if the mass ranges of these new particles are $10^2 \,\mathrm{GeV} - 10^3 \,\mathrm{GeV}$. The EWPT $SU(2) \rightarrow U(1)$ is strengthened by only the new bosons; its strength is about $1 - 1.15$ if the mass parts of $H^0_1$, $H^\pm_2$ and $Y^\pm$ are in the ranges $10 \,\mathrm{GeV} - 10^2 \,\mathrm{GeV}$. The contributions of $H^0_1$ and $H^{\pm}_2$ to the strengths of both EWPTs may make them sufficiently strong to provide large deviations from thermal equilibrium and B violation necessary for baryogenesis., Comment: 17 pages, 9 figures

We calculate the electroweak sphaleron rates in the reduced minimal 3-3-1 (RM331) model. In the context of the early Universe, this model undergoes a sequence of two first-order phase transitions, $SU(3) \rightarrow SU(2)$ at the TeV scale and $SU(2)\rightarrow U(1)$ at the $10^2$ GeV scale, as the Universe cools down from the hot big bang. By a thin-wall approximation, we show that for each phase transition in this sequence, the sphaleron rate is larger than the cosmological expansion rate at temperatures higher than the critical temperature, and after the phase transition, the sphaleron process is decoupled. This may provide baryon-number violation (B violation) necessary for baryogenesis in the relationship with nonequilibrium physics in the early Universe., Comment: 13 pages, 3 figures

The electroweak phase transition is considered in framework of the reduced minimal 3-3-1 model (RM331). Structure of phase transition in this model is divided into two periods. The first period is the phase transition SU(3) ---> SU(2) at TeV scale and the second one is SU(2)--> U(1), which is the like-Standard Model electroweak phase transition. When mass of the neutral Higgs boson (h_1) is taken to be equal to the LHC value: m_{h_1}=125 GeV, then these phase transitions are the first order phase transitions, the mass of Z_2 is about 4.8 TeV; and we find the region of parameter space with the first order phase transition at v_{\rho_0}=246 GeV scale, leading to an effective potential, where mass of the charged Higgs boson is in range of 4.154 TeV < m_{h_{++}} < 5.946 TeV. Therefore, with this approach, new bosons are the triggers of the first order electroweak phase transition with significant implications for the viability of electroweak baryogenesis scenarios., Comment: 21 pages, 3 figures

The rare kaon decay K^+ --> \pi^+ \nu \bar{\nu} is considered in the framework of the models based on the SU(3)_C X SU(3)_L X U(1)_N (3 - 3 - 1) gauge group. It is shown that a lower bound of the Z' mass in the 3 - 3 - 1 model with right-handed neutrinos at a value of 3 TeV is derived, while that in the minimal version -- 1.7 TeV., Comment: 7 pages, 1 figure, latex

Contribution from new gauge bosons in the 3 - 3 - 1 models to the anomalous magnetic moment of the muon, mass difference of the kaon system and rare kaon decay are calculated and numerically estimated. Bounds on masses of new gauge bosons: bileptons and Z' are derived., Comment: Latex, 10 pages, 2 figures, axodraw.sty used, Talk given at the 4-th Rencontres du Vietnam, 19 -25 July, 2000

Contributions of flavour-changing neutral currents in the 3 3 1 model with right-handed neutrinos to mass difference of the neutral meson system $\Delta m_P (P = K, D, B)$ are calculated. Using the Fritzsch anzats on quark mixing, we show that the third family should be different from the first two. We obtain a lower bound on mass of the new heavy neutral gauge boson as 1.02 TeV., Comment: 7 pages, no figures, to appear in J. Phys. G (1999), October issue