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Online Large Language Model (LLM) services such as ChatGPT and Claude 3 have transformed business operations and academic research by effortlessly enabling new opportunities. However, due to data-sharing restrictions, sectors such as healthcare and finance prefer to deploy local LLM applications using costly hardware resources. This scenario requires a balance between the effectiveness advantages of LLMs and significant financial burdens. Additionally, the rapid evolution of models increases the frequency and redundancy of benchmarking efforts. Existing benchmarking toolkits, which typically focus on effectiveness, often overlook economic considerations, making their findings less applicable to practical scenarios. To address these challenges, we introduce CEBench, an open-source toolkit specifically designed for multi-objective benchmarking that focuses on the critical trade-offs between expenditure and effectiveness required for LLM deployments. CEBench allows for easy modifications through configuration files, enabling stakeholders to effectively assess and optimize these trade-offs. This strategic capability supports crucial decision-making processes aimed at maximizing effectiveness while minimizing cost impacts. By streamlining the evaluation process and emphasizing cost-effectiveness, CEBench seeks to facilitate the development of economically viable AI solutions across various industries and research fields. The code and demonstration are available in \url{https://github.com/amademicnoboday12/CEBench}.

Solid-state spin qubits have emerged as promising quantum information platforms but are susceptible to magnetic noise. Despite extensive efforts in controlling noise in spin qubit quantum applications, one important but less controlled noise source is near-field electromagnetic fluctuations. Low-frequency (MHz and GHz) electromagnetic fluctuations are significantly enhanced near nanostructured lossy material components essential in quantum applications, including metallic/superconducting gates necessary for controlling spin qubits in quantum computing devices and materials/nanostructures to be probed in quantum sensing. Although controlling this low-frequency electromagnetic fluctuation noise is crucial for improving the performance of quantum sensing and computing, current efforts are hindered by computational challenges. In this paper, we leverage advanced computational electromagnetics techniques, especially fast and accurate volume integral equation based solvers, to overcome the computational obstacle. We introduce a theoretical and computational framework to control low-frequency magnetic fluctuation noise for enhancing spin qubit quantum sensing and computing performance. Our framework extends the application of computational electromagnetics to spin qubit quantum devices. We further apply our theoretical framework to control noise effects in realistic quantum computing devices and quantum sensing applications. Our work paves the way for device engineering to control magnetic fluctuations and improve the performance of spin qubit quantum sensing and computing., Comment: 9 pages, 5 figures

We establish sufficient and necessary conditions for the joint transitivity of linear iterates in a minimal topological dynamical system with commuting transformations. This result provides the first topological analogue of the classical Berend and Bergelson joint ergodicity criterion in measure-preserving systems., Comment: Comments welcome!

Pure dephasing and spontaneous emission are two non-unitary processes of atoms or spins interacting with fluctuating electromagnetic (EM) modes. Collective spontaneous emission (e.g., superradiance) originates from interactions with EM modes in resonance with atoms and has received considerable attention. Meanwhile, the analogous collective dephasing phenomena remain poorly understood. Here, we introduce the nano-EM super-dephasing phenomenon arising in the photonic environment near lossy material interfaces. We show that this effect is enhanced by over 10 orders of magnitude compared to free space or photonic cavities due to the presence of long-range correlations in low-frequency evanescent EM fluctuations. We unravel the universality of nano-EM super-dephasing behaviors near ferrimagnets, metals, and superconductors and their dependence on low-frequency material properties. We demonstrate that the scaling of nano-EM super-dephasing is independent of EM modes' wavelengths and differs from the conventional $N^2$ scaling of superradiance by analyzing the decoherence of entangled states, including GHZ states. Finally, we show how to experimentally isolate and control super-dephasing to open interesting frontiers for scalable quantum systems., Comment: 6+17 pages, 3+3 figures

Experimental observations of vacuum radiation and vacuum frictional torque are challenging due to their vanishingly small effects in practical systems. For example, a rotating nanosphere in free space slows down due to friction from vacuum fluctuations with a stopping time around the age of the universe. Here, we show that a spinning yttrium iron garnet (YIG) nanosphere near aluminum or YIG slabs exhibits vacuum radiation eight orders of magnitude larger than other metallic or dielectric spinning nanospheres. We achieve this giant enhancement by exploiting the large near-field magnetic local density of states in YIG systems, which occurs in the low-frequency GHz regime comparable to the rotation frequency. Furthermore, we propose a realistic experimental setup for observing the effects of this large vacuum radiation and frictional torque under experimentally accessible conditions., Comment: main text (5 pages, 3 figures) + appendices (11 pages, 1 figure) + supplementary material (11 pages, 3 figures)

This paper is the first part of the series "Spherical higher order Fourier analysis over finite fields", aiming to develop the higher order Fourier analysis method along spheres over finite fields, and to solve the geometric Ramsey conjecture in the finite field setting. In this paper, we prove a quantitative equidistribution theorem for polynomial sequences in a nilmanifold, where the average is taken along spheres instead of cubes. To be more precise, let $\Omega\subseteq \mathbb{Z}^{d}$ be the preimage of a sphere $\mathbb{F}_{p}^{d}$ under the natural embedding from $\mathbb{Z}^{d}$ to $\mathbb{F}_{p}^{d}$. We showed that if a rational polynomial sequence $(g(n)\Gamma)_{n\in\Omega}$ is not equidistributed on a nilmanifold $G/\Gamma$, then there exists a nontrivial horizontal character $\eta$ of $G/\Gamma$ such that $\eta\circ g \mod \mathbb{Z}$ vanishes on $\Omega$. We also prove quantitative equidistribution and factorization theorems for more general sets arising from quadratic forms defined over $\mathbb{F}_{p}^{d}$. These results will serve as fundamental tools in later parts of the series to proof the spherical Gowers inverse theorem and the geometric Ramsey conjecture., Comment: 133 pages, comments are welcome

This paper is the fourth and the last part of the series "Spherical higher order Fourier analysis over finite fields", aiming to develop the higher order Fourier analysis method along spheres over finite fields, and to solve the Geometric Ramsey Conjecture in the finite field setting. In this paper, we proof a conjecture of Graham on the Remsey properties for spherical configurations in the finite field setting. To be more precise, we show that for any spherical configuration $X$ of $\mathbb{F}_{p}^{d}$ of complexity at most $C$ with $d$ being sufficiently large with respect to $C$ and $\vert X\vert$, and for some prime $p$ being sufficiently large with respect to $C$, $\vert X\vert$ and $\epsilon>0$, any set $E\subseteq \mathbb{F}_{p}^{d}$ with $\vert E\vert>\epsilon p^{d}$ contains at least $\gg_{C,\epsilon,\vert X\vert}p^{(k+1)d-(k+1)k/2}$ congruent copies of $X$, where $k$ is the dimension of $\text{span}_{\mathbb{F}_{p}}(X-X)$. The novelty of our approach is that we avoid the use of harmonic analysis, and replace it by the theory of spherical higher order Fourier analysis developed in previous parts of the series., Comment: 61 pages, comments are welcome. arXiv admin note: text overlap with arXiv:2312.06636

This paper is the second part of the series "Spherical higher order Fourier analysis over finite fields", aiming to develop the higher order Fourier analysis method along spheres over finite fields, and to solve the geometric Ramsey conjecture in the finite field setting. In this paper, we study additive combinatorial properties for shifted modules, i.e. the structure of sets of the form $E\hat{+} E$, where $E$ is a collection of shifted modules of the polynomial ring $\mathbb{R}[x_{1},\dots,x_{d}]$ and we identify two modules if their difference contains the zero polynomial. We show that under appropriate definitions, the set $E\hat{+} E$ enjoys properties similar to the conventional setting where $E$ is a subset of an abelian group. In particular, among other results, we prove the Balog-Gowers-Szemer\'edi theorem, the Rusza's quasi triangle inequality and a weak form of the Pl\"unnecke-Rusza theorem in the setting of shifted modules. We also show that for a special class of maps $\xi$ from $\mathbb{Z}_{K}^{d}$ to the collection of all shifted modules of $\mathbb{R}[x_{1},\dots,x_{d}]$, if the set $\xi(\mathbb{Z}_{K}^{d})+\xi(\mathbb{Z}_{K}^{d})$ has large additive energy, then $\xi$ is an almost linear Freiman homomorphism. This result is the crucial additive combinatorial input we need to prove the spherical Gowers inverse theorem in later parts of the series., Comment: 91 pages, comments are welcome

This paper is the third part of the series "Spherical higher order Fourier analysis over finite fields", aiming to develop the higher order Fourier analysis method along spheres over finite fields, and to solve the geometric Ramsey conjecture in the finite field setting. In this paper, we prove an inverse theorem over finite field for spherical Gowers norms, i.e. a local Gowers norm supported on a sphere. We show that if the $(s+1)$-th spherical Gowers norm of a 1-bounded function $f\colon\mathbb{F}_{p}^{d}\to \mathbb{C}$ is at least $\epsilon$ and if $d$ is sufficiently large depending only on $s$, then $f$ correlates on the sphere with a $p$-periodic $s$-step nilsequence, where the bounds for the complexity and correlation depend only on $d$ and $\epsilon$. This result will be used in later parts of the series to prove the geometric Ramsey conjecture in the finite field setting., Comment: 108 pages, comments are welcome

There is an increase in interest to model driving maneuver patterns via the automatic unsupervised clustering of naturalistic sequential kinematic driving data. The patterns learned are often used in transportation research areas such as eco-driving, road safety, and intelligent vehicles. One such model capable of modeling these patterns is the Hierarchical Dirichlet Process Hidden Semi-Markov Model (HDP-HSMM), as it is often used to estimate data segmentation, state duration, and transition probabilities. While this model is a powerful tool for automatically clustering observed sequential data, the existing HDP-HSMM estimation suffers from an inherent tendency to overestimate the number of states. This can result in poor estimation, which can potentially impact impact transportation research through incorrect inference of driving patterns. In this paper, a new robust HDP-HSMM (rHDP-HSMM) method is proposed to reduce the number of redundant states and improve the consistency of the model's estimation. Both a simulation study and a case study using naturalistic driving data are presented to demonstrate the effectiveness of the proposed rHDP-HSMM in identifying and inference of driving maneuver patterns.

Current techniques for Out-of-Distribution (OoD) detection predominantly rely on quantifying predictive uncertainty and incorporating model regularization during the training phase, using either real or synthetic OoD samples. However, methods that utilize real OoD samples lack exploration and are prone to overfit the OoD samples at hand. Whereas synthetic samples are often generated based on features extracted from training data, rendering them less effective when the training and OoD data are highly overlapped in the feature space. In this work, we propose a Wasserstein-score-based generative adversarial training scheme to enhance OoD detection accuracy, which, for the first time, performs data augmentation and exploration simultaneously under the supervision of limited OoD samples. Specifically, the generator explores OoD spaces and generates synthetic OoD samples using feedback from the discriminator, while the discriminator exploits both the observed and synthesized samples for OoD detection using a predefined Wasserstein score. We provide theoretical guarantees that the optimal solutions of our generative scheme are statistically achievable through adversarial training in empirical settings. We then demonstrate that the proposed method outperforms state-of-the-art techniques on various computer vision datasets and exhibits superior generalizability to unseen OoD data.

We prove a pointwise convergence result for additive ergodic averages associated with certain multiplicative actions of the Gaussian integers. We derive several applications in dynamics and number theory, including: (i) Wirsing's theorem for Gaussian integers: if $f\colon \mathbb{G} \to \mathbb{R}$ is a bounded completely multiplicative function, then the following limit exists: $$\lim_{N \to \infty} \frac{1}{N^2} \sum_{1 \leq m, n \leq N} f(m + {\rm i} n).$$ (ii) An answer to a special case of a question of Frantzikinakis and Host: for any completely multiplicative real-valued function $f: \mathbb{N} \to \mathbb{R}$, the following limit exists: $$\lim_{N \to \infty} \frac{1}{N^2} \sum_{1 \leq m, n \leq N} f(m^2 + n^2).$$ (iii) A variant of a theorem of Bergelson and Richter on ergodic averages along the $\Omega$ function: if $(X,T)$ is a uniquely ergodic system with unique invariant measure $\mu$, then for any $x\in X$ and $f\in C(X)$, $$\lim_{N\to\infty}\frac{1}{N^2}\sum_{1 \leq m, n \leq N} f(T^{\Omega(m^2 + n^2)}x)=\int_Xf \ d\mu.$$, Comment: 32 pages. Suggestions and comments of the referee have been incorporated

Edge states occurring in Chern and quantum spin-Hall phases are signatures of the topological electronic band structure in two-dimensional (2D) materials. Recently, a new topological electromagnetic phase of graphene characterized by the optical N-invariant has been proposed. Optical N-invariant arises from repulsive Hall viscosity in hydrodynamic many-body electron systems, fundamentally different from the Chern and Z2 invariants. In this paper, we introduce the topologically protected edge excitation -- optical N-plasmon of interacting many-body electron systems in the topological optical N-phase. These optical N-plasmons are signatures of the topological plasmonic band structure in 2D materials. We demonstrate that optical N-plasmons exhibit fundamentally different dispersion relations, stability, and edge profiles from the topologically trivial edge magneto plasmons. Based on the optical N-plasmon, we design an ultra sub-wavelength broadband topological hydrodynamic circulator, which is a chiral quantum radio-frequency circuit component crucial for information routing and interfacing quantum-classical computing systems. Furthermore, we reveal that optical N-plasmons can be effectively tuned by the neighboring dielectric environment without breaking the topological properties. Our work provides a smoking gun signature of repulsive Hall viscosity and opens practical applications of topological electromagnetic phases of two-dimensional materials., Comment: 13 pages, 6 figures

The rapid growth of large-scale machine learning (ML) models has led numerous commercial companies to utilize ML models for generating predictive results to help business decision-making. As two primary components in traditional predictive pipelines, data processing, and model predictions often operate in separate execution environments, leading to redundant engineering and computations. Additionally, the diverging mathematical foundations of data processing and machine learning hinder cross-optimizations by combining these two components, thereby overlooking potential opportunities to expedite predictive pipelines. In this paper, we propose an operator fusing method based on GPU-accelerated linear algebraic evaluation of relational queries. Our method leverages linear algebra computation properties to merge operators in machine learning predictions and data processing, significantly accelerating predictive pipelines by up to 317x. We perform a complexity analysis to deliver quantitative insights into the advantages of operator fusion, considering various data and model dimensions. Furthermore, we extensively evaluate matrix multiplication query processing utilizing the widely-used Star Schema Benchmark. Through comprehensive evaluations, we demonstrate the effectiveness and potential of our approach in improving the efficiency of data processing and machine learning workloads on modern hardware.

Examining multiple ergodic averages whose iterates are integer parts of real valued polynomials for totally ergodic systems, we provide various characterizations of total joint ergodicity, meaning that an average converges to the "expected" limit along every arithmetic progression. In particular, we obtain a complete characterization when the number of iterates is at most two, and disprove a conjecture of the first author. We also improve a result of Frantzikinakis on joint ergodicity of Hardy field functions of at most polynomial growth for totally ergodic systems, which extends a conjecture of Bergelson-Moreira-Richter. Our method is to first use the methodology of Frantzikinakis, which allows one to reduce the systems to rotations on abelian groups without using deep tools from ergodic theory, then develop formulas for integrals of exponential functions over subtori, and finally, compute exponential sums for integer parts of real polynomials., Comment: 30 pages

We provide necessary and sufficient conditions for joint ergodicity results for systems of commuting measure preserving transformations for an iterated Hardy field function of polynomial growth. Our method builds on and improves recent techniques due to Frantzikinakis and Tsinas, who dealt with multiple ergodic averages along Hardy field functions; it also enhances an approach introduced by the authors and Ferr\'e Moragues to study polynomial iterates. The more general expression, in which the iterate is a linear combination of a Hardy field function of polynomial growth and a tempered function, is studied as well., Comment: 36 pages; Theorem 6.1 now covers the case where the iterate is a linear combination of a Hardy field and a tempered function of different polynomial growth rates, extending in particular Theorem 1.1

Subgraph isomorphism or subgraph matching is generally considered as an NP-complete problem, made more complex in practical applications where the edge weights take real values and are subject to measurement noise and possible anomalies. To the best of our knowledge, almost all subgraph matching methods utilize node labels to perform node-node matching. In the absence of such labels (in applications such as image matching and map matching among others), these subgraph matching methods do not work. We propose a method for identifying the node correspondence between a subgraph and a full graph in the inexact case without node labels in two steps - (a) extract the minimal unique topology preserving subset from the subgraph and find its feasible matching in the full graph, and (b) implement a consensus-based algorithm to expand the matched node set by pairing unique paths based on boundary commutativity. Going beyond the existing subgraph matching approaches, the proposed method is shown to have realistically sub-linear computational efficiency, robustness to random measurement noise, and good statistical properties. Our method is also readily applicable to the exact matching case without loss of generality. To demonstrate the effectiveness of the proposed method, a simulation and a case study is performed on the Erdos-Renyi random graphs and the image-based affine covariant features dataset respectively., Comment: Authors contributed equally. Names listed in alphabetical order

High-fidelity quantum gate operations are essential for achieving scalable quantum circuits. In spin qubit quantum computing systems, metallic gates and antennas which are necessary for qubit operation, initialization, and readout, also cause detriments by enhancing fluctuations of electromagnetic fields. Therefore evanescent wave Johnson noise (EWJN) caused by thermal and vacuum fluctuations becomes an important unmitigated noise, which induces the decay of spin qubits and limits the quantum gate operation fidelity. Here, we first develop a quantum electrodynamics theory of EWJN. Then we propose a numerical technique based on volume integral equations to quantify EWJN strength in the vicinity of nanofabricated metallic gates with arbitrary geometry. We study the limits to two spin-qubit gate fidelity from EWJN-induced relaxation processes in two experimentally relevant quantum computing platforms: (a) silicon quantum dot system and (b) NV centers in diamond. Finally, we introduce the Lindbladian engineering method to optimize the control pulse sequence design and show its enhanced performance over Hamiltonian engineering in mitigating the influence of thermal and vacuum fluctuations. Our work leverages advances in computational electromagnetics, fluctuational electrodynamics and open quantum systems to suppress the effects of thermal and vacuum fluctuations and reach the limits of two-spin-qubit gate fidelity., Comment: 24 pages, 12 figures

Low dimensional primitive feature extraction from LiDAR point clouds (such as planes) forms the basis of majority of LiDAR data processing tasks. A major challenge in LiDAR data analysis arises from the irregular nature of LiDAR data that forces practitioners to either regularize the data using some form of gridding or utilize a triangular mesh such as triangulated irregular network (TIN). While there have been a handful applications using LiDAR data as a connected graph, a principled treatment of utilizing graph-theoretical approach for LiDAR data modelling is still lacking. In this paper, we try to bridge this gap by utilizing graphical approach for normal estimation from LiDAR point clouds. We formulate the normal estimation problem in an optimization framework, where we find the corresponding normal vector for each LiDAR point by utilizing its nearest neighbors and simultaneously enforcing a graph smoothness assumption based on point samples. This is a non-linear constrained convex optimization problem which can then be solved using projected conjugate gradient descent to yield an unique solution. As an enhancement to our optimization problem, we also provide different weighted solutions based on the dot product of the normals and Euclidean distance between the points. In order to assess the performance of our proposed normal extraction method and weighting strategies, we first provide a detailed analysis on repeated randomly generated datasets with four different noise levels and four different tuning parameters. Finally, we benchmark our proposed method against existing state-of-the-art approaches on a large scale synthetic plane extraction dataset. The code for the proposed approach along with the simulations and benchmarking is available at https://github.com/arpan-kusari/graph-plane-extraction-simulation., Comment: Published at ISPRS Annals of Photogrammetry and Remote Sensing

The data needed for machine learning (ML) model training, can reside in different separate sites often termed data silos. For data-intensive ML applications, data silos pose a major challenge: the integration and transformation of data demand a lot of manual work and computational resources. With data privacy and security constraints, data often cannot leave the local sites, and a model has to be trained in a decentralized manner. In this work, we present a vision on how to bridge the traditional data integration (DI) techniques with the requirements of modern machine learning. We explore the possibilities of utilizing metadata obtained from data integration processes for improving the effectiveness and efficiency of ML models. We analyze two common use cases over data silos, feature augmentation and federated learning. Bringing data integration and machine learning together, we highlight the new research opportunities from the aspects of systems, representations, factorized learning and federated learning., Comment: Accepted at ICDE2023 -- Special track (Vision)

Machine-vision-based defect classification techniques have been widely adopted for automatic quality inspection in manufacturing processes. This article describes a general framework for classifying defects from high volume data batches with efficient inspection of unlabelled samples. The concept is to construct a detector to identify new defect types, send them to the inspection station for labelling, and dynamically update the classifier in an efficient manner that reduces both storage and computational needs imposed by data samples of previously observed batches. Both a simulation study on image classification and a case study on surface defect detection via 3D point clouds are performed to demonstrate the effectiveness of the proposed method., Comment: Journal of Quality Technology (2022)

In the precision medicine era, there is a growing need for precision radiotherapy where the planned radiation dose needs to be optimally determined by considering a myriad of patient-specific information in order to ensure treatment efficacy. Existing artificial-intelligence (AI) methods can recommend radiation dose prescriptions within the scope of this available information. However, treating physicians may not fully entrust the AI's recommended prescriptions due to known limitations or when the AI recommendation may go beyond physicians' current knowledge. This paper lays out a systematic method to integrate expert human knowledge with AI recommendations for optimizing clinical decision making. Towards this goal, Gaussian process (GP) models are integrated with deep neural networks (DNNs) to quantify the uncertainty of the treatment outcomes given by physicians and AI recommendations, respectively, which are further used as a guideline to educate clinical physicians and improve AI models performance. The proposed method is demonstrated in a comprehensive dataset where patient-specific information and treatment outcomes are prospectively collected during radiotherapy of $67$ non-small cell lung cancer patients and retrospectively analyzed.

In this paper we consider the problem of unsupervised anomaly segmentation in medical images, which has attracted increasing attention in recent years due to the expensive pixel-level annotations from experts and the existence of a large amount of unannotated normal and abnormal image scans. We introduce a segmentation network that utilizes adversarial learning to partition an image into two cuts, with one of them falling into a reference distribution provided by the user. This Adversarial-based Selective Cutting network (ASC-Net) bridges the two domains of cluster-based deep segmentation and adversarial-based anomaly/novelty detection algorithms. Our ASC-Net learns from normal and abnormal medical scans to segment anomalies in medical scans without any masks for supervision. We evaluate this unsupervised anomly segmentation model on three public datasets, i.e., BraTS 2019 for brain tumor segmentation, LiTS for liver lesion segmentation, and MS-SEG 2015 for brain lesion segmentation, and also on a private dataset for brain tumor segmentation. Compared to existing methods, our model demonstrates tremendous performance gains in unsupervised anomaly segmentation tasks. Although there is still room to further improve performance compared to supervised learning algorithms, the promising experimental results and interesting observations shed light on building an unsupervised learning algorithm for medical anomaly identification using user-defined knowledge., Comment: Currently in Submission to Medical Image Analysis Journal. Extension of DOI - 10.1007/978-3-030-87240-3_23 with more details and experiments and indepth analysis. arXiv admin note: substantial text overlap with arXiv:2103.03664

The training and test data for deep-neural-network-based classifiers are usually assumed to be sampled from the same distribution. When part of the test samples are drawn from a distribution that is sufficiently far away from that of the training samples (a.k.a. out-of-distribution (OOD) samples), the trained neural network has a tendency to make high confidence predictions for these OOD samples. Detection of the OOD samples is critical when training a neural network used for image classification, object detection, etc. It can enhance the classifier's robustness to irrelevant inputs, and improve the system resilience and security under different forms of attacks. Detection of OOD samples has three main challenges: (i) the proposed OOD detection method should be compatible with various architectures of classifiers (e.g., DenseNet, ResNet), without significantly increasing the model complexity and requirements on computational resources; (ii) the OOD samples may come from multiple distributions, whose class labels are commonly unavailable; (iii) a score function needs to be defined to effectively separate OOD samples from in-distribution (InD) samples. To overcome these challenges, we propose a Wasserstein-based out-of-distribution detection (WOOD) method. The basic idea is to define a Wasserstein-distance-based score that evaluates the dissimilarity between a test sample and the distribution of InD samples. An optimization problem is then formulated and solved based on the proposed score function. The statistical learning bound of the proposed method is investigated to guarantee that the loss value achieved by the empirical optimizer approximates the global optimum. The comparison study results demonstrate that the proposed WOOD consistently outperforms other existing OOD detection methods.

We show that, under finitely many ergodicity assumptions, any multicorrelation sequence defined by invertible measure preserving $\mathbb{Z}^d$-actions with multivariable integer polynomial iterates is the sum of a nilsequence and a null sequence, extending a recent result of the second author. To this end, we develop a new seminorm bound estimate for multiple averages by improving the results in a previous work of the first, third and fourth authors. We also use this approach to obtain new criteria for joint ergodicity of multiple averages with multivariable polynomial iterates on $\mathbb{Z}^{d}$-systems., Comment: comments welcome!