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In learning problems, the noise inherent to the task at hand hinders the possibility to infer without a certain degree of uncertainty. Quantifying this uncertainty, regardless of its wide use, assumes high relevance for security-sensitive applications. Within these scenarios, it becomes fundamental to guarantee good (i.e., trustworthy) uncertainty measures, which downstream modules can securely employ to drive the final decision-making process. However, an attacker may be interested in forcing the system to produce either (i) highly uncertain outputs jeopardizing the system's availability or (ii) low uncertainty estimates, making the system accept uncertain samples that would instead require a careful inspection (e.g., human intervention). Therefore, it becomes fundamental to understand how to obtain robust uncertainty estimates against these kinds of attacks. In this work, we reveal both empirically and theoretically that defending against adversarial examples, i.e., carefully perturbed samples that cause misclassification, additionally guarantees a more secure, trustworthy uncertainty estimate under common attack scenarios without the need for an ad-hoc defense strategy. To support our claims, we evaluate multiple adversarial-robust models from the publicly available benchmark RobustBench on the CIFAR-10 and ImageNet datasets.

Data poisoning attacks on clustering algorithms have received limited attention, with existing methods struggling to scale efficiently as dataset sizes and feature counts increase. These attacks typically require re-clustering the entire dataset multiple times to generate predictions and assess the attacker's objectives, significantly hindering their scalability. This paper addresses these limitations by proposing Sonic, a novel genetic data poisoning attack that leverages incremental and scalable clustering algorithms, e.g., FISHDBC, as surrogates to accelerate poisoning attacks against graph-based and density-based clustering methods, such as HDBSCAN. We empirically demonstrate the effectiveness and efficiency of Sonic in poisoning the target clustering algorithms. We then conduct a comprehensive analysis of the factors affecting the scalability and transferability of poisoning attacks against clustering algorithms, and we conclude by examining the robustness of hyperparameters in our attack strategy Sonic., Comment: preprint paper

Despite explainable AI (XAI) has recently become a hot topic and several different approaches have been developed, there is still a widespread belief that it lacks a convincing unifying foundation. On the other hand, over the past centuries, the very concept of explanation has been the subject of extensive philosophical analysis in an attempt to address the fundamental question of "why" in the context of scientific law. However, this discussion has rarely been connected with XAI. This paper tries to fill in this gap and aims to explore the concept of explanation in AI through an epistemological lens. By comparing the historical development of both the philosophy of science and AI, an intriguing picture emerges. Specifically, we show that a gradual progression has independently occurred in both domains from logical-deductive to statistical models of explanation, thereby experiencing in both cases a paradigm shift from deterministic to nondeterministic and probabilistic causality. Interestingly, we also notice that similar concepts have independently emerged in both realms such as, for example, the relation between explanation and understanding and the importance of pragmatic factors. Our study aims to be the first step towards understanding the philosophical underpinnings of the notion of explanation in AI, and we hope that our findings will shed some fresh light on the elusive nature of XAI., Comment: 10 pages

Neuromorphic processors are well-suited for efficiently handling sparse events from event-based cameras. However, they face significant challenges in the growth of computing demand and hardware costs as the input resolution increases. This paper proposes the Trainable Region-of-Interest Prediction (TRIP), the first hardware-efficient hard attention framework for event-based vision processing on a neuromorphic processor. Our TRIP framework actively produces low-resolution Region-of-Interest (ROIs) for efficient and accurate classification. The framework exploits sparse events' inherent low information density to reduce the overhead of ROI prediction. We introduced extensive hardware-aware optimizations for TRIP and implemented the hardware-optimized algorithm on the SENECA neuromorphic processor. We utilized multiple event-based classification datasets for evaluation. Our approach achieves state-of-the-art accuracies in all datasets and produces reasonable ROIs with varying locations and sizes. On the DvsGesture dataset, our solution requires 46x less computation than the state-of-the-art while achieving higher accuracy. Furthermore, TRIP enables more than 2x latency and energy improvements on the SENECA neuromorphic processor compared to the conventional solution., Comment: Accepted in ICONS 2024

Thanks to their extensive capacity, over-parameterized neural networks exhibit superior predictive capabilities and generalization. However, having a large parameter space is considered one of the main suspects of the neural networks' vulnerability to adversarial example -- input samples crafted ad-hoc to induce a desired misclassification. Relevant literature has claimed contradictory remarks in support of and against the robustness of over-parameterized networks. These contradictory findings might be due to the failure of the attack employed to evaluate the networks' robustness. Previous research has demonstrated that depending on the considered model, the algorithm employed to generate adversarial examples may not function properly, leading to overestimating the model's robustness. In this work, we empirically study the robustness of over-parameterized networks against adversarial examples. However, unlike the previous works, we also evaluate the considered attack's reliability to support the results' veracity. Our results show that over-parameterized networks are robust against adversarial attacks as opposed to their under-parameterized counterparts.

Matter-wave interferometry is essential to both science and technology. Phase-space squeezing has been shown to be an advantageous source of atoms, whereby the spread in momentum is decreased. Here, we show that the opposite squeezing may be just as advantageous. As an exemplification, we analyze the effect of such a source on point source atom interferometry (PSI), which enables rotation sensing. We describe how a squeezed PSI (SPSI) increases the sensitivity and dynamic range while facilitating short cycle times and high repetition rates. We present regions in parameter space for which the figures of merit are improved by orders of magnitude and show that under some definition of compactness, the SPSI is superior by more than four orders of magnitude. The SPSI thus enables either enhancing the performance for standard size devices or maintaining the performance while miniaturizing to a chip-scale device, opening the door to real-life applications.

Detecting out-of-distribution (OOD) instances is crucial for the reliable deployment of machine learning models in real-world scenarios. OOD inputs are commonly expected to cause a more uncertain prediction in the primary task; however, there are OOD cases for which the model returns a highly confident prediction. This phenomenon, denoted as "overconfidence", presents a challenge to OOD detection. Specifically, theoretical evidence indicates that overconfidence is an intrinsic property of certain neural network architectures, leading to poor OOD detection. In this work, we address this issue by measuring extreme activation values in the penultimate layer of neural networks and then leverage this proxy of overconfidence to improve on several OOD detection baselines. We test our method on a wide array of experiments spanning synthetic data and real-world data, tabular and image datasets, multiple architectures such as ResNet and Transformer, different training loss functions, and include the scenarios examined in previous theoretical work. Compared to the baselines, our method often grants substantial improvements, with double-digit increases in OOD detection AUC, and it does not damage performance in any scenario., Comment: Accepted for the 40th Conference on Uncertainty in Artificial Intelligence (UAI 2024)

Adversarial examples are typically optimized with gradient-based attacks. While novel attacks are continuously proposed, each is shown to outperform its predecessors using different experimental setups, hyperparameter settings, and number of forward and backward calls to the target models. This provides overly-optimistic and even biased evaluations that may unfairly favor one particular attack over the others. In this work, we aim to overcome these limitations by proposing AttackBench, i.e., the first evaluation framework that enables a fair comparison among different attacks. To this end, we first propose a categorization of gradient-based attacks, identifying their main components and differences. We then introduce our framework, which evaluates their effectiveness and efficiency. We measure these characteristics by (i) defining an optimality metric that quantifies how close an attack is to the optimal solution, and (ii) limiting the number of forward and backward queries to the model, such that all attacks are compared within a given maximum query budget. Our extensive experimental analysis compares more than $100$ attack implementations with a total of over $800$ different configurations against CIFAR-10 and ImageNet models, highlighting that only very few attacks outperform all the competing approaches. Within this analysis, we shed light on several implementation issues that prevent many attacks from finding better solutions or running at all. We release AttackBench as a publicly-available benchmark, aiming to continuously update it to include and evaluate novel gradient-based attacks for optimizing adversarial examples., Comment: https://attackbench.github.io

Prediction models are increasingly proposed for guiding treatment decisions, but most fail to address the special role of treatments, leading to inappropriate use. This paper highlights the limitations of using standard prediction models for treatment decision support. We identify `causal blind spots' in three common approaches to handling treatments in prediction modelling: including treatment as a predictor, restricting data based on treatment status and ignoring treatments. When predictions are used to inform treatment decisions, confounders, colliders and mediators, as well as changes in treatment protocols over time may lead to misinformed decision-making. We illustrate potential harmful consequences in several medical applications. We advocate for an extension of guidelines for development, reporting and evaluation of prediction models to ensure that the intended use of the model is matched to an appropriate risk estimand. When prediction models are intended to inform treatment decisions, prediction models should specify upfront the treatment decisions they aim to support and target a prediction estimand in line with that goal. This requires a shift towards developing predictions under the specific treatment options under consideration (`predictions under interventions'). Predictions under interventions need causal reasoning and inference techniques during development and validation. We argue that this will improve the efficacy of prediction models in guiding treatment decisions and prevent potential negative effects on patient outcomes.

Evaluating the adversarial robustness of deep networks to gradient-based attacks is challenging. While most attacks consider $\ell_2$- and $\ell_\infty$-norm constraints to craft input perturbations, only a few investigate sparse $\ell_1$- and $\ell_0$-norm attacks. In particular, $\ell_0$-norm attacks remain the least studied due to the inherent complexity of optimizing over a non-convex and non-differentiable constraint. However, evaluating adversarial robustness under these attacks could reveal weaknesses otherwise left untested with more conventional $\ell_2$- and $\ell_\infty$-norm attacks. In this work, we propose a novel $\ell_0$-norm attack, called $\sigma$-zero, which leverages a differentiable approximation of the $\ell_0$ norm to facilitate gradient-based optimization, and an adaptive projection operator to dynamically adjust the trade-off between loss minimization and perturbation sparsity. Extensive evaluations using MNIST, CIFAR10, and ImageNet datasets, involving robust and non-robust models, show that $\sigma$-zero finds minimum $\ell_0$-norm adversarial examples without requiring any time-consuming hyperparameter tuning, and that it outperforms all competing sparse attacks in terms of success rate, perturbation size, and efficiency., Comment: Code available at https://github.com/Cinofix/sigma-zero-adversarial-attack

Tracking ripening tomatoes is time consuming and labor intensive. Artificial intelligence technologies combined with those of computer vision can help users optimize the process of monitoring the ripening status of plants. To this end, we have proposed a tomato ripening monitoring approach based on deep learning in complex scenes. The objective is to detect mature tomatoes and harvest them in a timely manner. The proposed approach is declined in two parts. Firstly, the images of the scene are transmitted to the pre-processing layer. This process allows the detection of areas of interest (area of the image containing tomatoes). Then, these images are used as input to the maturity detection layer. This layer, based on a deep neural network learning algorithm, classifies the tomato thumbnails provided to it in one of the following five categories: green, brittle, pink, pale red, mature red. The experiments are based on images collected from the internet gathered through searches using tomato state across diverse languages including English, German, French, and Spanish. The experimental results of the maturity detection layer on a dataset composed of images of tomatoes taken under the extreme conditions, gave a good classification rate.

One of the fundamental problems of information theory, since its foundation by Shannon in 1948, has been the computation of the capacity of a discrete memoryless channel, a quantity expressing the maximum rate at which information can travel through the channel. In the literature, several algorithms were proposed to approximately compute the capacity of a discrete memoryless channel, being an analytical solution unavailable for the general discrete memoryless channel. This paper presents a novel approach to compute the capacity, which is based on a continuous-time dynamical system. Such a dynamical system can indeed be regarded as a continuous-time version of the Blahut-Arimoto algorithm. In fact, the updating map appearing in the Blahut-Arimoto algorithm is here obtained as a suitable discretization of the vector flow presented, using an analogy with some game-theoretical models. Finally, this analogy suggests a high-level hardware circuit design enabling analog computation to estimate the capacity., Comment: 13 pages, 15 figures. Submitted to IEEE Transactions on Information Theory

Prediction models are popular in medical research and practice. By predicting an outcome of interest for specific patients, these models may help inform difficult treatment decisions, and are often hailed as the poster children for personalized, data-driven healthcare. We show however, that using prediction models for decision making can lead to harmful decisions, even when the predictions exhibit good discrimination after deployment. These models are harmful self-fulfilling prophecies: their deployment harms a group of patients but the worse outcome of these patients does not invalidate the predictive power of the model. Our main result is a formal characterization of a set of such prediction models. Next we show that models that are well calibrated before and after deployment are useless for decision making as they made no change in the data distribution. These results point to the need to revise standard practices for validation, deployment and evaluation of prediction models that are used in medical decisions.

The current best practice approach for the retrospective diagnosis of adverse drug events (ADEs) in hospitalized patients relies on a full patient chart review and a formal causality assessment by multiple medical experts. This evaluation serves to qualitatively estimate the probability of causation (PC); the probability that a drug was a necessary cause of an adverse event. This practice is manual, resource intensive and prone to human biases, and may thus benefit from data-driven decision support. Here, we pioneer a causal modeling approach using observational data to estimate a lower bound of the PC (PC$_{low}$). This method includes two key causal inference components: (1) the target trial emulation framework and (2) estimation of individualized treatment effects using machine learning. We apply our method to the clinically relevant use-case of vancomycin-induced acute kidney injury in intensive care patients, and compare our causal model-based PC$_{low}$ estimates to qualitative estimates of the PC provided by a medical expert. Important limitations and potential improvements are discussed, and we conclude that future improved causal models could provide essential data-driven support for medication safety monitoring in hospitalized patients., Comment: Extended Abstract presented at Machine Learning for Health (ML4H) symposium 2023, December 10th, 2023, New Orleans, United States, 14 pages

Despite their success, Machine Learning (ML) models do not generalize effectively to data not originating from the training distribution. To reliably employ ML models in real-world healthcare systems and avoid inaccurate predictions on out-of-distribution (OOD) data, it is crucial to detect OOD samples. Numerous OOD detection approaches have been suggested in other fields - especially in computer vision - but it remains unclear whether the challenge is resolved when dealing with medical tabular data. To answer this pressing need, we propose an extensive reproducible benchmark to compare different methods across a suite of tests including both near and far OODs. Our benchmark leverages the latest versions of eICU and MIMIC-IV, two public datasets encompassing tens of thousands of ICU patients in several hospitals. We consider a wide array of density-based methods and SOTA post-hoc detectors across diverse predictive architectures, including MLP, ResNet, and Transformer. Our findings show that i) the problem appears to be solved for far-OODs, but remains open for near-OODs; ii) post-hoc methods alone perform poorly, but improve substantially when coupled with distance-based mechanisms; iii) the transformer architecture is far less overconfident compared to MLP and ResNet.

RGB-D object recognition systems improve their predictive performances by fusing color and depth information, outperforming neural network architectures that rely solely on colors. While RGB-D systems are expected to be more robust to adversarial examples than RGB-only systems, they have also been proven to be highly vulnerable. Their robustness is similar even when the adversarial examples are generated by altering only the original images' colors. Different works highlighted the vulnerability of RGB-D systems; however, there is a lacking of technical explanations for this weakness. Hence, in our work, we bridge this gap by investigating the learned deep representation of RGB-D systems, discovering that color features make the function learned by the network more complex and, thus, more sensitive to small perturbations. To mitigate this problem, we propose a defense based on a detection mechanism that makes RGB-D systems more robust against adversarial examples. We empirically show that this defense improves the performances of RGB-D systems against adversarial examples even when they are computed ad-hoc to circumvent this detection mechanism, and that is also more effective than adversarial training., Comment: Accepted for publication in the Information Sciences journal

The two-dimensional motion of an object on a moving rough horizontal plane is investigated. Two cases are studied: the plane having a translational acceleration, and a rotating plane. For the first case, the motions of a point particle and a sphere are studied, and it is shown that the solution to the latter problem can be expressed in terms of the solution to the former one. Examples of constant acceleration and periodic acceleration along a fixed line, and specifically sinusoidal acceleration along a fixed line, are studied in more detail. Also a situation is investigated where the friction is anisotropic, that is the friction coefficient depends on the direction of the velocity. In this situation, there may be stick-slip motions, and these are investigated in detail. For the second case, the motion of a point particle on a rough turntable is investigated.

Feature attribution methods have become a staple method to disentangle the complex behavior of black box models. Despite their success, some scholars have argued that such methods suffer from a serious flaw: they do not allow a reliable interpretation in terms of human concepts. Simply put, visualizing an array of feature contributions is not enough for humans to conclude something about a model's internal representations, and confirmation bias can trick users into false beliefs about model behavior. We argue that a structured approach is required to test whether our hypotheses on the model are confirmed by the feature attributions. This is what we call the "semantic match" between human concepts and (sub-symbolic) explanations. Building on the conceptual framework put forward in Cin\`a et al. [2023], we propose a structured approach to evaluate semantic match in practice. We showcase the procedure in a suite of experiments spanning tabular and image data, and show how the assessment of semantic match can give insight into both desirable (e.g., focusing on an object relevant for prediction) and undesirable model behaviors (e.g., focusing on a spurious correlation). We couple our experimental results with an analysis on the metrics to measure semantic match, and argue that this approach constitutes the first step towards resolving the issue of confirmation bias in XAI.

Deep learning models undergo a significant increase in the number of parameters they possess, leading to the execution of a larger number of operations during inference. This expansion significantly contributes to higher energy consumption and prediction latency. In this work, we propose EAT, a gradient-based algorithm that aims to reduce energy consumption during model training. To this end, we leverage a differentiable approximation of the $\ell_0$ norm, and use it as a sparse penalty over the training loss. Through our experimental analysis conducted on three datasets and two deep neural networks, we demonstrate that our energy-aware training algorithm EAT is able to train networks with a better trade-off between classification performance and energy efficiency., Comment: 12 pages, 3 figures. Paper accepted at the 22nd International Conference on Image Analysis and Processing (ICIAP) 2023

A long operational lifetime is required for the use of solar cells in real-life photovoltaic applications. The optimization of operational lifetimes is achieved through understanding the inherent degradation phenomena in solar cells. In this study, graphene/Si Schottky-junction solar cells were produced, utilizing liquid-phase-exfoliated graphene as an active surface. The operational and interface stability of these solar cells over a period of 5 years in ambient conditions (following ISOS-D protocols: dark storage/shelf life) was examined, and the origin of their degradation was reported. It was found that the dominant degradation mechanism could be attributed to the degradation of silver contacts. This was indicated by a decrease in shunt resistance, an increase in the ideality factor (due to a higher carrier recombination), and a constant defect density in graphene films for up to 4 years. Measurements across the solar cell's active area during the 5-year period revealed neither significant spatial inhomogeneity, nor shunt channel defects., Comment: 19 pages, 5 figures

Model stealing aims at inferring a victim model's functionality at a fraction of the original training cost. While the goal is clear, in practice the model's architecture, weight dimension, and original training data can not be determined exactly, leading to mutual uncertainty during stealing. In this work, we explicitly tackle this uncertainty by generating multiple possible networks and combining their predictions to improve the quality of the stolen model. For this, we compare five popular uncertainty quantification models in a model stealing task. Surprisingly, our results indicate that the considered models only lead to marginal improvements in terms of label agreement (i.e., fidelity) to the stolen model. To find the cause of this, we inspect the diversity of the model's prediction by looking at the prediction variance as a function of training iterations. We realize that during training, the models tend to have similar predictions, indicating that the network diversity we wanted to leverage using uncertainty quantification models is not (high) enough for improvements on the model stealing task., Comment: 6 pages, 1 figure, 2 table, paper submitted to European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning

Finding an optimum strategy to reach a certain destination by swimming in a background flow is an interesting question which leads to non-trivial results and swimming paths. Here we consider different strategies for various types of surface currents, including parallel currents, and currents resulting from spring sources, and sinks. Swimmers may instinctively swim toward the destination point. It turns out that this idea may not lead to the desired result in the presence of the background current. We will show in some cases the best strategy is to swim towards a certain point other than the actual destination. A different strategy may be to obtain the path of the least time and then follow the minimized path. We study this alternative strategy, too.

The recent spike in certified Artificial Intelligence (AI) tools for healthcare has renewed the debate around adoption of this technology. One thread of such debate concerns Explainable AI (XAI) and its promise to render AI devices more transparent and trustworthy. A few voices active in the medical AI space have expressed concerns on the reliability of Explainable AI techniques and especially feature attribution methods, questioning their use and inclusion in guidelines and standards. Despite valid concerns, we argue that existing criticism on the viability of post-hoc local explainability methods throws away the baby with the bathwater by generalizing a problem that is specific to image data. We begin by characterizing the problem as a lack of semantic match between explanations and human understanding. To understand when feature importance can be used reliably, we introduce a distinction between feature importance of low- and high-level features. We argue that for data types where low-level features come endowed with a clear semantics, such as tabular data like Electronic Health Records (EHRs), semantic match can be obtained, and thus feature attribution methods can still be employed in a meaningful and useful way. Finally, we sketch a procedure to test whether semantic match has been achieved.

A physics package for a compact cold atomic clock is hereby presented. The uniqueness of this package is its small dimensions that enable, for the first time, implementation of a primary cold atomic clock in a standard package of 3U height (=133mm). These dimensions are made possible by using an in-vacuum Microwave (MW) Loop Gap Resonator (LGR) whose length and diameter can be reduced from those of a typical resonator. Following our presentation of the design, we analyze the homogeneity of the MW field amplitude and phase. We find that the expected clock instability due to non-uniformity of the MW field is $\sim1.5\cdot10^{-14}$/day. Adding other clock errors, we estimate the total uncertainty of a cold atomic clock of this design will be around $\sim2\cdot10^{-14}$/day which results in a time drift of a few nanoseconds/day. Such a clock can serve as a primary-grade frequency reference, and may replace the cesium beam atomic clock and the GPS-disciplined rubidium atomic clocks.

The recent spike in certified Artificial Intelligence (AI) tools for healthcare has renewed the debate around adoption of this technology. One thread of such debate concerns Explainable AI and its promise to render AI devices more transparent and trustworthy. A few voices active in the medical AI space have expressed concerns on the reliability of Explainable AI techniques, questioning their use and inclusion in guidelines and standards. Revisiting such criticisms, this article offers a balanced and comprehensive perspective on the utility of Explainable AI, focusing on the specificity of clinical applications of AI and placing them in the context of healthcare interventions. Against its detractors and despite valid concerns, we argue that the Explainable AI research program is still central to human-machine interaction and ultimately our main tool against loss of control, a danger that cannot be prevented by rigorous clinical validation alone.

The success of machine learning is fueled by the increasing availability of computing power and large training datasets. The training data is used to learn new models or update existing ones, assuming that it is sufficiently representative of the data that will be encountered at test time. This assumption is challenged by the threat of poisoning, an attack that manipulates the training data to compromise the model's performance at test time. Although poisoning has been acknowledged as a relevant threat in industry applications, and a variety of different attacks and defenses have been proposed so far, a complete systematization and critical review of the field is still missing. In this survey, we provide a comprehensive systematization of poisoning attacks and defenses in machine learning, reviewing more than 100 papers published in the field in the last 15 years. We start by categorizing the current threat models and attacks, and then organize existing defenses accordingly. While we focus mostly on computer-vision applications, we argue that our systematization also encompasses state-of-the-art attacks and defenses for other data modalities. Finally, we discuss existing resources for research in poisoning, and shed light on the current limitations and open research questions in this research field., Comment: 35 pages, Accepted at ACM Computing Surveys

The recent success of machine learning (ML) has been fueled by the increasing availability of computing power and large amounts of data in many different applications. However, the trustworthiness of the resulting models can be compromised when such data is maliciously manipulated to mislead the learning process. In this article, we first review poisoning attacks that compromise the training data used to learn ML models, including attacks that aim to reduce the overall performance, manipulate the predictions on specific test samples, and even implant backdoors in the model. We then discuss how to mitigate these attacks using basic security principles, or by deploying ML-oriented defensive mechanisms. We conclude our article by formulating some relevant open challenges which are hindering the development of testing methods and benchmarks suitable for assessing and improving the trustworthiness of ML models against data poisoning attacks, Comment: preprint, 10 pages, 3 figures. Paper accepted to the IEEE Computer - Special Issue on Trustworthy AI

Sponge examples are test-time inputs carefully optimized to increase energy consumption and latency of neural networks when deployed on hardware accelerators. In this work, we are the first to demonstrate that sponge examples can also be injected at training time, via an attack that we call sponge poisoning. This attack allows one to increase the energy consumption and latency of machine-learning models indiscriminately on each test-time input. We present a novel formalization for sponge poisoning, overcoming the limitations related to the optimization of test-time sponge examples, and show that this attack is possible even if the attacker only controls a few model updates; for instance, if model training is outsourced to an untrusted third-party or distributed via federated learning. Our extensive experimental analysis shows that sponge poisoning can almost completely vanish the effect of hardware accelerators. We also analyze the activations of poisoned models, identifying which components are more vulnerable to this attack. Finally, we examine the feasibility of countermeasures against sponge poisoning to decrease energy consumption, showing that sanitization methods may be overly expensive for most of the users., Comment: Preprint;16 pages