We study the O($N$)$^*$ transitions that occur in the 3D $\mathbb{Z}_2$-gauge$N$-vector model, and the analogous Ising$^*$ transitions occurring in the 3D$\mathbb{Z}_2$-gauge Higgs model, corresponding to an $N$-vector model with$N=1$. At these transitions, gauge-invariant correlations behave as in theusual $N$-vector/Ising model. Instead, the nongauge invariant spin correlationsare trivial and therefore the spin order parameter that characterizes thespontaneous breaking of the O($N$) symmetry in standard $N$-vector/Isingsystems is apparently absent. We define a novel gauge fixing procedure -- wename it stochastic gauge fixing -- that allows us to define a gauge-dependentvector field that orders at the transition and is therefore the appropriateorder parameter for the O($N$) symmetry breaking. To substantiate thisapproach, we perform numerical simulations for $N=3$ and $N=1$. A finite-sizescaling analysis of the numerical data allows us to confirm the generalscenario: the gauge-fixed spin correlation functions behave as thecorresponding functions computed in the usual $N$-vector/Ising model. Theemergence of a critical vector order parameter in the gauge model shows thecomplete equivalence of the O($N$)$^*$/Ising$^*$ and O($N$)/Ising universalityclasses.
We consider a three-dimensional lattice Abelian Higgs gauge model for acharged $N$-component scalar field ${\phi}$, which is invariant under $SO(N)$global transformations for generic values of the parameters. We focus on thestrong-coupling regime, in which the kinetic Hamiltonian term for the gaugefield is a small perturbation, which is irrelevant for the critical behavior.The Hamiltonian depends on a parameter $v$ which determines the global symmetryof the model and the symmetry of the low-temperature phases. We presentrenormalization-group predictions, based on a Landau-Ginzburg-Wilson effectivedescription that relies on the identification of the appropriate orderparameter and on the symmetry-breaking patterns that occur at thestrong-coupling phase transitions. For $v=0$, the global symmetry group of themodel is $SU(N)$; the corresponding model may undergo continuous transitionsonly for $N=2$. For $v\not=0$, i.e., in the $SO(N)$ symmetric case, continuoustransitions (in the Heisenberg universality class) are possible also for $N=3$and 4. We perform Monte Carlo simulations for $N=2,3,4,6$, to verify therenormalization-group predictions. Finite-size scaling analyses of thenumerical data are in full agreement.
The pyroresistive response of conductive polymer composites (CPCs) hasattracted much interest because of its potential applications in manyelectronic devices requiring a significant responsiveness to changes inexternal physical parameters such as temperature or electric fields. Althoughextensive research has been conducted to study how the properties of thepolymeric matrix and conductive fillers affect the positive temperaturecoefficient pyroresistive effect, the understanding of the microscopicmechanism governing such a phenomenon is still incomplete. In particular, todate, there is little body of theoretical research devoted to investigating theeffect of the polymer thermal expansion on the electrical connectivity of theconductive phase. Here, we present the results of simulations of model CPCs inwhich rigid conductive fillers are dispersed in an insulating amorphous matrix.By employing a meshless algorithm to analyze the thermoelastic response of thesystem, we couple the computed strain field to the electrical connectedness ofthe percolating conductive particles. We show that the electrical conductivityresponds to the local strains that are generated by the mismatch between thethermal expansion of the polymeric and conductive phases and that theconductor-insulator transition is caused by a sudden and global disconnectionof the electrical contacts forming the percolating network.
Among the existing eXplainable AI (XAI) approaches, Feature Attribution methods are a popular option due to their interpretable nature. However, each method leads to a different solution, thus introducing uncertainty regarding their reliability and coherence with respect to the underlying model. This work introduces TextFocus , a metric for evaluating the faithfulness of Feature Attribution methods for Natural Language Processing (NLP) tasks involving classification. To address the absence of ground truth explanations for such methods, we introduce the concept of textual mosaics . A mosaic is composed of a combination of sentences belonging to different classes, which provides an implicit ground truth for attribution. The accuracy of explanations can be then evaluated by comparing feature attribution scores with the known class labels in the mosaic. The performance of six feature attribution methods is systematically compared on three sentence classification tasks by using TextFocus , with Integrated Gradients being the best overall method in terms of faithfulness and computational requirements. The proposed methodology fills a gap in NLP evaluation, by providing an objective way to assess Feature Attribution methods while finding their optimal parameters.
Anomaly detection is a topic of interest in several areas, ranging from Industry 4.0 to Energy Management, Smart Agriculture, Cybersecurity, and Bioinformatics. In a wide sense, detecting anomalies implies finding samples generated within a process that differs from its standard data generation mechanisms. Identifying these samples is extremely important for a variety of reasons, depending on the specific application and scenario, ranging from the minimization of production costs to maintaining the required safety standards. As such, the increasing availability of wide networks of sensors that yield large amounts of data characterizing the processes under observation allowed the large adoption of deep learning techniques, which proved worthy of attention due to their capability of identifying anomalies with large precision, accuracy and reproducibility. Consequently, there is an extensive need to consolidate research results to provide a common framework to understand the topic and ensure a common foundation to establish future research trends. To respond to this need, this work systematically reviews the state of the art of anomaly detection in Industry 4.0, evaluating gaps in the current knowledge and proposing future directions of interest. To pursue this objective, three main dimensions have been considered: the scenario where the anomaly detection methodologies were applied, the sensing equipment used to gather data characterizing the underlying process, and the algorithm employed to properly interpret the phenomena. The study was conducted following the PRISMA protocol, which allowed the identification of a relevant selection of papers by extracting a meaningful dataset of 78 papers of interest. The analysis highlighted the diffusion of autoencoders in several configurations and application scenarios, highlighting their effectiveness and flexibility for anomaly detection.
Approximate computing is a technique that sacrifices the accuracy of the result for an advantage in terms of power, area, and speed. It is useful for error-tolerant applications such as image and video processing. Many approximate arithmetic circuits can be devised using approximate versions of the basic binary full adder that simply adds three bits to generate carry and sum. Therefore, the approximate full adder has been the subject of extensive investigation in recent years. In this paper we present a comprehensive analysis of approximate full adders, by synthesizing in a FinFET 14 nm technology the whole set of possible designs, achievable by modifying one or more entries of the full adder truth-table. Our exhaustive analysis shows that only a few out of the many thousands of synthesized circuits perform reasonably well as approximate full adders. Our analysis re-discovers the approximate full adders already proposed in the literature and identifies some new ones. Examples of using the newly discovered approximate full adders in typical error resilient applications are provided, showing the performance and the usefulness of approximate arithmetic circuit designs in the real-world.