Correlation Clustering with Adaptive Similarity Queries

In correlation clustering, we are given $n$ objects together with a binary similarity score between each pair of them. The goal is to partition the objects into clusters so to minimise the disagreements with the scores. In this work we investigate correlation clustering as an active learning problem: each similarity score can be learned by making a query, and the goal is to minimise both the disagreements and the total number of queries. On the one hand, we describe simple active learning algorithms, which provably achieve an almost optimal trade-off while giving cluster recovery guarantees, and we test them on different datasets. On the other hand, we prove information-theoretical bounds on the number of queries necessary to guarantee a prescribed disagreement bound. These results give a rich characterization of the trade-off between queries and clustering error

A robust adaptive algebraic multigrid linear solver for structural mechanics

The numerical simulation of structural mechanics applications via finite elements usually requires the solution of large-size and ill-conditioned linear systems, especially when accurate results are sought for derived variables interpolated with lower order functions, like stress or deformation fields. Such task represents the most time-consuming kernel in commercial simulators; thus, it is of significant interest the development of robust and efficient linear solvers for such applications. In this context, direct solvers, which are based on LU factorization techniques, are often used due to their robustness and easy setup; however, they can reach only superlinear complexity, in the best case, thus, have limited applicability depending on the problem size. On the other hand, iterative solvers based on algebraic multigrid (AMG) preconditioners can reach up to linear complexity for sufficiently regular problems but do not always converge and require more knowledge from the user for an efficient setup. In this work, we present an adaptive AMG method specifically designed to improve its usability and efficiency in the solution of structural problems. We show numerical results for several practical applications with millions of unknowns and compare our method with two state-of-the-art linear solvers proving its efficiency and robustness.Comment: 50 pages, 16 figures, submitted to CMAM

Benchmarking integrated photonic architectures

Photonic platforms represent a promising technology for the realization of several quantum communication protocols and for experiments of quantum simulation. Moreover, large-scale integrated interferometers have recently gained a relevant role for restricted models of quantum computing, specifically with Boson Sampling devices. Indeed, various linear optical schemes have been proposed for the implementation of unitary transformations, each one suitable for a specific task. Notwithstanding, so far a comprehensive analysis of the state of the art under broader and realistic conditions is still lacking. In the present work we address this gap, providing in a unified framework a quantitative comparison of the three main photonic architectures, namely the ones with triangular and square designs and the so-called fast transformations. All layouts have been analyzed in presence of losses and imperfect control over the reflectivities and phases of the inner structure. Our results represent a further step ahead towards the implementation of quantum information protocols on large-scale integrated photonic devices.Comment: 10 pages, 6 figures + 2 pages Supplementary Informatio

Thermal Control of a Dual Mode Parametric Sapphire Transducer

We propose a method to control the thermal stability of a sapphire dielectric transducer made with two dielectric disks separated by a thin gap and resonating in the whispering gallery (WG) modes of the electromagnetic field. The simultaneous measurement of the frequencies of both a WGH mode and a WGE mode allows one to discriminate the frequency shifts due to gap variations from those due to temperature instability. A simple model, valid in quasi equilibrium conditions, describes the frequency shift of the two modes in terms of four tuning parameters. A procedure for the direct measurement of them is presented.Comment: 5 pages, 6 figures, presented at EFTF-IFCS joint conference 200

Relative contribution of chemico-osmosis and electro-osmosis to the experimental determination of the reflection coefficient in semipermeable clay soils

The containment performance of bentonite-based barriers is known to be influenced by the semipermeable membrane behaviour of the bentonite, which arises from the electrical interactions between the clay particles and the ionic species dissolved in the pore solution. Most of the experimental research conducted to date has provided evidence of the clay membrane behaviour, the extent of which is typically quantified through the reflection coefficient, , when the permeant (electrolyte) solution contains a monovalent or divalent salt. Under such conditions, the osmotic counter-flow of solution is controlled to a great extent by the solute exclusion, which is also referred to as the chemico-osmotic effect. However, theoretical simulations of coupled solute transport and solvent flow suggest that, when two or more cations with different diffusivities are contained in the permeant solution, the electro-osmotic effect, which stems from the condition of null electric current density, can be comparable to or even greater than the chemico-osmotic effect. The relative importance of the aforementioned contributions to multi-electrolyte systems is examined herein through the interpretation of laboratory test results from the literature pertaining to a bentonite-amended clay soil permeated with aqueous mixtures of potassium chloride (KCl) and hydrochloric acid (HCl)

Strain-controlled oedometer test for the measurement of the chemico-osmotic properties of bentonites

The possibility of relating the macroscopic transport properties and the swelling behaviour of bentonites to a limited number of physico-chemical and fabric parameters has been investigated by means of a new laboratory apparatus, which allows the reflection coefficient, which is also known as the membrane efficiency coefficient, and the swell coefficient to be simultaneously determined on the same clay specimen. The results of two multi-stage tests, which were performed on a natural sodium bentonite under fully saturated conditions, while varying both the specimen porosity and the salt concentration of the equilibrium solutions, have been interpreted through a physically-based model in which the pore-scale electro-chemical interactions be-tween the solid skeleton, the aqueous phase and the ion species are explicitly taken into account. The efficiency of the tested bentonite in acting as a semi-permeable membrane and its swelling behaviour have been found to be accurately simulated when a single fabric parameter, referred to as the solid charge coefficient, is calibrated on the available experimental dataset, thus suggesting that the containment performance of bentonite-based barriers, used for a number of geoenvironmental applications, may be predicted on the basis of the results of a strain-controlled oedometer test

The equality case in Cheeger's and Buser's inequalities on RCD\mathsf{RCD} spaces

We prove that the sharp Buser's inequality obtained in the framework of $\mathsf{RCD}(1,\infty)$ spaces by the first two authors is rigid, i.e. equality is obtained if and only if the space splits isomorphically a Gaussian. The result is new even in the smooth setting. We also show that the equality in Cheeger's inequality is never attained in the setting of $\mathsf{RCD}(K,\infty)$ spaces with finite diameter or positive curvature, and we provide several examples of spaces with Ricci curvature bounded below where these assumptions are not satisfied and the equality is attained.Comment: Added new results: the discussion on Cheeger's inequality now fits into the study of a family of inequalities relating eigenvalues of the p-Laplacian. To appear on Journal of Functional Analysi

Aligned and Non-Aligned Double JPEG Detection Using Convolutional Neural Networks

Due to the wide diffusion of JPEG coding standard, the image forensic community has devoted significant attention to the development of double JPEG (DJPEG) compression detectors through the years. The ability of detecting whether an image has been compressed twice provides paramount information toward image authenticity assessment. Given the trend recently gained by convolutional neural networks (CNN) in many computer vision tasks, in this paper we propose to use CNNs for aligned and non-aligned double JPEG compression detection. In particular, we explore the capability of CNNs to capture DJPEG artifacts directly from images. Results show that the proposed CNN-based detectors achieve good performance even with small size images (i.e., 64x64), outperforming state-of-the-art solutions, especially in the non-aligned case. Besides, good results are also achieved in the commonly-recognized challenging case in which the first quality factor is larger than the second one.Comment: Submitted to Journal of Visual Communication and Image Representation (first submission: March 20, 2017; second submission: August 2, 2017

Magnetic Control of Transmission and Helicity of Nano-Structured Optical Beams in Magnetoplasmonic Vortex Lenses

We theoretically investigate the generation of far-field propagating optical beams with a desired orbital angular momentum by using an archetypical magnetoplasmonic tip surrounded by a gold spiral slit. The use of a magnetic material can lead to important implications once magneto-optical activity is activated through the application of an external magnetic field. The physical model and the numerical study presented here introduce the concept of magnetically tunable plasmonic vortex lens, namely a magnetoplasmonic vortex lens, which ensures a tunable selectivity in the polarization state of the generated nanostructured beam. The presented system provides a promising platform for a localized excitation of plasmonic vortices followed by their beaming in the far-field with an active modulation of both light's transmittance and helicity

Stabilization of Discrete Time-Crystaline Response on a Superconducting Quantum Computer by increasing the Interaction Range

The simulation of complex quantum many-body systems is a promising short-term goal of noisy intermediate-scale quantum (NISQ) devices. However, the limited connectivity of native qubits hinders the implementation of quantum algorithms that require long-range interactions. We present the outcomes of a digital quantum simulation where we overcome the limitations of the qubit connectivity in NISQ devices. Utilizing the universality of quantum processor native gates, we demonstrate how to implement couplings among physically disconnected qubits at the cost of increasing the circuit depth. We apply this method to simulate a Floquet-driven quantum spin chain featuring interactions beyond nearest neighbors. Specifically, we benchmark the prethermal stabilization of the discrete Floquet time-crystalline response as the interaction range increases, a phenomenon never observed experimentally. Our quantum simulation addresses one of the significant limitations of superconducting quantum processors, namely, device connectivity. It reveals that nontrivial physics involving couplings beyond nearest neighbors can be extracted after the impact of noise is properly taken into account in the theoretical model and consequently mitigated from the experimental data