Playing the Lottery With Concave Regularizers for Sparse Trainable Neural Networks.

The design of sparse neural networks, i.e., of networks with a reduced number of parameters, has been attracting increasing research attention in the last few years. The use of sparse models may significantly reduce the computational and storage footprint in the inference phase. In this context, the lottery ticket hypothesis (LTH) constitutes a breakthrough result, that addresses not only the performance of the inference phase, but also of the training phase. It states that it is possible to extract effective sparse subnetworks, called winning tickets, that can be trained in isolation. The development of effective methods to play the lottery, i.e., to find winning tickets, is still an open problem. In this article, we propose a novel class of methods to play the lottery. The key point is the use of concave regularization to promote the sparsity of a relaxed binary mask, which represents the network topology. We theoretically analyze the effectiveness of the proposed method in the convex framework. Then, we propose extended numerical tests on various datasets and architectures, that show that the proposed method can improve the performance of state-of-the-art algorithms.

Short- to Mid-Term Clinical and Radiological Results of Selective Laser Melting Highly Porous Titanium Cup in Primary Total Hip Arthroplasty.

(1) Background: The aim of this study was to evaluate short- to mid-term clinical and radiological results in patients undergoing primary total hip arthroplasty (THA) with the use of a Selective Laser Melting 3D-printed highly porous titanium acetabular cup (Jump System Traser®, Permedica Orthopaedics). (2) Methods: We conducted a retrospective study and collected prospective data on 125 consecutive patients who underwent primary THA with the use of highly porous titanium cup. Each patient was evaluated preoperatively and postoperatively with a clinical and radiological assessment. (3) Results: The final cohort consisted of 104 patients evaluated after a correct value of 52 (38-74) months. The median Harris Hip Score (HHS) significantly improved from 63.7 (16-95.8) preoperatively to 94.8 (38.2-95.8) postoperatively (p < 0.001), with higher improvement associated with higher age at surgery (ß = 0.22, p = 0.025). On postoperative radiographs, the average acetabular cup inclination and anteversion were 46° (30°-57°) and 15° (1°-32°), respectively. All cups radiographically showed signs of osseointegration with no radiolucency observed, or component loosening. (4) Conclusions: The use of this highly porous acetabular cup in primary THA achieved excellent clinical, functional, and radiological results at mid-term follow-up. A better clinical recovery can be expected in older patients. The radiological evaluation showed excellent osseointegration of the cup with complete absence of periprosthetic radiolucent lines.

Dynamic planning of a two-dose vaccination campaign with uncertain supplies.

The ongoing COVID-19 pandemic has led public health authorities to face the unprecedented challenge of planning a global vaccination campaign, which for most protocols entails the administration of two doses, separated by a bounded but flexible time interval. The partial immunity already offered by the first dose and the high levels of uncertainty in the vaccine supplies have been characteristic of most of the vaccination campaigns implemented worldwide and made the planning of such interventions extremely complex. Motivated by this compelling challenge, we propose a stochastic optimization framework for optimally scheduling a two-dose vaccination campaign in the presence of uncertain supplies, taking into account constraints on the interval between the two doses and on the capacity of the healthcare system. The proposed framework seeks to maximize the vaccination coverage, considering the different levels of immunization obtained with partial (one dose only) and complete vaccination (two doses). We cast the optimization problem as a convex second-order cone program, which can be efficiently solved through numerical techniques. We demonstrate the potential of our framework on a case study calibrated on the COVID-19 vaccination campaign in Italy. The proposed method shows good performance when unrolled in a sliding-horizon fashion, thereby offering a powerful tool to help public health authorities calibrate the vaccination campaign, pursuing a trade-off between efficacy and the risk associated with shortages in supply.

Multiclass Sparse Centroids With Application to Fast Time Series Classification.

In this article, we propose an efficient multiclass classification scheme based on sparse centroids classifiers. The proposed strategy exhibits linear complexity with respect to both the number of classes and the cardinality of the feature space. The classifier we introduce is based on binary space partitioning, performed by a decision tree where the assignation law at each node is defined via a sparse centroid classifier. We apply the presented strategy to the time series classification problem, showing by experimental evidence that it achieves performance comparable to that of state-of-the-art methods, but with a significantly lower classification time. The proposed technique can be an effective option in resource-constrained environments where the classification time and the computational cost are critical or, in scenarios, where real-time classification is necessary.

Current Trends in Knee Arthroplasty: Are Italian Surgeons Doing What Is Expected?

OBJECTIVES: The purpose of this study is to evaluate Italian surgeons' behavior during knee arthroplasty. MATERIALS AND METHODS: All orthopedic surgeons who specialized in knee replacement surgeries and were members of the Italian Society of Knee, Arthroscopy, Sport, Cartilage and Orthopedic Technologies (SIGASCOT) between January 2019 and August 2019 were asked to complete a survey on the management of knee arthroplasty. Data were collected, analyzed, and presented as frequencies and percentages. RESULTS: One-hundred and seventy-seven surgeons completed the survey and were included in the study. Ninety-five (53.7%) surgeons were under 40 years of age. Eighty-five surgeons (48%) worked in public hospitals and 112 (63.3%) were considered "high volume surgeons", with more than 100 knee implants per year. Postero-stabilized total knee arthroplasty was the most commonly used, implanted with a fully cemented technique by 162 (91.5%) surgeons. Unicompartmental knee arthroplasty (UKA) was a rarer procedure compared to TKA, with 77% of surgeons performing less than 30% of UKAs. Most common TKA pre-operative radiological planning included complete antero-posterior (AP) weight-bearing lower limb radiographs, lateral view and patellofemoral view (used by 91%, 98.9% and 70.6% of surgeons, respectively). Pre-operative UKA radiological images included Rosenberg or Schuss views, patellofemoral view and magnetic resonance imaging (66.1%, 71.8% and 46.3% of surgeons, respectively). One hundred and thirty-two surgeons (74.6%) included an AP weight-bearing lower limb X-ray one year after surgery in the post-operative radiological follow-up. Furthermore, 119 surgeons (67.2%) did not perform a post-operative patellofemoral view because it was not considered useful for radiological follow-up. There was no uniformity in the timing and features of post-operative follow-up, with 13 different combinations. CONCLUSIONS: Italian surgeons perform TKA more commonly than UKA. Pre-operative TKA planning is quite uniform rather than UKA planning. Despite literature evidence, there is no agreement on follow-up. It may be useful to create a uniform checklist, including correct timing and exams needed. This analysis is also part of a society surgical educational project for training doctor.

Age structure in SIRD models for the COVID-19 pandemic-A case study on Italy data and effects on mortality.

The COVID-19 pandemic is bringing disruptive effects on the healthcare systems, economy and social life of countries all over the world. Even though the elder portion of the population is the most severely affected by the COVID-19 disease, the counter-measures introduced so far by governments took into little account the age structure, with restrictions that act uniformly on the population irrespectively of age. In this paper, we introduce a SIRD model with age classes for studying the impact on the epidemic evolution of lockdown policies applied heterogeneously on the different age groups of the population. The proposed model is then applied to age-stratified COVID-19 Italian data. The simulation results suggest that control measures focused to specific age groups may bring benefits in terms of reduction of the overall mortality rate.

Sparse ℓ1- and ℓ2-Center Classifiers.

In this article, we discuss two novel sparse versions of the classical nearest-centroid classifier. The proposed sparse classifiers are based on l1 and l2 distance criteria, respectively, and perform simultaneous feature selection and classification, by detecting the features that are most relevant for the classification purpose. We formally prove that the training of the proposed sparse models, with both distance criteria, can be performed exactly (i.e., the globally optimal set of features is selected) at a linear computational cost. Especially, the proposed sparse classifiers are trained in O(mn)+O(mlogk) operations, where n is the number of samples, m is the total number of features, and k ≤ m is the number of features to be retained in the classifier. Furthermore, the complexity of testing and classifying a new sample is simply O(k) for both methods. The proposed models can be employed either as stand-alone sparse classifiers or fast feature-selection techniques for prefiltering the features to be later fed to other types of classifiers (e.g., SVMs). The experimental results show that the proposed methods are competitive in accuracy with state-of-the-art feature selection and classification techniques while having a substantially lower computational cost.

A model predictive control approach to optimally devise a two-dose vaccination rollout: A case study on COVID-19 in Italy.

The COVID-19 pandemic has led to the unprecedented challenge of devising massive vaccination rollouts, toward slowing down and eventually extinguishing the diffusion of the virus. The two-dose vaccination procedure, speed requirements, and the scarcity of doses, suitable spaces, and personnel, make the optimal design of such rollouts a complex problem. Mathematical modeling, which has already proved to be determinant in the early phases of the pandemic, can again be a powerful tool to assist public health authorities in optimally planning the vaccination rollout. Here, we propose a novel epidemic model tailored to COVID-19, which includes the effect of nonpharmaceutical interventions and a concurrent two-dose vaccination campaign. Then, we leverage nonlinear model predictive control to devise optimal scheduling of first and second doses, accounting both for the healthcare needs and for the socio-economic costs associated with the epidemics. We calibrate our model to the 2021 COVID-19 vaccination campaign in Italy. Specifically, once identified the epidemic parameters from officially reported data, we numerically assess the effectiveness of the obtained optimal vaccination rollouts for the two most used vaccines. Determining the optimal vaccination strategy is nontrivial, as it depends on the efficacy and duration of the first-dose partial immunization, whereby the prioritization of first doses and the delay of second doses may be effective for vaccines with sufficiently strong first-dose immunization. Our model and optimization approach provide a flexible tool that can be adopted to help devise the current COVID-19 vaccination campaign, and increase preparedness for future epidemics.

Output Feedback Q-Learning for Linear-Quadratic Discrete-Time Finite-Horizon Control Problems.

An algorithm is proposed to determine output feedback policies that solve finite-horizon linear-quadratic (LQ) optimal control problems without requiring knowledge of the system dynamical matrices. To reach this goal, the Q -factors arising from finite-horizon LQ problems are first characterized in the state feedback case. It is then shown how they can be parameterized as functions of the input-output vectors. A procedure is then proposed for estimating these functions from input/output data and using these estimates for computing the optimal control via the measured inputs and outputs.

A time-varying SIRD model for the COVID-19 contagion in Italy.

The purpose of this work is to give a contribution to the understanding of the COVID-19 contagion in Italy. To this end, we developed a modified Susceptible-Infected-Recovered-Deceased (SIRD) model for the contagion, and we used official data of the pandemic for identifying the parameters of this model. Our approach features two main non-standard aspects. The first one is that model parameters can be time-varying, allowing us to capture possible changes of the epidemic behavior, due for example to containment measures enforced by authorities or modifications of the epidemic characteristics and to the effect of advanced antiviral treatments. The time-varying parameters are written as linear combinations of basis functions and are then inferred from data using sparse identification techniques. The second non-standard aspect resides in the fact that we consider as model parameters also the initial number of susceptible individuals, as well as the proportionality factor relating the detected number of positives with the actual (and unknown) number of infected individuals. Identifying the model parameters amounts to a non-convex identification problem that we solve by means of a nested approach, consisting in a one-dimensional grid search in the outer loop, with a Lasso optimization problem in the inner step.

A new metric for understanding hidden political influences from voting records.

Inspired by the increasing attention of the scientific community towards the understanding of human relationships and actions in social sciences, in this paper we address the problem of inferring from voting data the hidden influence on individuals from competing ideology groups. As a case study, we present an analysis of the closeness of members of the Italian Senate to political parties during the XVII Legislature. The proposed approach is aimed at automatic extraction of the relevant information by disentangling the actual influences from noise, via a two step procedure. First, a sparse principal component projection is performed on the standardized voting data. Then, the projected data is combined with a generative mixture model, and an information theoretic measure, which we refer to as Political Data-aNalytic Affinity (Political DNA), is finally derived. We show that the definition of this new affinity measure, together with suitable visualization tools for displaying the results of analysis, allows a better understanding and interpretability of the relationships among political groups.

A Universal Approximation Result for Difference of Log-Sum-Exp Neural Networks.

We show that a neural network whose output is obtained as the difference of the outputs of two feedforward networks with exponential activation function in the hidden layer and logarithmic activation function in the output node, referred to as log-sum-exp (LSE) network, is a smooth universal approximator of continuous functions over convex, compact sets. By using a logarithmic transform, this class of network maps to a family of subtraction-free ratios of generalized posynomials (GPOS), which we also show to be universal approximators of positive functions over log-convex, compact subsets of the positive orthant. The main advantage of difference-LSE networks with respect to classical feedforward neural networks is that, after a standard training phase, they provide surrogate models for a design that possesses a specific difference-of-convex-functions form, which makes them optimizable via relatively efficient numerical methods. In particular, by adapting an existing difference-of-convex algorithm to these models, we obtain an algorithm for performing an effective optimization-based design. We illustrate the proposed approach by applying it to the data-driven design of a diet for a patient with type-2 diabetes and to a nonconvex optimization problem.

Log-Sum-Exp Neural Networks and Posynomial Models for Convex and Log-Log-Convex Data.

In this paper, we show that a one-layer feedforward neural network with exponential activation functions in the inner layer and logarithmic activation in the output neuron is a universal approximator of convex functions. Such a network represents a family of scaled log-sum exponential functions, here named log-sum-exp ( LSET ). Under a suitable exponential transformation, the class of LSET functions maps to a family of generalized posynomials GPOST , which we similarly show to be universal approximators for log-log-convex functions. A key feature of an LSET network is that, once it is trained on data, the resulting model is convex in the variables, which makes it readily amenable to efficient design based on convex optimization. Similarly, once a GPOST model is trained on data, it yields a posynomial model that can be efficiently optimized with respect to its variables by using geometric programming (GP). The proposed methodology is illustrated by two numerical examples, in which, first, models are constructed from simulation data of the two physical processes (namely, the level of vibration in a vehicle suspension system, and the peak power generated by the combustion of propane), and then optimization-based design is performed on these models.

Very High Refractive Index Transition Metal Dichalcogenide Photonic Conformal Coatings by Conversion of ALD Metal Oxides.

Materials for nanophotonic devices ideally combine ease of deposition, very high refractive index, and facile pattern formation through lithographic templating and/or etching. In this work, we present a scalable method for producing high refractive index WS2 layers by chemical conversion of WO3 synthesized via atomic layer deposition (ALD). These conformal nanocrystalline thin films demonstrate a surprisingly high index of refraction (n > 3.9), and structural fidelity compatible with lithographically defined features down to ~10 nm. Although this process yields highly polycrystalline films, the optical constants are in agreement with those reported for single crystal bulk WS2. Subsequently, we demonstrate three photonic structures - first, a two-dimensional hole array made possible by patterning and etching an ALD WO3 thin film before conversion, second, an analogue of the 2D hole array first patterned into fused silica before conformal coating and conversion, and third, a three-dimensional inverse opal photonic crystal made by conformal coating of a self-assembled polystyrene bead template. These results can be trivially extended to other transition metal dichalcogenides, thus opening new opportunities for photonic devices based on high refractive index materials.

Erratum: Porous-Coated Metaphyseal Sleeves in Revision Total Knee Arthroplasty: Midterm Results.

[This corrects the article DOI: 10.1055/s-0041-1730377.].

A prospective, randomized, comparative study of intravenous alone and combined intravenous and intraarticular administration of tranexamic acid in primary total knee replacement.

BACKGROUND: Studies on the use of tranexamic acid (TXA) to improve clinical outcomes after joint arthroplasty have reported contrasting results between intravenous (IV) TXA alone and combined IV and intraarticular (IA) administration. We compared the effectiveness of the 2 methods in providing higher postoperative hemoglobin (Hb) levels in patients undergoing primary total knee arthroplasty (TKA). METHODS: A total of 100 TKA patients were randomly assigned to receive either IV TXA alone (group 1) or combined IV and topical IA TXA (group 2). Hb and hematocrit levels were measured before and after surgery. The amount of drained blood and transfused blood for the 2 groups was compared. RESULTS: The Hb level was significantly higher at postoperative day 4, together with a positive, albeit not significant, trend toward less postoperative blood loss in the group that received combined IV and IA TXA. No postoperative infections or deep venous thrombosis events occurred. CONCLUSIONS: This study reinforces evidence that, as compared to IV TXA alone, combined IV and IA administration of TXA has a synergic effect, leading to higher postoperative Hb levels without influencing drug safety in TKA patients.

Campanile Near-Field Probes Fabricated by Nanoimprint Lithography on the Facet of an Optical Fiber.

One of the major challenges to the widespread adoption of plasmonic and nano-optical devices in real-life applications is the difficulty to mass-fabricate nano-optical antennas in parallel and reproducible fashion, and the capability to precisely place nanoantennas into devices with nanometer-scale precision. In this study, we present a solution to this challenge using the state-of-the-art ultraviolet nanoimprint lithography (UV-NIL) to fabricate functional optical transformers onto the core of an optical fiber in a single step, mimicking the 'campanile' near-field probes. Imprinted probes were fabricated using a custom-built imprinter tool with co-axial alignment capability with sub <100 nm position accuracy, followed by a metallization step. Scanning electron micrographs confirm high imprint fidelity and precision with a thin residual layer to facilitate efficient optical coupling between the fiber and the imprinted optical transformer. The imprinted optical transformer probe was used in an actual NSOM measurement performing hyperspectral photoluminescence mapping of standard fluorescent beads. The calibration scans confirmed that imprinted probes enable sub-diffraction limited imaging with a spatial resolution consistent with the gap size. This novel nano-fabrication approach promises a low-cost, high-throughput, and reproducible manufacturing of advanced nano-optical devices.

Experimental evidence of Fano resonances in nanomechanical resonators.

Fano resonance refers to an interference between localized and continuum states that was firstly reported for atomic physics and solid-state quantum devices. In recent years, Fano interference gained more and more attention for its importance in metamaterials, nanoscale photonic devices, plasmonic nanoclusters and surface-enhanced Raman scattering (SERS). Despite such interest in nano-optics, no experimental evidence of Fano interference was reported up to now for purely nanomechanical resonators, even if classical mechanical analogies were referred from a theoretical point of view. Here we demonstrate for the first time that harmonic nanomechanical resonators with relatively high quality factors, such as cantilevers vibrating in vacuum, can show characteristic Fano asymmetric curves when coupled in arrays. The reported findings open new perspectives in fundamental aspects of classical nanomechanical resonators and pave the way to a new generation of chemical and biological nanoresonator sensors with higher parallelization capability.

Nanoimprint of a 3D structure on an optical fiber for light wavefront manipulation.

Integration of complex photonic structures onto optical fiber facets enables powerful platforms with unprecedented optical functionalities. Conventional nanofabrication technologies, however, do not permit viable integration of complex photonic devices onto optical fibers owing to their low throughput and high cost. In this paper we report the fabrication of a three-dimensional structure achieved by direct nanoimprint lithography on the facet of an optical fiber. Nanoimprint processes and tools were specifically developed to enable a high lithographic accuracy and coaxial alignment of the optical device with respect to the fiber core. To demonstrate the capability of this new approach, a 3D beam splitter has been designed, imprinted and optically characterized. Scanning electron microscopy and optical measurements confirmed the good lithographic capabilities of the proposed approach as well as the desired optical performance of the imprinted structure. The inexpensive solution presented here should enable advancements in areas such as integrated optics and sensing, achieving enhanced portability and versatility of fiber optic components.

High refractive index Fresnel lens on a fiber fabricated by nanoimprint lithography for immersion applications.

In this Letter, we present a Fresnel lens fabricated on the end of an optical fiber. The lens is fabricated using nanoimprint lithography of a functional high refractive index material, which is suitable for mass production. The main advantage of the presented Fresnel lens compared to a conventional fiber lens is its high refractive index (n=1.68), which enables efficient light focusing even inside other media, such as water or an adhesive. Measurement of the lens performance in an immersion liquid (n=1.51) shows a near diffraction limited focal spot of 810 nm in diameter at the 1/e2 intensity level for a wavelength of 660 nm. Applications of such fiber lenses include integrated optics, optical trapping, and fiber probes.