Elastic-Net Regularization in Learning Theory

Within the framework of statistical learning theory we analyze in detail the so-called elastic-net regularization scheme proposed by Zou and Hastie for the selection of groups of correlated variables. To investigate on the statistical properties of this scheme and in particular on its consistency properties, we set up a suitable mathematical framework. Our setting is random-design regression where we allow the response variable to be vector-valued and we consider prediction functions which are linear combination of elements ({\em features}) in an infinite-dimensional dictionary. Under the assumption that the regression function admits a sparse representation on the dictionary, we prove that there exists a particular ``{\em elastic-net representation}'' of the regression function such that, if the number of data increases, the elastic-net estimator is consistent not only for prediction but also for variable/feature selection. Our results include finite-sample bounds and an adaptive scheme to select the regularization parameter. Moreover, using convex analysis tools, we derive an iterative thresholding algorithm for computing the elastic-net solution which is different from the optimization procedure originally proposed by Zou and HastieComment: 32 pages, 3 figure

Ultrasound shear wave elastography for liver disease. A critical appraisal of the many actors on the stage

In the last 12\u200a-\u200a18 months nearly all ultrasound manufacturers have arrived to implement ultrasound shear wave elastography modality in their equipment for the assessment of chronic liver disease; the few remaining players are expected to follow in 2016.When all manufacturers rush to a new technology at the same time, it is evident that the clinical demand for this information is of utmost value. Around 1990, there was similar demand for color Doppler ultrasound; high demand for contrast-enhanced ultrasonography was evident at the beginning of this century, and around 2010 demand increased for strain elastography. However, some issues regarding the new shear wave ultrasound technologies must be noted to avoid misuse of the resulting information for clinical decisions. As new articles are expected to appear in 2016 reporting the findings of the new technologies from various companies, we felt that the beginning of this year was the right time to present an appraisal of these issues. We likewise expect that in the meantime EFSUMB will release a new update of the existing guidelines 1 2.The first ultrasound elastography method became available 13 years ago in the form of transient elastography with Fibroscan(\uae) 3. It was the first technique providing non-invasive quantitive information about the stiffness of the liver and hence regarding the amount of fibrosis in chronic liver disease 3. The innovation was enormous, since a non-invasive modality was finally available to provide findings otherwise achievable only by liver biopsy. In fact, prior to ultrasound elastography, a combination of conventional and Doppler ultrasound parameters were utilized to inform the physician about the presence of cirrhosis and portal hypertension 4. However, skilled operators were required, reproducibility and diagnostic accuracy were suboptimal, and it was not possible to differentiate the pre-cirrhotic stages of fibrosis. All these limitations were substantially improved by transient elastography, performed with Fibroscan(\uae), a technology dedicated exclusively to liver elastography. Since then, more than 1300 articles dealing with transient elastography have been listed in PubMed, some describing results with more than 10,000 patients 5. The technique has been tested in nearly all liver disease etiologies, with histology as the reference standard. Meta-analysis of data, available in many etiologies 6, showed good performance and reproducibility as well as some situations limiting reliability 5. Thresholds for the different fibrosis stages (F0 to F4) have been provided by many large-scale studies utilizing histology as the reference standard 7. Transient elastography tracks the velocity of shear waves generated by the gentle hit of a piston on the skin, with the resulting compression wave traveling in the liver along its longitudinal axis. The measurement is made in a 4\u200acm long section of the liver, thus able to average slightly inhomogeneous fibrotic deposition.In 2008 a new modality became available, Acoustic Radiation Force Impulse (ARFI) quantification, and classified by EFSUMB 1 as point shear wave elastography (pSWE), since the speed of the shear wave (perpendicular to the longitudinal axis) is measured in a small region (a "point", few millimeters) at a freely-choosen depth within 8\u200acm from the skin. This technology was the first to be implemented in a conventional ultrasound scanner by Siemens(\uae) 8. Several articles have been published regarding this technology, most with the best reference standards 9, some including findings on more than 1000 hepatitis C patients 10 or reporting meta-analysis of data 11. Although the correlation between Siemens pSWE and transient elastography appeared high 12 13, the calculated thresholds for the different fibrosis stages and the stiffness ranges between the two techniques are not superimposable.Interestingly, pSWE appears to provide greater applicability than transient elastography for measuring both liver 13 and spleen stiffness, which is a new application of elastography 14, of interest for the prediction of the degree of portal hypertension 15 16.Nowadays other companies have started producing equipment with pSWE technology, but only very few articles have been published so far, for instance describing the use of Philips(\uae) equipment, which was the second to provide pSWE. These articles show preliminary good results also in comparison with TE 17 18. Not enough evidence is currently available in the literature about the elastographic performance of the products most recently introduced to the market. Furthermore, with some products the shear wave velocities generated by a single ultrasound acoustic push pulse can be measured in a bidimensional area (a box in the range of 2\u200a-\u200a3\u200acm per side) rather than in a single small point, producing a so-called bidimensional 2D-SWE 1. The stiffness is depicted in color within the area and refreshing of the measurement occurs every 1\u200a-\u200a2 seconds. Once the best image is acquired, the operator chooses a Region Of Interest (ROI) within the color box, where the mean stiffness is then calculated. 2D-SWE can be performed as a "one shot" technique or as a semi-"real-time" technique for a few seconds (at about 1 frame per second) in order to obtain a stable elastogram. With either technique, there should be no motion/breathing during image acquisition. A bidimensional averaged area should overcome the limitation of pSWE to inadvertently investigate small regions of greater or lesser stiffness than average. A shear wave quality indicator could be useful to provide real-time feedback and optimize placement of the sampling ROIs, a technology recently presented by Toshiba(\uae), but which is still awaiting validation in the literature.Supersonic Imagine by Aixplorer(\uae) which works with a different modality of insonation and video analysis compared to the the previously-mentioned three techniques (i.\u200ae., transient elastography, pSWE and 2D-SWE), leading to a bidimensional assessment of liver stiffness in real time up to 5\u200aHz and in larger regions; thus this technique is also termed real-time 2\u200aD SWE. It has been available on the market for a few years 19 20, and many articles have been published showing stiffness values quite similar to those of Fibroscan(\uae) 21; likewise, defined thresholds based on histological findings have appeared in several articles 19 20 21.After this brief summary of the technological state of the art we would like to mention the following critical issues that we believe every user should note prior to providing liver stiffness reports. \ub7 The thresholds obtained from the "oldest" techniques for the various fibrosis stages based on hundreds of patients with histology as reference standard cannot be straightforwardly applied to the new ultrasound elastography techniques, even if based on the same principle (e.\u200ag. pSWE). In fact, the different manufacturers apply proprietary patented calculation modes, which might result in slightly to moderately different values. It should be kept in mind that the range for intermediate fibrosis stages (F1 to F3) is quite narrow, in the order of 2\u200a-\u200a3 kilopascal (over a total range spanning 2 to 75 kPa with Fibroscan), so that slightly different differences in outputs could shift the assessment of patients from one stage to another. Comparative studies using phantoms and healthy volunteers, as well as patients, are eagerly awaited. In fact, the equipment might not produce linear correlations of measurements at different degrees of severity of fibrosis. As a theoretical example, some equipment might well correlate in their values with an older technique, such as transient elastography, at low levels of liver fibrosis, but not as well in cases of more advanced fibrosis or vice versa. Consequentely, when elastography data are included in a report, the equipment utilized for the measurement should be clearly specified, and conclusions about the fibrosis stage should be withheld if an insufficient number of comparative studies with solid reference standards are available for that specific equipment.. \ub7 Future studies using histology as a reference might be biased in comparison to previous studies, since nowadays fewer patients with chronic hepatitis C or hepatitis B undergo biopsy. In fact, due to wide availability of effective drugs as well as the use of established elastography methods for patients with viral hepatitis, most cases submitted to biopsy today have uncertain etiology or inconsistent and inconclusive clinical data. Therefore, extrapolated thresholds from such inhomogeneous populations applied to more ordinary patients with viral hepatitis might become problematic in the future, although no better solution is currently anticipated. This situation might lead to the adoption of a standard validated elastographic method as reference, but this has to be agreed-upon at an international level.. \ub7 Ultrasound elastography embedded in conventional scanners usually allows the choice of where to place the ROI within the color stiffness box and whether to confirm or exclude each single measurement when determining the final value. Thus, the operator has a greater potential to influence the final findings than with Fibroscan\uae, where these choices are not available. This has to be kept in mind to avoid the possibility that an operator could, even inadvertently, tend to confirm an assumption about that specific patient or to confirm the patient's expectations.. \ub7 Quality criteria for the new technologies following transient elastography are absent (depending on the manufacturer) or have not been satisfactorily defined, so that the information potentially inserted in a report cannot currently be judged for its reliability by the clinician.. (ABSTRACT TRUNCATED

Vulnerability and Protection of Critical Infrastructures

Critical infrastructure networks are a key ingredient of modern society. We discuss a general method to spot the critical components of a critical infrastructure network, i.e. the nodes and the links fundamental to the perfect functioning of the network. Such nodes, and not the most connected ones, are the targets to protect from terrorist attacks. The method, used as an improvement analysis, can also help to better shape a planned expansion of the network.Comment: 4 pages, 1 figure, 3 table

Enhancement of cooperation in highly clustered scale-free networks

We study the effect of clustering on the organization of cooperation, by analyzing the evolutionary dynamics of the Prisoner's Dilemma on scale-free networks with a tunable value of clustering. We find that a high value of the clustering coefficient produces an overall enhancement of cooperation in the network, even for a very high temptation to defect. On the other hand, high clustering homogeneizes the process of invasion of degree classes by defectors, decreasing the chances of survival of low densities of cooperator strategists in the network.Comment: 4 pages, 3 figure

Deductive Evaluation: Implicit Code Verification With Low User Burden

We describe a framework for symbolically evaluating C code using a deductive approach that discovers and proves program properties. The framework applies Floyd-Hoare verification principles in its treatment of loops, with a library of iteration schemes serving to derive loop invariants. During evaluation, theorem proving is performed on-the-fly, obviating the generation of verification conditions normally needed to establish loop properties. A PVS-based prototype is presented along with results for sample C functions

Deductive Evaluation: Formal Code Analysis With Low User Burden

We describe a framework for symbolically evaluating iterative C code using a deductive approach that automatically discovers and proves program properties. Although verification is not performed, the method can infer detailed program behavior. Software engineering work flows could be enhanced by this type of analysis. Floyd-Hoare verification principles are applied to synthesize loop invariants, using a library of iteration-specific deductive knowledge. When needed, theorem proving is interleaved with evaluation and performed on the fly. Evaluation results take the form of inferred expressions and type constraints for values of program variables. An implementation using PVS (Prototype Verification System) is presented along with results for sample C functions

BIOECONOMIC MODELING OF THE GULF SHRIMP FISHERY: AN APPLICATION TO GALVESTON BAY AND ADJACENT OFFSHORE AREAS

Resource /Energy Economics and Policy,