Harnack Inequalities and Heat-kernel Estimates for Degenerate Diffusion Operators Arising in Population Biology

This paper continues the analysis, started in [2, 3], of a class of degenerate elliptic operators defined on manifolds with corners, which arise in Population Biology. Using techniques pioneered by J. Moser, and extended and refined by L. Saloff-Coste, Grigoryan, and Sturm, we show that weak solutions to the parabolic problem defined by a sub-class of these operators, which consists of those that can be defined by Dirichlet forms and have non-vanishing transverse vector field, satisfy a Harnack inequality. This allows us to conclude that the solutions to these equations belong, for positive times, to the natural anisotropic Holder spaces, and also leads to upper and, in some cases, lower bounds for the heat kernels of these operators. These results imply that these operators have a compact resolvent when acting on $C^0$ or $L^2.$ The proof relies upon a scale invariant Poincare inequality that we establish for a large class of weighted Dirichlet forms, as well as estimates to handle certain mildly singular perturbation terms. The weights that we consider are neither Ahlfors regular, nor do they generally belong to the Muckenhaupt class $A_2.$Comment: This version corrects a small gap in the argument used to estimate the contribution of vector fields and potentials with log-divergent coefficients (the old Lemma B.2

Degenerate Diffusion Operators Arising in Population Biology

We analyze a class of partial differential equations that arise as "backwards Kolmogorov operators" in infinite population limits of the Wright-Fisher models in population genetics and in mathematical finance. These are degenerate elliptic operators defined on manifolds with corners. The classical example is the Kimura diffusion operator, which acts on functions defined on the simplex in R^n. We introduce anisotropic Holder spaces, and prove existence, uniqueness and regularity results for the heat and resolvent equations defined by this class of operators. This suffices to prove that the C^0-graph closure generates a strongly continuous semigroup, and that the associated Martingale problem has a unique solution. We give a detailed description of the nullspace of the forward Kolmogorov operator.Comment: 1 figure, 341 page

Facing the blockchain endpoint vulnerability, an SGX-based solution for secure eHealth auditing

According to McAfee Labs, even in 2019, the eHealth sector is confirmed as one of the most critical in terms of cybersecurity incidents. It is estimated that more than 176 million patient records were target of attacks between 2009 and 2017, and with a single attack, in 2018, more than 1.4 million patient records were affected at UnityPoint Health. To cope with such a dramatic situation, one of the main strategic priority in the eHealth field is represented by the adoption of Blockchain. Specifically, according to a Deloittes survey, 55% of healthcare executives believe that blockchain technology will disrupt the healthcare industry. Unfortunately, while blockchain provides a valuable tool for enhancing the security of health applications and related data, it cannot be assumed as a panacea for data security. As an example, the so-called Endpoint Vulnerability issue is a well-known problem of Blockchain-based solutions: in such a case the attacker successful in gaining control of the end-point can tamper data off-chain during its generation and/or before it is sent to the chain. In this paper, we face such an issue by shielding the endpoint through the Intel Software Guard eXtension (SGX) technology. We demonstrate our solution for an auditing software belonging to the European eHealth management system (namely OpenNCP). We also discuss how our solution can be generalized to any other Blockchain-based solution. Finally, an experimental evaluation has been conducted to prove the actual feasibility of the proposed solution under the requirements of the real eHealth system

SGXTuner: Performance Enhancement of Intel SGX Applications via Stochastic Optimization

Intel SGX has started to be widely adopted. Cloud providers (Microsoft Azure, IBM Cloud, Alibaba Cloud) are offering new solutions, implementing data-in-use protection via SGX. A major challenge faced by both academia and industry is providing transparent SGX support to legacy applications. The approach with the highest consensus is linking the target software with SGX-extended libc libraries. Unfortunately, the increased security entails a dramatic performance penalty, which is mainly due to the intrinsic overhead of context switches, and the limited size of protected memory. Performance optimization is non-trivial since it depends on key parameters whose manual tuning is a very long process. We present the architecture of an automated tool, called SGXTuner, which is able to find the best setting of SGX-extended libc library parameters, by iteratively adjusting such parameters based on continuous monitoring of performance data. The tool is to a large extent algorithm agnostic. We decided to base the current implementation on a particular type of stochastic optimization algorithm, specifically Simulated Annealing. A massive experimental campaign was conducted on a relevant case study. Three client-server applications Memcached, Redis, and Apache were compiled with SCONE's sgx-musl and tuned for best performance. Results demonstrate the effectiveness of SGXTuner

On ``hyperboloidal'' Cauchy data for vacuum Einstein equations and obstructions to smoothness of ``null infinity''

Various works have suggested that the Bondi--Sachs--Penrose decay conditions on the gravitational field at null infinity are not generally representative of asymptotically flat space--times. We have made a detailed analysis of the constraint equations for ``asymptotically hyperboloidal'' initial data and find that log terms arise generically in asymptotic expansions. These terms are absent in the corresponding Bondi--Sachs--Penrose expansions, and can be related to explicit geometric quantities. We have nevertheless shown that there exists a large class of ``non--generic'' solutions of the constraint equations, the evolution of which leads to space--times satisfying the Bondi--Sachs--Penrose smoothness conditions.Comment: 8 pages, revtex styl

Measuring sap flow through small diameter stems

Most techniques for measuring xylem sap flow involve the use of heat as a tracer, and the insertion of linear probes radially into the secondary xylem. The disruption caused means probe based techniques can generally only be used with stems larger than approximately 10 mm in diameter. For smaller diameter stems, constant power heat balance gauges are available, but they can be difficult and expensive to use, and may not resolve very small flows. As part of our studies of kiwifruit fruit development we need to better understand factors affecting the movement of water and solutes into and out of the fruit via the pedicel. There are also many other potential applications for measurement of sap flow through small diameter stems and roots. We therefore set out to develop gauges capable of measuring sap flow in both directions through stems as small as 1 mm in diameter. We describe a modification of the ‘heat ratio’ heat pulse technique. Instead of probes as heating and sensing elements, a chip resistor is used as a miniature heater, and both the heater and temperature sensing thermocouples are pressed against the surface of the stem. For calibration, excised Actinidia deliciosa fruit pedicels were connected to a pressurized water supply and actual flow measured gravimetrically. Heat pulse velocity measured using the gauge was linearly related to actual sap flow in both the acropetal and basipetal directions. On intact fruit pedicels the gauges were used to measure sap flow into Actinidia fruit from shoot, and from the fruit to the shoot when the shoot was allowed to dehydrate. Development of the technique is continuing with further calibration and modelling of the propagation of the heat pulse through the bark, phloem and xylem

Approximation-Based Fault Tolerance in Image Processing Applications

Image processing applications exhibit an intrinsic degree of fault tolerance due to i) the redundant nature of images, and ii) the possible ability of the consumers of the application output to effectively carry out their task even when it is slightly corrupted. In this application scenario the classical Duplication with Comparison (DWC) scheme, that rejects images (and requires re-executions) when the two replicas' outputs differ in a per-pixel comparison, may be over-conservative. In this article, we propose a novel lightweight fault tolerant scheme specifically tailored for image processing applications. The proposed scheme enhances the state-of-the-art by: i) improving the DWC scheme by replacing one of the two exact replicas with an approximated counterpart, and ii) allowing to distinguish between usable and unusable images instead of corrupted and uncorrupted ones by means of a Convolutional Neural Network-based checker. To tune the proposed scheme we introduce a specific design methodology that optimizes both execution time and fault detection capability of the hardened system. We report the results of the application of the proposed approach on two case studies; our proposal achieves an average execution time reduction larger than 30% w.r.t. the DWC with re-execution, and less than 4% misclassified unusable images