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The Real-Time Mixed-Trust (RTMT) Framework [2] enables the use of untrusted components in safety-critical CPS functions (e.g., driving a car) by monitoring their actions with verified and trusted components (called enforcers ) that correct unsafe actions to guarantee critical safety properties (e.g., brake to prevent a crash). The enforcers are run within a verified hypervisor that protects them from security attacks or bugs and the untrusted components are run in an unverified virtual machine (VM) on top of the hypervisor. The untrusted and trusted components are executed as a single coordinated sporadic real-time task, called a mixed-trust task , where the untrusted part is known as the guest task (GT, because it runs in the guest VM) and the trusted part running in the hypervisor (HV) is known as the hypertask (HT). The GT is run by a preemptive fixed-priority scheduler in the VM and the HT by a non-preemptive fixed-priority scheduler in the HV. The non-preemptive scheduler prevents interleavings and simplifies the logical verification [4] , [5] . From a timing point of view, the HT monitors that the GT produces a valid output before the deadline, and if not, the HT itself produces a safe output before the deadline elapses. A new set of schedulability equations to evaluate their schedulability were presented in [2] along with a full discussion of the framework.

Consider fixed-priority preemptive partitioned scheduling of constrained-deadline sporadic tasks on a multiprocessor. A task generates a sequence of jobs and each job has a deadline that must be met. Assume tasks have Corunner-dependent execution times; i.e., the execution time of a job J depends on the set of jobs that happen to execute (on other processors) at instants when J executes. We present a model that describes Corunner-dependent execution times. For this model, we show that exact schedulability testing is co-NP-hard in the strong sense. Facing this complexity, we present a sufficient schedulability test, which has pseudo-polynomial-time complexity if the number of processors is fixed. We ran experiments with synthetic software benchmarks on a quad-core Intel multicore processor with the Linux/RK operating system and found that for each task, its maximum measured response time was bounded by the upper bound computed by our theory.

This article surveys the evolution of stock market trading over a 60-year period. It begins before 1960, when there was no database widely available to conduct a statistical analysis of stock price movements. This changed in the 1960s with the introduction of the Center for Research in Security Prices database. A major finding was the heavy-tailed nature of stock returns. The 1960s also brought major theoretical developments, including the martingale theory of stock price processes and the efficient market hypothesis. This hypothesis prevailed until the 1990s, when the discovery of market anomalies led to statistical arbitrage strategies. We describe the use of modern machine learning methods, such as AdaBoost and random forests, which can combine some of these strategies into an improved trading strategy. The twenty-first century was marked by the rapid evolution of electronic markets and the rise of computer-driven high-frequency trading based on computing technology, low latency access, and limit order book modeling.

Many solutions for composability and compositionality rely on specifying the interface for a component using bandwidth. Some previous works specify period (P) and budget (Q) as an interface for a component. Q/P provides us with a bandwidth (the share of a processor that this component may request); P specifies the time granularity of the allocation of this processing capacity. Other works add another parameter, deadline , which can help to provide tighter bounds on how this processing capacity is distributed. Yet other works use the parameters α and Δ where α is the bandwidth and Δ specifies how smoothly this bandwidth is distributed. It is known [4] that such bandwidth-like interfaces carry a cost: there are tasksets that could be guaranteed to be schedulable if tasks were scheduled directly on the processor, but with bandwidth-like interfaces, it is impossible to guarantee the taskset to be schedulable. It is known that this penalty can be infinite, i.e., the use of bandwidth-like interfaces may require the use of a processor that has a speed that is k times faster, and one can show this for any k. This brings the following question: "What is the average-case performance penalty of bandwidth-like interfaces?" A previous paper [5] has partially answered this question by stating an expression on this penalty as a function of taskset parameters and then randomly generated tasksets to obtain a probability distribution of this penalty. In this paper, we answer this question analytically for the case that the taskset has tasks with infinite minimum inter-arrival time, equal task density, uniformly distributed deadlines, and the number of tasks approaches infinity. For this specific case, we derive an expression; if deadlines are uniformly distributed in [0,1], then we find that the penalty is two. We also run experiments to explore systems with these assumptions but for finite number of tasks. From these experiments, we conclude that (i) the larger the number of tasks is, the larger the penalty is, (ii) the larger the number of tasks is, the less skewed the probability distribution is, and (iii) the larger the number of tasks is, the smaller the variance of the penalty is. We are currently working on the case where deadlines follow other distributions.

Verifying complex Cyber-Physical Systems (CPS) is increasingly important given the push to deploy safety-critical autonomous features. Unfortunately, traditional verification methods do not scale to the complexity of these systems and do not provide systematic methods to protect verified properties when not all the components can be verified. To address these challenges, this paper proposes a real-time mixed-trust computing framework that combines verification and protection. The framework introduces a new task model, where an application task can have both an untrusted and a trusted part. The untrusted part allows complex computations supported by a full OS with a realtime scheduler running in a VM hosted by a trusted hypervisor. The trusted part is executed by another scheduler within the hypervisor and is thus protected from the untrusted part. If the untrusted part fails to finish by a specific time, the trusted part is activated to preserve safety (e.g., prevent a crash) including its timing guarantees. This framework is the first allowing the use of untrusted components for CPS critical functions while preserving logical and timing guarantees, even in the presence of malicious attackers. We present the framework design and implementation along with the schedulability analysis and the coordination protocol between the trusted and untrusted parts. We also present our Raspberry Pi 3 implementation along with experiments showing the behavior of the system under failures of untrusted components, and a drone application to demonstrate its practicality.

The dependence structure in multivariate financial time series is of great importance in portfolio management. By studying daily return histories of 17 exchange-traded index funds, we identify important features of the data, and we propose two new models to capture these features. The first is an extension of the multivariate BEKK (Baba, Engle, Kraft, Kroner) model, which includes a multivariate t-type error distribution with different degrees of freedom. We demonstrate that this error distribution is able to accommodate different levels of heavy-tailed behaviour and thus provides a better fit than models based on a multivariate t-with a common degree of freedom. The second model is copula based, and can be regarded as an extension of the standard and the generalized dynamic conditional correlation model [Engle, Journal of Business and Economics Statistics (2002) Vol. 17, 425–446; Cappiello et al. (2003) Working paper, UCSD] to a Student copula. Model comparison is carried out using criteria including the Akaike information criteria and Bayesian information criteria. We also evaluate the two models from an asset-allocation perspective using a three-asset portfolio as an example, constructing optimal portfolios based on the Markowitz theory. Our results indicate that, for our data, the proposed models both outperform the standard BEKK model, with the copula model performing better than the extension of the BEKK model.