Robustness Definition, Meaning & Synonyms

But a lot has happened since then, and the drop in 2020 turned out to be not as deep as initially expected—4.4% rather than 7%—nor as robust as analysts hoped. Materials were chosen for their robustness and ease of maintenance. His mental robustness helped him to cope in the aftermath of the trial. Sensitivity analyses were undertaken to test the robustness of the results. The table results are very reassuring for the robustness of the main results.

Synopsys’s PrimeShield™ solution provides design robustness analysis and optimization at advanced nodes and enables designers to effectively improve design robustness in face of escalating process and voltage variability. It enables designers to reduce design power and boost frequency by minimizing over-pessimism, over-margin and over-design while ensuring design safety. It would be interesting to study whether this feature appears systematically for parameter variations improving the robustness of the desired behavior. The satisfaction degree is normalized such that it ranges between 0 and 1, with a satisfaction degree equal to 1 when the property is true and tending toward 0 when the system is far from satisfying the expected property. For some applications, the satisfaction degree might be normalized differently, using a given constant K instead of the ones in Equation . The atomic propositions in ϕ being linear constraints on free variables y, the satisfaction domains are finite unions and intersections of polytopes that can be computed with standard polyhedra libraries.

In System 1, perturbations degrade the system’s performance more severely than in System 2. So, with a different meaning of robustness, one could say that System 2 is more robust than System 1. These two robustness interpretations have been indiscriminately used in the literature (see e.g. Davidson et al., 2003; von Dassow et al., 2000). To reflect this second interpretation, let us define the relative robustness of a system with respect to a nominal behavior as the system’s robustness divided by its nominal performance, that is, by the satisfaction degree of the reference behavior. In computer science, robustness is the ability of a computer system to cope with errors during execution.

Other approaches have been proposed that use temporal logic to define robustness of biological systems (Batt et al., 2007; Shen et al., 2008). However, these approaches use a Boolean interpretation of temporal logic that mboxis not well-adapted to defining a quantitative notion of robustness. Although very interesting from a theoretical point of view, Kitano’s definition might be too general when applying it to particular problems. Indeed the definition relies on a so-called evaluation function, defined using an unspecified, problem-dependent real-valued performance function. Here, we propose to define the evaluation function using the newly introduced notion of violation degree of temporal logic formulae . Intuitively, the violation degree reflects the distance between a particular behavior of the perturbed system, given as a numerical timed trace, and the expected reference behavior, expressed by a temporal logic formula.

3 Robust satisfaction degree

For obvious reasons, achieving a robust behavior despite cell variability and environmental fluctuations is a central issue in synthetic biology. In this context, input/output robustness (Shinar et al., 2007) and insulation (Vecchio et al., 2008) are notions of particular interest. The robustness landscape appears like a blurred version of the satisfaction degree landscape. This corresponds to the fact definition of robustness that parameter variations corresponding to cell-to-cell variability used for computing the robustness are generally smaller than parameter perturbations considered when exploring the parameter space. However, one should also stress that the robustness takes into account parameter variations in all dimensions and with particular distributions (here log-normal, with various noise intensities σ).

The evaluation function needs to be defined for each specific problem in an ad hoc manner and re-implemented for the computation of the robustness. We first define the Boolean semantics of linear temporal logic on timed numerical traces (Section 2.1). Then, we show how using the variable abstraction technique of Section 2.2, we can define a continuous satisfaction degree for temporal logic formulae (Section 2.3) better adapted to a quantitative notion of robustness.

Robustness (glossary)

The patented fast statistical methods and breakthrough machine learning technology are used to firmly establish design robustness analysis as a method to minimize failure and maximize power, performance, and area . PrimeShield delivers 100X-10,000X faster design robustness analysis and optimization than existing solutions. It is scalable to volume production system- on-chips with billions of transistors, while using industry standard inputs for immediate deployment. In the next section, we provide a brief description of the violation degree notion introduced in Fages and Rizk . In Section 3, we present the proposed method for robustness estimation and its implementation in BIOCHAM 2.8. In Section 4, we detail the application of our method to the analysis of the robustness of the synthetic transcriptional cascade.

If you are an investor you will have used many financial models. If they are robust models they can provide more reliable information even as prices rise or fall, interest changes, or other unforeseen variables affect the market you are studying. Needs to review the security of your connection before proceeding. These example https://globalcloudteam.com/ sentences are selected automatically from various online news sources to reflect current usage of the word ‘robust.’ Views expressed in the examples do not represent the opinion of Merriam-Webster or its editors. Look up any word in the dictionary offline, anytime, anywhere with the Oxford Advanced Learner’s Dictionary app.

However, contrary to the sensitivities, the relative robustness takes into account a given perturbation model. The applicability and biological relevance of our approach is illustrated on the analysis of the robustness of the timed response of a synthetic transcriptional cascade built in Escherichia coli. This system presents a high cell-to-cell variability that prevents using it as a biological timer. We look for parameter modifications that improve the robustness of a ‘well-timed’ behavior. One considers a particular system, a particular function and a particular set of perturbations, and one assesses how perturbations affect the given function. However, with the notable exception of Kitano , no general formal definition of robustness has been proposed.

Robustness can also be defined as the ability of an algorithm to continue operating despite abnormalities in input, calculations, etc. Robustness can encompass many areas of computer science, such as robust programming, robust machine learning, and Robust Security Network. Formal techniques, such as fuzz testing, are essential to showing robustness since this type of testing involves invalid or unexpected inputs. Various commercial products perform robustness testing of software systems, and is a process of failure assessment analysis.

Benefits of Robustness Analysis

First and most significant second order sensitivity indices defined for the robustness with respect to large parameter variations and computed on 8D grids. The analysis of the first-order sensitivity indices corroborates our previous finding that γ variations have a very strong impact on the robust behavior of the cascade. The variations of this parameter alone are responsible for 20% of the robustness variations. In contrast, aTc variations seem to have a very low impact on the cascade behavior. To obtain a more comprehensive picture of the variations of the robustness of the expected behavior, we sample the parameter space for large parameter variations, and for each parameter, we compute the robustness.

We consider the design of a synthetic transcriptional cascade that could be used for the temporal sequencing of events in synthetic biology applications. This cascade has been build by Hooshangi and colleagues and here we investigate the robustness of a desired behavior, and the possibilities to make it more robust. We believe that distinguishing these two notions will help to clarify the analysis of robustness of biological systems. Undoubtedly, formal definitions are useful for making this distinction. Robustness can be defined as the capacity of a system to maintain a function in the face of perturbations. Robustness is now regarded as one of the fundamental characteristics of biological systems because it allows their correct functioning in presence of molecular noise and environmental fluctuations.

Because temporal logics are expressive languages to formalize temporal behavior of dynamical systems and the violation degree can be automatically computed, our instantiation of Kitano’s definition is both general and computational. The main contribution of our work is that we propose a computational approach for—and an implementation of—the automatic estimation of the robustness that applies to a broad class of dynamical properties and a large variety of possible perturbations. We simply require that the property describing the expected behavior can be expressed in temporal logic and that the behavior of the system can be represented by a numerical trace . The following algorithm is implemented in version 2.8 of the freely available tool BIOCHAM, a modeling environment for the analysis of biological systems (Calzone et al., 2006). The computation of the trace Tp is done by numerical integration. The computation of the satisfaction domain 𝒟Tp,ϕ is made by induction on the formula structure, using for each subformula a direct implementation of the definition.

Robustness

Architecture and inherent robustness of a bacterial cell-cycle control system. Reglatory gene networks and the properties of the developmental process. We thank Ron Weiss, Priscilla Purnick and other members of the Weiss lab for fruitful discussions and for providing experimental data. We acknowledge partial support from the European project Tempo, the INRIA Colage and INRA AgroBi projects. Numerical integrations illustrate that the expected behavior is indeed more robustly obtained (compare Figures 5c and ​ and6a). In the sequel, ϕ will denote the QFLTL formula obtained by variable abstraction from a LTL formula ϕ.

• Chin JW. Modular approaches to expanding the functions of living matter.
• In this context, input/output robustness (Shinar et al., 2007) and insulation (Vecchio et al., 2008) are notions of particular interest.
• We can help you reset your password using the email address linked to your Project Euclid account.
• We look for parameter modifications that improve the robustness of a ‘well-timed’ behavior.
• This could be compared with the sensitivity of satisfaction degree with respect to parameter perturbations.
• More generally, this variable abstraction/instantiation process allows us to view a LTL formula as a point in the QFLTL formula space ℝq, where q is the number of constants appearing in ϕ .
• When formalizing the robustness notion, we found that several definitions can be proposed.

Central to our approach is the notion of satisfaction degree of temporal logic formulae. In systems and synthetic biology, many computational approaches use a rather simple measure of the performance of the system, either for parameter searching, robustness computation or local and global sensitivity analysis. Finding a relevant measure of the system performance limits the applicability of the above-mentioned approaches. Examples of such measures are the gain of a response, and the perturbation of a steady state or of the period of oscillations (Felix and Wagner, 2008; Feng et al., 2004; Gonze et al., 2002). In contrast, using the satisfaction degree as a performance measure allows us to take advantage of the expressivity of temporal logics and consequently to significantly broaden the applicability of these techniques. In Rizk et al. , we showed that using the satisfaction degree, one can efficiently find parameter values for which complex dynamical behaviors are observed.

VIOLATION DEGREE OF TEMPORAL LOGIC PROPERTIES

Although generally efficient, these operations require in the worst case a time exponential in the formula space dimension. They are, however, independent on the number of state variables. Aicas aicas was founded to provide businesses with a flexible, more efficient approach to embedded realtime application development.

The effectiveness and robustness characteristics of our proposed method were verified successfully in both simulations and experiments. Improve your vocabulary with English Vocabulary in Use from Cambridge. The robustness of the furniture makes it suitable for a playroom.

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Systems having same absolute robustness or same relative robustness , assuming evenly distributed perturbations. Performance functions of Systems 1 and 2 have same the average, whereas the performance function of System 3 is half of the one of System 1. Each grid is defined by three parameter values in each dimension. These values—or more precisely their log—are obtained by dividing evenly the parameter domain [ln(pi/10), ln] in three subintervals and by choosing randomly a value in each subinterval.

2 Relative robustness

Synopsys is a leading provider of high-quality, silicon-proven semiconductor IP solutions for SoC designs. Nanotron Nanotron Technologies is a leader in the development of wireless products that combine high speed data transmission and location information at about 1 meter accuracy. Their wireless technology guarantees high signal Robustness and low energy consumption.

Please note that a Project Euclid web account does not automatically grant access to full-text content. An institutional or society member subscription is required to view non-Open Access content. You can test the robustness of a financial or economic model by dramatically changing the inputs of the model. If you continue to get the same results, the model can be considered robust.

This comes with no surprise, since as said earlier, the ratios κi/γi largely determine the steady state levels of the proteins. For the computation of validity domains and satisfaction degree in a given trace. To find out more about robustness, see our definitions of resilience, technical analysis and financial models. Ultrasensitivity and noise propagation in a synthetic transcriptional cascade. These sensitivity indices and higher order sensitivity indices quantify how the variations of a parameter Pi or a group of parameters contribute to the variance of R.

It seems that the nominal behavior, and even more the average behavior, is rather fragile to growth rate variations. In Figure 7c, it appears that the relative robustness that quantifies how different the average behavior is from the nominal one, efficiently identifies regions where the satisfaction degree changes significantly. In the context of system design, this information is of great interest. This could be compared with the sensitivity of satisfaction degree with respect to parameter perturbations.

The precise definition of robustness is generally highly problem-specific. This makes it difficult to discuss and compare the robustness found in different contexts, or even in similar contexts but computed using different formal definitions of robustness. In Kitano , the mathematical foundations of a theory of biological robustness is proposed, with the aim of providing a unified perspective on robustness. When comparing plots 1 and 2 of Figure 2, it appears that the consequences of perturbations of the nominal behavior are not the same, with T0 the nominal behavior.