Resilience of Bayesian Layer-Wise Explanations under Adversarial Attacks

We consider the problem of the stability of saliency-based explanations of Neural Network predictions under adversarial attacks in a classification task. Saliency interpretations of deterministic Neural Networks are remarkably brittle even when the attacks fail, i.e. for attacks that do not change the classification label. We empirically show that interpretations provided by Bayesian Neural Networks are considerably more stable under adversarial perturbations of the inputs and even under direct attacks to the explanations. By leveraging recent results, we also provide a theoretical explanation of this result in terms of the geometry of the data manifold. Additionally, we discuss the stability of the interpretations of high level representations of the inputs in the internal layers of a Network. Our results demonstrate that Bayesian methods, in addition to being more robust to adversarial attacks, have the potential to provide more stable and interpretable assessments of Neural Network predictions

Programmable models of growth and mutation of cancer-cell populations

In this paper we propose a systematic approach to construct mathematical models describing populations of cancer-cells at different stages of disease development. The methodology we propose is based on stochastic Concurrent Constraint Programming, a flexible stochastic modelling language. The methodology is tested on (and partially motivated by) the study of prostate cancer. In particular, we prove how our method is suitable to systematically reconstruct different mathematical models of prostate cancer growth - together with interactions with different kinds of hormone therapy - at different levels of refinement.Comment: In Proceedings CompMod 2011, arXiv:1109.104

Characterization methodology for re-using marble slurry in industrial applications

Nowadays calcium carbonate has a great importance in different industrial fields and currently there is the opportunity of appreciate the potential value of marble waste and convert it into marketable products. Marble slurry samples, collected from different dimension stone treatment plants in Orosei marble district (Sardinia - Italy), were chemically, physically, mineralogically, and morphologically analyzed and the obtained data were evaluated for compatibility with the marketable micronized CaCO3 specifications required by some industrial sectors, estimating the prospects of recovered CaCO3 utilization. Besides the economic benefits, transforming a waste into an important economic resource involves environmental advantages, due to reduced marble waste landfills, and sustainability promotion

Polarity assessment of reflection seismic data: a Deep Learning approach

We propose a procedure for the polarity assessment in reflection seismic data based on a Neural Network approach. The algorithm is based on a fully 1D approach, which does not require any input besides the seismic data since the necessary parameters are all automatically estimated. An added benefit is that the prediction has an associated probability, which automatically quantifies the reliability of the results. We tested the proposed procedure on synthetic and real reflection seismic data sets. The algorithm is able to correctly extract the seismic horizons also in case of complex conditions, such as along the flanks of salt domes, and is able to track polarity inversions

The Mean Drift: Tailoring the Mean Field Theory of Markov Processes for Real-World Applications

The statement of the mean field approximation theorem in the mean field theory of Markov processes particularly targets the behaviour of population processes with an unbounded number of agents. However, in most real-world engineering applications one faces the problem of analysing middle-sized systems in which the number of agents is bounded. In this paper we build on previous work in this area and introduce the mean drift. We present the concept of population processes and the conditions under which the approximation theorems apply, and then show how the mean drift is derived through a systematic application of the propagation of chaos. We then use the mean drift to construct a new set of ordinary differential equations which address the analysis of population processes with an arbitrary size

Experimental Biological Protocols with Formal Semantics

Both experimental and computational biology is becoming increasingly automated. Laboratory experiments are now performed automatically on high-throughput machinery, while computational models are synthesized or inferred automatically from data. However, integration between automated tasks in the process of biological discovery is still lacking, largely due to incompatible or missing formal representations. While theories are expressed formally as computational models, existing languages for encoding and automating experimental protocols often lack formal semantics. This makes it challenging to extract novel understanding by identifying when theory and experimental evidence disagree due to errors in the models or the protocols used to validate them. To address this, we formalize the syntax of a core protocol language, which provides a unified description for the models of biochemical systems being experimented on, together with the discrete events representing the liquid-handling steps of biological protocols. We present both a deterministic and a stochastic semantics to this language, both defined in terms of hybrid processes. In particular, the stochastic semantics captures uncertainties in equipment tolerances, making it a suitable tool for both experimental and computational biologists. We illustrate how the proposed protocol language can be used for automated verification and synthesis of laboratory experiments on case studies from the fields of chemistry and molecular programming

Lumping the approximate master equation for multistate processes on complex networks

Complex networks play an important role in human society and in nature. Stochastic multistate processes provide a powerful framework to model a variety of emerging phenomena such as the dynamics of an epidemic or the spreading of information on complex networks. In recent years, mean-field type approximations gained widespread attention as a tool to analyze and understand complex network dynamics. They reduce the model\u2019s complexity by assuming that all nodes with a similar local structure behave identically. Among these methods the approximate master equation (AME) provides the most accurate description of complex networks\u2019 dynamics by considering the whole neighborhood of a node. The size of a typical network though renders the numerical solution of multistate AME infeasible. Here, we propose an efficient approach for the numerical solution of the AME that exploits similarities between the differential equations of structurally similar groups of nodes. We cluster a large number of similar equations together and solve only a single lumped equation per cluster. Our method allows the application of the AME to real-world networks, while preserving its accuracy in computing estimates of global network properties, such as the fraction of nodes in a state at a given time

Approximate probabilistic verification of hybrid systems

Hybrid systems whose mode dynamics are governed by non-linear ordinary differential equations (ODEs) are often a natural model for biological processes. However such models are difficult to analyze. To address this, we develop a probabilistic analysis method by approximating the mode transitions as stochastic events. We assume that the probability of making a mode transition is proportional to the measure of the set of pairs of time points and value states at which the mode transition is enabled. To ensure a sound mathematical basis, we impose a natural continuity property on the non-linear ODEs. We also assume that the states of the system are observed at discrete time points but that the mode transitions may take place at any time between two successive discrete time points. This leads to a discrete time Markov chain as a probabilistic approximation of the hybrid system. We then show that for BLTL (bounded linear time temporal logic) specifications the hybrid system meets a specification iff its Markov chain approximation meets the same specification with probability $1$. Based on this, we formulate a sequential hypothesis testing procedure for verifying -approximately- that the Markov chain meets a BLTL specification with high probability. Our case studies on cardiac cell dynamics and the circadian rhythm indicate that our scheme can be applied in a number of realistic settings