Sciduction: Combining Induction, Deduction, and Structure for Verification and Synthesis

Even with impressive advances in automated formal methods, certain problems in system verification and synthesis remain challenging. Examples include the verification of quantitative properties of software involving constraints on timing and energy consumption, and the automatic synthesis of systems from specifications. The major challenges include environment modeling, incompleteness in specifications, and the complexity of underlying decision problems. This position paper proposes sciduction, an approach to tackle these challenges by integrating inductive inference, deductive reasoning, and structure hypotheses. Deductive reasoning, which leads from general rules or concepts to conclusions about specific problem instances, includes techniques such as logical inference and constraint solving. Inductive inference, which generalizes from specific instances to yield a concept, includes algorithmic learning from examples. Structure hypotheses are used to define the class of artifacts, such as invariants or program fragments, generated during verification or synthesis. Sciduction constrains inductive and deductive reasoning using structure hypotheses, and actively combines inductive and deductive reasoning: for instance, deductive techniques generate examples for learning, and inductive reasoning is used to guide the deductive engines. We illustrate this approach with three applications: (i) timing analysis of software; (ii) synthesis of loop-free programs, and (iii) controller synthesis for hybrid systems. Some future applications are also discussed

Efficient Mission Planning for Robot Networks in Communication Constrained Environments

Many robotic systems are remotely operated nowadays that require uninterrupted connection and safe mission planning. Such systems are commonly found in military drones, search and rescue operations, mining robotics, agriculture, and environmental monitoring. Different robotic systems may employ disparate communication modalities such as radio network, visible light communication, satellite, infrared, Wi-Fi. However, in an autonomous mission where the robots are expected to be interconnected, communication constrained environment frequently arises due to the out of range problem or unavailability of the signal. Furthermore, several automated projects (building construction, assembly line) do not guarantee uninterrupted communication, and a safe project plan is required that optimizes collision risks, cost, and duration. In this thesis, we propose four pronged approaches to alleviate some of these issues: 1) Communication aware world mapping; 2) Communication preserving using the Line-of-Sight (LoS); 3) Communication aware safe planning; and 4) Multi-Objective motion planning for navigation. First, we focus on developing a communication aware world map that integrates traditional world models with the planning of multi-robot placement. Our proposed communication map selects the optimal placement of a chain of intermediate relay vehicles in order to maximize communication quality to a remote unit. We also vi propose an algorithm to build a min-Arborescence tree when there are multiple remote units to be served. Second, in communication denied environments, we use Line-of-Sight (LoS) to establish communication between mobile robots, control their movements and relay information to other autonomous units. We formulate and study the complexity of a multi-robot relay network positioning problem and propose approximation algorithms that restore visibility based connectivity through the relocation of one or more robots. Third, we develop a framework to quantify the safety score of a fully automated robotic mission where the coexistence of human and robot may pose a collision risk. A number of alternate mission plans are analyzed using motion planning algorithms to select the safest one. Finally, an efficient multi-objective optimization based path planning for the robots is developed to deal with several Pareto optimal cost attributes

Dynamic discrete tomography

We consider the problem of reconstructing the paths of a set of points over time, where, at each of a finite set of moments in time the current positions of points in space are only accessible through some small number of their X-rays. This particular particle tracking problem, with applications, e.g., in plasma physics, is the basic problem in dynamic discrete tomography. We introduce and analyze various different algorithmic models. In particular, we determine the computational complexity of the problem (and various of its relatives) and derive algorithms that can be used in practice. As a byproduct we provide new results on constrained variants of min-cost flow and matching problems.Comment: In Pres

Multistage Shortest Path: Instances and Practical Evaluation

A multistage graph problem is a generalization of a traditional graph problem where, instead of a single input graph, we consider a sequence of graphs. We ask for a sequence of solutions, one for each input graph, such that consecutive solutions are as similar as possible. There are several theoretical results on different multistage problems and their complexities, as well as FPT and approximation algorithms. However, there is a severe lack of experimental validation and resulting feedback. Not only are there no algorithmic experiments in literature, we do not even know of any strong set of multistage benchmark instances. In this paper we want to improve on this situation. We consider the natural problem of multistage shortest path (MSP). First, we propose a rich benchmark set, ranging from synthetic to real-world data, and discuss relevant aspects to ensure non-trivial instances, which is a surprisingly delicate task. Secondly, we present an explorative study on heuristic, approximate, and exact algorithms for the MSP problem from a practical point of view. Our practical findings also inform theoretical research in arguing sensible further directions. For example, based on our study we propose to focus on algorithms for multistage instances that do not rely on 2-stage oracles

Cast Irons

The demand for cast iron components, with weights ranging from a few kilograms to several tons, has increased significantly in recent years, both for technical and economic reasons. In fact, the lower cost compared to other alloys, and the good castability, which allow one to obtain near-net shape components in as-cast conditions, and the mechanical properties that can be obtained, are just some of the motivations that attract mechanical designers. However, correct design requires a good knowledge of the intrinsic correlation among alloy chemical composition, process parameters, microstructure (with casting defects) and mechanical properties. This book is aimed at collecting excellent and recent research experimental and theoretical works in this filed. Technological (say, wear resistance and weldability) and mechanical properties (say, Young modulus, static and fatigue strength) of different grades of cast irons, ranging from solution strengthened ferritic ductile iron to compacted graphite iron as well as white and nodular cast irons, are correlated with the alloy chemical composition, process parameters and casting dimension

XMM-Newton X-ray study of early type stars in the Carina OB1 association

<p><b>Aims:</b> X-ray properties of the stellar population in the Carina OB1 association are examined with special emphasis on early-type stars. Their spectral characteristics provide some clues to understanding the nature of X-ray formation mechanisms in the winds of single and binary early-type stars.</p> <p><b>Methods:</b> A timing and spectral analysis of five observations with XMM-Newton is performed using various statistical tests and thermal spectral models.</p> <p><b>Results:</b> 235 point sources have been detected within the field of view. Several of these sources are probably pre-main sequence stars with characteristic short-term variability. Seven sources are possible background AGNs. Spectral analysis of twenty four sources of type OB and WR 25 was performed. We derived spectral parameters of the sources and their fluxes in three energy bands. Estimating the interstellar absorption for every source and the distance to the nebula, we derived X-ray luminosities of these stars and compared them to their bolometric luminosities. We discuss possible reasons for the fact that, on average, the observed X-ray properties of binary and single early type stars are not very different, and give several possible explanations.</p&gt

Trustworthy Deep Learning for Medical Image Segmentation

Despite the recent success of deep learning methods at achieving new state-of-the-art accuracy for medical image segmentation, some major limitations are still restricting their deployment into clinics. One major limitation of deep learning-based segmentation methods is their lack of robustness to variability in the image acquisition protocol and in the imaged anatomy that were not represented or were underrepresented in the training dataset. This suggests adding new manually segmented images to the training dataset to better cover the image variability. However, in most cases, the manual segmentation of medical images requires highly skilled raters and is time-consuming, making this solution prohibitively expensive. Even when manually segmented images from different sources are available, they are rarely annotated for exactly the same regions of interest. This poses an additional challenge for current state-of-the-art deep learning segmentation methods that rely on supervised learning and therefore require all the regions of interest to be segmented for all the images to be used for training. This thesis introduces new mathematical and optimization methods to mitigate those limitations.Comment: PhD thesis successfully defended on 1st July 2022. Examiners: Prof Sotirios Tsaftaris and Dr Wenjia Ba

Counting Solutions of a Polynomial System Locally and Exactly

We propose a symbolic-numeric algorithm to count the number of solutions of a polynomial system within a local region. More specifically, given a zero-dimensional system $f_1=\cdots=f_n=0$, with $f_i\in\mathbb{C}[x_1,\ldots,x_n]$, and a polydisc $\mathbf{\Delta}\subset\mathbb{C}^n$, our method aims to certify the existence of $k$ solutions (counted with multiplicity) within the polydisc. In case of success, it yields the correct result under guarantee. Otherwise, no information is given. However, we show that our algorithm always succeeds if $\mathbf{\Delta}$ is sufficiently small and well-isolating for a $k$-fold solution $\mathbf{z}$ of the system. Our analysis of the algorithm further yields a bound on the size of the polydisc for which our algorithm succeeds under guarantee. This bound depends on local parameters such as the size and multiplicity of $\mathbf{z}$ as well as the distances between $\mathbf{z}$ and all other solutions. Efficiency of our method stems from the fact that we reduce the problem of counting the roots in $\mathbf{\Delta}$ of the original system to the problem of solving a truncated system of degree $k$. In particular, if the multiplicity $k$ of $\mathbf{z}$ is small compared to the total degrees of the polynomials $f_i$, our method considerably improves upon known complete and certified methods. For the special case of a bivariate system, we report on an implementation of our algorithm, and show experimentally that our algorithm leads to a significant improvement, when integrated as inclusion predicate into an elimination method