This dialog paper offers a preview and provides a foretaste of an upcoming work on the axiomatization of basic interactive algorithms. The modern notion of algorithm was elucidated in the 1930s--1950s. It was axiomatized a quarter of a century ago as the notion of ``sequential algorithm'' or ``classical algorithm''; we prefer to call it ``basic algorithm" now. The axiomatization was used to show that for every basic algorithm there is a behaviorally equivalent abstract state machine. It was also used to prove the Church-Turing thesis as it has been understood by the logicians. Starting from the 1960s, the notion of algorithm has expanded -- probabilistic algorithms, quantum algorithms, etc. -- prompting introduction of a much more ambitious version of the Church-Turing thesis commonly known as the ``physical thesis.'' We emphasize the difference between the two versions of the Church-Turing thesis and illustrate how nondeterministic and probabilistic algorithms can be viewed as basic algorithms with appropriate oracles. The same view applies to quantum circuit algorithms and many other classes of algorithms.

Many real-world applications can be modelled as complex networks, and such networks include the Internet, epidemic disease networks, transport networks, power grids, protein-folding structures and others. Network integrity and robustness are important to ensure that crucial networks are protected and undesired harmful networks can be dismantled. Network structure and integrity can be controlled by a set of key nodes, and to find the optimal combination of nodes in a network to ensure network structure and integrity can be an NP-complete problem. Despite extensive studies, existing methods have many limitations and there are still many unresolved problems. This paper presents a probabilistic approach based on neighborhood information and node importance, namely, neighborhood information-based probabilistic algorithm (NIPA). We also define a new centrality-based importance measure (IM), which combines the contribution ratios of the neighbor nodes of each target node and two-hop node information. Our proposed NIPA has been tested for different network benchmarks and compared with three other methods: optimal attack strategy (OAS), high betweenness first (HBF) and high degree first (HDF). Experiments suggest that the proposed NIPA is most effective among all four methods. In general, NIPA can identify the most crucial node combination with higher effectiveness, and the set of optimal key nodes found by our proposed NIPA is much smaller than that by heuristic centrality prediction. In addition, many previously neglected weakly connected nodes are identified, which become a crucial part of the newly identified optimal nodes. Thus, revised strategies for protection are recommended to ensure the safeguard of network integrity. Further key issues and future research topics are also discussed.

In this paper, we take a new approach for time of arrival geo-localization. We show that the main sources of error in metropolitan areas are due to environmental imperfections that bias our solutions, and that we can rely on a probabilistic model to learn and compensate for them. The resulting localization error is validated using measurements from a live LTE cellular network to be less than 10 meters, representing an order-of-magnitude improvement.

This article describes a methodology for programming robots known as probabilistic robotics. The probabilistic paradigm pays tribute to the inherent uncertainty in robot perception, relying on explicit representations of uncertainty when determining what to do. This article surveys some of the progress in the field, using in-depth examples to illustrate some of the nuts and bolts of the basic approach.

We have developed a general Bayesian algorithm for determining the coordinates of points in a three-dimensional space. The algorithm takes as input a set of probabilistic constraints on the coordinates of the points, and an a priori distribution for each point location. The output is a maximum-likelihood estimate of the location of each point. We use the extended, iterated Kalman filter, and add a search heuristic for optimizing its solution under nonlinear conditions. This heuristic is based on the same principle as the simulated annealing heuristic for other optimization problems. Our method uses any probabilistic constraints that can be expressed as a function of the point coordinates (for example, distance, angles, dihedral angles, and planarity). It assumes that all constraints have Gaussian noise. In this paper, we describe the algorithm and show its performance on a set of synthetic data to illustrate its convergence properties, and its applicability to domains such ng molecular structure determination.

The games of prediction with expert advice are considered in this paper. We present some modification of Kalai and Vempala algorithm of following the perturbed leader for the case of unrestrictedly large one-step gains. We show that in general case the cumulative gain of any probabilistic prediction algorithm can be much worse than the gain of some expert of the pool. Nevertheless, we give the lower bound for this cumulative gain in general case and construct a universal algorithm which has the optimal performance; we also prove that in case when one-step gains of experts of the pool have ``limited deviations'' the performance of our algorithm is close to the performance of the best expert.

The remarkable results of Foster and Vohra was a starting point for a series of papers which show that any sequence of outcomes can be learned (with no prior knowledge) using some universal randomized forecasting algorithm and forecast-dependent checking rules. We show that for the class of all computationally efficient outcome-forecast-based checking rules, this property is violated. Moreover, we present a probabilistic algorithm generating with probability close to one a sequence with a subsequence which simultaneously miscalibrates all partially weakly computable randomized forecasting algorithms. %subsequences non-learnable by each randomized algorithm. According to the Dawid's prequential framework we consider partial recursive randomized algorithms.

This article describes a methodology for programming robots known as probabilistic robotics. The probabilistic paradigm pays tribute to the inherent uncertainty in robot perception, relying on explicit representations of uncertainty when determining what to do. This article surveys some of the progress in the field, using in-depth examples to illustrate some of the nuts and bolts of the basic approach. My central conjecture is that the probabilistic approach to robotics scales better to complex real-world applications than approaches that ignore a robot's uncertainty.

This article describes a methodology for programming robots known as probabilistic robotics. The probabilistic paradigm pays tribute to the inherent uncertainty in robot perception, relying on explicit representations of uncertainty when determining what to do. This article surveys some of the progress in the field, using in-depth examples to illustrate some of the nuts and bolts of the basic approach. My central conjecture is that the probabilistic approach to robotics scales better to complex real-world applications than approaches that ignore a robot's uncertainty.