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The shortest path problem in graphs is fundamental to AI. Nearly all variants of the problem and relevant algorithms that solve them ignore edge-weight computation time and its common relation to weight uncertainty. This implies that taking these factors into consideration can potentially lead to a performance boost in relevant applications. Recently, a generalized framework for weighted directed graphs was suggested, where edge-weight can be computed (estimated) multiple times, at increasing accuracy and run-time expense. We build on this framework to introduce the problem of finding the tightest admissible shortest path (TASP); a path with the tightest suboptimality bound on the optimal cost. This is a generalization of the shortest path problem to bounded uncertainty, where edge-weight uncertainty can be traded for computational cost. We present a complete algorithm for solving TASP, with guarantees on solution quality. Empirical evaluation supports the effectiveness of this approach., Comment: arXiv admin note: text overlap with arXiv:2208.11489

The shortest path problem in graphs is a cornerstone of AI theory and applications. Existing algorithms generally ignore edge weight computation time. We present a generalized framework for weighted directed graphs, where edge weight can be computed (estimated) multiple times, at increasing accuracy and run-time expense. This raises several generalized variants of the shortest path problem. We introduce the problem of finding a path with the tightest lower-bound on the optimal cost. We then present two complete algorithms for the generalized problem, and empirically demonstrate their efficacy.

Information about action costs is critical for real-world AI planning applications. Rather than rely solely on declarative action models, recent approaches also use black-box external action cost estimators, often learned from data, that are applied during the planning phase. These, however, can be computationally expensive, and produce uncertain values. In this paper we suggest a generalization of deterministic planning with action costs that allows selecting between multiple estimators for action cost, to balance computation time against bounded estimation uncertainty. This enables a much richer -- and correspondingly more realistic -- problem representation. Importantly, it allows planners to bound plan accuracy, thereby increasing reliability, while reducing unnecessary computational burden, which is critical for scaling to large problems. We introduce a search algorithm, generalizing $A^*$, that solves such planning problems, and additional algorithmic extensions. In addition to theoretical guarantees, extensive experiments show considerable savings in runtime compared to alternatives., Comment: 3 figures, 2 tables

The definition and representation of planning problems is at the heart of AI planning research. A key part is the representation of action models. Decades of advances improving declarative action model representations resulted in numerous theoretical advances, and capable, working, domain-independent planners. However, despite the maturity of the field, AI planning technology is still rarely used outside the research community, suggesting that current representations fail to capture real-world requirements, such as utilizing complex mathematical functions and models learned from data. We argue that this is because the modeling process is assumed to have taken place and completed prior to the planning process, i.e., offline modeling for offline planning. There are several challenges inherent to this approach, including: limited expressiveness of declarative modeling languages; early commitment to modeling choices and computation, that preclude using the most appropriate resolution for each action model -- which can only be known during planning; and difficulty in reliably using non-declarative, learned, models. We therefore suggest to change the AI planning process, such that is carries out online modeling in offline planning, i.e., the use of action models that are computed or even generated as part of the planning process, as they are accessed. This generalizes the existing approach (offline modeling). The proposed definition admits novel planning processes, and we suggest one concrete implementation, demonstrating the approach. We sketch initial results that were obtained as part of a first attempt to follow this approach by planning with action cost estimators. We conclude by discussing open challenges.

Magnetic surveys are conventionally performed by scanning a domain with a portable scalar magnetic sensor. Unfortunately, scalar magnetometers are expensive, power consuming and bulky. In many applications, calibrated vector magnetometers can be used to perform magnetic surveys. In recent years algorithms based on artificial intelligence (AI) achieve state-of-the-art results in many modern applications. In this work we investigate an AI algorithm for the classical scalar calibration of magnetometers. A simple, low cost method for performing a magnetic survey is presented. The method utilizes a low power consumption sensor with an AI calibration procedure that improves the common calibration methods and suggests an alternative to the conventional technology and algorithms. The setup of the survey system is optimized for quick deployment in-situ right before performing the magnetic survey. We present a calibration method based on a procedure of rotating the sensor in the natural earth magnetic field for an optimal time period. This technique can deal with a constant field offset and non-orthogonality issues and does not require any external reference. The calibration is done by finding an estimator that yields the calibration parameters and produces the best geometric fit to the sensor readings. A comprehensive model considering the physical, algorithmic and hardware properties of the magnetometer of the survey system is presented. The geometric ellipsoid fitting approach is parametrically tested. The calibration procedure reduced the root-mean-squared noise from the order of 104 nT to less than 10 nT with variance lower than 1 nT in a complete 360 degrees rotation in the natural earth magnetic field., Comment: Accepted to IEEE Transactions On Magnetics

Modern magnetic sensor arrays conventionally utilize state of the art low power magnetometers such as parallel and orthogonal fluxgates. Low power fluxgates tend to have large Barkhausen jumps that appear as a dc jump in the fluxgate output. This phenomenon deteriorates the signal fidelity and effectively increases the internal sensor noise. Even if sensors that are more prone to dc jumps can be screened during production, the conventional noise measurement does not always catch the dc jump because of its sparsity. Moreover, dc jumps persist in almost all the sensor cores although at a slower but still intolerable rate. Even if dc jumps can be easily detected in a shielded environment, when deployed in presence of natural noise and clutter, it can be hard to positively detect them. This work fills this gap and presents algorithms that distinguish dc jumps embedded in natural magnetic field data. To improve robustness to noise, we developed two machine learning algorithms that employ temporal and statistical physical-based features of a pre-acquired and well-known experimental data set. The first algorithm employs a support vector machine classifier, while the second is based on a neural network architecture. We compare these new approaches to a more classical kernel-based method. To that purpose, the receiver operating characteristic curve is generated, which allows diagnosis ability of the different classifiers by comparing their performances across various operation points. The accuracy of the machine learning-based algorithms over the classic method is highly emphasized. In addition, high generalization and robustness of the neural network can be concluded, based on the rapid convergence of the corresponding receiver operating characteristic curves., Comment: Accepted to IEEE Magnetics Letters

A linear dynamical system is called positive if its flow maps the non-negative orthant to itself. More precisely, it maps the set of vectors with zero sign variations to itself. A linear dynamical system is called $k$-positive if its flow maps the set of vectors with up to $k-1$ sign variations to itself. A nonlinear dynamical system is called $k$-cooperative if its variational system, which is a time-varying linear dynamical system, is $k$-positive. These systems have special asymptotic properties. For example, it was recently shown that strongly $2$-cooperative systems satisfy a strong Poincar\'{e}-Bendixson property. Positivity and~$k$-positivity are easy to verify in terms of the sign-pattern of the matrix in the dynamics. However, these sign conditions are not invariant under a coordinate transformation. A natural question is to determine if a given~$n$-dimensional system is $k$-positive up to a coordinate transformation. We study this problem for two special kinds of transformations: permutations and scaling by a signature matrix. For any $n\geq 4$ and~$k\in\{2,\dots, n-2\}$, we provide a graph-theoretical necessary and sufficient condition for $k$-positivity up to such coordinate transformations. We describe an application of our results to a specific class of Lotka-Volterra systems.

The dynamics of linear positive systems map the positive orthant to itself. In other words, it maps a set of vectors with zero sign variations to itself. This raises the following question: what linear systems map the set of vectors with $k$ sign variations to itself? We address this question using tools from the theory of cooperative dynamical systems and the theory of totally positive matrices. This yields a generalization of positive linear systems called $k$-positive linear systems, that reduces to positive systems for $k=1$. We describe applications of this new type of systems to the analysis of nonlinear dynamical systems. In particular, we show that such systems admit certain explicit invariant sets, and for the case $k=2$ establish the Poincar\'{e}-Bendixson property for any bounded trajectory.

Smillie (1984) proved an interesting result on the stability of nonlinear, time-invariant, strongly cooperative, and tridiagonal dynamical systems. This result has found many applications in models from various fields including biology, ecology, and chemistry. Smith (1991) has extended Smillie's result and proved entrainment in the case where the vector field is time-varying and periodic. We use the theory of linear totally nonnegative differential systems developed by Schwarz (1970) to give a generalization of these two results. This is based on weakening the requirement for strong cooperativity to cooperativity, and adding an additional observability-type condition., Comment: arXiv admin note: text overlap with arXiv:1802.09590

Using a graph-theoretic approach, we derive a new sufficient condition for observability of a Boolean control network (BCN). Based on this condition, we describe two algorithms: the first selects a set of nodes so that observing this set makes the BCN observable. The second algorithm builds an observer for the observable BCN. Both algorithms are sub-optimal, as they are based on a sufficient but not necessary condition for observability. Yet their time-complexity is linear in the length of the description of the BCN, rendering them feasible for large-scale networks. We discuss how these results can be used to provide a sub-optimal yet polynomial-complexity algorithm for the minimal observability problem in BCNs. Some of the theoretical results are demonstrated using a BCN model of the core network regulating the mammalian cell cycle., Comment: arXiv admin note: text overlap with arXiv:1706.04072

Many complex systems in biology, physics, and engineering include a large number of state-variables, and measuring the full state of the system is often impossible. Typically, a set of sensors is used to measure part of the state-variables. A system is called observable if these measurements allow to reconstruct the entire state of the system. When the system is not observable, an important and practical problem is how to add a \emph{minimal} number of sensors so that the system becomes observable. This minimal observability problem is practically useful and theoretically interesting, as it pinpoints the most informative nodes in the system. We consider the minimal observability problem for an important special class of Boolean networks, called conjunctive Boolean networks (CBNs). Using a graph-theoretic approach, we provide a necessary and sufficient condition for observability of a CBN with $n$ state-variables, and an efficient~$O(n^2)$-time algorithm for solving the minimal observability problem. We demonstrate the usefulness of these results by studying the properties of a class of random CBNs., Comment: Revised version. Date: Dec 6, 2017

Given a conjunctive Boolean network (CBN) with $n$ state-variables, we consider the problem of finding a minimal set of state-variables to directly affect with an input so that the resulting conjunctive Boolean control network (CBCN) is controllable. We give a necessary and sufficient condition for controllability of a CBCN; an $O(n^2)$-time algorithm for testing controllability; and prove that nonetheless the minimal controllability problem for CBNs is NP-hard.