1,253 research outputs found
On Measuring Non-Recursive Trade-Offs
We investigate the phenomenon of non-recursive trade-offs between
descriptional systems in an abstract fashion. We aim at categorizing
non-recursive trade-offs by bounds on their growth rate, and show how to deduce
such bounds in general. We also identify criteria which, in the spirit of
abstract language theory, allow us to deduce non-recursive tradeoffs from
effective closure properties of language families on the one hand, and
differences in the decidability status of basic decision problems on the other.
We develop a qualitative classification of non-recursive trade-offs in order to
obtain a better understanding of this very fundamental behaviour of
descriptional systems
Anytime Hierarchical Clustering
We propose a new anytime hierarchical clustering method that iteratively
transforms an arbitrary initial hierarchy on the configuration of measurements
along a sequence of trees we prove for a fixed data set must terminate in a
chain of nested partitions that satisfies a natural homogeneity requirement.
Each recursive step re-edits the tree so as to improve a local measure of
cluster homogeneity that is compatible with a number of commonly used (e.g.,
single, average, complete) linkage functions. As an alternative to the standard
batch algorithms, we present numerical evidence to suggest that appropriate
adaptations of this method can yield decentralized, scalable algorithms
suitable for distributed/parallel computation of clustering hierarchies and
online tracking of clustering trees applicable to large, dynamically changing
databases and anomaly detection.Comment: 13 pages, 6 figures, 5 tables, in preparation for submission to a
conferenc
Semi-autonomous Intersection Collision Avoidance through Job-shop Scheduling
In this paper, we design a supervisor to prevent vehicle collisions at
intersections. An intersection is modeled as an area containing multiple
conflict points where vehicle paths cross in the future. At every time step,
the supervisor determines whether there will be more than one vehicle in the
vicinity of a conflict point at the same time. If there is, then an impending
collision is detected, and the supervisor overrides the drivers to avoid
collision. A major challenge in the design of a supervisor as opposed to an
autonomous vehicle controller is to verify whether future collisions will occur
based on the current drivers choices. This verification problem is particularly
hard due to the large number of vehicles often involved in intersection
collision, to the multitude of conflict points, and to the vehicles dynamics.
In order to solve the verification problem, we translate the problem to a
job-shop scheduling problem that yields equivalent answers. The job-shop
scheduling problem can, in turn, be transformed into a mixed-integer linear
program when the vehicle dynamics are first-order dynamics, and can thus be
solved by using a commercial solver.Comment: Submitted to Hybrid Systems: Computation and Control (HSCC) 201
Compact atomic descriptors enable accurate predictions via linear models
We probe the accuracy of linear ridge regression employing a three-body local density representation derived from the atomic cluster expansion. We benchmark the accuracy of this framework in the prediction of formation energies and atomic forces in molecules and solids. We find that such a simple regression framework performs on par with state-of-the-art machine learning methods which are, in most cases, more complex and more computationally demanding. Subsequently, we look for ways to sparsify the descriptor and further improve the computational efficiency of the method. To this aim, we use both principal component analysis and least absolute shrinkage operator regression for energy fitting on six single-element datasets. Both methods highlight the possibility of constructing a descriptor that is four times smaller than the original with a similar or even improved accuracy. Furthermore, we find that the reduced descriptors share a sizable fraction of their features across the six independent datasets, hinting at the possibility of designing material-agnostic, optimally compressed, and accurate descriptors
On the equivalence, containment, and covering problems for the regular and context-free languages
We consider the complexity of the equivalence and containment problems for regular expressions and context-free grammars, concentrating on the relationship between complexity and various language properties. Finiteness and boundedness of languages are shown to play important roles in the complexity of these problems. An encoding into grammars of Turing machine computations exponential in the size of the grammar is used to prove several exponential lower bounds. These lower bounds include exponential time for testing equivalence of grammars generating finite sets, and exponential space for testing equivalence of non-self-embedding grammars. Several problems which might be complex because of this encoding are shown to simplify for linear grammars. Other problems considered include grammatical covering and structural equivalence for right-linear, linear, and arbitrary grammars
- …