On the Disambiguation of Weighted Automata

We present a disambiguation algorithm for weighted automata. The algorithm admits two main stages: a pre-disambiguation stage followed by a transition removal stage. We give a detailed description of the algorithm and the proof of its correctness. The algorithm is not applicable to all weighted automata but we prove sufficient conditions for its applicability in the case of the tropical semiring by introducing the *weak twins property*. In particular, the algorithm can be used with all acyclic weighted automata, relevant to applications. While disambiguation can sometimes be achieved using determinization, our disambiguation algorithm in some cases can return a result that is exponentially smaller than any equivalent deterministic automaton. We also present some empirical evidence of the space benefits of disambiguation over determinization in speech recognition and machine translation applications

Phase space polarization and the topological string: a case study

We review and elaborate on our discussion in hep-th/0606112 on the interplay between the target space and the worldsheet description of the open topological string partition function, for the example of the conifold. We discuss the appropriate phase space and canonical form for the system. We find a map between choices of polarization and the worldsheet description, based on which we study the behavior of the partition function under canonical transformations.Comment: 18 pages, invited review for MPL

Parallel Metric Tree Embedding based on an Algebraic View on Moore-Bellman-Ford

A \emph{metric tree embedding} of expected \emph{stretch~$\alpha \geq 1$} maps a weighted $n$-node graph $G = (V, E, \omega)$ to a weighted tree $T = (V_T, E_T, \omega_T)$ with $V \subseteq V_T$ such that, for all $v,w \in V$, $\operatorname{dist}(v, w, G) \leq \operatorname{dist}(v, w, T)$ and $operatorname{E}[\operatorname{dist}(v, w, T)] \leq \alpha \operatorname{dist}(v, w, G)$. Such embeddings are highly useful for designing fast approximation algorithms, as many hard problems are easy to solve on tree instances. However, to date the best parallel $(\operatorname{polylog} n)$-depth algorithm that achieves an asymptotically optimal expected stretch of $\alpha \in \operatorname{O}(\log n)$ requires $\operatorname{\Omega}(n^2)$ work and a metric as input. In this paper, we show how to achieve the same guarantees using $\operatorname{polylog} n$ depth and $\operatorname{\tilde{O}}(m^{1+\epsilon})$ work, where $m = |E|$ and $\epsilon > 0$ is an arbitrarily small constant. Moreover, one may further reduce the work to $\operatorname{\tilde{O}}(m + n^{1+\epsilon})$ at the expense of increasing the expected stretch to $\operatorname{O}(\epsilon^{-1} \log n)$. Our main tool in deriving these parallel algorithms is an algebraic characterization of a generalization of the classic Moore-Bellman-Ford algorithm. We consider this framework, which subsumes a variety of previous "Moore-Bellman-Ford-like" algorithms, to be of independent interest and discuss it in depth. In our tree embedding algorithm, we leverage it for providing efficient query access to an approximate metric that allows sampling the tree using $\operatorname{polylog} n$ depth and $\operatorname{\tilde{O}}(m)$ work. We illustrate the generality and versatility of our techniques by various examples and a number of additional results

Residues and Topological Yang-Mills Theory in Two Dimensions

A residue formula which evaluates any correlation function of topological $SU_n$ Yang-Mills theory with arbitrary magnetic flux insertion in two dimensions are obtained. Deformations of the system by two form operators are investigated in some detail. The method of the diagonalization of a matrix valued field turns out to be useful to compute various physical quantities. As an application we find the operator that contracts a handle of a Riemann surface and a genus recursion relation.Comment: 23 pages, some references added, to appear in Rev.Math.Phy

Liveness-Based Garbage Collection for Lazy Languages

We consider the problem of reducing the memory required to run lazy first-order functional programs. Our approach is to analyze programs for liveness of heap-allocated data. The result of the analysis is used to preserve only live data---a subset of reachable data---during garbage collection. The result is an increase in the garbage reclaimed and a reduction in the peak memory requirement of programs. While this technique has already been shown to yield benefits for eager first-order languages, the lack of a statically determinable execution order and the presence of closures pose new challenges for lazy languages. These require changes both in the liveness analysis itself and in the design of the garbage collector. To show the effectiveness of our method, we implemented a copying collector that uses the results of the liveness analysis to preserve live objects, both evaluated (i.e., in WHNF) and closures. Our experiments confirm that for programs running with a liveness-based garbage collector, there is a significant decrease in peak memory requirements. In addition, a sizable reduction in the number of collections ensures that in spite of using a more complex garbage collector, the execution times of programs running with liveness and reachability-based collectors remain comparable

Containment and equivalence of weighted automata: Probabilistic and max-plus cases

This paper surveys some results regarding decision problems for probabilistic and max-plus automata, such as containment and equivalence. Probabilistic and max-plus automata are part of the general family of weighted automata, whose semantics are maps from words to real values. Given two weighted automata, the equivalence problem asks whether their semantics are the same, and the containment problem whether one is point-wise smaller than the other one. These problems have been studied intensively and this paper will review some techniques used to show (un)decidability and state a list of open questions that still remain

4D printing of recoverable buckling-induced architected iron-based shape memory alloys

Architected materials exhibit extraordinary properties in comparison with conventional materials and structures, resulting in additional functionality and efficiency by engineering the geometry in harmony with the base material. Buckling-induced architected materials (BIAMs) are a class of architected materials that exhibit a significant potential to absorb and dissipate energy owing to their local instabilities. Previous studies have shown a trade-off between energy dissipation and geometrical recoverability in metallic BIAM, which limits their use in applications that require both of these features. This study, for the first time, presents 4D printing of buckling-induced architected iron-based shape memory alloys (BIA Fe-SMAs) using laser powder bed fusion (LPBF). The results show that 4D printing of BIA Fe-SMAs can offer both energy dissipation and geometrical recoverability (i.e., recentring). The study was conducted on two different alloy compositions of Fe-17Mn-5Si-10Cr-4Ni. Quasi-static cyclic tests were performed on the two BIA Fe-SMAs, and the samples were subsequently heated to 200 °C to activate the shape memory effect (SME) of the base material. The samples could recover the residual deformations accumulated during the cyclic load owing to the SME of the base material, which led to shape-recovery ratios of 96.8 and 98.7% for the studied BIA Fe-SMAs. The results of this study demonstrate that 4D printing of BIA Fe-SMAs can yield an enhanced multi-functional behavior by combining the material's inherent functional behavior with the functionalities of the architected structure. Notably, BIA Fe-SMA samples could reconfigure their initial shape without damage after densification, which sets them apart from conventional crushable lattices

Hybrid expansions for local structural relaxations

A model is constructed in which pair potentials are combined with the cluster expansion method in order to better describe the energetics of structurally relaxed substitutional alloys. The effect of structural relaxations away from the ideal crystal positions, and the effect of ordering is described by interatomic-distance dependent pair potentials, while more subtle configurational aspects associated with correlations of three- and more sites are described purely within the cluster expansion formalism. Implementation of such a hybrid expansion in the context of the cluster variation method or Monte Carlo method gives improved ability to model phase stability in alloys from first-principles.Comment: 8 pages, 1 figur

Assessing the Positional Planimetric Accuracy of DBpedia Georeferenced Resources

International audienceAssessing the quality of the main linked data sources on the Web like DBpedia or Yago is an important research topic. The existing approaches for quality assessment mostly focus on determining whether data sources are compliant with Web of data best practices or on their completeness, semantic accuracy, consistency, relevancy or trustworthi-ness. In this article, we aim at assessing the accuracy of a particular type of information often associated with Web of data resources: direct spatial references. We present the approaches currently used for assessing the planimetric accuracy of geographic databases. We explain why they cannot be directly applied to the resources of the Web of data. Eventually , we propose an approach for assessing the planimetric accuracy of DBpedia resources, adapted to the open nature of this knowledge base

Reachability problems for products of matrices in semirings

We consider the following matrix reachability problem: given $r$ square matrices with entries in a semiring, is there a product of these matrices which attains a prescribed matrix? We define similarly the vector (resp. scalar) reachability problem, by requiring that the matrix product, acting by right multiplication on a prescribed row vector, gives another prescribed row vector (resp. when multiplied at left and right by prescribed row and column vectors, gives a prescribed scalar). We show that over any semiring, scalar reachability reduces to vector reachability which is equivalent to matrix reachability, and that for any of these problems, the specialization to any $r\geq 2$ is equivalent to the specialization to $r=2$. As an application of this result and of a theorem of Krob, we show that when $r=2$, the vector and matrix reachability problems are undecidable over the max-plus semiring $(Z\cup\{-\infty\},\max,+)$. We also show that the matrix, vector, and scalar reachability problems are decidable over semirings whose elements are ``positive'', like the tropical semiring $(N\cup\{+\infty\},\min,+)$.Comment: 21 page