Seiberg-Witten Curve for the E-String Theory

We construct the Seiberg-Witten curve for the E-string theory in six-dimensions. The curve is expressed in terms of affine E_8 characters up to level 6 and is determined by using the mirror-type transformation so that it reproduces the number of holomorphic curves in the Calabi-Yau manifold and the amplitudes of N=4 U(n) Yang-Mills theory on 1/2 K3. We also show that our curve flows to known five- and four-dimensional Seiberg-Witten curves in suitable limits.Comment: 18 pages, 1 figure; appendix C adde

Exceptional String: Instanton Expansions and Seiberg-Witten Curve

We investigate instanton expansions of partition functions of several toric E-string models using local mirror symmetry and elliptic modular forms. We also develop a method to obtain the Seiberg--Witten curve of E-string with arbitrary Wilson lines with the help of elliptic functions.Comment: 71 pages, three Wilson line

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

Giant magnetoimpedance in Vitrovac amorphous ribbons over [0.3-400 MHz] frequency range

Giant magneto impedance (GMI) effect for as-cast Vitrovac$^{\textrm{\scriptsize\textregistered}}$ amorphous ribbons (Vacuumschmelze, Germany) in two configurations (parallel and normal to the ribbon axis) is studied over the frequency range [0.3-400 MHz] and under static magnetic fields -160 Oe $< H_{dc} <$+160 Oe. A variety of peak features and GMI ratio values, falling within a small field range, are observed and discussed.Comment: Paper submitted to International Conference on Magnetism 2003 (ICM Rome 2003

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

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

MQCD, ('Barely') G_2 Manifolds and (Orientifold of) a Compact Calabi-Yau

We begin with a discussion on two apparently disconnected topics - one related to nonperturbative superpotential generated from wrapping an M2-brane around a supersymmetric three cycle embedded in a G_2-manifold evaluated by the path-integral inside a path-integral approach of [1], and the other centered around the compact Calabi-Yau CY_3(3,243) expressed as a blow-up of a degree-24 Fermat hypersurface in WCP^4[1,1,2,8,12]. For the former, we compare the results with the ones of Witten on heterotic world-sheet instantons [2]. The subtopics covered in the latter include an N=1 triality between Heterotic, M- and F-theories, evaluation of RP^2-instanton superpotential, Picard-Fuchs equation for the mirror Landau-Ginsburg model corresponding to CY_3(3,243), D=11 supergravity corresponding to M-theory compactified on a `barely' G_2 manifold involving CY_3(3,243) and a conjecture related to the action of antiholomorphic involution on period integrals. We then show an indirect connection between the two topics by showing a connection between each one of the two and Witten's MQCD [3]. As an aside, we show that in the limit of vanishing "\zeta", a complex constant that appears in the Riemann surfaces relevant to definining the boundary conditions for the domain wall in MQCD, the infinite series of [4] used to represent a suitable embedding of a supersymmetric 3-cycle in a G_2-mannifold, can be summed.Comment: 37 pages, LaTex; PARTLY based on talks given at ``Seventh Workshop on QCD" [session on "Strings, Branes and (De-)Construction"], Jan 6-10, 2003, La Cittadelle, Villefranche-sur-Mer, France; Fourth Workshop on ``Gauge Fields and Strings", Feb 25-Mar 1, 2003, Jena, Germany; ``XII Oporto Meeting on Geometry, Topology and Strings", July 17-20, 2003, Oporto, Portugal; "SQS03" - International Workshop on "Supersymmetries and Quantum Symmetries', July 24-29, 2003, JINR, Dubna, Russia; poster presented at ``XIV International Congress on Mathematical Physics", July 28-Aug 2, 2003, Lisbon, Portuga

Finite Automata for the Sub- and Superword Closure of CFLs: Descriptional and Computational Complexity

We answer two open questions by (Gruber, Holzer, Kutrib, 2009) on the state-complexity of representing sub- or superword closures of context-free grammars (CFGs): (1) We prove a (tight) upper bound of $2^{\mathcal{O}(n)}$ on the size of nondeterministic finite automata (NFAs) representing the subword closure of a CFG of size $n$. (2) We present a family of CFGs for which the minimal deterministic finite automata representing their subword closure matches the upper-bound of $2^{2^{\mathcal{O}(n)}}$ following from (1). Furthermore, we prove that the inequivalence problem for NFAs representing sub- or superword-closed languages is only NP-complete as opposed to PSPACE-complete for general NFAs. Finally, we extend our results into an approximation method to attack inequivalence problems for CFGs