Virasoro Constraints for Toric Bundles

We show that the Virasoro conjecture in Gromov--Witten theory holds for the the total space of a toric bundle $E \to B$ if and only if it holds for the base $B$. The main steps are: (i) we establish a localization formula that expresses Gromov--Witten invariants of $E$, equivariant with respect to the fiberwise torus action, in terms of genus-zero invariants of the toric fiber and all-genus invariants of $B$; and (ii) we pass to the non-equivariant limit in this formula, using Brown's mirror theorem for toric bundles.Comment: 24 page

Computing Genus-Zero Twisted Gromov-Witten Invariants

Twisted Gromov-Witten invariants are intersection numbers in moduli spaces of stable maps to a manifold or orbifold X which depend in addition on a vector bundle over X and an invertible multiplicative characteristic class. Special cases are closely related to local Gromov-Witten invariants of the bundle, and to genus-zero one-point invariants of complete intersections in X. We develop tools for computing genus-zero twisted Gromov-Witten invariants of orbifolds and apply them to several examples. We prove a "quantum Lefschetz theorem" which expresses genus-zero one-point Gromov-Witten invariants of a complete intersection in terms of those of the ambient orbifold X. We determine the genus-zero Gromov-Witten potential of the type A surface singularity C^2/Z_n. We also compute some genus-zero invariants of C^3/Z_3, verifying predictions of Aganagic-Bouchard-Klemm. In a self-contained Appendix, we determine the relationship between the quantum cohomology of the A_n surface singularity and that of its crepant resolution, thereby proving the Crepant Resolution Conjectures of Ruan and Bryan-Graber in this case.Comment: 46 pages. v2: corrected our description of the work of Davesh Maulik. v3 is the refereed version, with many changes: a new appendix containing the results from our preprint arXiv:0704.2034; another new appendix containing foundational results on Givental's Lagrangian cone and formal geometry; also a number of typos were corrected and some references adde

A Mirror Theorem for Toric Stacks

We prove a Givental-style mirror theorem for toric Deligne--Mumford stacks X. This determines the genus-zero Gromov--Witten invariants of X in terms of an explicit hypergeometric function, called the I-function, that takes values in the Chen--Ruan orbifold cohomology of X.Comment: 35 pages. v2: key references added. v3: errors corrected; formal setup changed; proofs simplified, clarified, and shortened; references added. v4: references updated. v5: references update

Parallel Index-Based Structural Graph Clustering and Its Approximation

SCAN (Structural Clustering Algorithm for Networks) is a well-studied, widely used graph clustering algorithm. For large graphs, however, sequential SCAN variants are prohibitively slow, and parallel SCAN variants do not effectively share work among queries with different SCAN parameter settings. Since users of SCAN often explore many parameter settings to find good clusterings, it is worthwhile to precompute an index that speeds up queries. This paper presents a practical and provably efficient parallel index-based SCAN algorithm based on GS*-Index, a recent sequential algorithm. Our parallel algorithm improves upon the asymptotic work of the sequential algorithm by using integer sorting. It is also highly parallel, achieving logarithmic span (parallel time) for both index construction and clustering queries. Furthermore, we apply locality-sensitive hashing (LSH) to design a novel approximate SCAN algorithm and prove guarantees for its clustering behavior. We present an experimental evaluation of our algorithms on large real-world graphs. On a 48-core machine with two-way hyper-threading, our parallel index construction achieves 50--151$\times$ speedup over the construction of GS*-Index. In fact, even on a single thread, our index construction algorithm is faster than GS*-Index. Our parallel index query implementation achieves 5--32$\times$ speedup over GS*-Index queries across a range of SCAN parameter values, and our implementation is always faster than ppSCAN, a state-of-the-art parallel SCAN algorithm. Moreover, our experiments show that applying LSH results in faster index construction while maintaining good clustering quality

Wall-Crossings in Toric Gromov-Witten Theory I: Crepant Examples

Let X be a Gorenstein orbifold and let Y be a crepant resolution of X. We state a conjecture relating the genus-zero Gromov--Witten invariants of X to those of Y, which differs in general from the Crepant Resolution Conjectures of Ruan and Bryan--Graber, and prove our conjecture when X = P(1,1,2) and X = P(1,1,1,3). As a consequence, we see that the original form of the Bryan--Graber Conjecture holds for P(1,1,2) but is probably false for P(1,1,1,3). Our methods are based on mirror symmetry for toric orbifolds.Comment: 71 pages, v2: typos corrected and references modified, v3: corrected errors in Proposition 2.9 and in Summary, v4: major revision, exposition unified from a viewpoint of VSHS, many signpostings for the logical structure; the authorship has changed, with Alessio Corti withdrawin

Post-Fire Assessment of Prestressed Concrete Bridges in Indiana

This project focused on evaluating the effects of fire-induced damage on concrete bridge elements, including prestressed concrete bridge girders. A series of controlled heating experiments, pool fire tests, material tests, and structural loading tests were conducted. Experimental results indicate that the portion of concrete subjected to temperatures higher than 400°C loses significant amounts of calcium hydroxide (CH). Decomposition of CH increases porosity and causes significant cracking. The portion of concrete exposed to temperatures higher than 400°C should be repaired or replaced. When subjected to ISO-834 standard fire heating, approximately 0.25 in. and 0.75 in. of concrete from the exposed surface are damaged after 40 minutes and 80 minutes of heating, respectively. Prestressed concrete girders exposed to about 50 minutes of hydrocarbon fire undergo superficial concrete material damage with loss of CH and extensive cracking and spalling extending to the depth of 0.75–1.0 in. from the exposed surface. These girders do not undergo significant reduction in flexural strength or shear strength. The reduction in the initial stiffness may be notable due to concrete cracking and spalling. Bridge inspectors can use these findings to infer the extent of material and structural damage to prestressed concrete bridge girders in the event of a fire and develop a post-fire assessment plan

Adversarial Policies Beat Superhuman Go AIs

We attack the state-of-the-art Go-playing AI system KataGo by training adversarial policies against it, achieving a >97% win rate against KataGo running at superhuman settings. Our adversaries do not win by playing Go well. Instead, they trick KataGo into making serious blunders. Our attack transfers zero-shot to other superhuman Go-playing AIs, and is comprehensible to the extent that human experts can implement it without algorithmic assistance to consistently beat superhuman AIs. The core vulnerability uncovered by our attack persists even in KataGo agents adversarially trained to defend against our attack. Our results demonstrate that even superhuman AI systems may harbor surprising failure modes. Example games are available https://goattack.far.ai/.Comment: Accepted to ICML 2023, see paper for changelo