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Let $X$ be a compact manifold, $G$ a Lie group, $P \to X$ a principal $G$-bundle, and $\mathcal{B}_P$ the infinite-dimensional moduli space of connections on $P$ modulo gauge. For a real elliptic operator $E_\bullet$ we previously studied orientations on the real determinant line bundle over $\mathcal{B}_P$. These are used to construct orientations in the usual sense on smooth gauge theory moduli spaces, and have been extensively studied since the work of Donaldson. Here we consider complex elliptic operators $F_\bullet$ and introduce the idea of spin structures, square roots of the complex determinant line bundle of $F_\bullet$. These may be used to construct spin structures in the usual sense on smooth complex gauge theory moduli spaces. We study the existence and classification of such spin structures. Our main result identifies spin structures on $X$ with orientations on $X \times S^1$. Thus, if $P \to X$ and $Q \to X \times S^1$ are principal $G$-bundles with $Q|_{X\times\{1\}} \cong P$, we relate spin structures on $(\mathcal{B}_P,F_\bullet)$ to orientations on $(\mathcal{B}_Q,E_\bullet)$ for a certain class of operators $F_\bullet$ on $X$ and $E_\bullet$ on $X\times S^1$. Combined with arXiv:1811.02405, we obtain canonical spin structures for positive Diracians on spin 6-manifolds and gauge groups $G=U(m), SU(m)$. In a sequel arXiv:2001.00113 we apply this to define canonical orientation data for all Calabi-Yau 3-folds $X$ over the complex numbers, as in Kontsevich-Soibelman arXiv:0811.2435, solving a long-standing problem in Donaldson-Thomas theory., Comment: 53 pages. (v3) final version, to appear in Advances in Mathematics

The Web Conference 2019 : proceedings of The World Wide Web Conference WWW 2019 : May 13-17, 2019, San Francisco, CA, USA / editors: Ling Liu (Georgia Tech, USA), Ryen White (Microsoft Research, USA), Amin Mantrach (Criteo AI Lab, France), Fabrizio Silvestri (Facebook, UK), Julian McAuley (University of California at San Diego, USA), Ricardo Baeza-Yates (NTENT & Northeastern University, USA), Leila Zia (Wikimedia Foundation, USA) ; Association for Computing Machinery World Wide Web Conference, WWW 2019, San Francisco, CA, USA, 13 May 2019 - 17 May 2019; New York, NY : ACM Press 1634-1645 (2019). doi:10.1145/3308558.3313440, Published by ACM Press, New York, NY

We prove that the observational equivalence problem for a finitary fragment of the programming langauge ML is recursively equivalent to the reachability problem for extended branching vector addition systems with states (EBVASS). This result has two natural and independent parts. We first prove that the observational equivalence problem is equivalent to the emptiness problem for a new class of class memory automata equipped with a visibly pushdown stack, called Visibly Pushdown Class Memory Automata (VPCMA). Our proof uses the fully abstract game semantics of the language. We then prove that the VPCMA emptiness problem is equivalent to the reachability problem for EBVASS. The results of this article complete our programme to give an automata classification of the ML types with respect to the observational equivalence problem for closed terms.

Some of the most well-celebrated constructions of metastable de Sitter vacua from string theory, such as the KKLT proposal, involve the interplay of gaugino condensation on a D7-brane stack and an uplift by a positive tension object. These constructions have recently been challenged using arguments that rely on the trace-reversed and integrated 10d Einstein equation. We give a critical assessment of such concerns. We first relate an integrated 10d Einstein equation to the extremization condition for a 10d-derived 4d effective potential. Then we argue how to obtain the latter from a 10d action which incorporates gaugino condensation in a (recently proposed) manifestly finite, perfect-square form. This effective potential is consistent with 4d supergravity and does not present obstacles for an uplifted minimum. Moreover, within standard approximations, we understand the uplift explicitly in one of the popular versions of the integrated 10d equation. Our conclusion is that de Sitter constructions of the KKLT type cannot be dismissed simply based on the integrated 10d equations considered so far., 23 pages; v2: Refs. and more details on the chosen technical approach added; v3: published in JHEP

For a split reductive group G over a finite field, we show that the intersection (cohomology) motive of the moduli stack of iterated G-shtukas with bounded modification and level structure is defined independently of the standard conjectures on motivic t-structures on triangulated categories of motives. This is in accordance with general expectations on the independence of l in the Langlands correspondence for function fields., Added a comparison with equivariant higher Chow groups, further minor edits. Final version, to appear in Forum of Mathematics Sigma. The former section 6 on Motives on Witt vector affine flag varieties has been removed and will appear elsewhere

Passing argument to functions is simple when you have four or fewer non-floating-point arguments. You use rcx, rdx, r8, and r9 and provide shadow space on the stack before calling the function. After the call, you re-adjust the stack for the shadow space, and everything is fine. If you have more than four arguments, things are more complicated.

In the setting of the geometric Langlands conjecture, we argue that the phenomenon of divergence at infinity on Bun G {\operatorname{Bun}_{G}} (that is, the difference between ! {!} -extensions and * {*} -extensions) is controlled, Langlands-dually, by the locus of semisimple G ˇ {{\check{G}}} -local systems. To see this, we first rephrase the question in terms of Deligne–Lusztig duality and then study the Deligne–Lusztig functor 𝖣𝖫 G spec {\mathsf{DL}_{G}^{\mathrm{spec}}} acting on the spectral Langlands DG category IndCoh 𝒩 ⁢ ( LS G ) {{\mathrm{IndCoh}}_{\mathcal{N}}({\mathrm{LS}}_{G})} . We prove that 𝖣𝖫 G spec {\mathsf{DL}_{G}^{\mathrm{spec}}} is the projection IndCoh 𝒩 ⁢ ( LS G ) ↠ QCoh ⁢ ( LS G ) {{\mathrm{IndCoh}}_{\mathcal{N}}({\mathrm{LS}}_{G})\twoheadrightarrow{\mathrm{% QCoh}}({\mathrm{LS}}_{G})} , followed by the action of a coherent D-module St G ∈ 𝔇 ⁢ ( LS G ) {{\mathrm{St}}_{G}\in\mathfrak{D}({\mathrm{LS}}_{G})} , which we call the Steinberg D-module. We argue that St G {{\mathrm{St}}_{G}} might be regarded as the dualizing sheaf of the locus of semisimple G-local systems. We also show that 𝖣𝖫 G spec {\mathsf{DL}_{G}^{\mathrm{spec}}} , while far from being conservative, is fully faithful on the subcategory of compact objects.

We introduce a variant of the birational symbols group of Kontsevich, Pestun, and the second author, and use this to define birational invariants of algebraic orbifolds., Comment: 20 pages

We prove that K-polystable log Fano pairs have reductive automorphism groups. In fact, we deduce this statement by establishing more general results concerning the S-completeness and $\Theta$-reductivity of the moduli of K-semistable log Fano pairs. Assuming the conjecture that K-semistability is an open condition, we prove that the Artin stack parametrizing K-semistable Fano varieties admits a separated good moduli space., Comment: 32 pages. Final version. To appear in Inventiones Math

Refers toJoost EngelfrietIterated stack automata and complexity classesInformation and Computation, Volume 95, Issue 1, November 1991, Pages 21-75https://doi.org/10.1016/0890-5401(91)90015-T

We compute the Picard group of the universal abelian variety over the moduli stack $\mathscr A_{g,n}$ of principally polarized abelian varieties over $\mathbb{C}$ with a symplectic principal level $n$-structure. We then prove that over $\mathbb{C}$ the statement of the Franchetta conjecture holds in a suitable form for $\mathscr A_{g,n}$., Comment: 17 pages

We consider the model of pushdown vector addition systems with resets. These consist of vector addition systems that have access to a pushdown stack and have instructions to reset counters. For this model, we study the coverability problem. In the absence of resets, this problem is known to be decidable for one-dimensional pushdown vector addition systems, but decidability is open for general pushdown vector addition systems. Moreover, coverability is known to be decidable for reset vector addition systems without a pushdown stack. We show in this note that the problem is undecidable for one-dimensional pushdown vector addition systems with resets., Comment: 8 pages

This document defines a YANG module for the DS-Lite Address Family Transition Router (AFTR) and Basic Bridging BroadBand (B4) elements. Editorial Note (To be removed by RFC Editor) Please update these statements in the document with the RFC number to be assigned to this document: o "This version of this YANG module is part of RFC XXXX;" o "RFC XXXX: A YANG Data Model for Dual-Stack Lite (DS-Lite)"; o "reference: RFC XXXX" Please update the "revision" date of the YANG module. Also, update this sentence with the RFC number to be assigned to I- D.ietf-opsawg-nat-yang: o "RFC YYYY: A YANG Module for Network Address Translation (NAT) and Network Prefix Translation (NPT)"

We present our submission to the IWCS 2019 shared task on semantic parsing, a transition-based parser that uses explicit word-meaning pairings, but no explicit representation of syntax. Parsing decisions are made based on vector representations of parser states, encoded via stack-LSTMs (Ballesteros et al., 2017), as well as some heuristic rules. Our system reaches 70.88% f-score in the competition.

Let G be a connected reductive complex algebraic group, and E a complex elliptic curve. Let G E denote the connected component of the trivial bundle in the stack of semistable G-bundles on E. We introduce a complex analytic uniformization of G E by adjoint quotients of reductive subgroups of the loop group of G. This can be viewed as a nonabelian version of the classical complex analytic uniformization E ≃ C ⁎ / q Z . We similarly construct a complex analytic uniformization of G itself via the exponential map, providing a nonabelian version of the standard isomorphism C ⁎ ≃ C / Z , and a complex analytic uniformization of G E generalizing the standard presentation E ≃ C / ( Z ⊕ Z τ ) . Finally, we apply these results to the study of sheaves with nilpotent singular support. As an application to Betti geometric Langlands conjecture in genus 1, we define a functor from S h N ( G E ) (the semistable part of the automorphic category) to IndCoh N ˇ ( Locsys G ˇ ( E ) ) (the spectral category).

Triangulated derived categories are considered which establish a commutative scheme (triangle) for determine or compute a hypercohomology of motives for the obtaining of solutions of the field equations. The determination of this hypercohomology arises of the derived category $\textup{DM}_{\textup {gm}}(k)$, which is of the motivic objects whose image is under $\textup {Spec}(k)$ that is to say, an equivalence of the underlying triangulated tensor categories, compatible with respective functors on $\textup{Sm}_{k}^{\textup{Op}}$. The geometrical motives will be risked with the moduli stack to holomorphic bundles. Likewise, is analysed the special case where complexes $C=\mathbb{Q}(q)$, are obtained when cohomology groups of the isomorphism $H_{\acute{e}t}^{p}(X,F_{\acute{e}t})\cong (X,F_{Nis})$, can be vanished for $p>\textup{dim}(Y)$. We observe also the Beilinson-Soul$\acute{e}$ vanishing conjectures where we have the vanishing $H^{p}(F,\mathbb{Q}(q))=0, \ \ \textup{if} \ \ p\leq0,$ and $q>0$, which confirms the before established. Then survives a hypercohomology $\mathbb{H}^{q}(X,\mathbb{Q})$. Then its objects are in $\textup{Spec(Sm}_{k})$. Likewise, for the complex Riemannian manifold the integrals of this hypercohomology are those whose functors image will be in $\textup{Spec}_{H}\textup{SymT(OP}_{L_{G}}(D))$, which is the variety of opers on the formal disk $D$, or neighborhood of all point in a surface $\Sigma$. Likewise, will be proved that $\mathrm{H}^{\vee}$, has the decomposing in components as hyper-cohomology groups which can be characterized as H- states in Vec$_\mathbb{C}$, for field equations $d \textup{da}=0$, on the general linear group with $k=\mathbb{C}$. A physics re-interpretation of the superposing, to the dual of the spectrum $\mathrm{H}^{\vee}$, whose hypercohomology is a quantized version of the cohomology space $H^{q}(Bun_{G},\mathcal{D}^{s})=\mathbb{H}^{q}_{G[[z]]}(\mathrm{G},(\land^{\bullet}[\Sigma^{0}]\otimes \mathbb{V}_{critical},\partial))$ is the corresponding deformed derived category for densities $\mathrm{h} \in \mathrm{H}$, in quantum field theory.

In this paper we prove that every proper Lie groupoid admits a desingularization to a regular proper Lie groupoid. When equipped with a Riemannian metric, we show that it admits a desingularization to a regular Riemannian proper Lie groupoid, arbitrarily close to the original one in the Gromov-Hausdorff distance between the quotient spaces. We construct the desingularization via a successive blow-up construction on a proper Lie groupoid. We also prove that our construction of the desingularization is invariant under Morita equivalence of groupoids, showing that it is a desingularization of the underlying differentiable stack., Comment: 27 pages

We use a method for determining the number of preimages of any permutation under the stack-sorting map in order to obtain recursive upper bounds for the numbers $W_t(n)$ and $W_t(n,k)$ of $t$-stack sortable permutations of length $n$ and $t$-stack sortable permutations of length $n$ with exactly $k$ descents. From these bounds, we are able to significantly improve the best known upper bounds for $\displaystyle{\lim_{n\to\infty}\sqrt[n]{W_t(n)}}$ when $t=3$ and $t=4$., Comment: 15 pages, 3 figures

In the present paper we consider the following question: does there exist a Neron model for families of Jacobians of curves with sections? By applying a construction of the author of universal compactified Jacobians over the moduli stack of reduced curves with markings and a result by J. Kass, we give a positive answer to the question holding for curves with planar singularities.

We prove that the dg category of perfect complexes on a smooth, proper Deligne-Mumford stack over a field of characteristic zero is geometric in the sense of Orlov, and in particular smooth and proper. On the level of triangulated categories, this means that the derived category of perfect complexes embeds as an admissible subcategory into the bounded derived category of coherent sheaves on a smooth, projective variety. The same holds for a smooth, projective, tame Artin stack over an arbitrary field., 31 pages

We propose a conjectural determination of the Gromov–Witten theory of a root stack along a smooth divisor. We verify our conjecture under an additional assumption.

We present an underapproximation for context-free languages by filtering out runs of the underlying pushdown automaton depending on how the stack height evolves over time. In particular, we assign to each run a number quantifying the oscillating behavior of the stack along the run. We study languages accepted by pushdown automata restricted to k-oscillating runs. We relate oscillation on pushdown automata with a counterpart restriction on context-free grammars. We also provide a way to filter all but the k-oscillating runs from a given PDA by annotating stack symbols with information about the oscillation. Finally, we study closure properties of the defined class of languages and the complexity of the k-emptiness problem asking, given a pushdown automaton P and k >= 0, whether P has a k-oscillating run. We show that, when k is not part of the input, the k-emptiness problem is NLOGSPACE-complete., In Proceedings GandALF 2016, arXiv:1609.03648

These notes present and survey results about spaces and moduli spaces of complete Riemannian metrics with curvature bounds on open and closed manifolds, here focussing mainly on connectedness and disconnectedness properties. They also discuss several open problems and questions in the field.

We investigate the spaces of rational curves on a general hypersurface. In particular, we show that for a general degree d hypersurface in ℙ n {\mathbb{P}^{n}} with n ≥ d + 2 {n\geq d+2} , the space ℳ ¯ 0 , 0 ⁢ ( X , e ) {\overline{\mathcal{M}}_{0,0}(X,e)} of degree e Kontsevich stable maps from a rational curve to X is an irreducible local complete intersection stack of dimension e ⁢ ( n - d + 1 ) + n - 4 {e(n-d+1)+n-4} . This resolves all but one case of a conjecture of Coskun, Harris and Starr, and also proves that the Gromov–Witten invariants of these hypersurfaces are enumerative.

Born approximation is a commonly used approximation in the simulation of seismic wave propagation. Calculation of the Green's function in Born approximation integral is essential for Born modeling. We derive a new Born formula based on the Gaussian beam representations of Green's functions. This procedure can be used to mitigate the problems like the caustic, shadow region, and multivalued traveltime caused by multipathing that traditional geometric ray theory cannot deal with. However, due to the characteristic of complex traveltime in the Gaussian beam, we present a new isochronous stack method for Gaussian beam based Born modeling. Additionally, two basic issues, background velocity and integral region selection, are discussed. Numerical results demonstrate the accuracy and efficiency of the Gaussian beam based Born theory and implementation.

Supercompilation is a program transformation technique that was first described by V. F. Turchin in the 1970s. In supercompilation, Turchin's relation as a similarity relation on call-stack configurations is used both for call-by-value and call-by-name semantics to terminate unfolding of the program being transformed. In this paper, we give a formal grammar model of call-by-name stack behaviour. We classify the model in terms of the Chomsky hierarchy and then formally prove that Turchin's relation can terminate all computations generated by the model., Comment: In Proceedings VPT 2016, arXiv:1607.01835

The Chow quotient of a toric variety by a subtorus, as defined by Kapranov-Sturmfels-Zelevinsky, coarsely represents the main component of the moduli space of stable toric varieties with a map to a fixed projective toric variety, as constructed by Alexeev and Brion. We show that, after endowing both spaces with the structure of a logarithmic stack, the resulting spaces are isomorphic. Along the way, we construct the Chow quotient stack and demonstrate several properties that it satisfies., Comment: Minor revisions-- version to appear in Algebraic Geometry

In this paper, we describe explicit relations in the symplectomorphism groups of toric hypersurfaces. To define the elements involved, we construct a proper stack of toric hypersurfaces with compactifying boundary representing toric hypersurface degenerations. Our relations arise through the study of the one dimensional strata of this stack. The results are then examined from the perspective of homological mirror symmetry where we view sequences of relations as maximal degenerations of Landau-Ginzburg models. We then study the B-model mirror to these degenerations, which gives a new mirror symmetry approach to the minimal model program.

Exploiting the description of rings of differential operators as Azumaya algebras on cotangent bundles, we show that the moduli stack of flat connections on a curve (allowed to acquire orbifold points) defined over an algebraically closed field of positive characteristic is \'etale locally equivalent to a moduli stack of Higgs bundles over the Hitchin base. We then study the interplay with stability and generalize a result of Laszlo-Pauly, concerning properness of the Hitchin map. Using Arinkin's autoduality of compactified Jacobians we extend the main result of Bezrukavnikov-Braverman, the Langlands correspondence for D-modules in positive characteristic for smooth spectral curves, to the locus of integral spectral curves., Comment: New version corrects Theorem 3.2 and Proposition 3.15

A stack of n pancakes can be rearranged in all n! ways by a sequence of n ! - 1 flips, and a stack of n 'burnt' pancakes can be rearranged in all 2 n n ! ways by a sequence of 2 n n ! - 1 flips. In both cases, a computer program can efficiently generate suitable solutions. We approach these tasks instead from a human perspective. How can we determine the next flip directly from the current stack? How can we flip the minimum or maximum number of (burnt) pancakes overall? What if we are only allowed to flip the top n - 2 , n - 1 , or n (burnt) pancakes? We answer the first question with simple successor rules that take worst-case O ( n ) -time and amortized O ( 1 ) -time. Then we answer the second question exactly for minimization, and provide conjectures for maximization. For the third question, we prove that solutions almost certainly exist for pancakes and burnt pancakes using only these three flips. More broadly, we discuss how efficiency and optimality can shape iterative solutions to Hamilton cycle problems in highly symmetric graphs.

Michelle Stack’s book on global university rankings is a timely addition to the Canadian discourse on higher education policy and practices given the widespread use of rankings which took root in t...

Hou et al. introduced a (2, n) block-based progressive visual cryptographic scheme (BPVCS). In (2, n)-BPVCS, a secret image is subdivided into n non-overlapped image blocks. When t (2 ≤ t ≤ n) participants stack their shadow images, the image blocks belonged to these t participants will be recovered. Unfortunately, Hou et al.’s (2, n)-BPVCS suffers from the cheating problem. Additionally, Hou et al.’s scheme is only suitable for 2-out-of-n case, i.e., (k, n)-BPVCS where k = 2. In this paper, we propose a cheating immune (k, n)-BPVCS for k>2. The main contribution of our paper is that the proposed (k, n)-BPVCS is not only cheating immune, but also suitable for general k-out-of-n threshold, where k and n are integers with 2 ≤ k ≤ n. Theoretical analysis demonstrates that our scheme still holds progressive recovery and security, and meantime has cheating immune capability.

We analyse in detail the language of partially non-abelian Deligne cohomology and of twisted differential K-theory, in order to describe the geometry of type II superstring backgrounds with D-branes. This description will also provide the opportunity to show some mathematical results of independent interest. In particular, we begin classifying the possible gauge theories on a D-brane or on a stack of D-branes using the intrinsic tool of long exact sequences. Afterwards, we recall how to construct two relevant models of differential twisted K-theory, paying particular attention to the dependence on the twisting cocycle within its cohomology class. In this way we will be able to define twisted K-homology and twisted Cheeger-Simons K-characters in the category of simply-connected manifolds, eliminating any unnatural dependence on the cocycle. The ambiguity left for non simply-connected manifolds will naturally correspond to the ambiguity in the gauge theory, following the previous classification. This picture will allow for a complete characterization of D-brane world-volumes, the Wess-Zumino action and topological D-brane charges within the K-theoretical framework, that can be compared step by step to the old cohomological classification. This has already been done for backgrounds with vanishing B-field; here we remove this hypothesis., Comment: 75 pages, to appear in Nuclear Physics, Section B

We prove that the number of 01-fillings of a given stack polyomino (a polyomino with justified rows whose lengths form a unimodal sequence) with at most one 1 per column which do not contain a fixed-size northeast chain and a fixed-size southeast chain, depends only on the set of row lengths of the polyomino. The proof is via a bijection between fillings of stack polyominoes which differ only in the position of one row and uses the Hecke insertion algorithm by Buch, Kresch, Shimozono, Tamvakis, and Yong and the jeu de taquin for increasing tableaux of Thomas and Yong. Moreover, our bijection gives another proof of the result by Chen, Guo, and Pang that the crossing number and the nesting number have a symmetric joint distribution over linked partitions.

Skeleton-based action recognition aims to recognize human actions by exploring the inherent characteristics from the given skeleton sequences and has attracted far more attention due to its great important potentials in practical applications. Previous methods have illustrated that learning discriminative spatial and temporal features from the skeleton sequences is a crucial factor to recognize human actions. Nevertheless, how to model spatio-temporal evolutions is still a challenging problem. In this work, we propose a novel model with hierarchical spatial reasoning and temporal stack learning network (HSR-TSL) to explore the discriminative spatial and temporal features for human action recognition, which consists of a hierarchical spatial reasoning network (HSRN) and a temporal stack learning network (TSLN). Specifically, the HSRN employs a hierarchical residual graph neural network to capture two-level spatial features: intra spatial information of each part and body-level structural information between each part. The TSLN models the detailed temporal dynamics of skeleton sequences by a composition of multiple skip-clip LSTMs. During training, we develop a clip-based incremental loss to effectively optimize the model. We perform extensive experiments on five challenging benchmarks to verify the effectiveness of each component of our model. The comparison results illustrate that our approach significantly boosts the performances for skeleton-based action recognition.

We describe the moduli stack of Gushel–Mukai varieties as a global quotient stack and its coarse moduli space as the corresponding GIT quotient. The construction is based on a comprehensive study of the relation between this stack and the stack of so-called Lagrangian data defined in our previous works; roughly speaking, we show that the former is a generalized root stack of the latter. As an application, we define the period map for Gushel–Mukai varieties and construct some complete nonisotrivial families of smooth Gushel–Mukai varieties. In an appendix, we describe a generalization of the root stack construction used in our approach to the moduli stack.

We show that the Hopf algebra of quasisymmetric functions arises naturally as the integral Chow ring of the algebraic stack of expanded pairs originally described by J. Li, using a more combinatorial description in terms of configurations of line bundles. In particular, we exhibit a gluing map which gives rise to the comultiplication. We then apply the result to calculate the Chow rings of certain stacks of semistable curves.

Improved version. To appear in Results in Mathematics., 30 pages, 1 figure

We exhibit a bijection between recently-introduced combinatorial objects known as valid hook configurations and certain weighted set partitions. When restricting our attention to set partitions that are matchings, we obtain three new combinatorial interpretations of Lassalle's sequence. One of these interpretations involves permutations that have exactly one preimage under the (West) stack-sorting map. We prove that the sequences obtained by counting these permutations according to their first entries are symmetric, and we conjecture that they are log-concave. We also obtain new recurrence relations involving Lassalle's sequence and the sequence that enumerates valid hook configurations. We end with several suggestions for future work., 20 pages, 11 figures

This article is based in part on lecture notes prepared for the summer school "The Geometry, Topology and Physics of Moduli Spaces of Higgs Bundles" at the Institute for Mathematical Sciences at the National University of Singapore in July of 2014. The aim is to provide a brief introduction to algebraic stacks, and then to give several constructions of the moduli stack of Higgs bundles on algebraic curves. The first construction is via a "bootstrap" method from the algebraic stack of vector bundles on an algebraic curve. This construction is motivated in part by Nitsure's GIT construction of a projective moduli space of semi-stable Higgs bundles, and we describe the relationship between Nitsure's moduli space and the algebraic stacks constructed here. The third approach is via deformation theory, where we directly construct the stack of Higgs bundles using Artin's criterion.

We compute the Brauer group of the universal moduli stack of vector bundles on (possibly marked) smooth curves of genus at least three over the complex numbers. As consequence, we obtain an explicit description of the Brauer group of the smooth locus of the associated moduli space of semistable vector bundles, when the genus is at least four., 26 pages. Fixed a mistake in section 3.1 in the new version

We give an explicit presentation of the integral Chow ring of a stack of smooth plane cubics. We also determine some relations in the general case of hypersurfaces of any dimension and degree., Made some improvements to the exposition. Accepted for publication in the Michigan Mathematical Journal

In the present paper, we study the extent to which linear combinations of period matrices arising from stable curves are degenerate (i.e., as bilinear forms). We give a criterion to determine whether a stable curve admits such a degenerate linear combination of period matrices. In particular, this criterion can be interpreted as a certain analogue of the weight-monodromy conjecture for non-degenerate elements of pro-$\ell$ log étale fundamental groups of certain log points associated to the log stack $\overline{\mathcal{M}}_{g}^{log}$.

We propose to reduce the decoding complexity of polar codes with Reed-Solomon kernels by exploiting its algebraic similarity with Arikan kernel, and employing the stack algorithm for computing the probabilities of kernel input symbols. Simulation results show that polar codes with $8\times 8$ Reed-Solomon kernel under SC decoding provide performance comparable to Arikan polar codes with CRC under list SC decoding.

In complex inferential tasks like question answering, machine learning models must confront two challenges: the need to implement a compositional reasoning process, and, in many applications, the need for this reasoning process to be interpretable to assist users in both development and prediction. Existing models designed to produce interpretable traces of their decision-making process typically require these traces to be supervised at training time. In this paper, we present a novel neural modular approach that performs compositional reasoning by automatically inducing a desired sub-task decomposition without relying on strong supervision. Our model allows linking different reasoning tasks though shared modules that handle common routines across tasks. Experiments show that the model is more interpretable to human evaluators compared to other state-of-the-art models: users can better understand the model's underlying reasoning procedure and predict when it will succeed or fail based on observing its intermediate outputs., Comment: ECCV 2018

For a compact manifold M and a differentiable stack Open image in new window presented by a Lie groupoid X, we show the Hom-stack Open image in new window is presented by a Frechet–Lie groupoid Map(M, X) and so is an infinite-dimensional differentiable stack. We further show that if Open image in new window is an orbifold, presented by a proper etale Lie groupoid, then Map(M, X) is proper etale and so presents an infinite-dimensional orbifold.

We consider the spherical DG category $Sph_G$ attached to an affine algebraic group $G$. By definition, $Sph_G := IndCoh(LS_G(S^2))$ consists of ind-coherent sheaves of the stack of $G$-local systems on the $2$-sphere $S^2$. The $3$-dimensional version of the pair of pants endows $Sph_G$ with an $E_3$-monoidal structure. More generally, for an algebraic stack $Y$ (satisfying some mild conditions) and $n \geq -1$, we can look at the $E_{n+1}$-monoidal DG category $Sph(Y,n) := IndCoh_0((Y^{S^n})^\wedge_Y)$, where $IndCoh_0$ is the sheaf theory introduced in [AG2] and [centerH]. % The case of $Sph_G$ is recovered by setting $Y =BG$ and $n=2$. The cobordism hypothesis associates to $Sph(Y,n)$ an $(n+1)$-dimensional TQFT, whose value of a manifold $M^d$ of dimension $d \leq n+1$ (possibly with boundary) is given by the {topological chiral homology} $\int_{M^d} Sph(Y,n)$. % In this paper, we compute such homology (in virtually all cases): we have the Stokes style formula $$ \int_{M^d} Sph(Y,n) \simeq IndCoh_0 ( (Y^{\partial(M^d \times D^{n+1-d})})^\wedge_{Y^M} ) , $$ where the formal completion is constructed using the obvious projection $\partial(M^d \times D^{n+1-d}) \to M^d$. The most interesting instance of this formula is for $Sph_G \simeq Sph(BG,2)$, the original spherical category, and $X$ a Riemann surface. In this case, we obtain a monoidal equivalence $\int_X Sph_G \simeq H(LS_G^{Betti}(X))$, where $LS_G^{Betti}(X)$ is the stack of $G$-local systems on the topological space underlying $X$ and $H$ is the sheaf theory introduced in [centerH]., Comment: Accepted for publication by Journal of Topology

We study counting-regular languages—these are languages L for which there is a regular language \(L'\) such that the number of strings of length n in L and \(L'\) are the same for all n. Our main result is that the languages accepted by the class of one-way unambiguous, reversal-bounded pushdown automata (\(\textsf {PDA}\)’s) are counting-regular. This generalizes an old result of Baron and Kuich that such languages have rational generating functions. We show that this result is the best possible in the sense that the claim does not hold for either 2-ambiguous \(\textsf {PDA}\)’s, unambiguous \(\textsf {PDA}\)’s with no reversal-bound, and other generalizations. We provide a number of examples of languages that are (and are not) counting-regular. We study closure properties of the class of context-free languages that are counting-regular. We also show the undecidability of counting-regularity of \(\textsf {PDA}\)’s. The undecidability is shown to hold for even the subclass of 2-ambiguous \(\textsf {PDA}\)’s which make only one reversal on the stack.